1,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**2)**(5/2),x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**(5/2), x)","F",0
2,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**2)**(3/2),x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**(3/2), x)","F",0
3,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(b*tan(e + f*x)**2), x)","F",0
4,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**2)**(1/2),x)","\int \frac{1}{\sqrt{b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*tan(e + f*x)**2), x)","F",0
5,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**2)**(3/2),x)","\int \frac{1}{\left(b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**(-3/2), x)","F",0
6,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**2)**(5/2),x)","\int \frac{1}{\left(b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**(-5/2), x)","F",0
7,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**3)**(5/2),x)","\int \left(b \tan^{3}{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b*tan(e + f*x)**3)**(5/2), x)","F",0
8,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**3)**(3/2),x)","\int \left(b \tan^{3}{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*tan(e + f*x)**3)**(3/2), x)","F",0
9,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**3)**(1/2),x)","\int \sqrt{b \tan^{3}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(b*tan(e + f*x)**3), x)","F",0
10,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**3)**(1/2),x)","\int \frac{1}{\sqrt{b \tan^{3}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*tan(e + f*x)**3), x)","F",0
11,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**3)**(3/2),x)","\int \frac{1}{\left(b \tan^{3}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*tan(e + f*x)**3)**(-3/2), x)","F",0
12,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**3)**(5/2),x)","\int \frac{1}{\left(b \tan^{3}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*tan(e + f*x)**3)**(-5/2), x)","F",0
13,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**4)**(5/2),x)","\int \left(b \tan^{4}{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b*tan(e + f*x)**4)**(5/2), x)","F",0
14,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**4)**(3/2),x)","\int \left(b \tan^{4}{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*tan(e + f*x)**4)**(3/2), x)","F",0
15,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**4)**(1/2),x)","\int \sqrt{b \tan^{4}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(b*tan(e + f*x)**4), x)","F",0
16,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**4)**(1/2),x)","\int \frac{1}{\sqrt{b \tan^{4}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*tan(e + f*x)**4), x)","F",0
17,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**4)**(3/2),x)","\int \frac{1}{\left(b \tan^{4}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*tan(e + f*x)**4)**(-3/2), x)","F",0
18,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**4)**(5/2),x)","\int \frac{1}{\left(b \tan^{4}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*tan(e + f*x)**4)**(-5/2), x)","F",0
19,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**n)**(5/2),x)","\int \left(b \tan^{n}{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b*tan(e + f*x)**n)**(5/2), x)","F",0
20,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**n)**(3/2),x)","\int \left(b \tan^{n}{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*tan(e + f*x)**n)**(3/2), x)","F",0
21,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**n)**(1/2),x)","\int \sqrt{b \tan^{n}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(b*tan(e + f*x)**n), x)","F",0
22,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**n)**(1/2),x)","\int \frac{1}{\sqrt{b \tan^{n}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*tan(e + f*x)**n), x)","F",0
23,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**n)**(3/2),x)","\int \frac{1}{\left(b \tan^{n}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*tan(e + f*x)**n)**(-3/2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/(b*tan(f*x+e)**n)**(5/2),x)","\int \frac{1}{\left(b \tan^{n}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*tan(e + f*x)**n)**(-5/2), x)","F",0
25,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**n)**p,x)","\int \left(b \tan^{n}{\left(e + f x \right)}\right)^{p}\, dx"," ",0,"Integral((b*tan(e + f*x)**n)**p, x)","F",0
26,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**2)**p,x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{p}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**p, x)","F",0
27,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**3)**p,x)","\int \left(b \tan^{3}{\left(e + f x \right)}\right)^{p}\, dx"," ",0,"Integral((b*tan(e + f*x)**3)**p, x)","F",0
28,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**4)**p,x)","\int \left(b \tan^{4}{\left(e + f x \right)}\right)^{p}\, dx"," ",0,"Integral((b*tan(e + f*x)**4)**p, x)","F",0
29,0,0,0,0.000000," ","integrate((b*tan(f*x+e)**n)**(1/n),x)","\int \left(b \tan^{n}{\left(e + f x \right)}\right)^{\frac{1}{n}}\, dx"," ",0,"Integral((b*tan(e + f*x)**n)**(1/n), x)","F",0
30,0,0,0,0.000000," ","integrate(sin(f*x+e)**5*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \sin^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*sin(e + f*x)**5, x)","F",0
31,0,0,0,0.000000," ","integrate(sin(f*x+e)**3*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \sin^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*sin(e + f*x)**3, x)","F",0
32,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \sin{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*sin(e + f*x), x)","F",0
33,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*csc(e + f*x), x)","F",0
34,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*csc(e + f*x)**3, x)","F",0
35,0,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \csc^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*csc(e + f*x)**5, x)","F",0
36,0,0,0,0.000000," ","integrate(sin(f*x+e)**6*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \sin^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*sin(e + f*x)**6, x)","F",0
37,0,0,0,0.000000," ","integrate(sin(f*x+e)**4*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \sin^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*sin(e + f*x)**4, x)","F",0
38,0,0,0,0.000000," ","integrate(sin(f*x+e)**2*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*sin(e + f*x)**2, x)","F",0
39,1,20,0,0.139068," ","integrate(a+b*tan(f*x+e)**2,x)","a x + b \left(\begin{cases} - x + \frac{\tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \tan^{2}{\left(e \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-x + tan(e + f*x)/f, Ne(f, 0)), (x*tan(e)**2, True))","A",0
40,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*csc(e + f*x)**2, x)","F",0
41,0,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*csc(e + f*x)**4, x)","F",0
42,0,0,0,0.000000," ","integrate(csc(f*x+e)**6*(a+b*tan(f*x+e)**2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right) \csc^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)*csc(e + f*x)**6, x)","F",0
43,0,0,0,0.000000," ","integrate(sin(f*x+e)**5*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \sin^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*sin(e + f*x)**5, x)","F",0
44,0,0,0,0.000000," ","integrate(sin(f*x+e)**3*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \sin^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*sin(e + f*x)**3, x)","F",0
45,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*sin(e + f*x), x)","F",0
46,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*csc(e + f*x), x)","F",0
47,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*csc(e + f*x)**3, x)","F",0
48,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,0,0,0,0.000000," ","integrate(sin(f*x+e)**4*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \sin^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*sin(e + f*x)**4, x)","F",0
50,0,0,0,0.000000," ","integrate(sin(f*x+e)**2*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*sin(e + f*x)**2, x)","F",0
51,1,68,0,0.320476," ","integrate((a+b*tan(f*x+e)**2)**2,x)","\begin{cases} a^{2} x - 2 a b x + \frac{2 a b \tan{\left(e + f x \right)}}{f} + b^{2} x + \frac{b^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x - 2*a*b*x + 2*a*b*tan(e + f*x)/f + b**2*x + b**2*tan(e + f*x)**3/(3*f) - b**2*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e)**2)**2, True))","A",0
52,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*csc(e + f*x)**2, x)","F",0
53,0,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*tan(f*x+e)**2)**2,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2} \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**2*csc(e + f*x)**4, x)","F",0
54,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6*(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(a+b*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)**2),x)","\int \frac{\sin{\left(e + f x \right)}}{a + b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sin(e + f*x)/(a + b*tan(e + f*x)**2), x)","F",0
58,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)**2),x)","\int \frac{\csc{\left(e + f x \right)}}{a + b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(csc(e + f*x)/(a + b*tan(e + f*x)**2), x)","F",0
59,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*tan(f*x+e)**2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{a + b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(csc(e + f*x)**3/(a + b*tan(e + f*x)**2), x)","F",0
60,0,0,0,0.000000," ","integrate(csc(f*x+e)**5/(a+b*tan(f*x+e)**2),x)","\int \frac{\csc^{5}{\left(e + f x \right)}}{a + b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(csc(e + f*x)**5/(a + b*tan(e + f*x)**2), x)","F",0
61,-1,0,0,0.000000," ","integrate(sin(f*x+e)**6/(a+b*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,1,280,0,2.354039," ","integrate(1/(a+b*tan(f*x+e)**2),x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- x - \frac{1}{f \tan{\left(e + f x \right)}}}{b} & \text{for}\: a = 0 \\\frac{f x \tan^{2}{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{f x}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{\tan{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} & \text{for}\: a = b \\\frac{x}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{x}{a} & \text{for}\: b = 0 \\\frac{2 i \sqrt{a} f x \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b f \sqrt{\frac{1}{b}}} - \frac{\log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 i a^{\frac{3}{2}} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b f \sqrt{\frac{1}{b}}} + \frac{\log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 i a^{\frac{3}{2}} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b f \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-x - 1/(f*tan(e + f*x)))/b, Eq(a, 0)), (f*x*tan(e + f*x)**2/(2*b*f*tan(e + f*x)**2 + 2*b*f) + f*x/(2*b*f*tan(e + f*x)**2 + 2*b*f) + tan(e + f*x)/(2*b*f*tan(e + f*x)**2 + 2*b*f), Eq(a, b)), (x/(a + b*tan(e)**2), Eq(f, 0)), (x/a, Eq(b, 0)), (2*I*sqrt(a)*f*x*sqrt(1/b)/(2*I*a**(3/2)*f*sqrt(1/b) - 2*I*sqrt(a)*b*f*sqrt(1/b)) - log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*I*a**(3/2)*f*sqrt(1/b) - 2*I*sqrt(a)*b*f*sqrt(1/b)) + log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*I*a**(3/2)*f*sqrt(1/b) - 2*I*sqrt(a)*b*f*sqrt(1/b)), True))","A",0
65,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*tan(f*x+e)**2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{a + b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(csc(e + f*x)**2/(a + b*tan(e + f*x)**2), x)","F",0
66,0,0,0,0.000000," ","integrate(csc(f*x+e)**4/(a+b*tan(f*x+e)**2),x)","\int \frac{\csc^{4}{\left(e + f x \right)}}{a + b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(csc(e + f*x)**4/(a + b*tan(e + f*x)**2), x)","F",0
67,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6/(a+b*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)**2)**2,x)","\int \frac{\sin{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral(sin(e + f*x)/(a + b*tan(e + f*x)**2)**2, x)","F",0
71,-1,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,1,2322,0,28.540375," ","integrate(1/(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{4}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{x}{a^{2}} & \text{for}\: b = 0 \\\frac{x + \frac{1}{f \tan{\left(e + f x \right)}} - \frac{1}{3 f \tan^{3}{\left(e + f x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{3 f x \tan^{4}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{6 f x \tan^{2}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{3 f x}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{3 \tan^{3}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{5 \tan{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} & \text{for}\: a = b \\\frac{x}{\left(a + b \tan^{2}{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{4 i a^{\frac{5}{2}} f x \sqrt{\frac{1}{b}}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{4 i a^{\frac{3}{2}} b f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{2 i a^{\frac{3}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{2 i \sqrt{a} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{3 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{3 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{3 a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{3 a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**4, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (x/a**2, Eq(b, 0)), ((x + 1/(f*tan(e + f*x)) - 1/(3*f*tan(e + f*x)**3))/b**2, Eq(a, 0)), (3*f*x*tan(e + f*x)**4/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 6*f*x*tan(e + f*x)**2/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 3*f*x/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 3*tan(e + f*x)**3/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 5*tan(e + f*x)/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f), Eq(a, b)), (x/(a + b*tan(e)**2)**2, Eq(f, 0)), (4*I*a**(5/2)*f*x*sqrt(1/b)/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + 4*I*a**(3/2)*b*f*x*sqrt(1/b)*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - 2*I*a**(3/2)*b*sqrt(1/b)*tan(e + f*x)/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + 2*I*sqrt(a)*b**2*sqrt(1/b)*tan(e + f*x)/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - 3*a**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + 3*a**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - 3*a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + 3*a*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - a*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2), True))","A",0
77,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,1,9629,0,138.502299," ","integrate(1/(a+b*tan(f*x+e)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{6}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{x}{a^{3}} & \text{for}\: b = 0 \\\frac{- x - \frac{1}{f \tan{\left(e + f x \right)}} + \frac{1}{3 f \tan^{3}{\left(e + f x \right)}} - \frac{1}{5 f \tan^{5}{\left(e + f x \right)}}}{b^{3}} & \text{for}\: a = 0 \\\frac{15 f x \tan^{6}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{45 f x \tan^{4}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{45 f x \tan^{2}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{15 f x}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{15 \tan^{5}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{40 \tan^{3}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{33 \tan{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} & \text{for}\: a = b \\\frac{x}{\left(a + b \tan^{2}{\left(e \right)}\right)^{3}} & \text{for}\: f = 0 \\\frac{16 i a^{\frac{9}{2}} f x \sqrt{\frac{1}{b}}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{32 i a^{\frac{7}{2}} b f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{18 i a^{\frac{7}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{16 i a^{\frac{5}{2}} b^{2} f x \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{14 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{28 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{20 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 i \sqrt{a} b^{4} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{15 a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{15 a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{30 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{10 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{30 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{15 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{20 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{15 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{20 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{10 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 b^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 b^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**6, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (x/a**3, Eq(b, 0)), ((-x - 1/(f*tan(e + f*x)) + 1/(3*f*tan(e + f*x)**3) - 1/(5*f*tan(e + f*x)**5))/b**3, Eq(a, 0)), (15*f*x*tan(e + f*x)**6/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 45*f*x*tan(e + f*x)**4/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 45*f*x*tan(e + f*x)**2/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 15*f*x/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 15*tan(e + f*x)**5/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 40*tan(e + f*x)**3/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 33*tan(e + f*x)/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f), Eq(a, b)), (x/(a + b*tan(e)**2)**3, Eq(f, 0)), (16*I*a**(9/2)*f*x*sqrt(1/b)/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 32*I*a**(7/2)*b*f*x*sqrt(1/b)*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 18*I*a**(7/2)*b*sqrt(1/b)*tan(e + f*x)/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 16*I*a**(5/2)*b**2*f*x*sqrt(1/b)*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 14*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 28*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 20*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 10*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 6*I*sqrt(a)*b**4*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 15*a**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 15*a**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 30*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 10*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 30*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 10*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 15*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 20*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 3*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 15*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 20*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 3*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 10*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 10*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 3*b**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 3*b**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4), True))","A",0
89,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5*(a+b*tan(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(a+b*tan(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*sin(e + f*x), x)","F",0
95,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*csc(e + f*x), x)","F",0
96,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*csc(e + f*x)**3, x)","F",0
97,0,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \csc^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*csc(e + f*x)**5, x)","F",0
98,0,0,0,0.000000," ","integrate(sin(f*x+e)**4*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \sin^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*sin(e + f*x)**4, x)","F",0
99,0,0,0,0.000000," ","integrate(sin(f*x+e)**2*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*sin(e + f*x)**2, x)","F",0
100,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2), x)","F",0
101,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*csc(e + f*x)**2, x)","F",0
102,0,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*csc(e + f*x)**4, x)","F",0
103,0,0,0,0.000000," ","integrate(csc(f*x+e)**6*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \csc^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*csc(e + f*x)**6, x)","F",0
104,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,0,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*sin(e + f*x), x)","F",0
107,0,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*csc(e + f*x), x)","F",0
108,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,0,0,0,0.000000," ","integrate(sin(f*x+e)**2*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*sin(e + f*x)**2, x)","F",0
112,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2), x)","F",0
113,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(a+b*tan(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*tan(f*x+e)**2)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)/sqrt(a + b*tan(e + f*x)**2), x)","F",0
119,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)/sqrt(a + b*tan(e + f*x)**2), x)","F",0
120,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/sqrt(a + b*tan(e + f*x)**2), x)","F",0
121,0,0,0,0.000000," ","integrate(csc(f*x+e)**5/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\csc^{5}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**5/sqrt(a + b*tan(e + f*x)**2), x)","F",0
122,0,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\sin^{4}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)**4/sqrt(a + b*tan(e + f*x)**2), x)","F",0
123,0,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\sin^{2}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)**2/sqrt(a + b*tan(e + f*x)**2), x)","F",0
124,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*tan(e + f*x)**2), x)","F",0
125,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/sqrt(a + b*tan(e + f*x)**2), x)","F",0
126,0,0,0,0.000000," ","integrate(csc(f*x+e)**4/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\csc^{4}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**4/sqrt(a + b*tan(e + f*x)**2), x)","F",0
127,0,0,0,0.000000," ","integrate(csc(f*x+e)**6/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\csc^{6}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**6/sqrt(a + b*tan(e + f*x)**2), x)","F",0
128,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
131,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
132,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
133,0,0,0,0.000000," ","integrate(csc(f*x+e)**5/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\csc^{5}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**5/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
134,0,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\sin^{4}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**4/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
135,0,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\sin^{2}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**2/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
136,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{1}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(-3/2), x)","F",0
137,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
138,0,0,0,0.000000," ","integrate(csc(f*x+e)**4/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\csc^{4}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**4/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
139,0,0,0,0.000000," ","integrate(csc(f*x+e)**6/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\csc^{6}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**6/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
140,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(a+b*tan(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*tan(f*x+e)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
143,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
144,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
145,0,0,0,0.000000," ","integrate(csc(f*x+e)**5/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\csc^{5}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**5/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
146,0,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\sin^{4}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**4/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
147,0,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\sin^{2}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**2/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
148,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{1}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(-5/2), x)","F",0
149,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
150,0,0,0,0.000000," ","integrate(csc(f*x+e)**4/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\csc^{4}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**4/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
151,0,0,0,0.000000," ","integrate(csc(f*x+e)**6/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\csc^{6}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**6/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
152,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**m*(b*tan(f*x+e)**2)**p,x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{p} \left(d \sin{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**p*(d*sin(e + f*x))**m, x)","F",0
153,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate(sin(f*x+e)*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate(csc(f*x+e)*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**p,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**p, x)","F",0
161,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**m*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \left(d \sin{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*(d*sin(e + f*x))**m, x)","F",0
165,0,0,0,0.000000," ","integrate(sin(f*x+e)**2*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*sin(e + f*x)**2, x)","F",0
166,0,0,0,0.000000," ","integrate((b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p, x)","F",0
167,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*csc(e + f*x)**2, x)","F",0
168,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6*(b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,0,0,0,0.000000," ","integrate(sin(f*x+e)*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*sin(e + f*x), x)","F",0
172,0,0,0,0.000000," ","integrate(csc(f*x+e)*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*csc(e + f*x), x)","F",0
173,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*csc(e + f*x)**3, x)","F",0
174,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**m*(a+b*tan(f*x+e)**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,0,0,0,0.000000," ","integrate((d*cos(f*x+e))**m*(b*tan(f*x+e)**2)**p,x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{p} \left(d \cos{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**p*(d*cos(e + f*x))**m, x)","F",0
176,-1,0,0,0.000000," ","integrate((d*cos(f*x+e))**m*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,0,0,0,0.000000," ","integrate((d*cos(f*x+e))**m*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \left(d \cos{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*(d*cos(e + f*x))**m, x)","F",0
178,-1,0,0,0.000000," ","integrate((d*cos(f*x+e))**m*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,1,68,0,1.061969," ","integrate((a+a*tan(d*x+c)**2)**4,x)","\begin{cases} \frac{a^{4} \tan^{7}{\left(c + d x \right)}}{7 d} + \frac{3 a^{4} \tan^{5}{\left(c + d x \right)}}{5 d} + \frac{a^{4} \tan^{3}{\left(c + d x \right)}}{d} + \frac{a^{4} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \tan^{2}{\left(c \right)} + a\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*tan(c + d*x)**7/(7*d) + 3*a**4*tan(c + d*x)**5/(5*d) + a**4*tan(c + d*x)**3/d + a**4*tan(c + d*x)/d, Ne(d, 0)), (x*(a*tan(c)**2 + a)**4, True))","A",0
180,1,54,0,0.544880," ","integrate((a+a*tan(d*x+c)**2)**3,x)","\begin{cases} \frac{a^{3} \tan^{5}{\left(c + d x \right)}}{5 d} + \frac{2 a^{3} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{3} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \tan^{2}{\left(c \right)} + a\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*tan(c + d*x)**5/(5*d) + 2*a**3*tan(c + d*x)**3/(3*d) + a**3*tan(c + d*x)/d, Ne(d, 0)), (x*(a*tan(c)**2 + a)**3, True))","A",0
181,1,37,0,0.285345," ","integrate((a+a*tan(d*x+c)**2)**2,x)","\begin{cases} \frac{a^{2} \tan^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a \tan^{2}{\left(c \right)} + a\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*tan(c + d*x)**3/(3*d) + a**2*tan(c + d*x)/d, Ne(d, 0)), (x*(a*tan(c)**2 + a)**2, True))","A",0
182,1,87,0,0.543254," ","integrate(1/(a+a*tan(d*x+c)**2),x)","\begin{cases} \frac{d x \tan^{2}{\left(c + d x \right)}}{2 a d \tan^{2}{\left(c + d x \right)} + 2 a d} + \frac{d x}{2 a d \tan^{2}{\left(c + d x \right)} + 2 a d} + \frac{\tan{\left(c + d x \right)}}{2 a d \tan^{2}{\left(c + d x \right)} + 2 a d} & \text{for}\: d \neq 0 \\\frac{x}{a \tan^{2}{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((d*x*tan(c + d*x)**2/(2*a*d*tan(c + d*x)**2 + 2*a*d) + d*x/(2*a*d*tan(c + d*x)**2 + 2*a*d) + tan(c + d*x)/(2*a*d*tan(c + d*x)**2 + 2*a*d), Ne(d, 0)), (x/(a*tan(c)**2 + a), True))","A",0
183,1,248,0,0.897100," ","integrate(1/(a+a*tan(d*x+c)**2)**2,x)","\begin{cases} \frac{3 d x \tan^{4}{\left(c + d x \right)}}{8 a^{2} d \tan^{4}{\left(c + d x \right)} + 16 a^{2} d \tan^{2}{\left(c + d x \right)} + 8 a^{2} d} + \frac{6 d x \tan^{2}{\left(c + d x \right)}}{8 a^{2} d \tan^{4}{\left(c + d x \right)} + 16 a^{2} d \tan^{2}{\left(c + d x \right)} + 8 a^{2} d} + \frac{3 d x}{8 a^{2} d \tan^{4}{\left(c + d x \right)} + 16 a^{2} d \tan^{2}{\left(c + d x \right)} + 8 a^{2} d} + \frac{3 \tan^{3}{\left(c + d x \right)}}{8 a^{2} d \tan^{4}{\left(c + d x \right)} + 16 a^{2} d \tan^{2}{\left(c + d x \right)} + 8 a^{2} d} + \frac{5 \tan{\left(c + d x \right)}}{8 a^{2} d \tan^{4}{\left(c + d x \right)} + 16 a^{2} d \tan^{2}{\left(c + d x \right)} + 8 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x}{\left(a \tan^{2}{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*d*x*tan(c + d*x)**4/(8*a**2*d*tan(c + d*x)**4 + 16*a**2*d*tan(c + d*x)**2 + 8*a**2*d) + 6*d*x*tan(c + d*x)**2/(8*a**2*d*tan(c + d*x)**4 + 16*a**2*d*tan(c + d*x)**2 + 8*a**2*d) + 3*d*x/(8*a**2*d*tan(c + d*x)**4 + 16*a**2*d*tan(c + d*x)**2 + 8*a**2*d) + 3*tan(c + d*x)**3/(8*a**2*d*tan(c + d*x)**4 + 16*a**2*d*tan(c + d*x)**2 + 8*a**2*d) + 5*tan(c + d*x)/(8*a**2*d*tan(c + d*x)**4 + 16*a**2*d*tan(c + d*x)**2 + 8*a**2*d), Ne(d, 0)), (x/(a*tan(c)**2 + a)**2, True))","A",0
184,1,454,0,1.399502," ","integrate(1/(a+a*tan(d*x+c)**2)**3,x)","\begin{cases} \frac{15 d x \tan^{6}{\left(c + d x \right)}}{48 a^{3} d \tan^{6}{\left(c + d x \right)} + 144 a^{3} d \tan^{4}{\left(c + d x \right)} + 144 a^{3} d \tan^{2}{\left(c + d x \right)} + 48 a^{3} d} + \frac{45 d x \tan^{4}{\left(c + d x \right)}}{48 a^{3} d \tan^{6}{\left(c + d x \right)} + 144 a^{3} d \tan^{4}{\left(c + d x \right)} + 144 a^{3} d \tan^{2}{\left(c + d x \right)} + 48 a^{3} d} + \frac{45 d x \tan^{2}{\left(c + d x \right)}}{48 a^{3} d \tan^{6}{\left(c + d x \right)} + 144 a^{3} d \tan^{4}{\left(c + d x \right)} + 144 a^{3} d \tan^{2}{\left(c + d x \right)} + 48 a^{3} d} + \frac{15 d x}{48 a^{3} d \tan^{6}{\left(c + d x \right)} + 144 a^{3} d \tan^{4}{\left(c + d x \right)} + 144 a^{3} d \tan^{2}{\left(c + d x \right)} + 48 a^{3} d} + \frac{15 \tan^{5}{\left(c + d x \right)}}{48 a^{3} d \tan^{6}{\left(c + d x \right)} + 144 a^{3} d \tan^{4}{\left(c + d x \right)} + 144 a^{3} d \tan^{2}{\left(c + d x \right)} + 48 a^{3} d} + \frac{40 \tan^{3}{\left(c + d x \right)}}{48 a^{3} d \tan^{6}{\left(c + d x \right)} + 144 a^{3} d \tan^{4}{\left(c + d x \right)} + 144 a^{3} d \tan^{2}{\left(c + d x \right)} + 48 a^{3} d} + \frac{33 \tan{\left(c + d x \right)}}{48 a^{3} d \tan^{6}{\left(c + d x \right)} + 144 a^{3} d \tan^{4}{\left(c + d x \right)} + 144 a^{3} d \tan^{2}{\left(c + d x \right)} + 48 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x}{\left(a \tan^{2}{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*d*x*tan(c + d*x)**6/(48*a**3*d*tan(c + d*x)**6 + 144*a**3*d*tan(c + d*x)**4 + 144*a**3*d*tan(c + d*x)**2 + 48*a**3*d) + 45*d*x*tan(c + d*x)**4/(48*a**3*d*tan(c + d*x)**6 + 144*a**3*d*tan(c + d*x)**4 + 144*a**3*d*tan(c + d*x)**2 + 48*a**3*d) + 45*d*x*tan(c + d*x)**2/(48*a**3*d*tan(c + d*x)**6 + 144*a**3*d*tan(c + d*x)**4 + 144*a**3*d*tan(c + d*x)**2 + 48*a**3*d) + 15*d*x/(48*a**3*d*tan(c + d*x)**6 + 144*a**3*d*tan(c + d*x)**4 + 144*a**3*d*tan(c + d*x)**2 + 48*a**3*d) + 15*tan(c + d*x)**5/(48*a**3*d*tan(c + d*x)**6 + 144*a**3*d*tan(c + d*x)**4 + 144*a**3*d*tan(c + d*x)**2 + 48*a**3*d) + 40*tan(c + d*x)**3/(48*a**3*d*tan(c + d*x)**6 + 144*a**3*d*tan(c + d*x)**4 + 144*a**3*d*tan(c + d*x)**2 + 48*a**3*d) + 33*tan(c + d*x)/(48*a**3*d*tan(c + d*x)**6 + 144*a**3*d*tan(c + d*x)**4 + 144*a**3*d*tan(c + d*x)**2 + 48*a**3*d), Ne(d, 0)), (x/(a*tan(c)**2 + a)**3, True))","A",0
185,1,116,0,0.729626," ","integrate(tan(f*x+e)**5*(a+b*tan(f*x+e)**2),x)","\begin{cases} \frac{a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{a \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b \tan^{6}{\left(e + f x \right)}}{6 f} - \frac{b \tan^{4}{\left(e + f x \right)}}{4 f} + \frac{b \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \tan^{5}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(tan(e + f*x)**2 + 1)/(2*f) + a*tan(e + f*x)**4/(4*f) - a*tan(e + f*x)**2/(2*f) - b*log(tan(e + f*x)**2 + 1)/(2*f) + b*tan(e + f*x)**6/(6*f) - b*tan(e + f*x)**4/(4*f) + b*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e)**2)*tan(e)**5, True))","A",0
186,1,88,0,0.394203," ","integrate(tan(f*x+e)**3*(a+b*tan(f*x+e)**2),x)","\begin{cases} - \frac{a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{b \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \tan^{3}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*log(tan(e + f*x)**2 + 1)/(2*f) + a*tan(e + f*x)**2/(2*f) + b*log(tan(e + f*x)**2 + 1)/(2*f) + b*tan(e + f*x)**4/(4*f) - b*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e)**2)*tan(e)**3, True))","A",0
187,1,60,0,0.199281," ","integrate(tan(f*x+e)*(a+b*tan(f*x+e)**2),x)","\begin{cases} \frac{a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \tan{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*log(tan(e + f*x)**2 + 1)/(2*f) - b*log(tan(e + f*x)**2 + 1)/(2*f) + b*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e)**2)*tan(e), True))","A",0
188,1,58,0,0.411891," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)**2),x)","\begin{cases} - \frac{a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a \log{\left(\tan{\left(e + f x \right)} \right)}}{f} + \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \cot{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*log(tan(e + f*x)**2 + 1)/(2*f) + a*log(tan(e + f*x))/f + b*log(tan(e + f*x)**2 + 1)/(2*f), Ne(f, 0)), (x*(a + b*tan(e)**2)*cot(e), True))","A",0
189,1,97,0,1.292598," ","integrate(cot(f*x+e)**3*(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} a x & \text{for}\: e = 0 \wedge f = 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \cot^{3}{\left(e \right)} & \text{for}\: f = 0 \\\tilde{\infty} a x & \text{for}\: e = - f x \\\frac{a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - \frac{a \log{\left(\tan{\left(e + f x \right)} \right)}}{f} - \frac{a}{2 f \tan^{2}{\left(e + f x \right)}} - \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b \log{\left(\tan{\left(e + f x \right)} \right)}}{f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, Eq(e, 0) & Eq(f, 0)), (x*(a + b*tan(e)**2)*cot(e)**3, Eq(f, 0)), (zoo*a*x, Eq(e, -f*x)), (a*log(tan(e + f*x)**2 + 1)/(2*f) - a*log(tan(e + f*x))/f - a/(2*f*tan(e + f*x)**2) - b*log(tan(e + f*x)**2 + 1)/(2*f) + b*log(tan(e + f*x))/f, True))","A",0
190,1,124,0,2.932301," ","integrate(cot(f*x+e)**5*(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} a x & \text{for}\: e = 0 \wedge f = 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \cot^{5}{\left(e \right)} & \text{for}\: f = 0 \\\tilde{\infty} a x & \text{for}\: e = - f x \\- \frac{a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a \log{\left(\tan{\left(e + f x \right)} \right)}}{f} + \frac{a}{2 f \tan^{2}{\left(e + f x \right)}} - \frac{a}{4 f \tan^{4}{\left(e + f x \right)}} + \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - \frac{b \log{\left(\tan{\left(e + f x \right)} \right)}}{f} - \frac{b}{2 f \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, Eq(e, 0) & Eq(f, 0)), (x*(a + b*tan(e)**2)*cot(e)**5, Eq(f, 0)), (zoo*a*x, Eq(e, -f*x)), (-a*log(tan(e + f*x)**2 + 1)/(2*f) + a*log(tan(e + f*x))/f + a/(2*f*tan(e + f*x)**2) - a/(4*f*tan(e + f*x)**4) + b*log(tan(e + f*x)**2 + 1)/(2*f) - b*log(tan(e + f*x))/f - b/(2*f*tan(e + f*x)**2), True))","A",0
191,1,109,0,0.962845," ","integrate(tan(f*x+e)**6*(a+b*tan(f*x+e)**2),x)","\begin{cases} - a x + \frac{a \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{a \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{a \tan{\left(e + f x \right)}}{f} + b x + \frac{b \tan^{7}{\left(e + f x \right)}}{7 f} - \frac{b \tan^{5}{\left(e + f x \right)}}{5 f} + \frac{b \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \tan^{6}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*x + a*tan(e + f*x)**5/(5*f) - a*tan(e + f*x)**3/(3*f) + a*tan(e + f*x)/f + b*x + b*tan(e + f*x)**7/(7*f) - b*tan(e + f*x)**5/(5*f) + b*tan(e + f*x)**3/(3*f) - b*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e)**2)*tan(e)**6, True))","A",0
192,1,82,0,0.533932," ","integrate(tan(f*x+e)**4*(a+b*tan(f*x+e)**2),x)","\begin{cases} a x + \frac{a \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{a \tan{\left(e + f x \right)}}{f} - b x + \frac{b \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{b \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{b \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \tan^{4}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x + a*tan(e + f*x)**3/(3*f) - a*tan(e + f*x)/f - b*x + b*tan(e + f*x)**5/(5*f) - b*tan(e + f*x)**3/(3*f) + b*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e)**2)*tan(e)**4, True))","A",0
193,1,54,0,0.286757," ","integrate(tan(f*x+e)**2*(a+b*tan(f*x+e)**2),x)","\begin{cases} - a x + \frac{a \tan{\left(e + f x \right)}}{f} + b x + \frac{b \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right) \tan^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*x + a*tan(e + f*x)/f + b*x + b*tan(e + f*x)**3/(3*f) - b*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e)**2)*tan(e)**2, True))","A",0
194,1,20,0,0.139686," ","integrate(a+b*tan(f*x+e)**2,x)","a x + b \left(\begin{cases} - x + \frac{\tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \tan^{2}{\left(e \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-x + tan(e + f*x)/f, Ne(f, 0)), (x*tan(e)**2, True))","A",0
195,1,46,0,0.781758," ","integrate(cot(f*x+e)**2*(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} a x & \text{for}\: \left(e = 0 \vee e = - f x\right) \wedge \left(e = - f x \vee f = 0\right) \\x \left(a + b \tan^{2}{\left(e \right)}\right) \cot^{2}{\left(e \right)} & \text{for}\: f = 0 \\- a x - \frac{a}{f \tan{\left(e + f x \right)}} + b x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, (Eq(e, 0) | Eq(e, -f*x)) & (Eq(f, 0) | Eq(e, -f*x))), (x*(a + b*tan(e)**2)*cot(e)**2, Eq(f, 0)), (-a*x - a/(f*tan(e + f*x)) + b*x, True))","A",0
196,1,70,0,1.714346," ","integrate(cot(f*x+e)**4*(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} a x & \text{for}\: \left(e = 0 \vee e = - f x\right) \wedge \left(e = - f x \vee f = 0\right) \\x \left(a + b \tan^{2}{\left(e \right)}\right) \cot^{4}{\left(e \right)} & \text{for}\: f = 0 \\a x + \frac{a}{f \tan{\left(e + f x \right)}} - \frac{a}{3 f \tan^{3}{\left(e + f x \right)}} - b x - \frac{b}{f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, (Eq(e, 0) | Eq(e, -f*x)) & (Eq(f, 0) | Eq(e, -f*x))), (x*(a + b*tan(e)**2)*cot(e)**4, Eq(f, 0)), (a*x + a/(f*tan(e + f*x)) - a/(3*f*tan(e + f*x)**3) - b*x - b/(f*tan(e + f*x)), True))","A",0
197,1,97,0,4.421803," ","integrate(cot(f*x+e)**6*(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} a x & \text{for}\: \left(e = 0 \vee e = - f x\right) \wedge \left(e = - f x \vee f = 0\right) \\x \left(a + b \tan^{2}{\left(e \right)}\right) \cot^{6}{\left(e \right)} & \text{for}\: f = 0 \\- a x - \frac{a}{f \tan{\left(e + f x \right)}} + \frac{a}{3 f \tan^{3}{\left(e + f x \right)}} - \frac{a}{5 f \tan^{5}{\left(e + f x \right)}} + b x + \frac{b}{f \tan{\left(e + f x \right)}} - \frac{b}{3 f \tan^{3}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a*x, (Eq(e, 0) | Eq(e, -f*x)) & (Eq(f, 0) | Eq(e, -f*x))), (x*(a + b*tan(e)**2)*cot(e)**6, Eq(f, 0)), (-a*x - a/(f*tan(e + f*x)) + a/(3*f*tan(e + f*x)**3) - a/(5*f*tan(e + f*x)**5) + b*x + b/(f*tan(e + f*x)) - b/(3*f*tan(e + f*x)**3), True))","A",0
198,1,206,0,1.343155," ","integrate(tan(f*x+e)**5*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \frac{a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{a^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{a b \tan^{6}{\left(e + f x \right)}}{3 f} - \frac{a b \tan^{4}{\left(e + f x \right)}}{2 f} + \frac{a b \tan^{2}{\left(e + f x \right)}}{f} + \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{2} \tan^{8}{\left(e + f x \right)}}{8 f} - \frac{b^{2} \tan^{6}{\left(e + f x \right)}}{6 f} + \frac{b^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{b^{2} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \tan^{5}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*log(tan(e + f*x)**2 + 1)/(2*f) + a**2*tan(e + f*x)**4/(4*f) - a**2*tan(e + f*x)**2/(2*f) - a*b*log(tan(e + f*x)**2 + 1)/f + a*b*tan(e + f*x)**6/(3*f) - a*b*tan(e + f*x)**4/(2*f) + a*b*tan(e + f*x)**2/f + b**2*log(tan(e + f*x)**2 + 1)/(2*f) + b**2*tan(e + f*x)**8/(8*f) - b**2*tan(e + f*x)**6/(6*f) + b**2*tan(e + f*x)**4/(4*f) - b**2*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e)**2)**2*tan(e)**5, True))","A",0
199,1,160,0,0.788658," ","integrate(tan(f*x+e)**3*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} - \frac{a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{a b \tan^{4}{\left(e + f x \right)}}{2 f} - \frac{a b \tan^{2}{\left(e + f x \right)}}{f} - \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{2} \tan^{6}{\left(e + f x \right)}}{6 f} - \frac{b^{2} \tan^{4}{\left(e + f x \right)}}{4 f} + \frac{b^{2} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \tan^{3}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*log(tan(e + f*x)**2 + 1)/(2*f) + a**2*tan(e + f*x)**2/(2*f) + a*b*log(tan(e + f*x)**2 + 1)/f + a*b*tan(e + f*x)**4/(2*f) - a*b*tan(e + f*x)**2/f - b**2*log(tan(e + f*x)**2 + 1)/(2*f) + b**2*tan(e + f*x)**6/(6*f) - b**2*tan(e + f*x)**4/(4*f) + b**2*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e)**2)**2*tan(e)**3, True))","A",0
200,1,112,0,0.421116," ","integrate(tan(f*x+e)*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \frac{a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{a b \tan^{2}{\left(e + f x \right)}}{f} + \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{b^{2} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \tan{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*log(tan(e + f*x)**2 + 1)/(2*f) - a*b*log(tan(e + f*x)**2 + 1)/f + a*b*tan(e + f*x)**2/f + b**2*log(tan(e + f*x)**2 + 1)/(2*f) + b**2*tan(e + f*x)**4/(4*f) - b**2*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e)**2)**2*tan(e), True))","A",0
201,1,97,0,1.137928," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} - \frac{a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a^{2} \log{\left(\tan{\left(e + f x \right)} \right)}}{f} + \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{2} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \cot{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*log(tan(e + f*x)**2 + 1)/(2*f) + a**2*log(tan(e + f*x))/f + a*b*log(tan(e + f*x)**2 + 1)/f - b**2*log(tan(e + f*x)**2 + 1)/(2*f) + b**2*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e)**2)**2*cot(e), True))","A",0
202,1,129,0,2.798012," ","integrate(cot(f*x+e)**3*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \tilde{\infty} a^{2} x & \text{for}\: e = 0 \wedge f = 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \cot^{3}{\left(e \right)} & \text{for}\: f = 0 \\\tilde{\infty} a^{2} x & \text{for}\: e = - f x \\\frac{a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - \frac{a^{2} \log{\left(\tan{\left(e + f x \right)} \right)}}{f} - \frac{a^{2}}{2 f \tan^{2}{\left(e + f x \right)}} - \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{2 a b \log{\left(\tan{\left(e + f x \right)} \right)}}{f} + \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, Eq(e, 0) & Eq(f, 0)), (x*(a + b*tan(e)**2)**2*cot(e)**3, Eq(f, 0)), (zoo*a**2*x, Eq(e, -f*x)), (a**2*log(tan(e + f*x)**2 + 1)/(2*f) - a**2*log(tan(e + f*x))/f - a**2/(2*f*tan(e + f*x)**2) - a*b*log(tan(e + f*x)**2 + 1)/f + 2*a*b*log(tan(e + f*x))/f + b**2*log(tan(e + f*x)**2 + 1)/(2*f), True))","A",0
203,1,172,0,8.543146," ","integrate(cot(f*x+e)**5*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \tilde{\infty} a^{2} x & \text{for}\: e = 0 \wedge f = 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \cot^{5}{\left(e \right)} & \text{for}\: f = 0 \\\tilde{\infty} a^{2} x & \text{for}\: e = - f x \\- \frac{a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{a^{2} \log{\left(\tan{\left(e + f x \right)} \right)}}{f} + \frac{a^{2}}{2 f \tan^{2}{\left(e + f x \right)}} - \frac{a^{2}}{4 f \tan^{4}{\left(e + f x \right)}} + \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - \frac{2 a b \log{\left(\tan{\left(e + f x \right)} \right)}}{f} - \frac{a b}{f \tan^{2}{\left(e + f x \right)}} - \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{b^{2} \log{\left(\tan{\left(e + f x \right)} \right)}}{f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, Eq(e, 0) & Eq(f, 0)), (x*(a + b*tan(e)**2)**2*cot(e)**5, Eq(f, 0)), (zoo*a**2*x, Eq(e, -f*x)), (-a**2*log(tan(e + f*x)**2 + 1)/(2*f) + a**2*log(tan(e + f*x))/f + a**2/(2*f*tan(e + f*x)**2) - a**2/(4*f*tan(e + f*x)**4) + a*b*log(tan(e + f*x)**2 + 1)/f - 2*a*b*log(tan(e + f*x))/f - a*b/(f*tan(e + f*x)**2) - b**2*log(tan(e + f*x)**2 + 1)/(2*f) + b**2*log(tan(e + f*x))/f, True))","A",0
204,1,212,0,1.871881," ","integrate(tan(f*x+e)**6*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} - a^{2} x + \frac{a^{2} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{a^{2} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{a^{2} \tan{\left(e + f x \right)}}{f} + 2 a b x + \frac{2 a b \tan^{7}{\left(e + f x \right)}}{7 f} - \frac{2 a b \tan^{5}{\left(e + f x \right)}}{5 f} + \frac{2 a b \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 a b \tan{\left(e + f x \right)}}{f} - b^{2} x + \frac{b^{2} \tan^{9}{\left(e + f x \right)}}{9 f} - \frac{b^{2} \tan^{7}{\left(e + f x \right)}}{7 f} + \frac{b^{2} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{b^{2} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{b^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \tan^{6}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x + a**2*tan(e + f*x)**5/(5*f) - a**2*tan(e + f*x)**3/(3*f) + a**2*tan(e + f*x)/f + 2*a*b*x + 2*a*b*tan(e + f*x)**7/(7*f) - 2*a*b*tan(e + f*x)**5/(5*f) + 2*a*b*tan(e + f*x)**3/(3*f) - 2*a*b*tan(e + f*x)/f - b**2*x + b**2*tan(e + f*x)**9/(9*f) - b**2*tan(e + f*x)**7/(7*f) + b**2*tan(e + f*x)**5/(5*f) - b**2*tan(e + f*x)**3/(3*f) + b**2*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e)**2)**2*tan(e)**6, True))","A",0
205,1,165,0,1.075450," ","integrate(tan(f*x+e)**4*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} a^{2} x + \frac{a^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{a^{2} \tan{\left(e + f x \right)}}{f} - 2 a b x + \frac{2 a b \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{2 a b \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{2 a b \tan{\left(e + f x \right)}}{f} + b^{2} x + \frac{b^{2} \tan^{7}{\left(e + f x \right)}}{7 f} - \frac{b^{2} \tan^{5}{\left(e + f x \right)}}{5 f} + \frac{b^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \tan^{4}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + a**2*tan(e + f*x)**3/(3*f) - a**2*tan(e + f*x)/f - 2*a*b*x + 2*a*b*tan(e + f*x)**5/(5*f) - 2*a*b*tan(e + f*x)**3/(3*f) + 2*a*b*tan(e + f*x)/f + b**2*x + b**2*tan(e + f*x)**7/(7*f) - b**2*tan(e + f*x)**5/(5*f) + b**2*tan(e + f*x)**3/(3*f) - b**2*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e)**2)**2*tan(e)**4, True))","A",0
206,1,117,0,0.625619," ","integrate(tan(f*x+e)**2*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} - a^{2} x + \frac{a^{2} \tan{\left(e + f x \right)}}{f} + 2 a b x + \frac{2 a b \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 a b \tan{\left(e + f x \right)}}{f} - b^{2} x + \frac{b^{2} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{b^{2} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{b^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \tan^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*x + a**2*tan(e + f*x)/f + 2*a*b*x + 2*a*b*tan(e + f*x)**3/(3*f) - 2*a*b*tan(e + f*x)/f - b**2*x + b**2*tan(e + f*x)**5/(5*f) - b**2*tan(e + f*x)**3/(3*f) + b**2*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e)**2)**2*tan(e)**2, True))","A",0
207,1,68,0,0.317245," ","integrate((a+b*tan(f*x+e)**2)**2,x)","\begin{cases} a^{2} x - 2 a b x + \frac{2 a b \tan{\left(e + f x \right)}}{f} + b^{2} x + \frac{b^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{b^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x - 2*a*b*x + 2*a*b*tan(e + f*x)/f + b**2*x + b**2*tan(e + f*x)**3/(3*f) - b**2*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e)**2)**2, True))","A",0
208,1,73,0,1.704090," ","integrate(cot(f*x+e)**2*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \tilde{\infty} a^{2} x & \text{for}\: \left(e = 0 \vee e = - f x\right) \wedge \left(e = - f x \vee f = 0\right) \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \cot^{2}{\left(e \right)} & \text{for}\: f = 0 \\- a^{2} x - \frac{a^{2}}{f \tan{\left(e + f x \right)}} + 2 a b x - b^{2} x + \frac{b^{2} \tan{\left(e + f x \right)}}{f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, (Eq(e, 0) | Eq(e, -f*x)) & (Eq(f, 0) | Eq(e, -f*x))), (x*(a + b*tan(e)**2)**2*cot(e)**2, Eq(f, 0)), (-a**2*x - a**2/(f*tan(e + f*x)) + 2*a*b*x - b**2*x + b**2*tan(e + f*x)/f, True))","A",0
209,1,90,0,4.119662," ","integrate(cot(f*x+e)**4*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \tilde{\infty} a^{2} x & \text{for}\: \left(e = 0 \vee e = - f x\right) \wedge \left(e = - f x \vee f = 0\right) \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \cot^{4}{\left(e \right)} & \text{for}\: f = 0 \\a^{2} x + \frac{a^{2}}{f \tan{\left(e + f x \right)}} - \frac{a^{2}}{3 f \tan^{3}{\left(e + f x \right)}} - 2 a b x - \frac{2 a b}{f \tan{\left(e + f x \right)}} + b^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, (Eq(e, 0) | Eq(e, -f*x)) & (Eq(f, 0) | Eq(e, -f*x))), (x*(a + b*tan(e)**2)**2*cot(e)**4, Eq(f, 0)), (a**2*x + a**2/(f*tan(e + f*x)) - a**2/(3*f*tan(e + f*x)**3) - 2*a*b*x - 2*a*b/(f*tan(e + f*x)) + b**2*x, True))","A",0
210,1,134,0,8.464880," ","integrate(cot(f*x+e)**6*(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \tilde{\infty} a^{2} x & \text{for}\: \left(e = 0 \vee e = - f x\right) \wedge \left(e = - f x \vee f = 0\right) \\x \left(a + b \tan^{2}{\left(e \right)}\right)^{2} \cot^{6}{\left(e \right)} & \text{for}\: f = 0 \\- a^{2} x - \frac{a^{2}}{f \tan{\left(e + f x \right)}} + \frac{a^{2}}{3 f \tan^{3}{\left(e + f x \right)}} - \frac{a^{2}}{5 f \tan^{5}{\left(e + f x \right)}} + 2 a b x + \frac{2 a b}{f \tan{\left(e + f x \right)}} - \frac{2 a b}{3 f \tan^{3}{\left(e + f x \right)}} - b^{2} x - \frac{b^{2}}{f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*a**2*x, (Eq(e, 0) | Eq(e, -f*x)) & (Eq(f, 0) | Eq(e, -f*x))), (x*(a + b*tan(e)**2)**2*cot(e)**6, Eq(f, 0)), (-a**2*x - a**2/(f*tan(e + f*x)) + a**2/(3*f*tan(e + f*x)**3) - a**2/(5*f*tan(e + f*x)**5) + 2*a*b*x + 2*a*b/(f*tan(e + f*x)) - 2*a*b/(3*f*tan(e + f*x)**3) - b**2*x - b**2/(f*tan(e + f*x)), True))","A",0
211,1,348,0,16.360951," ","integrate(tan(f*x+e)**5/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x \tan^{3}{\left(e \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\- \frac{2 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} - \frac{2 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{\tan^{4}{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} - \frac{2}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} & \text{for}\: a = b \\\frac{\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\tan^{4}{\left(e + f x \right)}}{4 f} - \frac{\tan^{2}{\left(e + f x \right)}}{2 f}}{a} & \text{for}\: b = 0 \\\frac{x \tan^{5}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\- \frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a b^{2} f - 2 b^{3} f} - \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a b^{2} f - 2 b^{3} f} + \frac{a b \tan^{2}{\left(e + f x \right)}}{2 a b^{2} f - 2 b^{3} f} + \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a b^{2} f - 2 b^{3} f} - \frac{b^{2} \tan^{2}{\left(e + f x \right)}}{2 a b^{2} f - 2 b^{3} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(e)**3, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (-2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*b*f*tan(e + f*x)**2 + 2*b*f) - 2*log(tan(e + f*x)**2 + 1)/(2*b*f*tan(e + f*x)**2 + 2*b*f) + tan(e + f*x)**4/(2*b*f*tan(e + f*x)**2 + 2*b*f) - 2/(2*b*f*tan(e + f*x)**2 + 2*b*f), Eq(a, b)), ((log(tan(e + f*x)**2 + 1)/(2*f) + tan(e + f*x)**4/(4*f) - tan(e + f*x)**2/(2*f))/a, Eq(b, 0)), (x*tan(e)**5/(a + b*tan(e)**2), Eq(f, 0)), (-a**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a*b**2*f - 2*b**3*f) - a**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a*b**2*f - 2*b**3*f) + a*b*tan(e + f*x)**2/(2*a*b**2*f - 2*b**3*f) + b**2*log(tan(e + f*x)**2 + 1)/(2*a*b**2*f - 2*b**3*f) - b**2*tan(e + f*x)**2/(2*a*b**2*f - 2*b**3*f), True))","A",0
212,1,240,0,3.674612," ","integrate(tan(f*x+e)**3/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x \tan{\left(e \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\tan^{2}{\left(e + f x \right)}}{2 f}}{a} & \text{for}\: b = 0 \\\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{1}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} & \text{for}\: a = b \\\frac{x \tan^{3}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a b f - 2 b^{2} f} + \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a b f - 2 b^{2} f} - \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a b f - 2 b^{2} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-log(tan(e + f*x)**2 + 1)/(2*f) + tan(e + f*x)**2/(2*f))/a, Eq(b, 0)), (log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*b*f*tan(e + f*x)**2 + 2*b*f) + log(tan(e + f*x)**2 + 1)/(2*b*f*tan(e + f*x)**2 + 2*b*f) + 1/(2*b*f*tan(e + f*x)**2 + 2*b*f), Eq(a, b)), (x*tan(e)**3/(a + b*tan(e)**2), Eq(f, 0)), (a*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a*b*f - 2*b**2*f) + a*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a*b*f - 2*b**2*f) - b*log(tan(e + f*x)**2 + 1)/(2*a*b*f - 2*b**2*f), True))","A",0
213,1,143,0,2.112271," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)**2),x)","\begin{cases} \frac{\tilde{\infty} x}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a f} & \text{for}\: b = 0 \\- \frac{1}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} & \text{for}\: a = b \\\frac{x \tan{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\- \frac{\log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a f - 2 b f} - \frac{\log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a f - 2 b f} + \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a f - 2 b f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (log(tan(e + f*x)**2 + 1)/(2*a*f), Eq(b, 0)), (-1/(2*b*f*tan(e + f*x)**2 + 2*b*f), Eq(a, b)), (x*tan(e)/(a + b*tan(e)**2), Eq(f, 0)), (-log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a*f - 2*b*f) - log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a*f - 2*b*f) + log(tan(e + f*x)**2 + 1)/(2*a*f - 2*b*f), True))","A",0
214,1,398,0,8.378547," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)**2),x)","\begin{cases} \frac{\tilde{\infty} x \cot{\left(e \right)}}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - \frac{\log{\left(\tan{\left(e + f x \right)} \right)}}{f} - \frac{1}{2 f \tan^{2}{\left(e + f x \right)}}}{b} & \text{for}\: a = 0 \\- \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 a f \tan^{2}{\left(e + f x \right)} + 2 a f} - \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a f \tan^{2}{\left(e + f x \right)} + 2 a f} + \frac{2 \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a f \tan^{2}{\left(e + f x \right)} + 2 a f} + \frac{2 \log{\left(\tan{\left(e + f x \right)} \right)}}{2 a f \tan^{2}{\left(e + f x \right)} + 2 a f} + \frac{1}{2 a f \tan^{2}{\left(e + f x \right)} + 2 a f} & \text{for}\: a = b \\\frac{x \cot{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{- \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\log{\left(\tan{\left(e + f x \right)} \right)}}{f}}{a} & \text{for}\: b = 0 \\- \frac{a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} f - 2 a b f} + \frac{2 a \log{\left(\tan{\left(e + f x \right)} \right)}}{2 a^{2} f - 2 a b f} + \frac{b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} f - 2 a b f} + \frac{b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} f - 2 a b f} - \frac{2 b \log{\left(\tan{\left(e + f x \right)} \right)}}{2 a^{2} f - 2 a b f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*cot(e)/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((log(tan(e + f*x)**2 + 1)/(2*f) - log(tan(e + f*x))/f - 1/(2*f*tan(e + f*x)**2))/b, Eq(a, 0)), (-log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*a*f*tan(e + f*x)**2 + 2*a*f) - log(tan(e + f*x)**2 + 1)/(2*a*f*tan(e + f*x)**2 + 2*a*f) + 2*log(tan(e + f*x))*tan(e + f*x)**2/(2*a*f*tan(e + f*x)**2 + 2*a*f) + 2*log(tan(e + f*x))/(2*a*f*tan(e + f*x)**2 + 2*a*f) + 1/(2*a*f*tan(e + f*x)**2 + 2*a*f), Eq(a, b)), (x*cot(e)/(a + b*tan(e)**2), Eq(f, 0)), ((-log(tan(e + f*x)**2 + 1)/(2*f) + log(tan(e + f*x))/f)/a, Eq(b, 0)), (-a*log(tan(e + f*x)**2 + 1)/(2*a**2*f - 2*a*b*f) + 2*a*log(tan(e + f*x))/(2*a**2*f - 2*a*b*f) + b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**2*f - 2*a*b*f) + b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**2*f - 2*a*b*f) - 2*b*log(tan(e + f*x))/(2*a**2*f - 2*a*b*f), True))","A",0
215,1,743,0,28.088575," ","integrate(cot(f*x+e)**3/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge e = 0 \wedge f = 0 \\\frac{- \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\log{\left(\tan{\left(e + f x \right)} \right)}}{f} + \frac{1}{2 f \tan^{2}{\left(e + f x \right)}} - \frac{1}{4 f \tan^{4}{\left(e + f x \right)}}}{b} & \text{for}\: a = 0 \\\frac{2 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{4}{\left(e + f x \right)}}{2 a f \tan^{4}{\left(e + f x \right)} + 2 a f \tan^{2}{\left(e + f x \right)}} + \frac{2 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 a f \tan^{4}{\left(e + f x \right)} + 2 a f \tan^{2}{\left(e + f x \right)}} - \frac{4 \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{2 a f \tan^{4}{\left(e + f x \right)} + 2 a f \tan^{2}{\left(e + f x \right)}} - \frac{4 \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a f \tan^{4}{\left(e + f x \right)} + 2 a f \tan^{2}{\left(e + f x \right)}} - \frac{2 \tan^{2}{\left(e + f x \right)}}{2 a f \tan^{4}{\left(e + f x \right)} + 2 a f \tan^{2}{\left(e + f x \right)}} - \frac{1}{2 a f \tan^{4}{\left(e + f x \right)} + 2 a f \tan^{2}{\left(e + f x \right)}} & \text{for}\: a = b \\\frac{\tilde{\infty} x}{a} & \text{for}\: e = - f x \\\frac{x \cot^{3}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - \frac{\log{\left(\tan{\left(e + f x \right)} \right)}}{f} - \frac{1}{2 f \tan^{2}{\left(e + f x \right)}}}{a} & \text{for}\: b = 0 \\\frac{a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} b f \tan^{2}{\left(e + f x \right)}} - \frac{2 a^{2} \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} b f \tan^{2}{\left(e + f x \right)}} - \frac{a^{2}}{2 a^{3} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} b f \tan^{2}{\left(e + f x \right)}} + \frac{a b}{2 a^{3} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} b f \tan^{2}{\left(e + f x \right)}} - \frac{b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} b f \tan^{2}{\left(e + f x \right)}} - \frac{b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} b f \tan^{2}{\left(e + f x \right)}} + \frac{2 b^{2} \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} f \tan^{2}{\left(e + f x \right)} - 2 a^{2} b f \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(e, 0) & Eq(f, 0)), ((-log(tan(e + f*x)**2 + 1)/(2*f) + log(tan(e + f*x))/f + 1/(2*f*tan(e + f*x)**2) - 1/(4*f*tan(e + f*x)**4))/b, Eq(a, 0)), (2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**4/(2*a*f*tan(e + f*x)**4 + 2*a*f*tan(e + f*x)**2) + 2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*a*f*tan(e + f*x)**4 + 2*a*f*tan(e + f*x)**2) - 4*log(tan(e + f*x))*tan(e + f*x)**4/(2*a*f*tan(e + f*x)**4 + 2*a*f*tan(e + f*x)**2) - 4*log(tan(e + f*x))*tan(e + f*x)**2/(2*a*f*tan(e + f*x)**4 + 2*a*f*tan(e + f*x)**2) - 2*tan(e + f*x)**2/(2*a*f*tan(e + f*x)**4 + 2*a*f*tan(e + f*x)**2) - 1/(2*a*f*tan(e + f*x)**4 + 2*a*f*tan(e + f*x)**2), Eq(a, b)), (zoo*x/a, Eq(e, -f*x)), (x*cot(e)**3/(a + b*tan(e)**2), Eq(f, 0)), ((log(tan(e + f*x)**2 + 1)/(2*f) - log(tan(e + f*x))/f - 1/(2*f*tan(e + f*x)**2))/a, Eq(b, 0)), (a**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*a**3*f*tan(e + f*x)**2 - 2*a**2*b*f*tan(e + f*x)**2) - 2*a**2*log(tan(e + f*x))*tan(e + f*x)**2/(2*a**3*f*tan(e + f*x)**2 - 2*a**2*b*f*tan(e + f*x)**2) - a**2/(2*a**3*f*tan(e + f*x)**2 - 2*a**2*b*f*tan(e + f*x)**2) + a*b/(2*a**3*f*tan(e + f*x)**2 - 2*a**2*b*f*tan(e + f*x)**2) - b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*f*tan(e + f*x)**2 - 2*a**2*b*f*tan(e + f*x)**2) - b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*f*tan(e + f*x)**2 - 2*a**2*b*f*tan(e + f*x)**2) + 2*b**2*log(tan(e + f*x))*tan(e + f*x)**2/(2*a**3*f*tan(e + f*x)**2 - 2*a**2*b*f*tan(e + f*x)**2), True))","A",0
216,1,908,0,94.467824," ","integrate(cot(f*x+e)**5/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge e = 0 \wedge f = 0 \\\frac{\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - \frac{\log{\left(\tan{\left(e + f x \right)} \right)}}{f} - \frac{1}{2 f \tan^{2}{\left(e + f x \right)}} + \frac{1}{4 f \tan^{4}{\left(e + f x \right)}} - \frac{1}{6 f \tan^{6}{\left(e + f x \right)}}}{b} & \text{for}\: a = 0 \\- \frac{6 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{6}{\left(e + f x \right)}}{4 a f \tan^{6}{\left(e + f x \right)} + 4 a f \tan^{4}{\left(e + f x \right)}} - \frac{6 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{4}{\left(e + f x \right)}}{4 a f \tan^{6}{\left(e + f x \right)} + 4 a f \tan^{4}{\left(e + f x \right)}} + \frac{12 \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{6}{\left(e + f x \right)}}{4 a f \tan^{6}{\left(e + f x \right)} + 4 a f \tan^{4}{\left(e + f x \right)}} + \frac{12 \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a f \tan^{6}{\left(e + f x \right)} + 4 a f \tan^{4}{\left(e + f x \right)}} + \frac{6 \tan^{4}{\left(e + f x \right)}}{4 a f \tan^{6}{\left(e + f x \right)} + 4 a f \tan^{4}{\left(e + f x \right)}} + \frac{3 \tan^{2}{\left(e + f x \right)}}{4 a f \tan^{6}{\left(e + f x \right)} + 4 a f \tan^{4}{\left(e + f x \right)}} - \frac{1}{4 a f \tan^{6}{\left(e + f x \right)} + 4 a f \tan^{4}{\left(e + f x \right)}} & \text{for}\: a = b \\\frac{\tilde{\infty} x}{a} & \text{for}\: e = - f x \\\frac{x \cot^{5}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{- \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\log{\left(\tan{\left(e + f x \right)} \right)}}{f} + \frac{1}{2 f \tan^{2}{\left(e + f x \right)}} - \frac{1}{4 f \tan^{4}{\left(e + f x \right)}}}{a} & \text{for}\: b = 0 \\- \frac{2 a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} + \frac{4 a^{3} \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} + \frac{2 a^{3} \tan^{2}{\left(e + f x \right)}}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} - \frac{a^{3}}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} + \frac{a^{2} b}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} - \frac{2 a b^{2} \tan^{2}{\left(e + f x \right)}}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} + \frac{2 b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} + \frac{2 b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} - \frac{4 b^{3} \log{\left(\tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{4} f \tan^{4}{\left(e + f x \right)} - 4 a^{3} b f \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(e, 0) & Eq(f, 0)), ((log(tan(e + f*x)**2 + 1)/(2*f) - log(tan(e + f*x))/f - 1/(2*f*tan(e + f*x)**2) + 1/(4*f*tan(e + f*x)**4) - 1/(6*f*tan(e + f*x)**6))/b, Eq(a, 0)), (-6*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**6/(4*a*f*tan(e + f*x)**6 + 4*a*f*tan(e + f*x)**4) - 6*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**4/(4*a*f*tan(e + f*x)**6 + 4*a*f*tan(e + f*x)**4) + 12*log(tan(e + f*x))*tan(e + f*x)**6/(4*a*f*tan(e + f*x)**6 + 4*a*f*tan(e + f*x)**4) + 12*log(tan(e + f*x))*tan(e + f*x)**4/(4*a*f*tan(e + f*x)**6 + 4*a*f*tan(e + f*x)**4) + 6*tan(e + f*x)**4/(4*a*f*tan(e + f*x)**6 + 4*a*f*tan(e + f*x)**4) + 3*tan(e + f*x)**2/(4*a*f*tan(e + f*x)**6 + 4*a*f*tan(e + f*x)**4) - 1/(4*a*f*tan(e + f*x)**6 + 4*a*f*tan(e + f*x)**4), Eq(a, b)), (zoo*x/a, Eq(e, -f*x)), (x*cot(e)**5/(a + b*tan(e)**2), Eq(f, 0)), ((-log(tan(e + f*x)**2 + 1)/(2*f) + log(tan(e + f*x))/f + 1/(2*f*tan(e + f*x)**2) - 1/(4*f*tan(e + f*x)**4))/a, Eq(b, 0)), (-2*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**4/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4) + 4*a**3*log(tan(e + f*x))*tan(e + f*x)**4/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4) + 2*a**3*tan(e + f*x)**2/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4) - a**3/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4) + a**2*b/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4) - 2*a*b**2*tan(e + f*x)**2/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4) + 2*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4) + 2*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4) - 4*b**3*log(tan(e + f*x))*tan(e + f*x)**4/(4*a**4*f*tan(e + f*x)**4 - 4*a**3*b*f*tan(e + f*x)**4), True))","A",0
217,1,685,0,35.000128," ","integrate(tan(f*x+e)**6/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x \tan^{4}{\left(e \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- x + \frac{\tan^{5}{\left(e + f x \right)}}{5 f} - \frac{\tan^{3}{\left(e + f x \right)}}{3 f} + \frac{\tan{\left(e + f x \right)}}{f}}{a} & \text{for}\: b = 0 \\\frac{x + \frac{\tan^{3}{\left(e + f x \right)}}{3 f} - \frac{\tan{\left(e + f x \right)}}{f}}{b} & \text{for}\: a = 0 \\\frac{15 f x \tan^{2}{\left(e + f x \right)}}{6 b f \tan^{2}{\left(e + f x \right)} + 6 b f} + \frac{15 f x}{6 b f \tan^{2}{\left(e + f x \right)} + 6 b f} + \frac{2 \tan^{5}{\left(e + f x \right)}}{6 b f \tan^{2}{\left(e + f x \right)} + 6 b f} - \frac{10 \tan^{3}{\left(e + f x \right)}}{6 b f \tan^{2}{\left(e + f x \right)} + 6 b f} - \frac{15 \tan{\left(e + f x \right)}}{6 b f \tan^{2}{\left(e + f x \right)} + 6 b f} & \text{for}\: a = b \\\frac{x \tan^{6}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\- \frac{6 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{6 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} - 6 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}}} + \frac{2 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{6 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} - 6 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}}} - \frac{6 i \sqrt{a} b^{3} f x \sqrt{\frac{1}{b}}}{6 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} - 6 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}}} - \frac{2 i \sqrt{a} b^{3} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{6 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} - 6 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}}} + \frac{6 i \sqrt{a} b^{3} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{6 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} - 6 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}}} + \frac{3 a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{6 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} - 6 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}}} - \frac{3 a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{6 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} - 6 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(e)**4, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-x + tan(e + f*x)**5/(5*f) - tan(e + f*x)**3/(3*f) + tan(e + f*x)/f)/a, Eq(b, 0)), ((x + tan(e + f*x)**3/(3*f) - tan(e + f*x)/f)/b, Eq(a, 0)), (15*f*x*tan(e + f*x)**2/(6*b*f*tan(e + f*x)**2 + 6*b*f) + 15*f*x/(6*b*f*tan(e + f*x)**2 + 6*b*f) + 2*tan(e + f*x)**5/(6*b*f*tan(e + f*x)**2 + 6*b*f) - 10*tan(e + f*x)**3/(6*b*f*tan(e + f*x)**2 + 6*b*f) - 15*tan(e + f*x)/(6*b*f*tan(e + f*x)**2 + 6*b*f), Eq(a, b)), (x*tan(e)**6/(a + b*tan(e)**2), Eq(f, 0)), (-6*I*a**(5/2)*b*sqrt(1/b)*tan(e + f*x)/(6*I*a**(3/2)*b**3*f*sqrt(1/b) - 6*I*sqrt(a)*b**4*f*sqrt(1/b)) + 2*I*a**(3/2)*b**2*sqrt(1/b)*tan(e + f*x)**3/(6*I*a**(3/2)*b**3*f*sqrt(1/b) - 6*I*sqrt(a)*b**4*f*sqrt(1/b)) - 6*I*sqrt(a)*b**3*f*x*sqrt(1/b)/(6*I*a**(3/2)*b**3*f*sqrt(1/b) - 6*I*sqrt(a)*b**4*f*sqrt(1/b)) - 2*I*sqrt(a)*b**3*sqrt(1/b)*tan(e + f*x)**3/(6*I*a**(3/2)*b**3*f*sqrt(1/b) - 6*I*sqrt(a)*b**4*f*sqrt(1/b)) + 6*I*sqrt(a)*b**3*sqrt(1/b)*tan(e + f*x)/(6*I*a**(3/2)*b**3*f*sqrt(1/b) - 6*I*sqrt(a)*b**4*f*sqrt(1/b)) + 3*a**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(6*I*a**(3/2)*b**3*f*sqrt(1/b) - 6*I*sqrt(a)*b**4*f*sqrt(1/b)) - 3*a**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(6*I*a**(3/2)*b**3*f*sqrt(1/b) - 6*I*sqrt(a)*b**4*f*sqrt(1/b)), True))","A",0
218,1,493,0,6.761986," ","integrate(tan(f*x+e)**4/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x \tan^{2}{\left(e \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{x + \frac{\tan^{3}{\left(e + f x \right)}}{3 f} - \frac{\tan{\left(e + f x \right)}}{f}}{a} & \text{for}\: b = 0 \\\frac{- x + \frac{\tan{\left(e + f x \right)}}{f}}{b} & \text{for}\: a = 0 \\- \frac{3 f x \tan^{2}{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} - \frac{3 f x}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{2 \tan^{3}{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{3 \tan{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} & \text{for}\: a = b \\\frac{x \tan^{4}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 i a^{\frac{3}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{2 i a^{\frac{3}{2}} b^{2} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b^{3} f \sqrt{\frac{1}{b}}} + \frac{2 i \sqrt{a} b^{2} f x \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} b^{2} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b^{3} f \sqrt{\frac{1}{b}}} - \frac{2 i \sqrt{a} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{2 i a^{\frac{3}{2}} b^{2} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b^{3} f \sqrt{\frac{1}{b}}} - \frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 i a^{\frac{3}{2}} b^{2} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b^{3} f \sqrt{\frac{1}{b}}} + \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 i a^{\frac{3}{2}} b^{2} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b^{3} f \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((x + tan(e + f*x)**3/(3*f) - tan(e + f*x)/f)/a, Eq(b, 0)), ((-x + tan(e + f*x)/f)/b, Eq(a, 0)), (-3*f*x*tan(e + f*x)**2/(2*b*f*tan(e + f*x)**2 + 2*b*f) - 3*f*x/(2*b*f*tan(e + f*x)**2 + 2*b*f) + 2*tan(e + f*x)**3/(2*b*f*tan(e + f*x)**2 + 2*b*f) + 3*tan(e + f*x)/(2*b*f*tan(e + f*x)**2 + 2*b*f), Eq(a, b)), (x*tan(e)**4/(a + b*tan(e)**2), Eq(f, 0)), (2*I*a**(3/2)*b*sqrt(1/b)*tan(e + f*x)/(2*I*a**(3/2)*b**2*f*sqrt(1/b) - 2*I*sqrt(a)*b**3*f*sqrt(1/b)) + 2*I*sqrt(a)*b**2*f*x*sqrt(1/b)/(2*I*a**(3/2)*b**2*f*sqrt(1/b) - 2*I*sqrt(a)*b**3*f*sqrt(1/b)) - 2*I*sqrt(a)*b**2*sqrt(1/b)*tan(e + f*x)/(2*I*a**(3/2)*b**2*f*sqrt(1/b) - 2*I*sqrt(a)*b**3*f*sqrt(1/b)) - a**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*I*a**(3/2)*b**2*f*sqrt(1/b) - 2*I*sqrt(a)*b**3*f*sqrt(1/b)) + a**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*I*a**(3/2)*b**2*f*sqrt(1/b) - 2*I*sqrt(a)*b**3*f*sqrt(1/b)), True))","A",0
219,1,292,0,2.288626," ","integrate(tan(f*x+e)**2/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{x}{b} & \text{for}\: a = 0 \\\frac{f x \tan^{2}{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{f x}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} - \frac{\tan{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} & \text{for}\: a = b \\\frac{x \tan^{2}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{- x + \frac{\tan{\left(e + f x \right)}}{f}}{a} & \text{for}\: b = 0 \\- \frac{2 i \sqrt{a} b f x \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} b f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b^{2} f \sqrt{\frac{1}{b}}} + \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 i a^{\frac{3}{2}} b f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b^{2} f \sqrt{\frac{1}{b}}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 i a^{\frac{3}{2}} b f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b^{2} f \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (x/b, Eq(a, 0)), (f*x*tan(e + f*x)**2/(2*b*f*tan(e + f*x)**2 + 2*b*f) + f*x/(2*b*f*tan(e + f*x)**2 + 2*b*f) - tan(e + f*x)/(2*b*f*tan(e + f*x)**2 + 2*b*f), Eq(a, b)), (x*tan(e)**2/(a + b*tan(e)**2), Eq(f, 0)), ((-x + tan(e + f*x)/f)/a, Eq(b, 0)), (-2*I*sqrt(a)*b*f*x*sqrt(1/b)/(2*I*a**(3/2)*b*f*sqrt(1/b) - 2*I*sqrt(a)*b**2*f*sqrt(1/b)) + a*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*I*a**(3/2)*b*f*sqrt(1/b) - 2*I*sqrt(a)*b**2*f*sqrt(1/b)) - a*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*I*a**(3/2)*b*f*sqrt(1/b) - 2*I*sqrt(a)*b**2*f*sqrt(1/b)), True))","A",0
220,1,280,0,2.307165," ","integrate(1/(a+b*tan(f*x+e)**2),x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- x - \frac{1}{f \tan{\left(e + f x \right)}}}{b} & \text{for}\: a = 0 \\\frac{f x \tan^{2}{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{f x}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} + \frac{\tan{\left(e + f x \right)}}{2 b f \tan^{2}{\left(e + f x \right)} + 2 b f} & \text{for}\: a = b \\\frac{x}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{x}{a} & \text{for}\: b = 0 \\\frac{2 i \sqrt{a} f x \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b f \sqrt{\frac{1}{b}}} - \frac{\log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 i a^{\frac{3}{2}} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b f \sqrt{\frac{1}{b}}} + \frac{\log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 i a^{\frac{3}{2}} f \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b f \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-x - 1/(f*tan(e + f*x)))/b, Eq(a, 0)), (f*x*tan(e + f*x)**2/(2*b*f*tan(e + f*x)**2 + 2*b*f) + f*x/(2*b*f*tan(e + f*x)**2 + 2*b*f) + tan(e + f*x)/(2*b*f*tan(e + f*x)**2 + 2*b*f), Eq(a, b)), (x/(a + b*tan(e)**2), Eq(f, 0)), (x/a, Eq(b, 0)), (2*I*sqrt(a)*f*x*sqrt(1/b)/(2*I*a**(3/2)*f*sqrt(1/b) - 2*I*sqrt(a)*b*f*sqrt(1/b)) - log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*I*a**(3/2)*f*sqrt(1/b) - 2*I*sqrt(a)*b*f*sqrt(1/b)) + log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*I*a**(3/2)*f*sqrt(1/b) - 2*I*sqrt(a)*b*f*sqrt(1/b)), True))","A",0
221,1,570,0,14.921846," ","integrate(cot(f*x+e)**2/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge e = 0 \wedge f = 0 \\\frac{x + \frac{1}{f \tan{\left(e + f x \right)}} - \frac{1}{3 f \tan^{3}{\left(e + f x \right)}}}{b} & \text{for}\: a = 0 \\- \frac{3 f x \tan^{3}{\left(e + f x \right)}}{2 b f \tan^{3}{\left(e + f x \right)} + 2 b f \tan{\left(e + f x \right)}} - \frac{3 f x \tan{\left(e + f x \right)}}{2 b f \tan^{3}{\left(e + f x \right)} + 2 b f \tan{\left(e + f x \right)}} - \frac{3 \tan^{2}{\left(e + f x \right)}}{2 b f \tan^{3}{\left(e + f x \right)} + 2 b f \tan{\left(e + f x \right)}} - \frac{2}{2 b f \tan^{3}{\left(e + f x \right)} + 2 b f \tan{\left(e + f x \right)}} & \text{for}\: a = b \\\frac{\tilde{\infty} x}{a} & \text{for}\: e = - f x \\\frac{x \cot^{2}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{- x - \frac{\cot{\left(e + f x \right)}}{f}}{a} & \text{for}\: b = 0 \\- \frac{2 i a^{\frac{3}{2}} f x \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{2 i a^{\frac{5}{2}} f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)} - 2 i a^{\frac{3}{2}} b f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}} - \frac{2 i a^{\frac{3}{2}} \sqrt{\frac{1}{b}}}{2 i a^{\frac{5}{2}} f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)} - 2 i a^{\frac{3}{2}} b f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}} + \frac{2 i \sqrt{a} b \sqrt{\frac{1}{b}}}{2 i a^{\frac{5}{2}} f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)} - 2 i a^{\frac{3}{2}} b f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}} + \frac{b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 i a^{\frac{5}{2}} f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)} - 2 i a^{\frac{3}{2}} b f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}} - \frac{b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 i a^{\frac{5}{2}} f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)} - 2 i a^{\frac{3}{2}} b f \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(e, 0) & Eq(f, 0)), ((x + 1/(f*tan(e + f*x)) - 1/(3*f*tan(e + f*x)**3))/b, Eq(a, 0)), (-3*f*x*tan(e + f*x)**3/(2*b*f*tan(e + f*x)**3 + 2*b*f*tan(e + f*x)) - 3*f*x*tan(e + f*x)/(2*b*f*tan(e + f*x)**3 + 2*b*f*tan(e + f*x)) - 3*tan(e + f*x)**2/(2*b*f*tan(e + f*x)**3 + 2*b*f*tan(e + f*x)) - 2/(2*b*f*tan(e + f*x)**3 + 2*b*f*tan(e + f*x)), Eq(a, b)), (zoo*x/a, Eq(e, -f*x)), (x*cot(e)**2/(a + b*tan(e)**2), Eq(f, 0)), ((-x - cot(e + f*x)/f)/a, Eq(b, 0)), (-2*I*a**(3/2)*f*x*sqrt(1/b)*tan(e + f*x)/(2*I*a**(5/2)*f*sqrt(1/b)*tan(e + f*x) - 2*I*a**(3/2)*b*f*sqrt(1/b)*tan(e + f*x)) - 2*I*a**(3/2)*sqrt(1/b)/(2*I*a**(5/2)*f*sqrt(1/b)*tan(e + f*x) - 2*I*a**(3/2)*b*f*sqrt(1/b)*tan(e + f*x)) + 2*I*sqrt(a)*b*sqrt(1/b)/(2*I*a**(5/2)*f*sqrt(1/b)*tan(e + f*x) - 2*I*a**(3/2)*b*f*sqrt(1/b)*tan(e + f*x)) + b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)/(2*I*a**(5/2)*f*sqrt(1/b)*tan(e + f*x) - 2*I*a**(3/2)*b*f*sqrt(1/b)*tan(e + f*x)) - b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)/(2*I*a**(5/2)*f*sqrt(1/b)*tan(e + f*x) - 2*I*a**(3/2)*b*f*sqrt(1/b)*tan(e + f*x)), True))","A",0
222,1,823,0,57.334500," ","integrate(cot(f*x+e)**4/(a+b*tan(f*x+e)**2),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge e = 0 \wedge f = 0 \\\frac{- x - \frac{1}{f \tan{\left(e + f x \right)}} + \frac{1}{3 f \tan^{3}{\left(e + f x \right)}} - \frac{1}{5 f \tan^{5}{\left(e + f x \right)}}}{b} & \text{for}\: a = 0 \\\frac{15 f x \tan^{5}{\left(e + f x \right)}}{6 b f \tan^{5}{\left(e + f x \right)} + 6 b f \tan^{3}{\left(e + f x \right)}} + \frac{15 f x \tan^{3}{\left(e + f x \right)}}{6 b f \tan^{5}{\left(e + f x \right)} + 6 b f \tan^{3}{\left(e + f x \right)}} + \frac{15 \tan^{4}{\left(e + f x \right)}}{6 b f \tan^{5}{\left(e + f x \right)} + 6 b f \tan^{3}{\left(e + f x \right)}} + \frac{10 \tan^{2}{\left(e + f x \right)}}{6 b f \tan^{5}{\left(e + f x \right)} + 6 b f \tan^{3}{\left(e + f x \right)}} - \frac{2}{6 b f \tan^{5}{\left(e + f x \right)} + 6 b f \tan^{3}{\left(e + f x \right)}} & \text{for}\: a = b \\\frac{\tilde{\infty} x}{a} & \text{for}\: e = - f x \\\frac{x \cot^{4}{\left(e \right)}}{a + b \tan^{2}{\left(e \right)}} & \text{for}\: f = 0 \\\frac{x - \frac{\cot^{3}{\left(e + f x \right)}}{3 f} + \frac{\cot{\left(e + f x \right)}}{f}}{a} & \text{for}\: b = 0 \\\frac{6 i a^{\frac{5}{2}} f x \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{6 i a^{\frac{7}{2}} f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)} - 6 i a^{\frac{5}{2}} b f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}} + \frac{6 i a^{\frac{5}{2}} \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{6 i a^{\frac{7}{2}} f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)} - 6 i a^{\frac{5}{2}} b f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}} - \frac{2 i a^{\frac{5}{2}} \sqrt{\frac{1}{b}}}{6 i a^{\frac{7}{2}} f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)} - 6 i a^{\frac{5}{2}} b f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}} + \frac{2 i a^{\frac{3}{2}} b \sqrt{\frac{1}{b}}}{6 i a^{\frac{7}{2}} f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)} - 6 i a^{\frac{5}{2}} b f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}} - \frac{6 i \sqrt{a} b^{2} \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{6 i a^{\frac{7}{2}} f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)} - 6 i a^{\frac{5}{2}} b f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}} - \frac{3 b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{3}{\left(e + f x \right)}}{6 i a^{\frac{7}{2}} f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)} - 6 i a^{\frac{5}{2}} b f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}} + \frac{3 b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{3}{\left(e + f x \right)}}{6 i a^{\frac{7}{2}} f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)} - 6 i a^{\frac{5}{2}} b f \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(e, 0) & Eq(f, 0)), ((-x - 1/(f*tan(e + f*x)) + 1/(3*f*tan(e + f*x)**3) - 1/(5*f*tan(e + f*x)**5))/b, Eq(a, 0)), (15*f*x*tan(e + f*x)**5/(6*b*f*tan(e + f*x)**5 + 6*b*f*tan(e + f*x)**3) + 15*f*x*tan(e + f*x)**3/(6*b*f*tan(e + f*x)**5 + 6*b*f*tan(e + f*x)**3) + 15*tan(e + f*x)**4/(6*b*f*tan(e + f*x)**5 + 6*b*f*tan(e + f*x)**3) + 10*tan(e + f*x)**2/(6*b*f*tan(e + f*x)**5 + 6*b*f*tan(e + f*x)**3) - 2/(6*b*f*tan(e + f*x)**5 + 6*b*f*tan(e + f*x)**3), Eq(a, b)), (zoo*x/a, Eq(e, -f*x)), (x*cot(e)**4/(a + b*tan(e)**2), Eq(f, 0)), ((x - cot(e + f*x)**3/(3*f) + cot(e + f*x)/f)/a, Eq(b, 0)), (6*I*a**(5/2)*f*x*sqrt(1/b)*tan(e + f*x)**3/(6*I*a**(7/2)*f*sqrt(1/b)*tan(e + f*x)**3 - 6*I*a**(5/2)*b*f*sqrt(1/b)*tan(e + f*x)**3) + 6*I*a**(5/2)*sqrt(1/b)*tan(e + f*x)**2/(6*I*a**(7/2)*f*sqrt(1/b)*tan(e + f*x)**3 - 6*I*a**(5/2)*b*f*sqrt(1/b)*tan(e + f*x)**3) - 2*I*a**(5/2)*sqrt(1/b)/(6*I*a**(7/2)*f*sqrt(1/b)*tan(e + f*x)**3 - 6*I*a**(5/2)*b*f*sqrt(1/b)*tan(e + f*x)**3) + 2*I*a**(3/2)*b*sqrt(1/b)/(6*I*a**(7/2)*f*sqrt(1/b)*tan(e + f*x)**3 - 6*I*a**(5/2)*b*f*sqrt(1/b)*tan(e + f*x)**3) - 6*I*sqrt(a)*b**2*sqrt(1/b)*tan(e + f*x)**2/(6*I*a**(7/2)*f*sqrt(1/b)*tan(e + f*x)**3 - 6*I*a**(5/2)*b*f*sqrt(1/b)*tan(e + f*x)**3) - 3*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**3/(6*I*a**(7/2)*f*sqrt(1/b)*tan(e + f*x)**3 - 6*I*a**(5/2)*b*f*sqrt(1/b)*tan(e + f*x)**3) + 3*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**3/(6*I*a**(7/2)*f*sqrt(1/b)*tan(e + f*x)**3 - 6*I*a**(5/2)*b*f*sqrt(1/b)*tan(e + f*x)**3), True))","A",0
223,-1,0,0,0.000000," ","integrate(cot(f*x+e)**6/(a+b*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,1,1583,0,55.479479," ","integrate(tan(f*x+e)**5/(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \tilde{\infty} x \tan{\left(e \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{2 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{4}{\left(e + f x \right)}}{4 b^{2} f \tan^{4}{\left(e + f x \right)} + 8 b^{2} f \tan^{2}{\left(e + f x \right)} + 4 b^{2} f} + \frac{4 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{4 b^{2} f \tan^{4}{\left(e + f x \right)} + 8 b^{2} f \tan^{2}{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{4 b^{2} f \tan^{4}{\left(e + f x \right)} + 8 b^{2} f \tan^{2}{\left(e + f x \right)} + 4 b^{2} f} + \frac{4 \tan^{2}{\left(e + f x \right)}}{4 b^{2} f \tan^{4}{\left(e + f x \right)} + 8 b^{2} f \tan^{2}{\left(e + f x \right)} + 4 b^{2} f} + \frac{3}{4 b^{2} f \tan^{4}{\left(e + f x \right)} + 8 b^{2} f \tan^{2}{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = b \\\frac{\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\tan^{4}{\left(e + f x \right)}}{4 f} - \frac{\tan^{2}{\left(e + f x \right)}}{2 f}}{a^{2}} & \text{for}\: b = 0 \\\frac{x \tan^{5}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} + \frac{a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} + \frac{a^{3}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} + \frac{a^{2} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} - \frac{2 a^{2} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} + \frac{a^{2} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} - \frac{2 a^{2} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} - \frac{a^{2} b}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} - \frac{2 a b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} - \frac{2 a b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} + \frac{a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} + \frac{b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} b^{2} f + 2 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f - 4 a b^{4} f \tan^{2}{\left(e + f x \right)} + 2 a b^{4} f + 2 b^{5} f \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**4/(4*b**2*f*tan(e + f*x)**4 + 8*b**2*f*tan(e + f*x)**2 + 4*b**2*f) + 4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(4*b**2*f*tan(e + f*x)**4 + 8*b**2*f*tan(e + f*x)**2 + 4*b**2*f) + 2*log(tan(e + f*x)**2 + 1)/(4*b**2*f*tan(e + f*x)**4 + 8*b**2*f*tan(e + f*x)**2 + 4*b**2*f) + 4*tan(e + f*x)**2/(4*b**2*f*tan(e + f*x)**4 + 8*b**2*f*tan(e + f*x)**2 + 4*b**2*f) + 3/(4*b**2*f*tan(e + f*x)**4 + 8*b**2*f*tan(e + f*x)**2 + 4*b**2*f), Eq(a, b)), ((log(tan(e + f*x)**2 + 1)/(2*f) + tan(e + f*x)**4/(4*f) - tan(e + f*x)**2/(2*f))/a**2, Eq(b, 0)), (x*tan(e)**5/(a + b*tan(e)**2)**2, Eq(f, 0)), (a**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) + a**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) + a**3/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) + a**2*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) - 2*a**2*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) + a**2*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) - 2*a**2*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) - a**2*b/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) - 2*a*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) - 2*a*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) + a*b**2*log(tan(e + f*x)**2 + 1)/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2) + b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*a**3*b**2*f + 2*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f - 4*a*b**4*f*tan(e + f*x)**2 + 2*a*b**4*f + 2*b**5*f*tan(e + f*x)**2), True))","A",0
225,1,930,0,26.505940," ","integrate(tan(f*x+e)**3/(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\tan^{2}{\left(e + f x \right)}}{2 f}}{a^{2}} & \text{for}\: b = 0 \\- \frac{2 \tan^{2}{\left(e + f x \right)}}{4 b^{2} f \tan^{4}{\left(e + f x \right)} + 8 b^{2} f \tan^{2}{\left(e + f x \right)} + 4 b^{2} f} - \frac{1}{4 b^{2} f \tan^{4}{\left(e + f x \right)} + 8 b^{2} f \tan^{2}{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = b \\\frac{x \tan^{3}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\- \frac{a^{2}}{2 a^{3} b f + 2 a^{2} b^{2} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{2} f - 4 a b^{3} f \tan^{2}{\left(e + f x \right)} + 2 a b^{3} f + 2 b^{4} f \tan^{2}{\left(e + f x \right)}} + \frac{a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} b f + 2 a^{2} b^{2} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{2} f - 4 a b^{3} f \tan^{2}{\left(e + f x \right)} + 2 a b^{3} f + 2 b^{4} f \tan^{2}{\left(e + f x \right)}} + \frac{a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} b f + 2 a^{2} b^{2} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{2} f - 4 a b^{3} f \tan^{2}{\left(e + f x \right)} + 2 a b^{3} f + 2 b^{4} f \tan^{2}{\left(e + f x \right)}} - \frac{a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{3} b f + 2 a^{2} b^{2} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{2} f - 4 a b^{3} f \tan^{2}{\left(e + f x \right)} + 2 a b^{3} f + 2 b^{4} f \tan^{2}{\left(e + f x \right)}} + \frac{a b}{2 a^{3} b f + 2 a^{2} b^{2} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{2} f - 4 a b^{3} f \tan^{2}{\left(e + f x \right)} + 2 a b^{3} f + 2 b^{4} f \tan^{2}{\left(e + f x \right)}} + \frac{b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} b f + 2 a^{2} b^{2} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{2} f - 4 a b^{3} f \tan^{2}{\left(e + f x \right)} + 2 a b^{3} f + 2 b^{4} f \tan^{2}{\left(e + f x \right)}} + \frac{b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} b f + 2 a^{2} b^{2} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{2} f - 4 a b^{3} f \tan^{2}{\left(e + f x \right)} + 2 a b^{3} f + 2 b^{4} f \tan^{2}{\left(e + f x \right)}} - \frac{b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} b f + 2 a^{2} b^{2} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{2} f - 4 a b^{3} f \tan^{2}{\left(e + f x \right)} + 2 a b^{3} f + 2 b^{4} f \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-log(tan(e + f*x)**2 + 1)/(2*f) + tan(e + f*x)**2/(2*f))/a**2, Eq(b, 0)), (-2*tan(e + f*x)**2/(4*b**2*f*tan(e + f*x)**4 + 8*b**2*f*tan(e + f*x)**2 + 4*b**2*f) - 1/(4*b**2*f*tan(e + f*x)**4 + 8*b**2*f*tan(e + f*x)**2 + 4*b**2*f), Eq(a, b)), (x*tan(e)**3/(a + b*tan(e)**2)**2, Eq(f, 0)), (-a**2/(2*a**3*b*f + 2*a**2*b**2*f*tan(e + f*x)**2 - 4*a**2*b**2*f - 4*a*b**3*f*tan(e + f*x)**2 + 2*a*b**3*f + 2*b**4*f*tan(e + f*x)**2) + a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**3*b*f + 2*a**2*b**2*f*tan(e + f*x)**2 - 4*a**2*b**2*f - 4*a*b**3*f*tan(e + f*x)**2 + 2*a*b**3*f + 2*b**4*f*tan(e + f*x)**2) + a*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**3*b*f + 2*a**2*b**2*f*tan(e + f*x)**2 - 4*a**2*b**2*f - 4*a*b**3*f*tan(e + f*x)**2 + 2*a*b**3*f + 2*b**4*f*tan(e + f*x)**2) - a*b*log(tan(e + f*x)**2 + 1)/(2*a**3*b*f + 2*a**2*b**2*f*tan(e + f*x)**2 - 4*a**2*b**2*f - 4*a*b**3*f*tan(e + f*x)**2 + 2*a*b**3*f + 2*b**4*f*tan(e + f*x)**2) + a*b/(2*a**3*b*f + 2*a**2*b**2*f*tan(e + f*x)**2 - 4*a**2*b**2*f - 4*a*b**3*f*tan(e + f*x)**2 + 2*a*b**3*f + 2*b**4*f*tan(e + f*x)**2) + b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*b*f + 2*a**2*b**2*f*tan(e + f*x)**2 - 4*a**2*b**2*f - 4*a*b**3*f*tan(e + f*x)**2 + 2*a*b**3*f + 2*b**4*f*tan(e + f*x)**2) + b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*b*f + 2*a**2*b**2*f*tan(e + f*x)**2 - 4*a**2*b**2*f - 4*a*b**3*f*tan(e + f*x)**2 + 2*a*b**3*f + 2*b**4*f*tan(e + f*x)**2) - b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*a**3*b*f + 2*a**2*b**2*f*tan(e + f*x)**2 - 4*a**2*b**2*f - 4*a*b**3*f*tan(e + f*x)**2 + 2*a*b**3*f + 2*b**4*f*tan(e + f*x)**2), True))","A",0
226,1,816,0,26.390285," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{3}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\- \frac{1}{4 b^{2} f \tan^{4}{\left(e + f x \right)} + 8 b^{2} f \tan^{2}{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = b \\\frac{x \tan{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} f} & \text{for}\: b = 0 \\- \frac{a \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} f + 2 a^{2} b f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b f - 4 a b^{2} f \tan^{2}{\left(e + f x \right)} + 2 a b^{2} f + 2 b^{3} f \tan^{2}{\left(e + f x \right)}} - \frac{a \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{2 a^{3} f + 2 a^{2} b f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b f - 4 a b^{2} f \tan^{2}{\left(e + f x \right)} + 2 a b^{2} f + 2 b^{3} f \tan^{2}{\left(e + f x \right)}} + \frac{a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f + 2 a^{2} b f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b f - 4 a b^{2} f \tan^{2}{\left(e + f x \right)} + 2 a b^{2} f + 2 b^{3} f \tan^{2}{\left(e + f x \right)}} + \frac{a}{2 a^{3} f + 2 a^{2} b f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b f - 4 a b^{2} f \tan^{2}{\left(e + f x \right)} + 2 a b^{2} f + 2 b^{3} f \tan^{2}{\left(e + f x \right)}} - \frac{b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} f + 2 a^{2} b f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b f - 4 a b^{2} f \tan^{2}{\left(e + f x \right)} + 2 a b^{2} f + 2 b^{3} f \tan^{2}{\left(e + f x \right)}} - \frac{b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} f + 2 a^{2} b f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b f - 4 a b^{2} f \tan^{2}{\left(e + f x \right)} + 2 a b^{2} f + 2 b^{3} f \tan^{2}{\left(e + f x \right)}} + \frac{b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{2 a^{3} f + 2 a^{2} b f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b f - 4 a b^{2} f \tan^{2}{\left(e + f x \right)} + 2 a b^{2} f + 2 b^{3} f \tan^{2}{\left(e + f x \right)}} - \frac{b}{2 a^{3} f + 2 a^{2} b f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b f - 4 a b^{2} f \tan^{2}{\left(e + f x \right)} + 2 a b^{2} f + 2 b^{3} f \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**3, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (-1/(4*b**2*f*tan(e + f*x)**4 + 8*b**2*f*tan(e + f*x)**2 + 4*b**2*f), Eq(a, b)), (x*tan(e)/(a + b*tan(e)**2)**2, Eq(f, 0)), (log(tan(e + f*x)**2 + 1)/(2*a**2*f), Eq(b, 0)), (-a*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**3*f + 2*a**2*b*f*tan(e + f*x)**2 - 4*a**2*b*f - 4*a*b**2*f*tan(e + f*x)**2 + 2*a*b**2*f + 2*b**3*f*tan(e + f*x)**2) - a*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(2*a**3*f + 2*a**2*b*f*tan(e + f*x)**2 - 4*a**2*b*f - 4*a*b**2*f*tan(e + f*x)**2 + 2*a*b**2*f + 2*b**3*f*tan(e + f*x)**2) + a*log(tan(e + f*x)**2 + 1)/(2*a**3*f + 2*a**2*b*f*tan(e + f*x)**2 - 4*a**2*b*f - 4*a*b**2*f*tan(e + f*x)**2 + 2*a*b**2*f + 2*b**3*f*tan(e + f*x)**2) + a/(2*a**3*f + 2*a**2*b*f*tan(e + f*x)**2 - 4*a**2*b*f - 4*a*b**2*f*tan(e + f*x)**2 + 2*a*b**2*f + 2*b**3*f*tan(e + f*x)**2) - b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*f + 2*a**2*b*f*tan(e + f*x)**2 - 4*a**2*b*f - 4*a*b**2*f*tan(e + f*x)**2 + 2*a*b**2*f + 2*b**3*f*tan(e + f*x)**2) - b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(2*a**3*f + 2*a**2*b*f*tan(e + f*x)**2 - 4*a**2*b*f - 4*a*b**2*f*tan(e + f*x)**2 + 2*a*b**2*f + 2*b**3*f*tan(e + f*x)**2) + b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(2*a**3*f + 2*a**2*b*f*tan(e + f*x)**2 - 4*a**2*b*f - 4*a*b**2*f*tan(e + f*x)**2 + 2*a*b**2*f + 2*b**3*f*tan(e + f*x)**2) - b/(2*a**3*f + 2*a**2*b*f*tan(e + f*x)**2 - 4*a**2*b*f - 4*a*b**2*f*tan(e + f*x)**2 + 2*a*b**2*f + 2*b**3*f*tan(e + f*x)**2), True))","A",0
227,-1,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
228,-1,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
229,-1,0,0,0.000000," ","integrate(cot(f*x+e)**5/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,1,3198,0,78.023185," ","integrate(tan(f*x+e)**6/(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \tilde{\infty} x \tan^{2}{\left(e \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- x + \frac{\tan{\left(e + f x \right)}}{f}}{b^{2}} & \text{for}\: a = 0 \\- \frac{15 f x \tan^{4}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} - \frac{30 f x \tan^{2}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} - \frac{15 f x}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{8 \tan^{5}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{25 \tan^{3}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{15 \tan{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} & \text{for}\: a = b \\\frac{x \tan^{6}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{- x + \frac{\tan^{5}{\left(e + f x \right)}}{5 f} - \frac{\tan^{3}{\left(e + f x \right)}}{3 f} + \frac{\tan{\left(e + f x \right)}}{f}}{a^{2}} & \text{for}\: b = 0 \\\frac{6 i a^{\frac{7}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{4 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{10 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{4 i a^{\frac{3}{2}} b^{3} f x \sqrt{\frac{1}{b}}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{8 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{4 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{4 i \sqrt{a} b^{4} f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{4 i \sqrt{a} b^{4} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{3 a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{3 a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{3 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{5 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{3 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{5 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{5 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{5 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{4} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{5} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-x + tan(e + f*x)/f)/b**2, Eq(a, 0)), (-15*f*x*tan(e + f*x)**4/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) - 30*f*x*tan(e + f*x)**2/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) - 15*f*x/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 8*tan(e + f*x)**5/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 25*tan(e + f*x)**3/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 15*tan(e + f*x)/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f), Eq(a, b)), (x*tan(e)**6/(a + b*tan(e)**2)**2, Eq(f, 0)), ((-x + tan(e + f*x)**5/(5*f) - tan(e + f*x)**3/(3*f) + tan(e + f*x)/f)/a**2, Eq(b, 0)), (6*I*a**(7/2)*b*sqrt(1/b)*tan(e + f*x)/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) + 4*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)**3/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) - 10*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) - 4*I*a**(3/2)*b**3*f*x*sqrt(1/b)/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) - 8*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)**3/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) + 4*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) - 4*I*sqrt(a)*b**4*f*x*sqrt(1/b)*tan(e + f*x)**2/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) + 4*I*sqrt(a)*b**4*sqrt(1/b)*tan(e + f*x)**3/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) - 3*a**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) + 3*a**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) - 3*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) + 5*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) + 3*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) - 5*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) + 5*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2) - 5*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b**3*f*sqrt(1/b) + 4*I*a**(5/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**4*f*sqrt(1/b) - 8*I*a**(3/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**5*f*sqrt(1/b) + 4*I*sqrt(a)*b**6*f*sqrt(1/b)*tan(e + f*x)**2), True))","A",0
231,1,2416,0,28.759405," ","integrate(tan(f*x+e)**4/(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{x}{b^{2}} & \text{for}\: a = 0 \\\frac{3 f x \tan^{4}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{6 f x \tan^{2}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{3 f x}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} - \frac{5 \tan^{3}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} - \frac{3 \tan{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} & \text{for}\: a = b \\\frac{x \tan^{4}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{x + \frac{\tan^{3}{\left(e + f x \right)}}{3 f} - \frac{\tan{\left(e + f x \right)}}{f}}{a^{2}} & \text{for}\: b = 0 \\- \frac{2 i a^{\frac{5}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{4 i a^{\frac{3}{2}} b^{2} f x \sqrt{\frac{1}{b}}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{2 i a^{\frac{3}{2}} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{4 i \sqrt{a} b^{3} f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{a^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{a^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{a^{2} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{3 a^{2} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{a^{2} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{3 a^{2} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{3 a b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{3 a b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{3} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{4} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (x/b**2, Eq(a, 0)), (3*f*x*tan(e + f*x)**4/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 6*f*x*tan(e + f*x)**2/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 3*f*x/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) - 5*tan(e + f*x)**3/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) - 3*tan(e + f*x)/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f), Eq(a, b)), (x*tan(e)**4/(a + b*tan(e)**2)**2, Eq(f, 0)), ((x + tan(e + f*x)**3/(3*f) - tan(e + f*x)/f)/a**2, Eq(b, 0)), (-2*I*a**(5/2)*b*sqrt(1/b)*tan(e + f*x)/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) + 4*I*a**(3/2)*b**2*f*x*sqrt(1/b)/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) + 2*I*a**(3/2)*b**2*sqrt(1/b)*tan(e + f*x)/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) + 4*I*sqrt(a)*b**3*f*x*sqrt(1/b)*tan(e + f*x)**2/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) + a**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) - a**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) + a**2*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) - 3*a**2*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) - a**2*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) + 3*a**2*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) - 3*a*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2) + 3*a*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b**2*f*sqrt(1/b) + 4*I*a**(5/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**3*f*sqrt(1/b) - 8*I*a**(3/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**4*f*sqrt(1/b) + 4*I*sqrt(a)*b**5*f*sqrt(1/b)*tan(e + f*x)**2), True))","A",0
232,1,2375,0,28.287715," ","integrate(tan(f*x+e)**2/(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- x - \frac{1}{f \tan{\left(e + f x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{f x \tan^{4}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{2 f x \tan^{2}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{f x}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{\tan^{3}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} - \frac{\tan{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} & \text{for}\: a = b \\\frac{x \tan^{2}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{- x + \frac{\tan{\left(e + f x \right)}}{f}}{a^{2}} & \text{for}\: b = 0 \\- \frac{4 i a^{\frac{3}{2}} b f x \sqrt{\frac{1}{b}}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{2 i a^{\frac{3}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{4 i \sqrt{a} b^{2} f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{2 i \sqrt{a} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} - 8 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} + 4 i \sqrt{a} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-x - 1/(f*tan(e + f*x)))/b**2, Eq(a, 0)), (f*x*tan(e + f*x)**4/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 2*f*x*tan(e + f*x)**2/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + f*x/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + tan(e + f*x)**3/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) - tan(e + f*x)/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f), Eq(a, b)), (x*tan(e)**2/(a + b*tan(e)**2)**2, Eq(f, 0)), ((-x + tan(e + f*x)/f)/a**2, Eq(b, 0)), (-4*I*a**(3/2)*b*f*x*sqrt(1/b)/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) + 2*I*a**(3/2)*b*sqrt(1/b)*tan(e + f*x)/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) - 4*I*sqrt(a)*b**2*f*x*sqrt(1/b)*tan(e + f*x)**2/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) - 2*I*sqrt(a)*b**2*sqrt(1/b)*tan(e + f*x)/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) + a**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) - a**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) + a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) + a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) - a*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) - a*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) + b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2) - b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(7/2)*b*f*sqrt(1/b) + 4*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(5/2)*b**2*f*sqrt(1/b) - 8*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(3/2)*b**3*f*sqrt(1/b) + 4*I*sqrt(a)*b**4*f*sqrt(1/b)*tan(e + f*x)**2), True))","A",0
233,1,2322,0,27.874673," ","integrate(1/(a+b*tan(f*x+e)**2)**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{4}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{x}{a^{2}} & \text{for}\: b = 0 \\\frac{x + \frac{1}{f \tan{\left(e + f x \right)}} - \frac{1}{3 f \tan^{3}{\left(e + f x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{3 f x \tan^{4}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{6 f x \tan^{2}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{3 f x}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{3 \tan^{3}{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} + \frac{5 \tan{\left(e + f x \right)}}{8 b^{2} f \tan^{4}{\left(e + f x \right)} + 16 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 b^{2} f} & \text{for}\: a = b \\\frac{x}{\left(a + b \tan^{2}{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{4 i a^{\frac{5}{2}} f x \sqrt{\frac{1}{b}}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{4 i a^{\frac{3}{2}} b f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{2 i a^{\frac{3}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{2 i \sqrt{a} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{3 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{3 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{3 a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{3 a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} + \frac{b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} - \frac{b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 i a^{\frac{9}{2}} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 8 i a^{\frac{7}{2}} b f \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 4 i a^{\frac{5}{2}} b^{2} f \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**4, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (x/a**2, Eq(b, 0)), ((x + 1/(f*tan(e + f*x)) - 1/(3*f*tan(e + f*x)**3))/b**2, Eq(a, 0)), (3*f*x*tan(e + f*x)**4/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 6*f*x*tan(e + f*x)**2/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 3*f*x/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 3*tan(e + f*x)**3/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f) + 5*tan(e + f*x)/(8*b**2*f*tan(e + f*x)**4 + 16*b**2*f*tan(e + f*x)**2 + 8*b**2*f), Eq(a, b)), (x/(a + b*tan(e)**2)**2, Eq(f, 0)), (4*I*a**(5/2)*f*x*sqrt(1/b)/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + 4*I*a**(3/2)*b*f*x*sqrt(1/b)*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - 2*I*a**(3/2)*b*sqrt(1/b)*tan(e + f*x)/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + 2*I*sqrt(a)*b**2*sqrt(1/b)*tan(e + f*x)/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - 3*a**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + 3*a**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - 3*a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + 3*a*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - a*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) + b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2) - b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*I*a**(9/2)*f*sqrt(1/b) + 4*I*a**(7/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 8*I*a**(7/2)*b*f*sqrt(1/b) - 8*I*a**(5/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 4*I*a**(5/2)*b**2*f*sqrt(1/b) + 4*I*a**(3/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2), True))","A",0
234,-1,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate(cot(f*x+e)**6/(a+b*tan(f*x+e)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,1,3346,0,133.670700," ","integrate(tan(f*x+e)**5/(a+b*tan(f*x+e)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\- \frac{3 \tan^{4}{\left(e + f x \right)}}{6 b^{3} f \tan^{6}{\left(e + f x \right)} + 18 b^{3} f \tan^{4}{\left(e + f x \right)} + 18 b^{3} f \tan^{2}{\left(e + f x \right)} + 6 b^{3} f} - \frac{3 \tan^{2}{\left(e + f x \right)}}{6 b^{3} f \tan^{6}{\left(e + f x \right)} + 18 b^{3} f \tan^{4}{\left(e + f x \right)} + 18 b^{3} f \tan^{2}{\left(e + f x \right)} + 6 b^{3} f} - \frac{1}{6 b^{3} f \tan^{6}{\left(e + f x \right)} + 18 b^{3} f \tan^{4}{\left(e + f x \right)} + 18 b^{3} f \tan^{2}{\left(e + f x \right)} + 6 b^{3} f} & \text{for}\: a = b \\\frac{\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\tan^{4}{\left(e + f x \right)}}{4 f} - \frac{\tan^{2}{\left(e + f x \right)}}{2 f}}{a^{3}} & \text{for}\: b = 0 \\\frac{x \tan^{5}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{3}} & \text{for}\: f = 0 \\- \frac{a^{4}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{2 a^{3} b \tan^{2}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} + \frac{4 a^{3} b}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{2 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{2 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} + \frac{2 a^{2} b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} + \frac{6 a^{2} b^{2} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{3 a^{2} b^{2}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{4 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{4 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} + \frac{4 a b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{4 a b^{3} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{2 b^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} - \frac{2 b^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} + \frac{2 b^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} b^{2} f + 8 a^{4} b^{3} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{3} f + 4 a^{3} b^{4} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{4} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{4} f - 12 a^{2} b^{5} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{5} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{5} f + 12 a b^{6} f \tan^{4}{\left(e + f x \right)} - 8 a b^{6} f \tan^{2}{\left(e + f x \right)} - 4 b^{7} f \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (-3*tan(e + f*x)**4/(6*b**3*f*tan(e + f*x)**6 + 18*b**3*f*tan(e + f*x)**4 + 18*b**3*f*tan(e + f*x)**2 + 6*b**3*f) - 3*tan(e + f*x)**2/(6*b**3*f*tan(e + f*x)**6 + 18*b**3*f*tan(e + f*x)**4 + 18*b**3*f*tan(e + f*x)**2 + 6*b**3*f) - 1/(6*b**3*f*tan(e + f*x)**6 + 18*b**3*f*tan(e + f*x)**4 + 18*b**3*f*tan(e + f*x)**2 + 6*b**3*f), Eq(a, b)), ((log(tan(e + f*x)**2 + 1)/(2*f) + tan(e + f*x)**4/(4*f) - tan(e + f*x)**2/(2*f))/a**3, Eq(b, 0)), (x*tan(e)**5/(a + b*tan(e)**2)**3, Eq(f, 0)), (-a**4/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 2*a**3*b*tan(e + f*x)**2/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) + 4*a**3*b/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 2*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 2*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) + 2*a**2*b**2*log(tan(e + f*x)**2 + 1)/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) + 6*a**2*b**2*tan(e + f*x)**2/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 3*a**2*b**2/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 4*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 4*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) + 4*a*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 4*a*b**3*tan(e + f*x)**2/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 2*b**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) - 2*b**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4) + 2*b**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**4/(4*a**5*b**2*f + 8*a**4*b**3*f*tan(e + f*x)**2 - 12*a**4*b**3*f + 4*a**3*b**4*f*tan(e + f*x)**4 - 24*a**3*b**4*f*tan(e + f*x)**2 + 12*a**3*b**4*f - 12*a**2*b**5*f*tan(e + f*x)**4 + 24*a**2*b**5*f*tan(e + f*x)**2 - 4*a**2*b**5*f + 12*a*b**6*f*tan(e + f*x)**4 - 8*a*b**6*f*tan(e + f*x)**2 - 4*b**7*f*tan(e + f*x)**4), True))","A",0
238,1,2849,0,132.459665," ","integrate(tan(f*x+e)**3/(a+b*tan(f*x+e)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{3}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- \frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{\tan^{2}{\left(e + f x \right)}}{2 f}}{a^{3}} & \text{for}\: b = 0 \\- \frac{3 \tan^{2}{\left(e + f x \right)}}{12 b^{3} f \tan^{6}{\left(e + f x \right)} + 36 b^{3} f \tan^{4}{\left(e + f x \right)} + 36 b^{3} f \tan^{2}{\left(e + f x \right)} + 12 b^{3} f} - \frac{1}{12 b^{3} f \tan^{6}{\left(e + f x \right)} + 36 b^{3} f \tan^{4}{\left(e + f x \right)} + 36 b^{3} f \tan^{2}{\left(e + f x \right)} + 12 b^{3} f} & \text{for}\: a = b \\\frac{x \tan^{3}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{3}} & \text{for}\: f = 0 \\- \frac{a^{3}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} + \frac{2 a^{2} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} + \frac{2 a^{2} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} - \frac{2 a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} + \frac{4 a b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} + \frac{4 a b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} - \frac{4 a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} - \frac{2 a b^{2} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} + \frac{a b^{2}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} + \frac{2 b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} + \frac{2 b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} - \frac{2 b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} + \frac{2 b^{3} \tan^{2}{\left(e + f x \right)}}{4 a^{5} b f + 8 a^{4} b^{2} f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b^{2} f + 4 a^{3} b^{3} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{3} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{3} f - 12 a^{2} b^{4} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{4} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{4} f + 12 a b^{5} f \tan^{4}{\left(e + f x \right)} - 8 a b^{5} f \tan^{2}{\left(e + f x \right)} - 4 b^{6} f \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**3, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-log(tan(e + f*x)**2 + 1)/(2*f) + tan(e + f*x)**2/(2*f))/a**3, Eq(b, 0)), (-3*tan(e + f*x)**2/(12*b**3*f*tan(e + f*x)**6 + 36*b**3*f*tan(e + f*x)**4 + 36*b**3*f*tan(e + f*x)**2 + 12*b**3*f) - 1/(12*b**3*f*tan(e + f*x)**6 + 36*b**3*f*tan(e + f*x)**4 + 36*b**3*f*tan(e + f*x)**2 + 12*b**3*f), Eq(a, b)), (x*tan(e)**3/(a + b*tan(e)**2)**3, Eq(f, 0)), (-a**3/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) + 2*a**2*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) + 2*a**2*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) - 2*a**2*b*log(tan(e + f*x)**2 + 1)/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) + 4*a*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) + 4*a*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) - 4*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) - 2*a*b**2*tan(e + f*x)**2/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) + a*b**2/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) + 2*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) + 2*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) - 2*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**4/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4) + 2*b**3*tan(e + f*x)**2/(4*a**5*b*f + 8*a**4*b**2*f*tan(e + f*x)**2 - 12*a**4*b**2*f + 4*a**3*b**3*f*tan(e + f*x)**4 - 24*a**3*b**3*f*tan(e + f*x)**2 + 12*a**3*b**3*f - 12*a**2*b**4*f*tan(e + f*x)**4 + 24*a**2*b**4*f*tan(e + f*x)**2 - 4*a**2*b**4*f + 12*a*b**5*f*tan(e + f*x)**4 - 8*a*b**5*f*tan(e + f*x)**2 - 4*b**6*f*tan(e + f*x)**4), True))","A",0
239,1,2876,0,133.351502," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{5}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{\log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f} & \text{for}\: b = 0 \\- \frac{1}{6 b^{3} f \tan^{6}{\left(e + f x \right)} + 18 b^{3} f \tan^{4}{\left(e + f x \right)} + 18 b^{3} f \tan^{2}{\left(e + f x \right)} + 6 b^{3} f} & \text{for}\: a = b \\\frac{x \tan{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{3}} & \text{for}\: f = 0 \\- \frac{2 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} - \frac{2 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} + \frac{2 a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} + \frac{3 a^{2}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} - \frac{4 a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} - \frac{4 a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} + \frac{4 a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} + \frac{2 a b \tan^{2}{\left(e + f x \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} - \frac{4 a b}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} - \frac{2 b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} - \frac{2 b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} + \frac{2 b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{4}{\left(e + f x \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} - \frac{2 b^{2} \tan^{2}{\left(e + f x \right)}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} + \frac{b^{2}}{4 a^{5} f + 8 a^{4} b f \tan^{2}{\left(e + f x \right)} - 12 a^{4} b f + 4 a^{3} b^{2} f \tan^{4}{\left(e + f x \right)} - 24 a^{3} b^{2} f \tan^{2}{\left(e + f x \right)} + 12 a^{3} b^{2} f - 12 a^{2} b^{3} f \tan^{4}{\left(e + f x \right)} + 24 a^{2} b^{3} f \tan^{2}{\left(e + f x \right)} - 4 a^{2} b^{3} f + 12 a b^{4} f \tan^{4}{\left(e + f x \right)} - 8 a b^{4} f \tan^{2}{\left(e + f x \right)} - 4 b^{5} f \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**5, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (log(tan(e + f*x)**2 + 1)/(2*a**3*f), Eq(b, 0)), (-1/(6*b**3*f*tan(e + f*x)**6 + 18*b**3*f*tan(e + f*x)**4 + 18*b**3*f*tan(e + f*x)**2 + 6*b**3*f), Eq(a, b)), (x*tan(e)/(a + b*tan(e)**2)**3, Eq(f, 0)), (-2*a**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) - 2*a**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) + 2*a**2*log(tan(e + f*x)**2 + 1)/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) + 3*a**2/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) - 4*a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) - 4*a*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) + 4*a*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) + 2*a*b*tan(e + f*x)**2/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) - 4*a*b/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) - 2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) - 2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) + 2*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**4/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) - 2*b**2*tan(e + f*x)**2/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4) + b**2/(4*a**5*f + 8*a**4*b*f*tan(e + f*x)**2 - 12*a**4*b*f + 4*a**3*b**2*f*tan(e + f*x)**4 - 24*a**3*b**2*f*tan(e + f*x)**2 + 12*a**3*b**2*f - 12*a**2*b**3*f*tan(e + f*x)**4 + 24*a**2*b**3*f*tan(e + f*x)**2 - 4*a**2*b**3*f + 12*a*b**4*f*tan(e + f*x)**4 - 8*a*b**4*f*tan(e + f*x)**2 - 4*b**5*f*tan(e + f*x)**4), True))","A",0
240,-1,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate(cot(f*x+e)**5/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,1,9823,0,141.170531," ","integrate(tan(f*x+e)**6/(a+b*tan(f*x+e)**2)**3,x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{x}{b^{3}} & \text{for}\: a = 0 \\\frac{15 f x \tan^{6}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{45 f x \tan^{4}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{45 f x \tan^{2}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{15 f x}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} - \frac{33 \tan^{5}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} - \frac{40 \tan^{3}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} - \frac{15 \tan{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} & \text{for}\: a = b \\\frac{x \tan^{6}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{3}} & \text{for}\: f = 0 \\\frac{- x + \frac{\tan^{5}{\left(e + f x \right)}}{5 f} - \frac{\tan^{3}{\left(e + f x \right)}}{3 f} + \frac{\tan{\left(e + f x \right)}}{f}}{a^{3}} & \text{for}\: b = 0 \\- \frac{6 i a^{\frac{9}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{20 i a^{\frac{7}{2}} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{16 i a^{\frac{5}{2}} b^{3} f x \sqrt{\frac{1}{b}}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{28 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{14 i a^{\frac{5}{2}} b^{3} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{32 i a^{\frac{3}{2}} b^{4} f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{18 i a^{\frac{3}{2}} b^{4} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{16 i \sqrt{a} b^{5} f x \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 a^{5} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 a^{5} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a^{4} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 a^{4} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a^{4} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{10 a^{4} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 a^{3} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{20 a^{3} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{15 a^{3} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 a^{3} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{20 a^{3} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{15 a^{3} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 a^{2} b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{30 a^{2} b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{10 a^{2} b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{30 a^{2} b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{15 a b^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{15 a b^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{3} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{4} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{5} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{6} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{7} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{8} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (x/b**3, Eq(a, 0)), (15*f*x*tan(e + f*x)**6/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 45*f*x*tan(e + f*x)**4/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 45*f*x*tan(e + f*x)**2/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 15*f*x/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) - 33*tan(e + f*x)**5/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) - 40*tan(e + f*x)**3/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) - 15*tan(e + f*x)/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f), Eq(a, b)), (x*tan(e)**6/(a + b*tan(e)**2)**3, Eq(f, 0)), ((-x + tan(e + f*x)**5/(5*f) - tan(e + f*x)**3/(3*f) + tan(e + f*x)/f)/a**3, Eq(b, 0)), (-6*I*a**(9/2)*b*sqrt(1/b)*tan(e + f*x)/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 10*I*a**(7/2)*b**2*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 20*I*a**(7/2)*b**2*sqrt(1/b)*tan(e + f*x)/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 16*I*a**(5/2)*b**3*f*x*sqrt(1/b)/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 28*I*a**(5/2)*b**3*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 14*I*a**(5/2)*b**3*sqrt(1/b)*tan(e + f*x)/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 32*I*a**(3/2)*b**4*f*x*sqrt(1/b)*tan(e + f*x)**2/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 18*I*a**(3/2)*b**4*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 16*I*sqrt(a)*b**5*f*x*sqrt(1/b)*tan(e + f*x)**4/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 3*a**5*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 3*a**5*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a**4*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 10*a**4*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a**4*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 10*a**4*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 3*a**3*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 20*a**3*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 15*a**3*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 3*a**3*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 20*a**3*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 15*a**3*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 10*a**2*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 30*a**2*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 10*a**2*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 30*a**2*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) + 15*a*b**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4) - 15*a*b**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**3*f*sqrt(1/b) + 32*I*a**(9/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**4*f*sqrt(1/b) + 16*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**5*f*sqrt(1/b) - 48*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**6*f*sqrt(1/b) + 48*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**7*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**8*f*sqrt(1/b)*tan(e + f*x)**4), True))","A",0
244,1,9811,0,140.857267," ","integrate(tan(f*x+e)**4/(a+b*tan(f*x+e)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- x - \frac{1}{f \tan{\left(e + f x \right)}}}{b^{3}} & \text{for}\: a = 0 \\\frac{3 f x \tan^{6}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{9 f x \tan^{4}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{9 f x \tan^{2}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{3 f x}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{3 \tan^{5}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} - \frac{8 \tan^{3}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} - \frac{3 \tan{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} & \text{for}\: a = b \\\frac{x \tan^{4}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{3}} & \text{for}\: f = 0 \\\frac{x + \frac{\tan^{3}{\left(e + f x \right)}}{3 f} - \frac{\tan{\left(e + f x \right)}}{f}}{a^{3}} & \text{for}\: b = 0 \\- \frac{2 i a^{\frac{7}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{16 i a^{\frac{5}{2}} b^{2} f x \sqrt{\frac{1}{b}}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{2 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{4 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{32 i a^{\frac{3}{2}} b^{3} f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{12 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{16 i \sqrt{a} b^{4} f x \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{10 i \sqrt{a} b^{4} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{2 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{2 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{12 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{12 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 b^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 b^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i \sqrt{a} b^{7} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-x - 1/(f*tan(e + f*x)))/b**3, Eq(a, 0)), (3*f*x*tan(e + f*x)**6/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 9*f*x*tan(e + f*x)**4/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 9*f*x*tan(e + f*x)**2/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 3*f*x/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 3*tan(e + f*x)**5/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) - 8*tan(e + f*x)**3/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) - 3*tan(e + f*x)/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f), Eq(a, b)), (x*tan(e)**4/(a + b*tan(e)**2)**3, Eq(f, 0)), ((x + tan(e + f*x)**3/(3*f) - tan(e + f*x)/f)/a**3, Eq(b, 0)), (-2*I*a**(7/2)*b*sqrt(1/b)*tan(e + f*x)/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 16*I*a**(5/2)*b**2*f*x*sqrt(1/b)/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 2*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 4*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 32*I*a**(3/2)*b**3*f*x*sqrt(1/b)*tan(e + f*x)**2/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 12*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 6*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 16*I*sqrt(a)*b**4*f*x*sqrt(1/b)*tan(e + f*x)**4/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 10*I*sqrt(a)*b**4*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + a**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - a**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 2*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 2*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 12*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 3*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 12*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 3*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) - 3*b**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4) + 3*b**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(11/2)*b**2*f*sqrt(1/b) + 32*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(9/2)*b**3*f*sqrt(1/b) + 16*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(7/2)*b**4*f*sqrt(1/b) - 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b) + 48*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*sqrt(a)*b**7*f*sqrt(1/b)*tan(e + f*x)**4), True))","A",0
245,1,9763,0,140.009116," ","integrate(tan(f*x+e)**2/(a+b*tan(f*x+e)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{4}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{- x + \frac{\tan{\left(e + f x \right)}}{f}}{a^{3}} & \text{for}\: b = 0 \\\frac{x + \frac{1}{f \tan{\left(e + f x \right)}} - \frac{1}{3 f \tan^{3}{\left(e + f x \right)}}}{b^{3}} & \text{for}\: a = 0 \\\frac{3 f x \tan^{6}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{9 f x \tan^{4}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{9 f x \tan^{2}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{3 f x}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{3 \tan^{5}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{8 \tan^{3}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} - \frac{3 \tan{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} & \text{for}\: a = b \\\frac{x \tan^{2}{\left(e \right)}}{\left(a + b \tan^{2}{\left(e \right)}\right)^{3}} & \text{for}\: f = 0 \\- \frac{16 i a^{\frac{7}{2}} b f x \sqrt{\frac{1}{b}}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{10 i a^{\frac{7}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{32 i a^{\frac{5}{2}} b^{2} f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{12 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{16 i a^{\frac{3}{2}} b^{3} f x \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{4 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{2 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{2 i \sqrt{a} b^{4} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{12 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{12 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{2 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{2 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{b^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{b^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 32 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} + 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{3}{2}} b^{6} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**4, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), ((-x + tan(e + f*x)/f)/a**3, Eq(b, 0)), ((x + 1/(f*tan(e + f*x)) - 1/(3*f*tan(e + f*x)**3))/b**3, Eq(a, 0)), (3*f*x*tan(e + f*x)**6/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 9*f*x*tan(e + f*x)**4/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 9*f*x*tan(e + f*x)**2/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 3*f*x/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 3*tan(e + f*x)**5/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 8*tan(e + f*x)**3/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) - 3*tan(e + f*x)/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f), Eq(a, b)), (x*tan(e)**2/(a + b*tan(e)**2)**3, Eq(f, 0)), (-16*I*a**(7/2)*b*f*x*sqrt(1/b)/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 10*I*a**(7/2)*b*sqrt(1/b)*tan(e + f*x)/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 32*I*a**(5/2)*b**2*f*x*sqrt(1/b)*tan(e + f*x)**2/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 6*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 12*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 16*I*a**(3/2)*b**3*f*x*sqrt(1/b)*tan(e + f*x)**4/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 4*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 2*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 2*I*sqrt(a)*b**4*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 3*a**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 3*a**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 3*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 12*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 3*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 12*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 2*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + 2*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) - b**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4) + b**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(13/2)*b*f*sqrt(1/b) + 32*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(11/2)*b**2*f*sqrt(1/b) + 16*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(9/2)*b**3*f*sqrt(1/b) - 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(7/2)*b**4*f*sqrt(1/b) + 48*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(3/2)*b**6*f*sqrt(1/b)*tan(e + f*x)**4), True))","A",0
246,1,9629,0,138.067520," ","integrate(1/(a+b*tan(f*x+e)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{6}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{x}{a^{3}} & \text{for}\: b = 0 \\\frac{- x - \frac{1}{f \tan{\left(e + f x \right)}} + \frac{1}{3 f \tan^{3}{\left(e + f x \right)}} - \frac{1}{5 f \tan^{5}{\left(e + f x \right)}}}{b^{3}} & \text{for}\: a = 0 \\\frac{15 f x \tan^{6}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{45 f x \tan^{4}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{45 f x \tan^{2}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{15 f x}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{15 \tan^{5}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{40 \tan^{3}{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} + \frac{33 \tan{\left(e + f x \right)}}{48 b^{3} f \tan^{6}{\left(e + f x \right)} + 144 b^{3} f \tan^{4}{\left(e + f x \right)} + 144 b^{3} f \tan^{2}{\left(e + f x \right)} + 48 b^{3} f} & \text{for}\: a = b \\\frac{x}{\left(a + b \tan^{2}{\left(e \right)}\right)^{3}} & \text{for}\: f = 0 \\\frac{16 i a^{\frac{9}{2}} f x \sqrt{\frac{1}{b}}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{32 i a^{\frac{7}{2}} b f x \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{18 i a^{\frac{7}{2}} b \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{16 i a^{\frac{5}{2}} b^{2} f x \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{14 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{28 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{20 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 i \sqrt{a} b^{4} \sqrt{\frac{1}{b}} \tan^{3}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{15 a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{15 a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{30 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{10 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{30 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{15 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{20 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{15 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{20 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{10 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{6 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{10 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{6 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{2}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} - \frac{3 b^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} + \frac{3 b^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(e + f x \right)} \right)} \tan^{4}{\left(e + f x \right)}}{16 i a^{\frac{15}{2}} f \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 48 i a^{\frac{13}{2}} b f \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 96 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} + 48 i a^{\frac{11}{2}} b^{2} f \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} + 96 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{9}{2}} b^{3} f \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)} - 32 i a^{\frac{7}{2}} b^{4} f \sqrt{\frac{1}{b}} \tan^{2}{\left(e + f x \right)} - 16 i a^{\frac{5}{2}} b^{5} f \sqrt{\frac{1}{b}} \tan^{4}{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(e)**6, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (x/a**3, Eq(b, 0)), ((-x - 1/(f*tan(e + f*x)) + 1/(3*f*tan(e + f*x)**3) - 1/(5*f*tan(e + f*x)**5))/b**3, Eq(a, 0)), (15*f*x*tan(e + f*x)**6/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 45*f*x*tan(e + f*x)**4/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 45*f*x*tan(e + f*x)**2/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 15*f*x/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 15*tan(e + f*x)**5/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 40*tan(e + f*x)**3/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f) + 33*tan(e + f*x)/(48*b**3*f*tan(e + f*x)**6 + 144*b**3*f*tan(e + f*x)**4 + 144*b**3*f*tan(e + f*x)**2 + 48*b**3*f), Eq(a, b)), (x/(a + b*tan(e)**2)**3, Eq(f, 0)), (16*I*a**(9/2)*f*x*sqrt(1/b)/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 32*I*a**(7/2)*b*f*x*sqrt(1/b)*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 18*I*a**(7/2)*b*sqrt(1/b)*tan(e + f*x)/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 16*I*a**(5/2)*b**2*f*x*sqrt(1/b)*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 14*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 28*I*a**(5/2)*b**2*sqrt(1/b)*tan(e + f*x)/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 20*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 10*I*a**(3/2)*b**3*sqrt(1/b)*tan(e + f*x)/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 6*I*sqrt(a)*b**4*sqrt(1/b)*tan(e + f*x)**3/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 15*a**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 15*a**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 30*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 10*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 30*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 10*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 15*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 20*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 3*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 15*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 20*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 3*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 10*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 6*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 10*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 6*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**2/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) - 3*b**4*log(-I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4) + 3*b**4*log(I*sqrt(a)*sqrt(1/b) + tan(e + f*x))*tan(e + f*x)**4/(16*I*a**(15/2)*f*sqrt(1/b) + 32*I*a**(13/2)*b*f*sqrt(1/b)*tan(e + f*x)**2 - 48*I*a**(13/2)*b*f*sqrt(1/b) + 16*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**4 - 96*I*a**(11/2)*b**2*f*sqrt(1/b)*tan(e + f*x)**2 + 48*I*a**(11/2)*b**2*f*sqrt(1/b) - 48*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**4 + 96*I*a**(9/2)*b**3*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(9/2)*b**3*f*sqrt(1/b) + 48*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**4 - 32*I*a**(7/2)*b**4*f*sqrt(1/b)*tan(e + f*x)**2 - 16*I*a**(5/2)*b**5*f*sqrt(1/b)*tan(e + f*x)**4), True))","A",0
247,-1,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
248,-1,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
249,-1,0,0,0.000000," ","integrate(cot(f*x+e)**6/(a+b*tan(f*x+e)**2)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,1,209,0,1.268461," ","integrate((a+b*tan(d*x+c)**2)**4,x)","\begin{cases} a^{4} x - 4 a^{3} b x + \frac{4 a^{3} b \tan{\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} - 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} + b^{4} x + \frac{b^{4} \tan^{7}{\left(c + d x \right)}}{7 d} - \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^{2}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x - 4*a**3*b*x + 4*a**3*b*tan(c + d*x)/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 - 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*x + b**4*tan(c + d*x)**7/(7*d) - 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)**2)**4, True))","A",0
251,1,126,0,0.673727," ","integrate((a+b*tan(d*x+c)**2)**3,x)","\begin{cases} a^{3} x - 3 a^{2} b x + \frac{3 a^{2} b \tan{\left(c + d x \right)}}{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} - 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^{2}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x - 3*a**2*b*x + 3*a**2*b*tan(c + d*x)/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*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)**2)**3, True))","A",0
252,1,68,0,0.313960," ","integrate((a+b*tan(d*x+c)**2)**2,x)","\begin{cases} a^{2} x - 2 a b x + \frac{2 a b \tan{\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^{2}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x - 2*a*b*x + 2*a*b*tan(c + d*x)/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)**2, True))","A",0
253,1,20,0,0.139065," ","integrate(a+b*tan(d*x+c)**2,x)","a x + b \left(\begin{cases} - x + \frac{\tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \tan^{2}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-x + tan(c + d*x)/d, Ne(d, 0)), (x*tan(c)**2, True))","A",0
254,1,280,0,2.397378," ","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{x}{a} & \text{for}\: b = 0 \\\frac{- x - \frac{1}{d \tan{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\\frac{d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 b d} + \frac{d x}{2 b d \tan^{2}{\left(c + d x \right)} + 2 b d} + \frac{\tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 b d} & \text{for}\: a = b \\\frac{x}{a + b \tan^{2}{\left(c \right)}} & \text{for}\: d = 0 \\\frac{2 i \sqrt{a} d x \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} d \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b d \sqrt{\frac{1}{b}}} - \frac{\log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{2 i a^{\frac{3}{2}} d \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b d \sqrt{\frac{1}{b}}} + \frac{\log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{2 i a^{\frac{3}{2}} d \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b d \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (x/a, Eq(b, 0)), ((-x - 1/(d*tan(c + d*x)))/b, Eq(a, 0)), (d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*b*d) + d*x/(2*b*d*tan(c + d*x)**2 + 2*b*d) + tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*b*d), Eq(a, b)), (x/(a + b*tan(c)**2), Eq(d, 0)), (2*I*sqrt(a)*d*x*sqrt(1/b)/(2*I*a**(3/2)*d*sqrt(1/b) - 2*I*sqrt(a)*b*d*sqrt(1/b)) - log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(2*I*a**(3/2)*d*sqrt(1/b) - 2*I*sqrt(a)*b*d*sqrt(1/b)) + log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(2*I*a**(3/2)*d*sqrt(1/b) - 2*I*sqrt(a)*b*d*sqrt(1/b)), True))","A",0
255,1,2322,0,20.593933," ","integrate(1/(a+b*tan(d*x+c)**2)**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{4}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 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{3 d x \tan^{4}{\left(c + d x \right)}}{8 b^{2} d \tan^{4}{\left(c + d x \right)} + 16 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d} + \frac{6 d x \tan^{2}{\left(c + d x \right)}}{8 b^{2} d \tan^{4}{\left(c + d x \right)} + 16 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d} + \frac{3 d x}{8 b^{2} d \tan^{4}{\left(c + d x \right)} + 16 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d} + \frac{3 \tan^{3}{\left(c + d x \right)}}{8 b^{2} d \tan^{4}{\left(c + d x \right)} + 16 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d} + \frac{5 \tan{\left(c + d x \right)}}{8 b^{2} d \tan^{4}{\left(c + d x \right)} + 16 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d} & \text{for}\: a = b \\\frac{x}{\left(a + b \tan^{2}{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{x}{a^{2}} & \text{for}\: b = 0 \\\frac{4 i a^{\frac{5}{2}} d x \sqrt{\frac{1}{b}}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} + \frac{4 i a^{\frac{3}{2}} b d x \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} - \frac{2 i a^{\frac{3}{2}} b \sqrt{\frac{1}{b}} \tan{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} + \frac{2 i \sqrt{a} b^{2} \sqrt{\frac{1}{b}} \tan{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} - \frac{3 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} + \frac{3 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} - \frac{3 a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} + \frac{a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} + \frac{3 a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} - \frac{a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} + \frac{b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}} - \frac{b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\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 + 1/(d*tan(c + d*x)) - 1/(3*d*tan(c + d*x)**3))/b**2, Eq(a, 0)), (3*d*x*tan(c + d*x)**4/(8*b**2*d*tan(c + d*x)**4 + 16*b**2*d*tan(c + d*x)**2 + 8*b**2*d) + 6*d*x*tan(c + d*x)**2/(8*b**2*d*tan(c + d*x)**4 + 16*b**2*d*tan(c + d*x)**2 + 8*b**2*d) + 3*d*x/(8*b**2*d*tan(c + d*x)**4 + 16*b**2*d*tan(c + d*x)**2 + 8*b**2*d) + 3*tan(c + d*x)**3/(8*b**2*d*tan(c + d*x)**4 + 16*b**2*d*tan(c + d*x)**2 + 8*b**2*d) + 5*tan(c + d*x)/(8*b**2*d*tan(c + d*x)**4 + 16*b**2*d*tan(c + d*x)**2 + 8*b**2*d), Eq(a, b)), (x/(a + b*tan(c)**2)**2, Eq(d, 0)), (x/a**2, Eq(b, 0)), (4*I*a**(5/2)*d*x*sqrt(1/b)/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) + 4*I*a**(3/2)*b*d*x*sqrt(1/b)*tan(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) - 2*I*a**(3/2)*b*sqrt(1/b)*tan(c + d*x)/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) + 2*I*sqrt(a)*b**2*sqrt(1/b)*tan(c + d*x)/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) - 3*a**2*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) + 3*a**2*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) - 3*a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) + a*b*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) + 3*a*b*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) - a*b*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) + b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2) - b**2*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2), True))","A",0
256,1,9629,0,99.075763," ","integrate(1/(a+b*tan(d*x+c)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\tan^{6}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 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)}} - \frac{1}{5 d \tan^{5}{\left(c + d x \right)}}}{b^{3}} & \text{for}\: a = 0 \\\frac{15 d x \tan^{6}{\left(c + d x \right)}}{48 b^{3} d \tan^{6}{\left(c + d x \right)} + 144 b^{3} d \tan^{4}{\left(c + d x \right)} + 144 b^{3} d \tan^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{45 d x \tan^{4}{\left(c + d x \right)}}{48 b^{3} d \tan^{6}{\left(c + d x \right)} + 144 b^{3} d \tan^{4}{\left(c + d x \right)} + 144 b^{3} d \tan^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{45 d x \tan^{2}{\left(c + d x \right)}}{48 b^{3} d \tan^{6}{\left(c + d x \right)} + 144 b^{3} d \tan^{4}{\left(c + d x \right)} + 144 b^{3} d \tan^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{15 d x}{48 b^{3} d \tan^{6}{\left(c + d x \right)} + 144 b^{3} d \tan^{4}{\left(c + d x \right)} + 144 b^{3} d \tan^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{15 \tan^{5}{\left(c + d x \right)}}{48 b^{3} d \tan^{6}{\left(c + d x \right)} + 144 b^{3} d \tan^{4}{\left(c + d x \right)} + 144 b^{3} d \tan^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{40 \tan^{3}{\left(c + d x \right)}}{48 b^{3} d \tan^{6}{\left(c + d x \right)} + 144 b^{3} d \tan^{4}{\left(c + d x \right)} + 144 b^{3} d \tan^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{33 \tan{\left(c + d x \right)}}{48 b^{3} d \tan^{6}{\left(c + d x \right)} + 144 b^{3} d \tan^{4}{\left(c + d x \right)} + 144 b^{3} d \tan^{2}{\left(c + d x \right)} + 48 b^{3} d} & \text{for}\: a = b \\\frac{x}{\left(a + b \tan^{2}{\left(c \right)}\right)^{3}} & \text{for}\: d = 0 \\\frac{x}{a^{3}} & \text{for}\: b = 0 \\\frac{16 i a^{\frac{9}{2}} d x \sqrt{\frac{1}{b}}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{32 i a^{\frac{7}{2}} b d x \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{18 i a^{\frac{7}{2}} b \sqrt{\frac{1}{b}} \tan{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{16 i a^{\frac{5}{2}} b^{2} d x \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{14 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan^{3}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{28 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \tan{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{20 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan^{3}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{10 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \tan{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{6 i \sqrt{a} b^{4} \sqrt{\frac{1}{b}} \tan^{3}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{15 a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{15 a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{30 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{10 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{30 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{10 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{15 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{20 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{3 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{15 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{20 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{3 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{10 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{6 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{10 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{6 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} - \frac{3 b^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} + \frac{3 b^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \tan{\left(c + d x \right)} \right)} \tan^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \tan^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \tan^{4}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/tan(c)**6, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-x - 1/(d*tan(c + d*x)) + 1/(3*d*tan(c + d*x)**3) - 1/(5*d*tan(c + d*x)**5))/b**3, Eq(a, 0)), (15*d*x*tan(c + d*x)**6/(48*b**3*d*tan(c + d*x)**6 + 144*b**3*d*tan(c + d*x)**4 + 144*b**3*d*tan(c + d*x)**2 + 48*b**3*d) + 45*d*x*tan(c + d*x)**4/(48*b**3*d*tan(c + d*x)**6 + 144*b**3*d*tan(c + d*x)**4 + 144*b**3*d*tan(c + d*x)**2 + 48*b**3*d) + 45*d*x*tan(c + d*x)**2/(48*b**3*d*tan(c + d*x)**6 + 144*b**3*d*tan(c + d*x)**4 + 144*b**3*d*tan(c + d*x)**2 + 48*b**3*d) + 15*d*x/(48*b**3*d*tan(c + d*x)**6 + 144*b**3*d*tan(c + d*x)**4 + 144*b**3*d*tan(c + d*x)**2 + 48*b**3*d) + 15*tan(c + d*x)**5/(48*b**3*d*tan(c + d*x)**6 + 144*b**3*d*tan(c + d*x)**4 + 144*b**3*d*tan(c + d*x)**2 + 48*b**3*d) + 40*tan(c + d*x)**3/(48*b**3*d*tan(c + d*x)**6 + 144*b**3*d*tan(c + d*x)**4 + 144*b**3*d*tan(c + d*x)**2 + 48*b**3*d) + 33*tan(c + d*x)/(48*b**3*d*tan(c + d*x)**6 + 144*b**3*d*tan(c + d*x)**4 + 144*b**3*d*tan(c + d*x)**2 + 48*b**3*d), Eq(a, b)), (x/(a + b*tan(c)**2)**3, Eq(d, 0)), (x/a**3, Eq(b, 0)), (16*I*a**(9/2)*d*x*sqrt(1/b)/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 32*I*a**(7/2)*b*d*x*sqrt(1/b)*tan(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 18*I*a**(7/2)*b*sqrt(1/b)*tan(c + d*x)/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 16*I*a**(5/2)*b**2*d*x*sqrt(1/b)*tan(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 14*I*a**(5/2)*b**2*sqrt(1/b)*tan(c + d*x)**3/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 28*I*a**(5/2)*b**2*sqrt(1/b)*tan(c + d*x)/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 20*I*a**(3/2)*b**3*sqrt(1/b)*tan(c + d*x)**3/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 10*I*a**(3/2)*b**3*sqrt(1/b)*tan(c + d*x)/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 6*I*sqrt(a)*b**4*sqrt(1/b)*tan(c + d*x)**3/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 15*a**4*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 15*a**4*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 30*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 10*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 30*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 10*a**3*b*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 15*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 20*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 3*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 15*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 20*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 3*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 10*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 6*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 10*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 6*a*b**3*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) - 3*b**4*log(-I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4) + 3*b**4*log(I*sqrt(a)*sqrt(1/b) + tan(c + d*x))*tan(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*tan(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*tan(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*tan(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*tan(c + d*x)**4), True))","A",0
257,0,0,0,0.000000," ","integrate((a+a*tan(x)**2)**(1/2)*tan(x)**4,x)","\int \sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)} \tan^{4}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a*(tan(x)**2 + 1))*tan(x)**4, x)","F",0
258,0,0,0,0.000000," ","integrate((a+a*tan(x)**2)**(1/2)*tan(x)**3,x)","\int \sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)} \tan^{3}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a*(tan(x)**2 + 1))*tan(x)**3, x)","F",0
259,0,0,0,0.000000," ","integrate((a+a*tan(x)**2)**(1/2)*tan(x)**2,x)","\int \sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)} \tan^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a*(tan(x)**2 + 1))*tan(x)**2, x)","F",0
260,1,10,0,0.598817," ","integrate((a+a*tan(x)**2)**(1/2)*tan(x),x)","\sqrt{a \tan^{2}{\left(x \right)} + a}"," ",0,"sqrt(a*tan(x)**2 + a)","A",0
261,0,0,0,0.000000," ","integrate(cot(x)*(a+a*tan(x)**2)**(1/2),x)","\int \sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)} \cot{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a*(tan(x)**2 + 1))*cot(x), x)","F",0
262,0,0,0,0.000000," ","integrate(cot(x)**2*(a+a*tan(x)**2)**(1/2),x)","\int \sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a*(tan(x)**2 + 1))*cot(x)**2, x)","F",0
263,0,0,0,0.000000," ","integrate(cot(x)**3*(a+a*tan(x)**2)**(1/2),x)","\int \sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)} \cot^{3}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a*(tan(x)**2 + 1))*cot(x)**3, x)","F",0
264,0,0,0,0.000000," ","integrate(cot(x)**4*(a+a*tan(x)**2)**(1/2),x)","\int \sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)} \cot^{4}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a*(tan(x)**2 + 1))*cot(x)**4, x)","F",0
265,0,0,0,0.000000," ","integrate((a+a*tan(d*x+c)**2)**(1/2),x)","\int \sqrt{a \tan^{2}{\left(c + d x \right)} + a}\, dx"," ",0,"Integral(sqrt(a*tan(c + d*x)**2 + a), x)","F",0
266,0,0,0,0.000000," ","integrate(tan(x)**3*(a+a*tan(x)**2)**(3/2),x)","\int \left(a \left(\tan^{2}{\left(x \right)} + 1\right)\right)^{\frac{3}{2}} \tan^{3}{\left(x \right)}\, dx"," ",0,"Integral((a*(tan(x)**2 + 1))**(3/2)*tan(x)**3, x)","F",0
267,0,0,0,0.000000," ","integrate(tan(x)**2*(a+a*tan(x)**2)**(3/2),x)","\int \left(a \left(\tan^{2}{\left(x \right)} + 1\right)\right)^{\frac{3}{2}} \tan^{2}{\left(x \right)}\, dx"," ",0,"Integral((a*(tan(x)**2 + 1))**(3/2)*tan(x)**2, x)","F",0
268,1,12,0,1.939571," ","integrate(tan(x)*(a+a*tan(x)**2)**(3/2),x)","\frac{\left(a \tan^{2}{\left(x \right)} + a\right)^{\frac{3}{2}}}{3}"," ",0,"(a*tan(x)**2 + a)**(3/2)/3","A",0
269,0,0,0,0.000000," ","integrate(cot(x)*(a+a*tan(x)**2)**(3/2),x)","\int \left(a \left(\tan^{2}{\left(x \right)} + 1\right)\right)^{\frac{3}{2}} \cot{\left(x \right)}\, dx"," ",0,"Integral((a*(tan(x)**2 + 1))**(3/2)*cot(x), x)","F",0
270,0,0,0,0.000000," ","integrate(cot(x)**2*(a+a*tan(x)**2)**(3/2),x)","\int \left(a \left(\tan^{2}{\left(x \right)} + 1\right)\right)^{\frac{3}{2}} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral((a*(tan(x)**2 + 1))**(3/2)*cot(x)**2, x)","F",0
271,0,0,0,0.000000," ","integrate((a+a*tan(d*x+c)**2)**(3/2),x)","\int \left(a \tan^{2}{\left(c + d x \right)} + a\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a*tan(c + d*x)**2 + a)**(3/2), x)","F",0
272,0,0,0,0.000000," ","integrate((a+a*tan(d*x+c)**2)**(5/2),x)","\int \left(a \tan^{2}{\left(c + d x \right)} + a\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a*tan(c + d*x)**2 + a)**(5/2), x)","F",0
273,0,0,0,0.000000," ","integrate(tan(x)**3/(a+a*tan(x)**2)**(1/2),x)","\int \frac{\tan^{3}{\left(x \right)}}{\sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(x)**3/sqrt(a*(tan(x)**2 + 1)), x)","F",0
274,0,0,0,0.000000," ","integrate(tan(x)**2/(a+a*tan(x)**2)**(1/2),x)","\int \frac{\tan^{2}{\left(x \right)}}{\sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(x)**2/sqrt(a*(tan(x)**2 + 1)), x)","F",0
275,1,14,0,0.569828," ","integrate(tan(x)/(a+a*tan(x)**2)**(1/2),x)","- \frac{1}{\sqrt{a \tan^{2}{\left(x \right)} + a}}"," ",0,"-1/sqrt(a*tan(x)**2 + a)","A",0
276,0,0,0,0.000000," ","integrate(cot(x)/(a+a*tan(x)**2)**(1/2),x)","\int \frac{\cot{\left(x \right)}}{\sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(x)/sqrt(a*(tan(x)**2 + 1)), x)","F",0
277,0,0,0,0.000000," ","integrate(cot(x)**2/(a+a*tan(x)**2)**(1/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\sqrt{a \left(\tan^{2}{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(x)**2/sqrt(a*(tan(x)**2 + 1)), x)","F",0
278,1,36,0,3.574785," ","integrate(tan(x)**3/(a+a*tan(x)**2)**(3/2),x)","\begin{cases} \frac{\frac{a}{3 \left(a \tan^{2}{\left(x \right)} + a\right)^{\frac{3}{2}}} - \frac{1}{\sqrt{a \tan^{2}{\left(x \right)} + a}}}{a} & \text{for}\: a \neq 0 \\\tilde{\infty} \tan^{4}{\left(x \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a/(3*(a*tan(x)**2 + a)**(3/2)) - 1/sqrt(a*tan(x)**2 + a))/a, Ne(a, 0)), (zoo*tan(x)**4, True))","A",0
279,0,0,0,0.000000," ","integrate(tan(x)**2/(a+a*tan(x)**2)**(3/2),x)","\int \frac{\tan^{2}{\left(x \right)}}{\left(a \left(\tan^{2}{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(x)**2/(a*(tan(x)**2 + 1))**(3/2), x)","F",0
280,1,15,0,3.315698," ","integrate(tan(x)/(a+a*tan(x)**2)**(3/2),x)","- \frac{1}{3 \left(a \tan^{2}{\left(x \right)} + a\right)^{\frac{3}{2}}}"," ",0,"-1/(3*(a*tan(x)**2 + a)**(3/2))","A",0
281,0,0,0,0.000000," ","integrate(cot(x)/(a+a*tan(x)**2)**(3/2),x)","\int \frac{\cot{\left(x \right)}}{\left(a \left(\tan^{2}{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(x)/(a*(tan(x)**2 + 1))**(3/2), x)","F",0
282,0,0,0,0.000000," ","integrate(cot(x)**2/(a+a*tan(x)**2)**(3/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\left(a \left(\tan^{2}{\left(x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(x)**2/(a*(tan(x)**2 + 1))**(3/2), x)","F",0
283,0,0,0,0.000000," ","integrate(1/(a+a*tan(d*x+c)**2)**(1/2),x)","\int \frac{1}{\sqrt{a \tan^{2}{\left(c + d x \right)} + a}}\, dx"," ",0,"Integral(1/sqrt(a*tan(c + d*x)**2 + a), x)","F",0
284,0,0,0,0.000000," ","integrate(1/(a+a*tan(d*x+c)**2)**(3/2),x)","\int \frac{1}{\left(a \tan^{2}{\left(c + d x \right)} + a\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*tan(c + d*x)**2 + a)**(-3/2), x)","F",0
285,0,0,0,0.000000," ","integrate(1/(a+a*tan(d*x+c)**2)**(5/2),x)","\int \frac{1}{\left(a \tan^{2}{\left(c + d x \right)} + a\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a*tan(c + d*x)**2 + a)**(-5/2), x)","F",0
286,0,0,0,0.000000," ","integrate(1/(a+a*tan(d*x+c)**2)**(7/2),x)","\int \frac{1}{\left(a \tan^{2}{\left(c + d x \right)} + a\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a*tan(c + d*x)**2 + a)**(-7/2), x)","F",0
287,0,0,0,0.000000," ","integrate((1+tan(x)**2)**(3/2),x)","\int \left(\tan^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((tan(x)**2 + 1)**(3/2), x)","F",0
288,0,0,0,0.000000," ","integrate((1+tan(x)**2)**(1/2),x)","\int \sqrt{\tan^{2}{\left(x \right)} + 1}\, dx"," ",0,"Integral(sqrt(tan(x)**2 + 1), x)","F",0
289,1,12,0,0.361344," ","integrate(1/(1+tan(x)**2)**(1/2),x)","\frac{\tan{\left(x \right)}}{\sqrt{\tan^{2}{\left(x \right)} + 1}}"," ",0,"tan(x)/sqrt(tan(x)**2 + 1)","A",0
290,0,0,0,0.000000," ","integrate((-1-tan(x)**2)**(3/2),x)","\int \left(- \tan^{2}{\left(x \right)} - 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-tan(x)**2 - 1)**(3/2), x)","F",0
291,0,0,0,0.000000," ","integrate((-1-tan(x)**2)**(1/2),x)","\int \sqrt{- \tan^{2}{\left(x \right)} - 1}\, dx"," ",0,"Integral(sqrt(-tan(x)**2 - 1), x)","F",0
292,0,0,0,0.000000," ","integrate(1/(-1-tan(x)**2)**(1/2),x)","\int \frac{1}{\sqrt{- \tan^{2}{\left(x \right)} - 1}}\, dx"," ",0,"Integral(1/sqrt(-tan(x)**2 - 1), x)","F",0
293,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(1/2)*tan(f*x+e)**5,x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \tan^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*tan(e + f*x)**5, x)","F",0
294,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(1/2)*tan(f*x+e)**3,x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*tan(e + f*x)**3, x)","F",0
295,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(1/2)*tan(f*x+e),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*tan(e + f*x), x)","F",0
296,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*cot(e + f*x), x)","F",0
297,0,0,0,0.000000," ","integrate(cot(f*x+e)**3*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \cot^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*cot(e + f*x)**3, x)","F",0
298,0,0,0,0.000000," ","integrate(cot(f*x+e)**5*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \cot^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*cot(e + f*x)**5, x)","F",0
299,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(1/2)*tan(f*x+e)**6,x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \tan^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*tan(e + f*x)**6, x)","F",0
300,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(1/2)*tan(f*x+e)**4,x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \tan^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*tan(e + f*x)**4, x)","F",0
301,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(1/2)*tan(f*x+e)**2,x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*tan(e + f*x)**2, x)","F",0
302,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2), x)","F",0
303,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*cot(e + f*x)**2, x)","F",0
304,0,0,0,0.000000," ","integrate(cot(f*x+e)**4*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \cot^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*cot(e + f*x)**4, x)","F",0
305,0,0,0,0.000000," ","integrate(cot(f*x+e)**6*(a+b*tan(f*x+e)**2)**(1/2),x)","\int \sqrt{a + b \tan^{2}{\left(e + f x \right)}} \cot^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x)**2)*cot(e + f*x)**6, x)","F",0
306,0,0,0,0.000000," ","integrate(tan(f*x+e)**5*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{5}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*tan(e + f*x)**5, x)","F",0
307,0,0,0,0.000000," ","integrate(tan(f*x+e)**3*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*tan(e + f*x)**3, x)","F",0
308,0,0,0,0.000000," ","integrate(tan(f*x+e)*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*tan(e + f*x), x)","F",0
309,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*cot(e + f*x), x)","F",0
310,0,0,0,0.000000," ","integrate(cot(f*x+e)**3*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \cot^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*cot(e + f*x)**3, x)","F",0
311,-1,0,0,0.000000," ","integrate(cot(f*x+e)**5*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
312,0,0,0,0.000000," ","integrate(tan(f*x+e)**6*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*tan(e + f*x)**6, x)","F",0
313,0,0,0,0.000000," ","integrate(tan(f*x+e)**4*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*tan(e + f*x)**4, x)","F",0
314,0,0,0,0.000000," ","integrate(tan(f*x+e)**2*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*tan(e + f*x)**2, x)","F",0
315,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2), x)","F",0
316,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*cot(e + f*x)**2, x)","F",0
317,0,0,0,0.000000," ","integrate(cot(f*x+e)**4*(a+b*tan(f*x+e)**2)**(3/2),x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}} \cot^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(3/2)*cot(e + f*x)**4, x)","F",0
318,-1,0,0,0.000000," ","integrate(cot(f*x+e)**6*(a+b*tan(f*x+e)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
319,0,0,0,0.000000," ","integrate((a+b*tan(d*x+c)**2)**(5/2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**(5/2), x)","F",0
320,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**5/sqrt(a + b*tan(e + f*x)**2), x)","F",0
321,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**3/sqrt(a + b*tan(e + f*x)**2), x)","F",0
322,0,0,0,0.000000," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\tan{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)/sqrt(a + b*tan(e + f*x)**2), x)","F",0
323,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)/sqrt(a + b*tan(e + f*x)**2), x)","F",0
324,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**3/sqrt(a + b*tan(e + f*x)**2), x)","F",0
325,0,0,0,0.000000," ","integrate(cot(f*x+e)**5/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{5}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**5/sqrt(a + b*tan(e + f*x)**2), x)","F",0
326,0,0,0,0.000000," ","integrate(tan(f*x+e)**6/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{6}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**6/sqrt(a + b*tan(e + f*x)**2), x)","F",0
327,0,0,0,0.000000," ","integrate(tan(f*x+e)**4/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{4}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**4/sqrt(a + b*tan(e + f*x)**2), x)","F",0
328,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(tan(e + f*x)**2/sqrt(a + b*tan(e + f*x)**2), x)","F",0
329,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*tan(e + f*x)**2), x)","F",0
330,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**2/sqrt(a + b*tan(e + f*x)**2), x)","F",0
331,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**4/sqrt(a + b*tan(e + f*x)**2), x)","F",0
332,0,0,0,0.000000," ","integrate(cot(f*x+e)**6/(a+b*tan(f*x+e)**2)**(1/2),x)","\int \frac{\cot^{6}{\left(e + f x \right)}}{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cot(e + f*x)**6/sqrt(a + b*tan(e + f*x)**2), x)","F",0
333,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**5/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
334,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**3/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
335,1,56,0,24.732932," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)**2)**(3/2),x)","\frac{1}{f \left(a - b\right) \sqrt{a + b \tan^{2}{\left(e + f x \right)}}} + \frac{\operatorname{atan}{\left(\frac{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}{\sqrt{- a + b}} \right)}}{f \sqrt{- a + b} \left(a - b\right)}"," ",0,"1/(f*(a - b)*sqrt(a + b*tan(e + f*x)**2)) + atan(sqrt(a + b*tan(e + f*x)**2)/sqrt(-a + b))/(f*sqrt(-a + b)*(a - b))","A",0
336,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
337,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**3/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
338,0,0,0,0.000000," ","integrate(cot(f*x+e)**5/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{5}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**5/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
339,0,0,0,0.000000," ","integrate(tan(f*x+e)**6/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{6}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**6/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
340,0,0,0,0.000000," ","integrate(tan(f*x+e)**4/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{4}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**4/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
341,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**2/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
342,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{1}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(-3/2), x)","F",0
343,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**2/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
344,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**4/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
345,0,0,0,0.000000," ","integrate(cot(f*x+e)**6/(a+b*tan(f*x+e)**2)**(3/2),x)","\int \frac{\cot^{6}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**6/(a + b*tan(e + f*x)**2)**(3/2), x)","F",0
346,0,0,0,0.000000," ","integrate(tan(f*x+e)**5/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{5}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**5/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
347,0,0,0,0.000000," ","integrate(tan(f*x+e)**3/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{3}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**3/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
348,1,83,0,31.490128," ","integrate(tan(f*x+e)/(a+b*tan(f*x+e)**2)**(5/2),x)","\frac{1}{3 f \left(a - b\right) \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{3}{2}}} + \frac{1}{f \left(a - b\right)^{2} \sqrt{a + b \tan^{2}{\left(e + f x \right)}}} + \frac{\operatorname{atan}{\left(\frac{\sqrt{a + b \tan^{2}{\left(e + f x \right)}}}{\sqrt{- a + b}} \right)}}{f \sqrt{- a + b} \left(a - b\right)^{2}}"," ",0,"1/(3*f*(a - b)*(a + b*tan(e + f*x)**2)**(3/2)) + 1/(f*(a - b)**2*sqrt(a + b*tan(e + f*x)**2)) + atan(sqrt(a + b*tan(e + f*x)**2)/sqrt(-a + b))/(f*sqrt(-a + b)*(a - b)**2)","A",0
349,0,0,0,0.000000," ","integrate(cot(f*x+e)/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\cot{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
350,0,0,0,0.000000," ","integrate(cot(f*x+e)**3/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{3}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**3/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
351,0,0,0,0.000000," ","integrate(cot(f*x+e)**5/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{5}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**5/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
352,0,0,0,0.000000," ","integrate(tan(f*x+e)**6/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{6}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**6/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
353,0,0,0,0.000000," ","integrate(tan(f*x+e)**4/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{4}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**4/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
354,0,0,0,0.000000," ","integrate(tan(f*x+e)**2/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\tan^{2}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(e + f*x)**2/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
355,0,0,0,0.000000," ","integrate(1/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{1}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**(-5/2), x)","F",0
356,0,0,0,0.000000," ","integrate(cot(f*x+e)**2/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{2}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**2/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
357,0,0,0,0.000000," ","integrate(cot(f*x+e)**4/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{4}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**4/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
358,0,0,0,0.000000," ","integrate(cot(f*x+e)**6/(a+b*tan(f*x+e)**2)**(5/2),x)","\int \frac{\cot^{6}{\left(e + f x \right)}}{\left(a + b \tan^{2}{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(e + f*x)**6/(a + b*tan(e + f*x)**2)**(5/2), x)","F",0
359,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**m*(b*tan(f*x+e)**2)**p,x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{p} \left(d \tan{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**p*(d*tan(e + f*x))**m, x)","F",0
360,-1,0,0,0.000000," ","integrate((d*tan(f*x+e))**m*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate(tan(f*x+e)**5*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,0,0,0,0.000000," ","integrate(tan(f*x+e)**3*(a+b*tan(f*x+e)**2)**p,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{p} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**p*tan(e + f*x)**3, x)","F",0
363,0,0,0,0.000000," ","integrate(tan(f*x+e)*(a+b*tan(f*x+e)**2)**p,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{p} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**p*tan(e + f*x), x)","F",0
364,0,0,0,0.000000," ","integrate(cot(f*x+e)*(a+b*tan(f*x+e)**2)**p,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{p} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**p*cot(e + f*x), x)","F",0
365,-1,0,0,0.000000," ","integrate(cot(f*x+e)**3*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate(cot(f*x+e)**5*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate(tan(f*x+e)**6*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,0,0,0,0.000000," ","integrate(tan(f*x+e)**4*(a+b*tan(f*x+e)**2)**p,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{p} \tan^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**p*tan(e + f*x)**4, x)","F",0
369,0,0,0,0.000000," ","integrate(tan(f*x+e)**2*(a+b*tan(f*x+e)**2)**p,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{p} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**p*tan(e + f*x)**2, x)","F",0
370,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e)**2)**p,x)","\int \left(a + b \tan^{2}{\left(e + f x \right)}\right)^{p}\, dx"," ",0,"Integral((a + b*tan(e + f*x)**2)**p, x)","F",0
371,-1,0,0,0.000000," ","integrate(cot(f*x+e)**2*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(cot(f*x+e)**4*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(cot(f*x+e)**6*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,1,301,0,3.583918," ","integrate((a+b*tan(d*x+c)**3)**4,x)","\begin{cases} a^{4} x - \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{6 a^{2} b^{2} \tan^{5}{\left(c + d x \right)}}{5 d} - \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^{8}{\left(c + d x \right)}}{2 d} - \frac{2 a b^{3} \tan^{6}{\left(c + d x \right)}}{3 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^{11}{\left(c + d x \right)}}{11 d} - \frac{b^{4} \tan^{9}{\left(c + d x \right)}}{9 d} + \frac{b^{4} \tan^{7}{\left(c + d x \right)}}{7 d} - \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^{3}{\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 + 2*a**3*b*tan(c + d*x)**2/d - 6*a**2*b**2*x + 6*a**2*b**2*tan(c + d*x)**5/(5*d) - 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)**8/(2*d) - 2*a*b**3*tan(c + d*x)**6/(3*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)**11/(11*d) - b**4*tan(c + d*x)**9/(9*d) + b**4*tan(c + d*x)**7/(7*d) - 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)**3)**4, True))","A",0
375,1,194,0,1.650707," ","integrate((a+b*tan(d*x+c)**3)**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} + \frac{3 a^{2} b \tan^{2}{\left(c + d x \right)}}{2 d} - 3 a b^{2} x + \frac{3 a b^{2} \tan^{5}{\left(c + d x \right)}}{5 d} - \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^{8}{\left(c + d x \right)}}{8 d} - \frac{b^{3} \tan^{6}{\left(c + d x \right)}}{6 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^{3}{\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**2*b*tan(c + d*x)**2/(2*d) - 3*a*b**2*x + 3*a*b**2*tan(c + d*x)**5/(5*d) - 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)**8/(8*d) - b**3*tan(c + d*x)**6/(6*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)**3, True))","A",0
376,1,94,0,0.596564," ","integrate((a+b*tan(d*x+c)**3)**2,x)","\begin{cases} a^{2} x - \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^{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^{3}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x - 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)**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)**3)**2, True))","A",0
377,1,37,0,0.182188," ","integrate(a+b*tan(d*x+c)**3,x)","a x + b \left(\begin{cases} - \frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{\tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \tan^{3}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-log(tan(c + d*x)**2 + 1)/(2*d) + tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*tan(c)**3, True))","A",0
378,0,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c)**3),x)","\int \frac{1}{a + b \tan^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(a + b*tan(c + d*x)**3), x)","F",0
379,-1,0,0,0.000000," ","integrate(1/(a+b*tan(d*x+c)**3)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
380,1,34,0,0.179866," ","integrate(1/(1+tan(x)**3),x)","\frac{x}{2} + \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{6} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4} - \frac{\log{\left(\tan^{2}{\left(x \right)} - \tan{\left(x \right)} + 1 \right)}}{3}"," ",0,"x/2 + log(tan(x) + 1)/6 + log(tan(x)**2 + 1)/4 - log(tan(x)**2 - tan(x) + 1)/3","A",0
381,1,386,0,7.070303," ","integrate((a+tan(d*x+c)**4*b)**4,x)","\begin{cases} a^{4} x + 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} + 6 a^{2} b^{2} x + \frac{6 a^{2} b^{2} \tan^{7}{\left(c + d x \right)}}{7 d} - \frac{6 a^{2} b^{2} \tan^{5}{\left(c + d x \right)}}{5 d} + \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} + 4 a b^{3} x + \frac{4 a b^{3} \tan^{11}{\left(c + d x \right)}}{11 d} - \frac{4 a b^{3} \tan^{9}{\left(c + d x \right)}}{9 d} + \frac{4 a b^{3} \tan^{7}{\left(c + d x \right)}}{7 d} - \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} + b^{4} x + \frac{b^{4} \tan^{15}{\left(c + d x \right)}}{15 d} - \frac{b^{4} \tan^{13}{\left(c + d x \right)}}{13 d} + \frac{b^{4} \tan^{11}{\left(c + d x \right)}}{11 d} - \frac{b^{4} \tan^{9}{\left(c + d x \right)}}{9 d} + \frac{b^{4} \tan^{7}{\left(c + d x \right)}}{7 d} - \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^{4}{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + 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 + 6*a**2*b**2*x + 6*a**2*b**2*tan(c + d*x)**7/(7*d) - 6*a**2*b**2*tan(c + d*x)**5/(5*d) + 2*a**2*b**2*tan(c + d*x)**3/d - 6*a**2*b**2*tan(c + d*x)/d + 4*a*b**3*x + 4*a*b**3*tan(c + d*x)**11/(11*d) - 4*a*b**3*tan(c + d*x)**9/(9*d) + 4*a*b**3*tan(c + d*x)**7/(7*d) - 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*x + b**4*tan(c + d*x)**15/(15*d) - b**4*tan(c + d*x)**13/(13*d) + b**4*tan(c + d*x)**11/(11*d) - b**4*tan(c + d*x)**9/(9*d) + b**4*tan(c + d*x)**7/(7*d) - 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)**4, True))","A",0
382,1,224,0,3.175594," ","integrate((a+tan(d*x+c)**4*b)**3,x)","\begin{cases} a^{3} x + 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} + 3 a b^{2} x + \frac{3 a b^{2} \tan^{7}{\left(c + d x \right)}}{7 d} - \frac{3 a b^{2} \tan^{5}{\left(c + d x \right)}}{5 d} + \frac{a b^{2} \tan^{3}{\left(c + d x \right)}}{d} - \frac{3 a b^{2} \tan{\left(c + d x \right)}}{d} + b^{3} x + \frac{b^{3} \tan^{11}{\left(c + d x \right)}}{11 d} - \frac{b^{3} \tan^{9}{\left(c + d x \right)}}{9 d} + \frac{b^{3} \tan^{7}{\left(c + d x \right)}}{7 d} - \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^{4}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + 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*x + 3*a*b**2*tan(c + d*x)**7/(7*d) - 3*a*b**2*tan(c + d*x)**5/(5*d) + a*b**2*tan(c + d*x)**3/d - 3*a*b**2*tan(c + d*x)/d + b**3*x + b**3*tan(c + d*x)**11/(11*d) - b**3*tan(c + d*x)**9/(9*d) + b**3*tan(c + d*x)**7/(7*d) - 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)**4)**3, True))","A",0
383,1,116,0,1.083573," ","integrate((a+tan(d*x+c)**4*b)**2,x)","\begin{cases} a^{2} x + 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} + b^{2} x + \frac{b^{2} \tan^{7}{\left(c + d x \right)}}{7 d} - \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^{4}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + 2*a*b*x + 2*a*b*tan(c + d*x)**3/(3*d) - 2*a*b*tan(c + d*x)/d + b**2*x + b**2*tan(c + d*x)**7/(7*d) - 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)**4)**2, True))","A",0
384,1,32,0,0.221286," ","integrate(a+tan(d*x+c)**4*b,x)","a x + b \left(\begin{cases} x + \frac{\tan^{3}{\left(c + d x \right)}}{3 d} - \frac{\tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \tan^{4}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((x + tan(c + d*x)**3/(3*d) - tan(c + d*x)/d, Ne(d, 0)), (x*tan(c)**4, True))","A",0
385,0,0,0,0.000000," ","integrate(1/(a+tan(d*x+c)**4*b),x)","\int \frac{1}{a + b \tan^{4}{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(a + b*tan(c + d*x)**4), x)","F",0
386,0,0,0,0.000000," ","integrate(1/(a+tan(d*x+c)**4*b)**2,x)","\int \frac{1}{\left(a + b \tan^{4}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**4)**(-2), x)","F",0
387,0,0,0,0.000000," ","integrate((a+tan(d*x+c)**4*b)**(1/2),x)","\int \sqrt{a + b \tan^{4}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*tan(c + d*x)**4), x)","F",0
388,0,0,0,0.000000," ","integrate(1/(a+tan(d*x+c)**4*b)**(1/2),x)","\int \frac{1}{\sqrt{a + b \tan^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*tan(c + d*x)**4), x)","F",0
389,0,0,0,0.000000," ","integrate((a+b*tan(x)**4)**(1/2)*tan(x)**3,x)","\int \sqrt{a + b \tan^{4}{\left(x \right)}} \tan^{3}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(x)**4)*tan(x)**3, x)","F",0
390,0,0,0,0.000000," ","integrate((a+b*tan(x)**4)**(1/2)*tan(x),x)","\int \sqrt{a + b \tan^{4}{\left(x \right)}} \tan{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(x)**4)*tan(x), x)","F",0
391,0,0,0,0.000000," ","integrate(cot(x)*(a+b*tan(x)**4)**(1/2),x)","\int \sqrt{a + b \tan^{4}{\left(x \right)}} \cot{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(x)**4)*cot(x), x)","F",0
392,0,0,0,0.000000," ","integrate((a+b*tan(x)**4)**(1/2)*tan(x)**2,x)","\int \sqrt{a + b \tan^{4}{\left(x \right)}} \tan^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*tan(x)**4)*tan(x)**2, x)","F",0
393,0,0,0,0.000000," ","integrate(tan(x)**3*(a+b*tan(x)**4)**(3/2),x)","\int \left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{3}{2}} \tan^{3}{\left(x \right)}\, dx"," ",0,"Integral((a + b*tan(x)**4)**(3/2)*tan(x)**3, x)","F",0
394,0,0,0,0.000000," ","integrate(tan(x)*(a+b*tan(x)**4)**(3/2),x)","\int \left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{3}{2}} \tan{\left(x \right)}\, dx"," ",0,"Integral((a + b*tan(x)**4)**(3/2)*tan(x), x)","F",0
395,0,0,0,0.000000," ","integrate(cot(x)*(a+b*tan(x)**4)**(3/2),x)","\int \left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{3}{2}} \cot{\left(x \right)}\, dx"," ",0,"Integral((a + b*tan(x)**4)**(3/2)*cot(x), x)","F",0
396,0,0,0,0.000000," ","integrate(tan(x)**3/(a+b*tan(x)**4)**(1/2),x)","\int \frac{\tan^{3}{\left(x \right)}}{\sqrt{a + b \tan^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(tan(x)**3/sqrt(a + b*tan(x)**4), x)","F",0
397,0,0,0,0.000000," ","integrate(tan(x)/(a+b*tan(x)**4)**(1/2),x)","\int \frac{\tan{\left(x \right)}}{\sqrt{a + b \tan^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(tan(x)/sqrt(a + b*tan(x)**4), x)","F",0
398,0,0,0,0.000000," ","integrate(cot(x)/(a+b*tan(x)**4)**(1/2),x)","\int \frac{\cot{\left(x \right)}}{\sqrt{a + b \tan^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(cot(x)/sqrt(a + b*tan(x)**4), x)","F",0
399,0,0,0,0.000000," ","integrate(tan(x)**2/(a+b*tan(x)**4)**(1/2),x)","\int \frac{\tan^{2}{\left(x \right)}}{\sqrt{a + b \tan^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(tan(x)**2/sqrt(a + b*tan(x)**4), x)","F",0
400,0,0,0,0.000000," ","integrate(tan(x)**3/(a+b*tan(x)**4)**(3/2),x)","\int \frac{\tan^{3}{\left(x \right)}}{\left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(x)**3/(a + b*tan(x)**4)**(3/2), x)","F",0
401,0,0,0,0.000000," ","integrate(tan(x)/(a+b*tan(x)**4)**(3/2),x)","\int \frac{\tan{\left(x \right)}}{\left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(x)/(a + b*tan(x)**4)**(3/2), x)","F",0
402,0,0,0,0.000000," ","integrate(cot(x)/(a+b*tan(x)**4)**(3/2),x)","\int \frac{\cot{\left(x \right)}}{\left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(x)/(a + b*tan(x)**4)**(3/2), x)","F",0
403,0,0,0,0.000000," ","integrate(tan(x)**3/(a+b*tan(x)**4)**(5/2),x)","\int \frac{\tan^{3}{\left(x \right)}}{\left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(x)**3/(a + b*tan(x)**4)**(5/2), x)","F",0
404,0,0,0,0.000000," ","integrate(tan(x)/(a+b*tan(x)**4)**(5/2),x)","\int \frac{\tan{\left(x \right)}}{\left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(x)/(a + b*tan(x)**4)**(5/2), x)","F",0
405,0,0,0,0.000000," ","integrate(cot(x)/(a+b*tan(x)**4)**(5/2),x)","\int \frac{\cot{\left(x \right)}}{\left(a + b \tan^{4}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(x)/(a + b*tan(x)**4)**(5/2), x)","F",0
406,0,0,0,0.000000," ","integrate((a+b*(c*tan(f*x+e))**(1/2))**2*(d*tan(f*x+e))**m,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{m} \left(a + b \sqrt{c \tan{\left(e + f x \right)}}\right)^{2}\, dx"," ",0,"Integral((d*tan(e + f*x))**m*(a + b*sqrt(c*tan(e + f*x)))**2, x)","F",0
407,0,0,0,0.000000," ","integrate((a+b*(c*tan(f*x+e))**(1/2))*(d*tan(f*x+e))**m,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{m} \left(a + b \sqrt{c \tan{\left(e + f x \right)}}\right)\, dx"," ",0,"Integral((d*tan(e + f*x))**m*(a + b*sqrt(c*tan(e + f*x))), x)","F",0
408,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**m/(a+b*(c*tan(f*x+e))**(1/2)),x)","\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{m}}{a + b \sqrt{c \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((d*tan(e + f*x))**m/(a + b*sqrt(c*tan(e + f*x))), x)","F",0
409,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**m/(a+b*(c*tan(f*x+e))**(1/2))**2,x)","\int \frac{\left(d \tan{\left(e + f x \right)}\right)^{m}}{\left(a + b \sqrt{c \tan{\left(e + f x \right)}}\right)^{2}}\, dx"," ",0,"Integral((d*tan(e + f*x))**m/(a + b*sqrt(c*tan(e + f*x)))**2, x)","F",0
410,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**m*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \left(d \tan{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*(d*tan(e + f*x))**m, x)","F",0
411,0,0,0,0.000000," ","integrate(tan(f*x+e)**2*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \tan^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*tan(e + f*x)**2, x)","F",0
412,0,0,0,0.000000," ","integrate((b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p, x)","F",0
413,0,0,0,0.000000," ","integrate(cot(f*x+e)**2*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \cot^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*cot(e + f*x)**2, x)","F",0
414,0,0,0,0.000000," ","integrate(cot(f*x+e)**4*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \cot^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*cot(e + f*x)**4, x)","F",0
415,-1,0,0,0.000000," ","integrate(cot(f*x+e)**6*(b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
416,0,0,0,0.000000," ","integrate(tan(f*x+e)**3*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \tan^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*tan(e + f*x)**3, x)","F",0
417,0,0,0,0.000000," ","integrate(tan(f*x+e)*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \tan{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*tan(e + f*x), x)","F",0
418,0,0,0,0.000000," ","integrate(cot(f*x+e)*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \cot{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*cot(e + f*x), x)","F",0
419,0,0,0,0.000000," ","integrate(cot(f*x+e)**3*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \cot^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*cot(e + f*x)**3, x)","F",0
420,0,0,0,0.000000," ","integrate((d*tan(f*x+e))**m*(a+b*(c*tan(f*x+e))**n)**p,x)","\int \left(d \tan{\left(e + f x \right)}\right)^{m} \left(a + b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p}\, dx"," ",0,"Integral((d*tan(e + f*x))**m*(a + b*(c*tan(e + f*x))**n)**p, x)","F",0
421,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**m*(b*tan(f*x+e)**2)**p,x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{p} \left(d \cot{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**p*(d*cot(e + f*x))**m, x)","F",0
422,-1,0,0,0.000000," ","integrate((d*cot(f*x+e))**m*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
423,0,0,0,0.000000," ","integrate((d*cot(f*x+e))**m*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \left(d \cot{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*(d*cot(e + f*x))**m, x)","F",0
424,-1,0,0,0.000000," ","integrate((d*cot(f*x+e))**m*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*sec(c + d*x)**3, x)","F",0
426,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*sec(c + d*x), x)","F",0
427,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*cos(c + d*x), x)","F",0
428,0,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \cos^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*cos(c + d*x)**3, x)","F",0
429,0,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \cos^{5}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*cos(c + d*x)**5, x)","F",0
430,0,0,0,0.000000," ","integrate(cos(d*x+c)**7*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \cos^{7}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*cos(c + d*x)**7, x)","F",0
431,0,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \sec^{6}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*sec(c + d*x)**6, x)","F",0
432,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*sec(c + d*x)**4, x)","F",0
433,1,36,0,1.745136," ","integrate(sec(d*x+c)**2*(a+b*tan(d*x+c)**2),x)","\begin{cases} \frac{a \tan{\left(c + d x \right)} + \frac{b \tan^{3}{\left(c + d x \right)}}{3}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan^{2}{\left(c \right)}\right) \sec^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((a*tan(c + d*x) + b*tan(c + d*x)**3/3)/d, Ne(d, 0)), (x*(a + b*tan(c)**2)*sec(c)**2, True))","A",0
434,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*cos(c + d*x)**2, x)","F",0
435,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \cos^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*cos(c + d*x)**4, x)","F",0
436,0,0,0,0.000000," ","integrate(cos(d*x+c)**6*(a+b*tan(d*x+c)**2),x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right) \cos^{6}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)*cos(c + d*x)**6, x)","F",0
437,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*sec(c + d*x)**3, x)","F",0
438,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*sec(c + d*x), x)","F",0
439,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*cos(c + d*x), x)","F",0
440,0,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \cos^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*cos(c + d*x)**3, x)","F",0
441,0,0,0,0.000000," ","integrate(cos(d*x+c)**5*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \cos^{5}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*cos(c + d*x)**5, x)","F",0
442,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*(a+b*tan(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,-1,0,0,0.000000," ","integrate(cos(d*x+c)**9*(a+b*tan(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
444,0,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \sec^{6}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*sec(c + d*x)**6, x)","F",0
445,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*sec(c + d*x)**4, x)","F",0
446,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*sec(c + d*x)**2, x)","F",0
447,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*cos(c + d*x)**2, x)","F",0
448,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*(a+b*tan(d*x+c)**2)**2,x)","\int \left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2} \cos^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*tan(c + d*x)**2)**2*cos(c + d*x)**4, x)","F",0
449,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*(a+b*tan(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+b*tan(d*x+c)**2),x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a + b*tan(c + d*x)**2), x)","F",0
451,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*tan(d*x+c)**2),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*tan(c + d*x)**2), x)","F",0
452,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c)**2),x)","\int \frac{\sec{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*tan(c + d*x)**2), x)","F",0
453,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c)**2),x)","\int \frac{\cos{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)/(a + b*tan(c + d*x)**2), x)","F",0
454,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*tan(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
455,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a+b*tan(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,0,0,0,0.000000," ","integrate(sec(d*x+c)**8/(a+b*tan(d*x+c)**2),x)","\int \frac{\sec^{8}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**8/(a + b*tan(c + d*x)**2), x)","F",0
457,0,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a+b*tan(d*x+c)**2),x)","\int \frac{\sec^{6}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**6/(a + b*tan(c + d*x)**2), x)","F",0
458,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*tan(d*x+c)**2),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*tan(c + d*x)**2), x)","F",0
459,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*tan(d*x+c)**2),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a + b \tan^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*tan(c + d*x)**2), x)","F",0
460,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*tan(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*tan(d*x+c)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7/(a+b*tan(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a+b*tan(d*x+c)**2)**2,x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a + b*tan(c + d*x)**2)**2, x)","F",0
464,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a+b*tan(d*x+c)**2)**2,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a + b*tan(c + d*x)**2)**2, x)","F",0
465,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a+b*tan(d*x+c)**2)**2,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)/(a + b*tan(c + d*x)**2)**2, x)","F",0
466,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a+b*tan(d*x+c)**2)**2,x)","\int \frac{\cos{\left(c + d x \right)}}{\left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)/(a + b*tan(c + d*x)**2)**2, x)","F",0
467,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a+b*tan(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8/(a+b*tan(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,0,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a+b*tan(d*x+c)**2)**2,x)","\int \frac{\sec^{6}{\left(c + d x \right)}}{\left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**6/(a + b*tan(c + d*x)**2)**2, x)","F",0
470,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a+b*tan(d*x+c)**2)**2,x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a + b*tan(c + d*x)**2)**2, x)","F",0
471,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a+b*tan(d*x+c)**2)**2,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a + b \tan^{2}{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a + b*tan(c + d*x)**2)**2, x)","F",0
472,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a+b*tan(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a+b*tan(d*x+c)**2)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,0,0,0,0.000000," ","integrate((d*sec(f*x+e))**m*(b*tan(f*x+e)**2)**p,x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{p} \left(d \sec{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**p*(d*sec(e + f*x))**m, x)","F",0
475,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))**m*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,0,0,0,0.000000," ","integrate((d*sec(f*x+e))**m*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \left(d \sec{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*(d*sec(e + f*x))**m, x)","F",0
477,0,0,0,0.000000," ","integrate(sec(f*x+e)**6*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \sec^{6}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*sec(e + f*x)**6, x)","F",0
478,0,0,0,0.000000," ","integrate(sec(f*x+e)**4*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \sec^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*sec(e + f*x)**4, x)","F",0
479,0,0,0,0.000000," ","integrate(sec(f*x+e)**2*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \sec^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*sec(e + f*x)**2, x)","F",0
480,0,0,0,0.000000," ","integrate((b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p, x)","F",0
481,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \cos^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*cos(e + f*x)**2, x)","F",0
482,0,0,0,0.000000," ","integrate(sec(f*x+e)**3*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \sec^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*sec(e + f*x)**3, x)","F",0
483,0,0,0,0.000000," ","integrate(sec(f*x+e)*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \sec{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*sec(e + f*x), x)","F",0
484,0,0,0,0.000000," ","integrate(cos(f*x+e)*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \cos{\left(e + f x \right)}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*cos(e + f*x), x)","F",0
485,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3*(b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate((d*sec(f*x+e))**m*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(sec(f*x+e)**3*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+b*(c*tan(f*x+e))**n)**p,x)","\int \left(a + b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \sec{\left(e + f x \right)}\, dx"," ",0,"Integral((a + b*(c*tan(e + f*x))**n)**p*sec(e + f*x), x)","F",0
489,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,-1,0,0,0.000000," ","integrate(cos(f*x+e)**3*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,-1,0,0,0.000000," ","integrate(sec(f*x+e)**6*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,0,0,0,0.000000," ","integrate((a+b*(c*tan(f*x+e))**n)**p,x)","\int \left(a + b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p}\, dx"," ",0,"Integral((a + b*(c*tan(e + f*x))**n)**p, x)","F",0
495,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
496,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**m*(b*tan(f*x+e)**2)**p,x)","\int \left(b \tan^{2}{\left(e + f x \right)}\right)^{p} \left(d \csc{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*tan(e + f*x)**2)**p*(d*csc(e + f*x))**m, x)","F",0
497,-1,0,0,0.000000," ","integrate((d*csc(f*x+e))**m*(a+b*tan(f*x+e)**2)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**m*(b*(c*tan(f*x+e))**n)**p,x)","\int \left(b \left(c \tan{\left(e + f x \right)}\right)^{n}\right)^{p} \left(d \csc{\left(e + f x \right)}\right)^{m}\, dx"," ",0,"Integral((b*(c*tan(e + f*x))**n)**p*(d*csc(e + f*x))**m, x)","F",0
499,-1,0,0,0.000000," ","integrate((d*csc(f*x+e))**m*(a+b*(c*tan(f*x+e))**n)**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
