1,1,139,0,0.374140," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} - B a x + \frac{B a \tan{\left(c + d x \right)}}{d} - \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b \tan^{2}{\left(c + d x \right)}}{2 d} - \frac{C a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C a \tan^{2}{\left(c + d x \right)}}{2 d} + C b x + \frac{C b \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{C b \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*a*x + B*a*tan(c + d*x)/d - B*b*log(tan(c + d*x)**2 + 1)/(2*d) + B*b*tan(c + d*x)**2/(2*d) - C*a*log(tan(c + d*x)**2 + 1)/(2*d) + C*a*tan(c + d*x)**2/(2*d) + C*b*x + C*b*tan(c + d*x)**3/(3*d) - C*b*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))*(B*tan(c) + C*tan(c)**2)*tan(c), True))","A",0
2,1,105,0,0.243598," ","integrate((a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - B b x + \frac{B b \tan{\left(c + d x \right)}}{d} - C a x + \frac{C a \tan{\left(c + d x \right)}}{d} - \frac{C b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C b \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a*log(tan(c + d*x)**2 + 1)/(2*d) - B*b*x + B*b*tan(c + d*x)/d - C*a*x + C*a*tan(c + d*x)/d - C*b*log(tan(c + d*x)**2 + 1)/(2*d) + C*b*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))*(B*tan(c) + C*tan(c)**2), True))","A",0
3,1,82,0,0.647391," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} B a x + \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - C b x + \frac{C b \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a*x + B*b*log(tan(c + d*x)**2 + 1)/(2*d) + C*a*log(tan(c + d*x)**2 + 1)/(2*d) - C*b*x + C*b*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))*(B*tan(c) + C*tan(c)**2)*cot(c), True))","A",0
4,1,85,0,0.979158," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} - \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B b x + C a x + \frac{C b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right) \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*a*log(tan(c + d*x)**2 + 1)/(2*d) + B*a*log(tan(c + d*x))/d + B*b*x + C*a*x + C*b*log(tan(c + d*x)**2 + 1)/(2*d), Ne(d, 0)), (x*(a + b*tan(c))*(B*tan(c) + C*tan(c)**2)*cot(c)**2, True))","A",0
5,1,116,0,1.664248," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: c = 0 \wedge d = 0 \\x \left(a + b \tan{\left(c \right)}\right) \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\text{NaN} & \text{for}\: c = - d x \\- B a x - \frac{B a}{d \tan{\left(c + d x \right)}} - \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{C a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + C b x & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(c, 0) & Eq(d, 0)), (x*(a + b*tan(c))*(B*tan(c) + C*tan(c)**2)*cot(c)**3, Eq(d, 0)), (nan, Eq(c, -d*x)), (-B*a*x - B*a/(d*tan(c + d*x)) - B*b*log(tan(c + d*x)**2 + 1)/(2*d) + B*b*log(tan(c + d*x))/d - C*a*log(tan(c + d*x)**2 + 1)/(2*d) + C*a*log(tan(c + d*x))/d + C*b*x, True))","A",0
6,1,150,0,2.334637," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right) \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\\frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a}{2 d \tan^{2}{\left(c + d x \right)}} - B b x - \frac{B b}{d \tan{\left(c + d x \right)}} - C a x - \frac{C a}{d \tan{\left(c + d x \right)}} - \frac{C b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))*(B*tan(c) + C*tan(c)**2)*cot(c)**4, Eq(d, 0)), (B*a*log(tan(c + d*x)**2 + 1)/(2*d) - B*a*log(tan(c + d*x))/d - B*a/(2*d*tan(c + d*x)**2) - B*b*x - B*b/(d*tan(c + d*x)) - C*a*x - C*a/(d*tan(c + d*x)) - C*b*log(tan(c + d*x)**2 + 1)/(2*d) + C*b*log(tan(c + d*x))/d, True))","A",0
7,1,180,0,4.428793," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right) \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\B a x + \frac{B a}{d \tan{\left(c + d x \right)}} - \frac{B a}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B b}{2 d \tan^{2}{\left(c + d x \right)}} + \frac{C a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{C a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{C a}{2 d \tan^{2}{\left(c + d x \right)}} - C b x - \frac{C b}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))*(B*tan(c) + C*tan(c)**2)*cot(c)**5, Eq(d, 0)), (B*a*x + B*a/(d*tan(c + d*x)) - B*a/(3*d*tan(c + d*x)**3) + B*b*log(tan(c + d*x)**2 + 1)/(2*d) - B*b*log(tan(c + d*x))/d - B*b/(2*d*tan(c + d*x)**2) + C*a*log(tan(c + d*x)**2 + 1)/(2*d) - C*a*log(tan(c + d*x))/d - C*a/(2*d*tan(c + d*x)**2) - C*b*x - C*b/(d*tan(c + d*x)), True))","A",0
8,1,211,0,5.867883," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c))*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right) \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{B a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{B a}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{B a}{4 d \tan^{4}{\left(c + d x \right)}} + B b x + \frac{B b}{d \tan{\left(c + d x \right)}} - \frac{B b}{3 d \tan^{3}{\left(c + d x \right)}} + C a x + \frac{C a}{d \tan{\left(c + d x \right)}} - \frac{C a}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{C b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{C b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{C b}{2 d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))*(B*tan(c) + C*tan(c)**2)*cot(c)**6, Eq(d, 0)), (-B*a*log(tan(c + d*x)**2 + 1)/(2*d) + B*a*log(tan(c + d*x))/d + B*a/(2*d*tan(c + d*x)**2) - B*a/(4*d*tan(c + d*x)**4) + B*b*x + B*b/(d*tan(c + d*x)) - B*b/(3*d*tan(c + d*x)**3) + C*a*x + C*a/(d*tan(c + d*x)) - C*a/(3*d*tan(c + d*x)**3) + C*b*log(tan(c + d*x)**2 + 1)/(2*d) - C*b*log(tan(c + d*x))/d - C*b/(2*d*tan(c + d*x)**2), True))","A",0
9,1,250,0,0.600008," ","integrate(tan(d*x+c)*(a+b*tan(d*x+c))**2*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} - B a^{2} x + \frac{B a^{2} \tan{\left(c + d x \right)}}{d} - \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{B a b \tan^{2}{\left(c + d x \right)}}{d} + B b^{2} x + \frac{B b^{2} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{B b^{2} \tan{\left(c + d x \right)}}{d} - \frac{C a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C a^{2} \tan^{2}{\left(c + d x \right)}}{2 d} + 2 C a b x + \frac{2 C a b \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{2 C a b \tan{\left(c + d x \right)}}{d} + \frac{C b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C b^{2} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{C b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \tan{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*a**2*x + B*a**2*tan(c + d*x)/d - B*a*b*log(tan(c + d*x)**2 + 1)/d + B*a*b*tan(c + d*x)**2/d + B*b**2*x + B*b**2*tan(c + d*x)**3/(3*d) - B*b**2*tan(c + d*x)/d - C*a**2*log(tan(c + d*x)**2 + 1)/(2*d) + C*a**2*tan(c + d*x)**2/(2*d) + 2*C*a*b*x + 2*C*a*b*tan(c + d*x)**3/(3*d) - 2*C*a*b*tan(c + d*x)/d + C*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + C*b**2*tan(c + d*x)**4/(4*d) - C*b**2*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**2*(B*tan(c) + C*tan(c)**2)*tan(c), True))","A",0
10,1,194,0,0.434729," ","integrate((a+b*tan(d*x+c))**2*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 2 B a b x + \frac{2 B a b \tan{\left(c + d x \right)}}{d} - \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} - C a^{2} x + \frac{C a^{2} \tan{\left(c + d x \right)}}{d} - \frac{C a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{C a b \tan^{2}{\left(c + d x \right)}}{d} + C b^{2} x + \frac{C b^{2} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{C b^{2} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**2*log(tan(c + d*x)**2 + 1)/(2*d) - 2*B*a*b*x + 2*B*a*b*tan(c + d*x)/d - B*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**2*tan(c + d*x)**2/(2*d) - C*a**2*x + C*a**2*tan(c + d*x)/d - C*a*b*log(tan(c + d*x)**2 + 1)/d + C*a*b*tan(c + d*x)**2/d + C*b**2*x + C*b**2*tan(c + d*x)**3/(3*d) - C*b**2*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**2*(B*tan(c) + C*tan(c)**2), True))","A",0
11,1,151,0,1.085504," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**2*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} B a^{2} x + \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - B b^{2} x + \frac{B b^{2} \tan{\left(c + d x \right)}}{d} + \frac{C a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 2 C a b x + \frac{2 C a b \tan{\left(c + d x \right)}}{d} - \frac{C b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**2*x + B*a*b*log(tan(c + d*x)**2 + 1)/d - B*b**2*x + B*b**2*tan(c + d*x)/d + C*a**2*log(tan(c + d*x)**2 + 1)/(2*d) - 2*C*a*b*x + 2*C*a*b*tan(c + d*x)/d - C*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + C*b**2*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**2*(B*tan(c) + C*tan(c)**2)*cot(c), True))","A",0
12,1,136,0,1.612448," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**2*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} - \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 2 B a b x + \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + C a^{2} x + \frac{C a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - C b^{2} x + \frac{C b^{2} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*a**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**2*log(tan(c + d*x))/d + 2*B*a*b*x + B*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + C*a**2*x + C*a*b*log(tan(c + d*x)**2 + 1)/d - C*b**2*x + C*b**2*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**2*(B*tan(c) + C*tan(c)**2)*cot(c)**2, True))","A",0
13,1,158,0,2.297875," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**2*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: c = 0 \wedge d = 0 \\x \left(a + b \tan{\left(c \right)}\right)^{2} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\text{NaN} & \text{for}\: c = - d x \\- B a^{2} x - \frac{B a^{2}}{d \tan{\left(c + d x \right)}} - \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 B a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B b^{2} x - \frac{C a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 2 C a b x + \frac{C b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(c, 0) & Eq(d, 0)), (x*(a + b*tan(c))**2*(B*tan(c) + C*tan(c)**2)*cot(c)**3, Eq(d, 0)), (nan, Eq(c, -d*x)), (-B*a**2*x - B*a**2/(d*tan(c + d*x)) - B*a*b*log(tan(c + d*x)**2 + 1)/d + 2*B*a*b*log(tan(c + d*x))/d + B*b**2*x - C*a**2*log(tan(c + d*x)**2 + 1)/(2*d) + C*a**2*log(tan(c + d*x))/d + 2*C*a*b*x + C*b**2*log(tan(c + d*x)**2 + 1)/(2*d), True))","A",0
14,1,212,0,4.312186," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**2*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right)^{2} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\\frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - 2 B a b x - \frac{2 B a b}{d \tan{\left(c + d x \right)}} - \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - C a^{2} x - \frac{C a^{2}}{d \tan{\left(c + d x \right)}} - \frac{C a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 C a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + C b^{2} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**2*(B*tan(c) + C*tan(c)**2)*cot(c)**4, Eq(d, 0)), (B*a**2*log(tan(c + d*x)**2 + 1)/(2*d) - B*a**2*log(tan(c + d*x))/d - B*a**2/(2*d*tan(c + d*x)**2) - 2*B*a*b*x - 2*B*a*b/(d*tan(c + d*x)) - B*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**2*log(tan(c + d*x))/d - C*a**2*x - C*a**2/(d*tan(c + d*x)) - C*a*b*log(tan(c + d*x)**2 + 1)/d + 2*C*a*b*log(tan(c + d*x))/d + C*b**2*x, True))","A",0
15,1,258,0,5.678645," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**2*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right)^{2} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\B a^{2} x + \frac{B a^{2}}{d \tan{\left(c + d x \right)}} - \frac{B a^{2}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{2 B a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a b}{d \tan^{2}{\left(c + d x \right)}} - B b^{2} x - \frac{B b^{2}}{d \tan{\left(c + d x \right)}} + \frac{C a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{C a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{C a^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - 2 C a b x - \frac{2 C a b}{d \tan{\left(c + d x \right)}} - \frac{C b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**2*(B*tan(c) + C*tan(c)**2)*cot(c)**5, Eq(d, 0)), (B*a**2*x + B*a**2/(d*tan(c + d*x)) - B*a**2/(3*d*tan(c + d*x)**3) + B*a*b*log(tan(c + d*x)**2 + 1)/d - 2*B*a*b*log(tan(c + d*x))/d - B*a*b/(d*tan(c + d*x)**2) - B*b**2*x - B*b**2/(d*tan(c + d*x)) + C*a**2*log(tan(c + d*x)**2 + 1)/(2*d) - C*a**2*log(tan(c + d*x))/d - C*a**2/(2*d*tan(c + d*x)**2) - 2*C*a*b*x - 2*C*a*b/(d*tan(c + d*x)) - C*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + C*b**2*log(tan(c + d*x))/d, True))","A",0
16,1,311,0,8.800955," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c))**2*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right)^{2} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{B a^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{2}}{4 d \tan^{4}{\left(c + d x \right)}} + 2 B a b x + \frac{2 B a b}{d \tan{\left(c + d x \right)}} - \frac{2 B a b}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{B b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B b^{2}}{2 d \tan^{2}{\left(c + d x \right)}} + C a^{2} x + \frac{C a^{2}}{d \tan{\left(c + d x \right)}} - \frac{C a^{2}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{C a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{d} - \frac{2 C a b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{C a b}{d \tan^{2}{\left(c + d x \right)}} - C b^{2} x - \frac{C b^{2}}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**2*(B*tan(c) + C*tan(c)**2)*cot(c)**6, Eq(d, 0)), (-B*a**2*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**2*log(tan(c + d*x))/d + B*a**2/(2*d*tan(c + d*x)**2) - B*a**2/(4*d*tan(c + d*x)**4) + 2*B*a*b*x + 2*B*a*b/(d*tan(c + d*x)) - 2*B*a*b/(3*d*tan(c + d*x)**3) + B*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - B*b**2*log(tan(c + d*x))/d - B*b**2/(2*d*tan(c + d*x)**2) + C*a**2*x + C*a**2/(d*tan(c + d*x)) - C*a**2/(3*d*tan(c + d*x)**3) + C*a*b*log(tan(c + d*x)**2 + 1)/d - 2*C*a*b*log(tan(c + d*x))/d - C*a*b/(d*tan(c + d*x)**2) - C*b**2*x - C*b**2/(d*tan(c + d*x)), True))","A",0
17,1,313,0,0.666858," ","integrate((a+b*tan(d*x+c))**3*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 B a^{2} b x + \frac{3 B a^{2} b \tan{\left(c + d x \right)}}{d} - \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} + B b^{3} x + \frac{B b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{B b^{3} \tan{\left(c + d x \right)}}{d} - C a^{3} x + \frac{C a^{3} \tan{\left(c + d x \right)}}{d} - \frac{3 C a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 C a^{2} b \tan^{2}{\left(c + d x \right)}}{2 d} + 3 C a b^{2} x + \frac{C a b^{2} \tan^{3}{\left(c + d x \right)}}{d} - \frac{3 C a b^{2} \tan{\left(c + d x \right)}}{d} + \frac{C b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C b^{3} \tan^{4}{\left(c + d x \right)}}{4 d} - \frac{C b^{3} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{3} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) - 3*B*a**2*b*x + 3*B*a**2*b*tan(c + d*x)/d - 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a*b**2*tan(c + d*x)**2/(2*d) + B*b**3*x + B*b**3*tan(c + d*x)**3/(3*d) - B*b**3*tan(c + d*x)/d - C*a**3*x + C*a**3*tan(c + d*x)/d - 3*C*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*C*a**2*b*tan(c + d*x)**2/(2*d) + 3*C*a*b**2*x + C*a*b**2*tan(c + d*x)**3/d - 3*C*a*b**2*tan(c + d*x)/d + C*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + C*b**3*tan(c + d*x)**4/(4*d) - C*b**3*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**3*(B*tan(c) + C*tan(c)**2), True))","A",0
18,1,248,0,1.817376," ","integrate(cot(d*x+c)*(a+b*tan(d*x+c))**3*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} B a^{3} x + \frac{3 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 B a b^{2} x + \frac{3 B a b^{2} \tan{\left(c + d x \right)}}{d} - \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{3} \tan^{2}{\left(c + d x \right)}}{2 d} + \frac{C a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 C a^{2} b x + \frac{3 C a^{2} b \tan{\left(c + d x \right)}}{d} - \frac{3 C a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 C a b^{2} \tan^{2}{\left(c + d x \right)}}{2 d} + C b^{3} x + \frac{C b^{3} \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{C b^{3} \tan{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{3} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((B*a**3*x + 3*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*B*a*b**2*x + 3*B*a*b**2*tan(c + d*x)/d - B*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**3*tan(c + d*x)**2/(2*d) + C*a**3*log(tan(c + d*x)**2 + 1)/(2*d) - 3*C*a**2*b*x + 3*C*a**2*b*tan(c + d*x)/d - 3*C*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*C*a*b**2*tan(c + d*x)**2/(2*d) + C*b**3*x + C*b**3*tan(c + d*x)**3/(3*d) - C*b**3*tan(c + d*x)/d, Ne(d, 0)), (x*(a + b*tan(c))**3*(B*tan(c) + C*tan(c)**2)*cot(c), True))","A",0
19,1,211,0,2.322221," ","integrate(cot(d*x+c)**2*(a+b*tan(d*x+c))**3*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} - \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 B a^{2} b x + \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - B b^{3} x + \frac{B b^{3} \tan{\left(c + d x \right)}}{d} + C a^{3} x + \frac{3 C a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - 3 C a b^{2} x + \frac{3 C a b^{2} \tan{\left(c + d x \right)}}{d} - \frac{C b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C b^{3} \tan^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a + b \tan{\left(c \right)}\right)^{3} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**3*log(tan(c + d*x))/d + 3*B*a**2*b*x + 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - B*b**3*x + B*b**3*tan(c + d*x)/d + C*a**3*x + 3*C*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*C*a*b**2*x + 3*C*a*b**2*tan(c + d*x)/d - C*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + C*b**3*tan(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a + b*tan(c))**3*(B*tan(c) + C*tan(c)**2)*cot(c)**2, True))","A",0
20,1,214,0,4.424268," ","integrate(cot(d*x+c)**3*(a+b*tan(d*x+c))**3*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: c = 0 \wedge d = 0 \\x \left(a + b \tan{\left(c \right)}\right)^{3} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{3}{\left(c \right)} & \text{for}\: d = 0 \\\text{NaN} & \text{for}\: c = - d x \\- B a^{3} x - \frac{B a^{3}}{d \tan{\left(c + d x \right)}} - \frac{3 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 B a b^{2} x + \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{C a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 C a^{2} b x + \frac{3 C a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - C b^{3} x + \frac{C b^{3} \tan{\left(c + d x \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(c, 0) & Eq(d, 0)), (x*(a + b*tan(c))**3*(B*tan(c) + C*tan(c)**2)*cot(c)**3, Eq(d, 0)), (nan, Eq(c, -d*x)), (-B*a**3*x - B*a**3/(d*tan(c + d*x)) - 3*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a**2*b*log(tan(c + d*x))/d + 3*B*a*b**2*x + B*b**3*log(tan(c + d*x)**2 + 1)/(2*d) - C*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + C*a**3*log(tan(c + d*x))/d + 3*C*a**2*b*x + 3*C*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - C*b**3*x + C*b**3*tan(c + d*x)/d, True))","A",0
21,1,260,0,5.602032," ","integrate(cot(d*x+c)**4*(a+b*tan(d*x+c))**3*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right)^{3} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{4}{\left(c \right)} & \text{for}\: d = 0 \\\frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - 3 B a^{2} b x - \frac{3 B a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + B b^{3} x - C a^{3} x - \frac{C a^{3}}{d \tan{\left(c + d x \right)}} - \frac{3 C a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 C a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + 3 C a b^{2} x + \frac{C b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**3*(B*tan(c) + C*tan(c)**2)*cot(c)**4, Eq(d, 0)), (B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) - B*a**3*log(tan(c + d*x))/d - B*a**3/(2*d*tan(c + d*x)**2) - 3*B*a**2*b*x - 3*B*a**2*b/(d*tan(c + d*x)) - 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a*b**2*log(tan(c + d*x))/d + B*b**3*x - C*a**3*x - C*a**3/(d*tan(c + d*x)) - 3*C*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*C*a**2*b*log(tan(c + d*x))/d + 3*C*a*b**2*x + C*b**3*log(tan(c + d*x)**2 + 1)/(2*d), True))","A",0
22,1,330,0,8.559063," ","integrate(cot(d*x+c)**5*(a+b*tan(d*x+c))**3*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right)^{3} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{5}{\left(c \right)} & \text{for}\: d = 0 \\B a^{3} x + \frac{B a^{3}}{d \tan{\left(c + d x \right)}} - \frac{B a^{3}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{3 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 B a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 B a^{2} b}{2 d \tan^{2}{\left(c + d x \right)}} - 3 B a b^{2} x - \frac{3 B a b^{2}}{d \tan{\left(c + d x \right)}} - \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{C a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{C a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{C a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - 3 C a^{2} b x - \frac{3 C a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{3 C a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 C a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + C b^{3} x & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**3*(B*tan(c) + C*tan(c)**2)*cot(c)**5, Eq(d, 0)), (B*a**3*x + B*a**3/(d*tan(c + d*x)) - B*a**3/(3*d*tan(c + d*x)**3) + 3*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*B*a**2*b*log(tan(c + d*x))/d - 3*B*a**2*b/(2*d*tan(c + d*x)**2) - 3*B*a*b**2*x - 3*B*a*b**2/(d*tan(c + d*x)) - B*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*b**3*log(tan(c + d*x))/d + C*a**3*log(tan(c + d*x)**2 + 1)/(2*d) - C*a**3*log(tan(c + d*x))/d - C*a**3/(2*d*tan(c + d*x)**2) - 3*C*a**2*b*x - 3*C*a**2*b/(d*tan(c + d*x)) - 3*C*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) + 3*C*a*b**2*log(tan(c + d*x))/d + C*b**3*x, True))","A",0
23,1,398,0,11.005249," ","integrate(cot(d*x+c)**6*(a+b*tan(d*x+c))**3*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right)^{3} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{6}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{B a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{B a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{3}}{4 d \tan^{4}{\left(c + d x \right)}} + 3 B a^{2} b x + \frac{3 B a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{B a^{2} b}{d \tan^{3}{\left(c + d x \right)}} + \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 B a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 B a b^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - B b^{3} x - \frac{B b^{3}}{d \tan{\left(c + d x \right)}} + C a^{3} x + \frac{C a^{3}}{d \tan{\left(c + d x \right)}} - \frac{C a^{3}}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{3 C a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 C a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 C a^{2} b}{2 d \tan^{2}{\left(c + d x \right)}} - 3 C a b^{2} x - \frac{3 C a b^{2}}{d \tan{\left(c + d x \right)}} - \frac{C b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**3*(B*tan(c) + C*tan(c)**2)*cot(c)**6, Eq(d, 0)), (-B*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + B*a**3*log(tan(c + d*x))/d + B*a**3/(2*d*tan(c + d*x)**2) - B*a**3/(4*d*tan(c + d*x)**4) + 3*B*a**2*b*x + 3*B*a**2*b/(d*tan(c + d*x)) - B*a**2*b/(d*tan(c + d*x)**3) + 3*B*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - 3*B*a*b**2*log(tan(c + d*x))/d - 3*B*a*b**2/(2*d*tan(c + d*x)**2) - B*b**3*x - B*b**3/(d*tan(c + d*x)) + C*a**3*x + C*a**3/(d*tan(c + d*x)) - C*a**3/(3*d*tan(c + d*x)**3) + 3*C*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) - 3*C*a**2*b*log(tan(c + d*x))/d - 3*C*a**2*b/(2*d*tan(c + d*x)**2) - 3*C*a*b**2*x - 3*C*a*b**2/(d*tan(c + d*x)) - C*b**3*log(tan(c + d*x)**2 + 1)/(2*d) + C*b**3*log(tan(c + d*x))/d, True))","A",0
24,1,469,0,27.645885," ","integrate(cot(d*x+c)**7*(a+b*tan(d*x+c))**3*(B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\begin{cases} \text{NaN} & \text{for}\: \left(c = 0 \vee c = - d x\right) \wedge \left(c = - d x \vee d = 0\right) \\x \left(a + b \tan{\left(c \right)}\right)^{3} \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{7}{\left(c \right)} & \text{for}\: d = 0 \\- B a^{3} x - \frac{B a^{3}}{d \tan{\left(c + d x \right)}} + \frac{B a^{3}}{3 d \tan^{3}{\left(c + d x \right)}} - \frac{B a^{3}}{5 d \tan^{5}{\left(c + d x \right)}} - \frac{3 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{3 B a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{3 B a^{2} b}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{3 B a^{2} b}{4 d \tan^{4}{\left(c + d x \right)}} + 3 B a b^{2} x + \frac{3 B a b^{2}}{d \tan{\left(c + d x \right)}} - \frac{B a b^{2}}{d \tan^{3}{\left(c + d x \right)}} + \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B b^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B b^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{C a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C a^{3} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + \frac{C a^{3}}{2 d \tan^{2}{\left(c + d x \right)}} - \frac{C a^{3}}{4 d \tan^{4}{\left(c + d x \right)}} + 3 C a^{2} b x + \frac{3 C a^{2} b}{d \tan{\left(c + d x \right)}} - \frac{C a^{2} b}{d \tan^{3}{\left(c + d x \right)}} + \frac{3 C a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{3 C a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{3 C a b^{2}}{2 d \tan^{2}{\left(c + d x \right)}} - C b^{3} x - \frac{C b^{3}}{d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, (Eq(c, 0) | Eq(c, -d*x)) & (Eq(d, 0) | Eq(c, -d*x))), (x*(a + b*tan(c))**3*(B*tan(c) + C*tan(c)**2)*cot(c)**7, Eq(d, 0)), (-B*a**3*x - B*a**3/(d*tan(c + d*x)) + B*a**3/(3*d*tan(c + d*x)**3) - B*a**3/(5*d*tan(c + d*x)**5) - 3*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*d) + 3*B*a**2*b*log(tan(c + d*x))/d + 3*B*a**2*b/(2*d*tan(c + d*x)**2) - 3*B*a**2*b/(4*d*tan(c + d*x)**4) + 3*B*a*b**2*x + 3*B*a*b**2/(d*tan(c + d*x)) - B*a*b**2/(d*tan(c + d*x)**3) + B*b**3*log(tan(c + d*x)**2 + 1)/(2*d) - B*b**3*log(tan(c + d*x))/d - B*b**3/(2*d*tan(c + d*x)**2) - C*a**3*log(tan(c + d*x)**2 + 1)/(2*d) + C*a**3*log(tan(c + d*x))/d + C*a**3/(2*d*tan(c + d*x)**2) - C*a**3/(4*d*tan(c + d*x)**4) + 3*C*a**2*b*x + 3*C*a**2*b/(d*tan(c + d*x)) - C*a**2*b/(d*tan(c + d*x)**3) + 3*C*a*b**2*log(tan(c + d*x)**2 + 1)/(2*d) - 3*C*a*b**2*log(tan(c + d*x))/d - 3*C*a*b**2/(2*d*tan(c + d*x)**2) - C*b**3*x - C*b**3/(d*tan(c + d*x)), True))","A",0
25,1,1309,0,2.029816," ","integrate(tan(d*x+c)**2*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \tan{\left(c \right)} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{3 i B d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 B d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{2 i B \tan^{2}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 i B}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 C d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 i C d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i C \tan^{3}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{C \tan^{2}{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 C}{2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = - i b \\\frac{3 i B d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 B d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 i B \tan^{2}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 i B}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 C d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{3 i C d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{2 i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i C \tan^{3}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{C \tan^{2}{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{3 C}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = i b \\\frac{- \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \tan^{2}{\left(c + d x \right)}}{2 d} + C x + \frac{C \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{C \tan{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \tan^{2}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{2 B a^{3} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 B a^{2} b^{2} \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 B b^{4} d x}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 B b^{4} \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 C a^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 C a^{3} b \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{C a^{2} b^{2} \tan^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{2 C a b^{3} d x}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{2 C a b^{3} \tan{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} - \frac{C b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} + \frac{C b^{4} \tan^{2}{\left(c + d x \right)}}{2 a^{2} b^{3} d + 2 b^{5} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2)*tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-3*I*B*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3*B*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*B*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) + 2*I*B*tan(c + d*x)**2/(2*I*b*d*tan(c + d*x) + 2*b*d) + 3*I*B/(2*I*b*d*tan(c + d*x) + 2*b*d) + 3*C*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3*I*C*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*C*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*C*tan(c + d*x)**3/(2*I*b*d*tan(c + d*x) + 2*b*d) - C*tan(c + d*x)**2/(2*I*b*d*tan(c + d*x) + 2*b*d) - 3*C/(2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, -I*b)), (3*I*B*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 3*B*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) - B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*B*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*I*B*tan(c + d*x)**2/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 3*I*B/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 3*C*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 3*I*C*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) + 2*I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*C*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*C*tan(c + d*x)**3/(-2*I*b*d*tan(c + d*x) + 2*b*d) - C*tan(c + d*x)**2/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 3*C/(-2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, I*b)), ((-B*log(tan(c + d*x)**2 + 1)/(2*d) + B*tan(c + d*x)**2/(2*d) + C*x + C*tan(c + d*x)**3/(3*d) - C*tan(c + d*x)/d)/a, Eq(b, 0)), (x*(B*tan(c) + C*tan(c)**2)*tan(c)**2/(a + b*tan(c)), Eq(d, 0)), (-2*B*a**3*b*log(a/b + tan(c + d*x))/(2*a**2*b**3*d + 2*b**5*d) + 2*B*a**2*b**2*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) - B*a*b**3*log(tan(c + d*x)**2 + 1)/(2*a**2*b**3*d + 2*b**5*d) - 2*B*b**4*d*x/(2*a**2*b**3*d + 2*b**5*d) + 2*B*b**4*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) + 2*C*a**4*log(a/b + tan(c + d*x))/(2*a**2*b**3*d + 2*b**5*d) - 2*C*a**3*b*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) + C*a**2*b**2*tan(c + d*x)**2/(2*a**2*b**3*d + 2*b**5*d) + 2*C*a*b**3*d*x/(2*a**2*b**3*d + 2*b**5*d) - 2*C*a*b**3*tan(c + d*x)/(2*a**2*b**3*d + 2*b**5*d) - C*b**4*log(tan(c + d*x)**2 + 1)/(2*a**2*b**3*d + 2*b**5*d) + C*b**4*tan(c + d*x)**2/(2*a**2*b**3*d + 2*b**5*d), True))","A",0
26,1,1020,0,1.454405," ","integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c)),x)","\begin{cases} \tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{i B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{B d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{3 C d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{3 i C d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{2 C \tan^{2}{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{3 C}{2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = - i b \\- \frac{i B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{B d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{3 C d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{3 i C d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{2 C \tan^{2}{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{3 C}{2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = i b \\\frac{- B x + \frac{B \tan{\left(c + d x \right)}}{d} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C \tan^{2}{\left(c + d x \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \tan{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{2 B a^{2} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{2 B a b^{2} d x}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{B b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{2 C a^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{2 C a^{2} b \tan{\left(c + d x \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{C a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} - \frac{2 C b^{3} d x}{2 a^{2} b^{2} d + 2 b^{4} d} + \frac{2 C b^{3} \tan{\left(c + d x \right)}}{2 a^{2} b^{2} d + 2 b^{4} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (I*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + B*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) + B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*B*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*B/(2*b*d*tan(c + d*x) - 2*I*b*d) - 3*C*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 3*I*C*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) + I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + C*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) - 2*I*b*d) + 2*C*tan(c + d*x)**2/(2*b*d*tan(c + d*x) - 2*I*b*d) + 3*C/(2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, -I*b)), (-I*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + B*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) + B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*B*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*B/(2*b*d*tan(c + d*x) + 2*I*b*d) - 3*C*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) - 3*I*C*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) - I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + C*log(tan(c + d*x)**2 + 1)/(2*b*d*tan(c + d*x) + 2*I*b*d) + 2*C*tan(c + d*x)**2/(2*b*d*tan(c + d*x) + 2*I*b*d) + 3*C/(2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, I*b)), ((-B*x + B*tan(c + d*x)/d - C*log(tan(c + d*x)**2 + 1)/(2*d) + C*tan(c + d*x)**2/(2*d))/a, Eq(b, 0)), (x*(B*tan(c) + C*tan(c)**2)*tan(c)/(a + b*tan(c)), Eq(d, 0)), (2*B*a**2*b*log(a/b + tan(c + d*x))/(2*a**2*b**2*d + 2*b**4*d) - 2*B*a*b**2*d*x/(2*a**2*b**2*d + 2*b**4*d) + B*b**3*log(tan(c + d*x)**2 + 1)/(2*a**2*b**2*d + 2*b**4*d) - 2*C*a**3*log(a/b + tan(c + d*x))/(2*a**2*b**2*d + 2*b**4*d) + 2*C*a**2*b*tan(c + d*x)/(2*a**2*b**2*d + 2*b**4*d) - C*a*b**2*log(tan(c + d*x)**2 + 1)/(2*a**2*b**2*d + 2*b**4*d) - 2*C*b**3*d*x/(2*a**2*b**2*d + 2*b**4*d) + 2*C*b**3*tan(c + d*x)/(2*a**2*b**2*d + 2*b**4*d), True))","A",0
27,1,724,0,1.121760," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right)}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{B d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i B d x}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{B}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{i C d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{C d x}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i C}{- 2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = - i b \\- \frac{B d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i B d x}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{B}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{i C d x \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{C d x}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i C}{- 2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = i b \\\frac{\frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - C x + \frac{C \tan{\left(c + d x \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right)}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{2 B a b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b d + 2 b^{3} d} + \frac{B a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b d + 2 b^{3} d} + \frac{2 B b^{2} d x}{2 a^{2} b d + 2 b^{3} d} + \frac{2 C a^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} b d + 2 b^{3} d} - \frac{2 C a b d x}{2 a^{2} b d + 2 b^{3} d} + \frac{C b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} b d + 2 b^{3} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2)/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-B*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*B*d*x/(-2*b*d*tan(c + d*x) + 2*I*b*d) + B/(-2*b*d*tan(c + d*x) + 2*I*b*d) - I*C*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) - C*d*x/(-2*b*d*tan(c + d*x) + 2*I*b*d) - C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*C*log(tan(c + d*x)**2 + 1)/(-2*b*d*tan(c + d*x) + 2*I*b*d) + I*C/(-2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, -I*b)), (-B*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*B*d*x/(-2*b*d*tan(c + d*x) - 2*I*b*d) + B/(-2*b*d*tan(c + d*x) - 2*I*b*d) + I*C*d*x*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - C*d*x/(-2*b*d*tan(c + d*x) - 2*I*b*d) - C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*C*log(tan(c + d*x)**2 + 1)/(-2*b*d*tan(c + d*x) - 2*I*b*d) - I*C/(-2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, I*b)), ((B*log(tan(c + d*x)**2 + 1)/(2*d) - C*x + C*tan(c + d*x)/d)/a, Eq(b, 0)), (x*(B*tan(c) + C*tan(c)**2)/(a + b*tan(c)), Eq(d, 0)), (-2*B*a*b*log(a/b + tan(c + d*x))/(2*a**2*b*d + 2*b**3*d) + B*a*b*log(tan(c + d*x)**2 + 1)/(2*a**2*b*d + 2*b**3*d) + 2*B*b**2*d*x/(2*a**2*b*d + 2*b**3*d) + 2*C*a**2*log(a/b + tan(c + d*x))/(2*a**2*b*d + 2*b**3*d) - 2*C*a*b*d*x/(2*a**2*b*d + 2*b**3*d) + C*b**2*log(tan(c + d*x)**2 + 1)/(2*a**2*b*d + 2*b**3*d), True))","A",0
28,1,541,0,2.954171," ","integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot{\left(c \right)}}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{i B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{B d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{i B}{2 b d \tan{\left(c + d x \right)} - 2 i b d} + \frac{C d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{i C d x}{2 b d \tan{\left(c + d x \right)} - 2 i b d} - \frac{C}{2 b d \tan{\left(c + d x \right)} - 2 i b d} & \text{for}\: a = - i b \\- \frac{i B d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{B d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{i B}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{C d x \tan{\left(c + d x \right)}}{2 b d \tan{\left(c + d x \right)} + 2 i b d} + \frac{i C d x}{2 b d \tan{\left(c + d x \right)} + 2 i b d} - \frac{C}{2 b d \tan{\left(c + d x \right)} + 2 i b d} & \text{for}\: a = i b \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{B x + \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{2 B a d x}{2 a^{2} d + 2 b^{2} d} + \frac{2 B b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} d + 2 b^{2} d} - \frac{B b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} - \frac{2 C a \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{C a \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d + 2 b^{2} d} + \frac{2 C b d x}{2 a^{2} d + 2 b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2)*cot(c)/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (I*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) + B*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) + I*B/(2*b*d*tan(c + d*x) - 2*I*b*d) + C*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) - 2*I*b*d) - I*C*d*x/(2*b*d*tan(c + d*x) - 2*I*b*d) - C/(2*b*d*tan(c + d*x) - 2*I*b*d), Eq(a, -I*b)), (-I*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + B*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) - I*B/(2*b*d*tan(c + d*x) + 2*I*b*d) + C*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x) + 2*I*b*d) + I*C*d*x/(2*b*d*tan(c + d*x) + 2*I*b*d) - C/(2*b*d*tan(c + d*x) + 2*I*b*d), Eq(a, I*b)), (x*(B*tan(c) + C*tan(c)**2)*cot(c)/(a + b*tan(c)), Eq(d, 0)), ((B*x + C*log(tan(c + d*x)**2 + 1)/(2*d))/a, Eq(b, 0)), (2*B*a*d*x/(2*a**2*d + 2*b**2*d) + 2*B*b*log(a/b + tan(c + d*x))/(2*a**2*d + 2*b**2*d) - B*b*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d) - 2*C*a*log(a/b + tan(c + d*x))/(2*a**2*d + 2*b**2*d) + C*a*log(tan(c + d*x)**2 + 1)/(2*a**2*d + 2*b**2*d) + 2*C*b*d*x/(2*a**2*d + 2*b**2*d), True))","A",0
29,1,966,0,5.745524," ","integrate(cot(d*x+c)**2*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{2}{\left(c \right)}}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- B x - \frac{B}{d \tan{\left(c + d x \right)}} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C \log{\left(\tan{\left(c + d x \right)} \right)}}{d}}{b} & \text{for}\: a = 0 \\\frac{i B d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{B d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i B}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{C d x \tan{\left(c + d x \right)}}{2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i C d x}{2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{C}{2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = - i b \\- \frac{i B d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{B d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i B}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{C d x \tan{\left(c + d x \right)}}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{i C d x}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} - \frac{C}{- 2 i b d \tan{\left(c + d x \right)} + 2 b d} & \text{for}\: a = i b \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{2}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{- \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + C x}{a} & \text{for}\: b = 0 \\- \frac{B a^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{2 B a^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} - \frac{2 B a b d x}{2 a^{3} d + 2 a b^{2} d} - \frac{2 B b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{2 B b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} + \frac{2 C a^{2} d x}{2 a^{3} d + 2 a b^{2} d} + \frac{2 C a b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{3} d + 2 a b^{2} d} - \frac{C a b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d + 2 a b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2)*cot(c)**2/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-B*x - B/(d*tan(c + d*x)) - C*log(tan(c + d*x)**2 + 1)/(2*d) + C*log(tan(c + d*x))/d)/b, Eq(a, 0)), (I*B*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + B*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) + B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) - I*B*log(tan(c + d*x)**2 + 1)/(2*I*b*d*tan(c + d*x) + 2*b*d) - 2*B*log(tan(c + d*x))*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + 2*I*B*log(tan(c + d*x))/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*B/(2*I*b*d*tan(c + d*x) + 2*b*d) - C*d*x*tan(c + d*x)/(2*I*b*d*tan(c + d*x) + 2*b*d) + I*C*d*x/(2*I*b*d*tan(c + d*x) + 2*b*d) - C/(2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, -I*b)), (-I*B*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + B*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) + B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) + I*B*log(tan(c + d*x)**2 + 1)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*B*log(tan(c + d*x))*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - 2*I*B*log(tan(c + d*x))/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*B/(-2*I*b*d*tan(c + d*x) + 2*b*d) - C*d*x*tan(c + d*x)/(-2*I*b*d*tan(c + d*x) + 2*b*d) - I*C*d*x/(-2*I*b*d*tan(c + d*x) + 2*b*d) - C/(-2*I*b*d*tan(c + d*x) + 2*b*d), Eq(a, I*b)), (x*(B*tan(c) + C*tan(c)**2)*cot(c)**2/(a + b*tan(c)), Eq(d, 0)), ((-B*log(tan(c + d*x)**2 + 1)/(2*d) + B*log(tan(c + d*x))/d + C*x)/a, Eq(b, 0)), (-B*a**2*log(tan(c + d*x)**2 + 1)/(2*a**3*d + 2*a*b**2*d) + 2*B*a**2*log(tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) - 2*B*a*b*d*x/(2*a**3*d + 2*a*b**2*d) - 2*B*b**2*log(a/b + tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) + 2*B*b**2*log(tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) + 2*C*a**2*d*x/(2*a**3*d + 2*a*b**2*d) + 2*C*a*b*log(a/b + tan(c + d*x))/(2*a**3*d + 2*a*b**2*d) - C*a*b*log(tan(c + d*x)**2 + 1)/(2*a**3*d + 2*a*b**2*d), True))","A",0
30,1,2064,0,12.100558," ","integrate(cot(d*x+c)**3*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c)),x)","\begin{cases} \text{NaN} & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{- B x - \frac{B}{d \tan{\left(c + d x \right)}} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C \log{\left(\tan{\left(c + d x \right)} \right)}}{d}}{a} & \text{for}\: b = 0 \\\frac{\frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B}{2 d \tan^{2}{\left(c + d x \right)}} - C x - \frac{C}{d \tan{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\- \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{3 B d x \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{3 i B \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{2 B}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{C d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{i C d x \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{2 i C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{2 C \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} + \frac{C \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} - 2 i b d \tan{\left(c + d x \right)}} & \text{for}\: a = - i b \\\frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{3 B d x \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{2 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{2 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{3 i B \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{2 B}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{C d x \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{i C d x \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} - \frac{2 i C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{2 C \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} + \frac{C \tan{\left(c + d x \right)}}{2 b d \tan^{2}{\left(c + d x \right)} + 2 i b d \tan{\left(c + d x \right)}} & \text{for}\: a = i b \\\text{NaN} & \text{for}\: c = - d x \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{3}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{2 B a^{3} d x \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B a^{3}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B a b^{2}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{2 B b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 B b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{C a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{2 C a^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 C a^{2} b d x \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} - \frac{2 C a b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} + \frac{2 C a b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{4} d \tan{\left(c + d x \right)} + 2 a^{2} b^{2} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((-B*x - B/(d*tan(c + d*x)) - C*log(tan(c + d*x)**2 + 1)/(2*d) + C*log(tan(c + d*x))/d)/a, Eq(b, 0)), ((B*log(tan(c + d*x)**2 + 1)/(2*d) - B*log(tan(c + d*x))/d - B/(2*d*tan(c + d*x)**2) - C*x - C/(d*tan(c + d*x)))/b, Eq(a, 0)), (-3*I*B*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 3*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + 2*B*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 2*I*B*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 3*I*B*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - 2*B/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + C*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - I*C*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) - C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + 2*I*C*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + 2*C*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)) + C*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 - 2*I*b*d*tan(c + d*x)), Eq(a, -I*b)), (3*I*B*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 3*B*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 2*B*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 2*I*B*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 3*I*B*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 2*B/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + C*d*x*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + I*C*d*x*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) - 2*I*C*log(tan(c + d*x))*tan(c + d*x)**2/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + 2*C*log(tan(c + d*x))*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)) + C*tan(c + d*x)/(2*b*d*tan(c + d*x)**2 + 2*I*b*d*tan(c + d*x)), Eq(a, I*b)), (nan, Eq(c, -d*x)), (x*(B*tan(c) + C*tan(c)**2)*cot(c)**3/(a + b*tan(c)), Eq(d, 0)), (-2*B*a**3*d*x*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*a**3/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + B*a**2*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*a**2*b*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*a*b**2/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 2*B*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*B*b**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - C*a**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 2*C*a**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*C*a**2*b*d*x*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) - 2*C*a*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)) + 2*C*a*b**2*log(tan(c + d*x))*tan(c + d*x)/(2*a**4*d*tan(c + d*x) + 2*a**2*b**2*d*tan(c + d*x)), True))","A",0
31,1,2621,0,33.891354," ","integrate(cot(d*x+c)**4*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c)),x)","\begin{cases} \text{NaN} & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{B x + \frac{B}{d \tan{\left(c + d x \right)}} - \frac{B}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{C \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{C}{2 d \tan^{2}{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\\frac{3 B d x \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{4 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 B \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{i B \tan{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{B}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 i C d x \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 C d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 i C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 i C \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 C \tan{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} + 2 i b d \tan^{2}{\left(c + d x \right)}} & \text{for}\: a = - i b \\\frac{3 B d x \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{4 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 B \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{i B \tan{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{B}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 i C d x \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{3 C d x \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{2 i C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} - \frac{3 i C \tan^{2}{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} + \frac{2 C \tan{\left(c + d x \right)}}{- 2 b d \tan^{3}{\left(c + d x \right)} - 2 i b d \tan^{2}{\left(c + d x \right)}} & \text{for}\: a = i b \\\text{NaN} & \text{for}\: c = - d x \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{4}{\left(c \right)}}{a + b \tan{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B}{2 d \tan^{2}{\left(c + d x \right)}} - C x - \frac{C}{d \tan{\left(c + d x \right)}}}{a} & \text{for}\: b = 0 \\\frac{B a^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{4}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{3} b d x \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{3} b \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{B a^{2} b^{2}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a b^{3} \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 C a^{4} d x \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 C a^{4} \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{C a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 C a^{3} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 C a^{2} b^{2} \tan{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} + \frac{2 C a b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} - \frac{2 C a b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{5} d \tan^{2}{\left(c + d x \right)} + 2 a^{3} b^{2} d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((B*x + B/(d*tan(c + d*x)) - B/(3*d*tan(c + d*x)**3) + C*log(tan(c + d*x)**2 + 1)/(2*d) - C*log(tan(c + d*x))/d - C/(2*d*tan(c + d*x)**2))/b, Eq(a, 0)), (3*B*d*x*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 3*I*B*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 4*I*B*log(tan(c + d*x))*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 4*B*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 3*B*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - I*B*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + B/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 3*I*C*d*x*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 3*C*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) - 2*C*log(tan(c + d*x))*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 2*I*C*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 3*I*C*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2) + 2*C*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 + 2*I*b*d*tan(c + d*x)**2), Eq(a, -I*b)), (3*B*d*x*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 3*I*B*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 4*I*B*log(tan(c + d*x))*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 4*B*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 3*B*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + I*B*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + B/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 3*I*C*d*x*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 3*C*d*x*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 2*C*log(tan(c + d*x))*tan(c + d*x)**3/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 2*I*C*log(tan(c + d*x))*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) - 3*I*C*tan(c + d*x)**2/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2) + 2*C*tan(c + d*x)/(-2*b*d*tan(c + d*x)**3 - 2*I*b*d*tan(c + d*x)**2), Eq(a, I*b)), (nan, Eq(c, -d*x)), (x*(B*tan(c) + C*tan(c)**2)*cot(c)**4/(a + b*tan(c)), Eq(d, 0)), ((B*log(tan(c + d*x)**2 + 1)/(2*d) - B*log(tan(c + d*x))/d - B/(2*d*tan(c + d*x)**2) - C*x - C/(d*tan(c + d*x)))/a, Eq(b, 0)), (B*a**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*a**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - B*a**4/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*a**3*b*d*x*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*a**3*b*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - B*a**2*b**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*a*b**3*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*B*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*B*b**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*C*a**4*d*x*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*C*a**4*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + C*a**3*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*C*a**3*b*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*C*a**2*b**2*tan(c + d*x)/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) + 2*C*a*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2) - 2*C*a*b**3*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**5*d*tan(c + d*x)**2 + 2*a**3*b**2*d*tan(c + d*x)**2), True))","A",0
32,1,4602,0,2.978310," ","integrate(tan(d*x+c)**2*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**2,x)","\begin{cases} \tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \tan^{2}{\left(c + d x \right)}}{2 d} + C x + \frac{C \tan^{3}{\left(c + d x \right)}}{3 d} - \frac{C \tan{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\- \frac{3 B d x \tan^{2}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{6 i B d x \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{3 B d x}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{4 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{5 B \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{4 i B}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{9 i C d x \tan^{2}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{18 C d x \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{9 i C d x}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} - \frac{4 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{8 i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{4 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{4 i C \tan^{3}{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{19 i C \tan{\left(c + d x \right)}}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} + \frac{14 C}{4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} - 4 i b^{2} d} & \text{for}\: a = - i b \\- \frac{3 B d x \tan^{2}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{6 i B d x \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{3 B d x}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{4 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{2 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{5 B \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{4 i B}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{9 i C d x \tan^{2}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{18 C d x \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{9 i C d x}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{4 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{8 i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{4 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{4 i C \tan^{3}{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} - \frac{19 i C \tan{\left(c + d x \right)}}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} + \frac{14 C}{- 4 i b^{2} d \tan^{2}{\left(c + d x \right)} + 8 b^{2} d \tan{\left(c + d x \right)} + 4 i b^{2} d} & \text{for}\: a = i b \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \tan^{2}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{2 B a^{5} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 B a^{5} b}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 B a^{4} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{6 B a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{B a^{3} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 B a^{3} b^{3}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 B a^{2} b^{4} d x}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{6 B a^{2} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{B a^{2} b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 B a b^{5} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{B a b^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{B b^{6} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 C a^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 C a^{6}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{4 C a^{5} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{8 C a^{4} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 C a^{4} b^{2} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{6 C a^{4} b^{2}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 C a^{3} b^{3} d x}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{8 C a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 C a^{2} b^{4} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 C a^{2} b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{4 C a^{2} b^{4} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 C a^{2} b^{4}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 C a b^{5} d x}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 C a b^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} - \frac{2 C b^{6} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} + \frac{2 C b^{6} \tan^{2}{\left(c + d x \right)}}{2 a^{5} b^{3} d + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 4 a^{3} b^{5} d + 4 a^{2} b^{6} d \tan{\left(c + d x \right)} + 2 a b^{7} d + 2 b^{8} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-B*log(tan(c + d*x)**2 + 1)/(2*d) + B*tan(c + d*x)**2/(2*d) + C*x + C*tan(c + d*x)**3/(3*d) - C*tan(c + d*x)/d)/a**2, Eq(b, 0)), (-3*B*d*x*tan(c + d*x)**2/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 6*I*B*d*x*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 3*B*d*x/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 4*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 2*I*B*log(tan(c + d*x)**2 + 1)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 5*B*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 4*I*B/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 9*I*C*d*x*tan(c + d*x)**2/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 18*C*d*x*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 9*I*C*d*x/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) - 4*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 8*I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 4*C*log(tan(c + d*x)**2 + 1)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 4*I*C*tan(c + d*x)**3/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 19*I*C*tan(c + d*x)/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d) + 14*C/(4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) - 4*I*b**2*d), Eq(a, -I*b)), (-3*B*d*x*tan(c + d*x)**2/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 6*I*B*d*x*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 3*B*d*x/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 2*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 4*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 2*I*B*log(tan(c + d*x)**2 + 1)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 5*B*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 4*I*B/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 9*I*C*d*x*tan(c + d*x)**2/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 18*C*d*x*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 9*I*C*d*x/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 4*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 8*I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 4*C*log(tan(c + d*x)**2 + 1)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 4*I*C*tan(c + d*x)**3/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) - 19*I*C*tan(c + d*x)/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d) + 14*C/(-4*I*b**2*d*tan(c + d*x)**2 + 8*b**2*d*tan(c + d*x) + 4*I*b**2*d), Eq(a, I*b)), (x*(B*tan(c) + C*tan(c)**2)*tan(c)**2/(a + b*tan(c))**2, Eq(d, 0)), (2*B*a**5*b*log(a/b + tan(c + d*x))/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*B*a**5*b/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*B*a**4*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 6*B*a**3*b**3*log(a/b + tan(c + d*x))/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - B*a**3*b**3*log(tan(c + d*x)**2 + 1)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*B*a**3*b**3/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*B*a**2*b**4*d*x/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 6*B*a**2*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - B*a**2*b**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*B*a*b**5*d*x*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + B*a*b**5*log(tan(c + d*x)**2 + 1)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + B*b**6*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*C*a**6*log(a/b + tan(c + d*x))/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*C*a**6/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 4*C*a**5*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 8*C*a**4*b**2*log(a/b + tan(c + d*x))/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*C*a**4*b**2*tan(c + d*x)**2/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 6*C*a**4*b**2/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*C*a**3*b**3*d*x/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 8*C*a**3*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*C*a**2*b**4*d*x*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*C*a**2*b**4*log(tan(c + d*x)**2 + 1)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 4*C*a**2*b**4*tan(c + d*x)**2/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*C*a**2*b**4/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*C*a*b**5*d*x/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*C*a*b**5*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) - 2*C*b**6*d*x*tan(c + d*x)/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)) + 2*C*b**6*tan(c + d*x)**2/(2*a**5*b**3*d + 2*a**4*b**4*d*tan(c + d*x) + 4*a**3*b**5*d + 4*a**2*b**6*d*tan(c + d*x) + 2*a*b**7*d + 2*b**8*d*tan(c + d*x)), True))","A",0
33,1,3497,0,2.289341," ","integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right)}{\tan{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- B x + \frac{B \tan{\left(c + d x \right)}}{d} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C \tan^{2}{\left(c + d x \right)}}{2 d}}{a^{2}} & \text{for}\: b = 0 \\- \frac{B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i B d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{B d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i B}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{3 i C d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{6 C d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 i C d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{4 i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{5 i C \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{4 C}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = - i b \\- \frac{B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i B d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{B d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i B}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 i C d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{6 C d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{3 i C d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{4 i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{5 i C \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{4 C}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = i b \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \tan{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{2 B a^{4} b}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{2 B a^{3} b^{2} d x}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{3} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{4 B a^{2} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 B a^{2} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{3}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{4} d x}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{4 B a b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 B b^{5} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 C a^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 C a^{5}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 C a^{4} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{6 C a^{3} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{C a^{3} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{2 C a^{3} b^{2}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{4 C a^{2} b^{3} d x}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{6 C a^{2} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{C a^{2} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} - \frac{4 C a b^{4} d x \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{C a b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} + \frac{C b^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b^{2} d + 2 a^{4} b^{3} d \tan{\left(c + d x \right)} + 4 a^{3} b^{4} d + 4 a^{2} b^{5} d \tan{\left(c + d x \right)} + 2 a b^{6} d + 2 b^{7} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2)/tan(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-B*x + B*tan(c + d*x)/d - C*log(tan(c + d*x)**2 + 1)/(2*d) + C*tan(c + d*x)**2/(2*d))/a**2, Eq(b, 0)), (-B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*I*B*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + B*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 3*B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*I*B/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 3*I*C*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 6*C*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 3*I*C*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 4*I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*C*log(tan(c + d*x)**2 + 1)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 5*I*C*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 4*C/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d), Eq(a, -I*b)), (-B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*I*B*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + B*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 3*B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*I*B/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 3*I*C*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 6*C*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 3*I*C*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 4*I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*C*log(tan(c + d*x)**2 + 1)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 5*I*C*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 4*C/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d), Eq(a, I*b)), (x*(B*tan(c) + C*tan(c)**2)*tan(c)/(a + b*tan(c))**2, Eq(d, 0)), (-2*B*a**4*b/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 2*B*a**3*b**2*d*x/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 2*B*a**2*b**3*d*x*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 4*B*a**2*b**3*log(a/b + tan(c + d*x))/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*B*a**2*b**3*log(tan(c + d*x)**2 + 1)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 2*B*a**2*b**3/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*B*a*b**4*d*x/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 4*B*a*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*B*a*b**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*B*b**5*d*x*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*C*a**5*log(a/b + tan(c + d*x))/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*C*a**5/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*C*a**4*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 6*C*a**3*b**2*log(a/b + tan(c + d*x))/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - C*a**3*b**2*log(tan(c + d*x)**2 + 1)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 2*C*a**3*b**2/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 4*C*a**2*b**3*d*x/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + 6*C*a**2*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - C*a**2*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) - 4*C*a*b**4*d*x*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + C*a*b**4*log(tan(c + d*x)**2 + 1)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)) + C*b**5*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b**2*d + 2*a**4*b**3*d*tan(c + d*x) + 4*a**3*b**4*d + 4*a**2*b**5*d*tan(c + d*x) + 2*a*b**6*d + 2*b**7*d*tan(c + d*x)), True))","A",0
34,1,2995,0,1.839255," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right)}{\tan^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{\frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - C x + \frac{C \tan{\left(c + d x \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\\frac{i B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{i B d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{i B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{C d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 i C d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{C d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{3 C \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 i C}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} & \text{for}\: a = - i b \\- \frac{i B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{i B d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{i B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{C d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 i C d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{C d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{3 C \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 i C}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} & \text{for}\: a = i b \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right)}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{2 B a^{3} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{B a^{3} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 B a^{3} b}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{4 B a^{2} b^{2} d x}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{B a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{4 B a b^{3} d x \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{B a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{3}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 B b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{B b^{4} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 C a^{4}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 C a^{3} b d x}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 C a^{2} b^{2} d x \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{4 C a^{2} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 C a^{2} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{2 C a^{2} b^{2}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 C a b^{3} d x}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} - \frac{4 C a b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 C a b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} + \frac{2 C b^{4} d x \tan{\left(c + d x \right)}}{2 a^{5} b d + 2 a^{4} b^{2} d \tan{\left(c + d x \right)} + 4 a^{3} b^{3} d + 4 a^{2} b^{4} d \tan{\left(c + d x \right)} + 2 a b^{5} d + 2 b^{6} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2)/tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((B*log(tan(c + d*x)**2 + 1)/(2*d) - C*x + C*tan(c + d*x)/d)/a**2, Eq(b, 0)), (I*B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - I*B*d*x/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + I*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + C*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*I*C*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - C*d*x/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 3*C*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*I*C/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d), Eq(a, -I*b)), (-I*B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + I*B*d*x/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - I*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + C*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*I*C*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - C*d*x/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 3*C*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*I*C/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d), Eq(a, I*b)), (x*(B*tan(c) + C*tan(c)**2)/(a + b*tan(c))**2, Eq(d, 0)), (-2*B*a**3*b*log(a/b + tan(c + d*x))/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + B*a**3*b*log(tan(c + d*x)**2 + 1)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*B*a**3*b/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 4*B*a**2*b**2*d*x/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*B*a**2*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + B*a**2*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 4*B*a*b**3*d*x*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*B*a*b**3*log(a/b + tan(c + d*x))/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - B*a*b**3*log(tan(c + d*x)**2 + 1)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*B*a*b**3/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*B*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - B*b**4*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*C*a**4/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*C*a**3*b*d*x/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*C*a**2*b**2*d*x*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 4*C*a**2*b**2*log(a/b + tan(c + d*x))/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*C*a**2*b**2*log(tan(c + d*x)**2 + 1)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 2*C*a**2*b**2/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*C*a*b**3*d*x/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) - 4*C*a*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*C*a*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)) + 2*C*b**4*d*x*tan(c + d*x)/(2*a**5*b*d + 2*a**4*b**2*d*tan(c + d*x) + 4*a**3*b**3*d + 4*a**2*b**4*d*tan(c + d*x) + 2*a*b**5*d + 2*b**6*d*tan(c + d*x)), True))","A",0
35,1,2895,0,4.994780," ","integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot{\left(c \right)}}{\tan^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i B d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{B d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 i B}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{i C d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 C d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{i C d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{i C \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = - i b \\\frac{B d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i B d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{B d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{B \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 i B}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{i C d x \tan^{2}{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 C d x \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} - \frac{i C d x}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} + \frac{i C \tan{\left(c + d x \right)}}{- 4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = i b \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{B x + \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d}}{a^{2}} & \text{for}\: b = 0 \\\frac{2 B a^{3} d x}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a^{2} b d x \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{4 B a^{2} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a^{2} b}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a b^{2} d x}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{4 B a b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B b^{3} d x \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B b^{3}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 C a^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{C a^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 C a^{3}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{4 C a^{2} b d x}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{2 C a^{2} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{C a^{2} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{4 C a b^{2} d x \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 C a b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{C a b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 C a b^{2}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} + \frac{2 C b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} - \frac{C b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{5} d + 2 a^{4} b d \tan{\left(c + d x \right)} + 4 a^{3} b^{2} d + 4 a^{2} b^{3} d \tan{\left(c + d x \right)} + 2 a b^{4} d + 2 b^{5} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2)*cot(c)/tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*I*B*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - B*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*I*B/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - I*C*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*C*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + I*C*d*x/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - I*C*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) + 4*b**2*d), Eq(a, -I*b)), (B*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*I*B*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - B*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + B*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + 2*I*B/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + I*C*d*x*tan(c + d*x)**2/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - 2*C*d*x*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) - I*C*d*x/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d) + I*C*tan(c + d*x)/(-4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) + 4*b**2*d), Eq(a, I*b)), (x*(B*tan(c) + C*tan(c)**2)*cot(c)/(a + b*tan(c))**2, Eq(d, 0)), ((B*x + C*log(tan(c + d*x)**2 + 1)/(2*d))/a**2, Eq(b, 0)), (2*B*a**3*d*x/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*B*a**2*b*d*x*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 4*B*a**2*b*log(a/b + tan(c + d*x))/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*B*a**2*b*log(tan(c + d*x)**2 + 1)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*B*a**2*b/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*B*a*b**2*d*x/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 4*B*a*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*B*a*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*B*b**3*d*x*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*B*b**3/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*C*a**3*log(a/b + tan(c + d*x))/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + C*a**3*log(tan(c + d*x)**2 + 1)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*C*a**3/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 4*C*a**2*b*d*x/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - 2*C*a**2*b*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + C*a**2*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 4*C*a*b**2*d*x*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*C*a*b**2*log(a/b + tan(c + d*x))/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - C*a*b**2*log(tan(c + d*x)**2 + 1)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*C*a*b**2/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) + 2*C*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)) - C*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**5*d + 2*a**4*b*d*tan(c + d*x) + 4*a**3*b**2*d + 4*a**2*b**3*d*tan(c + d*x) + 2*a*b**4*d + 2*b**5*d*tan(c + d*x)), True))","A",0
36,1,4461,0,9.510500," ","integrate(cot(d*x+c)**2*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{2}{\left(c \right)}}{\tan^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- \frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} + C x}{a^{2}} & \text{for}\: b = 0 \\\frac{\frac{B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{B \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{B}{2 d \tan^{2}{\left(c + d x \right)}} - C x - \frac{C}{d \tan{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{6 B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{3 i B d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{3 i B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 B}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{C d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 i C d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{C d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{C \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 i C}{4 b^{2} d \tan^{2}{\left(c + d x \right)} - 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} & \text{for}\: a = - i b \\- \frac{3 i B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{6 B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{3 i B d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 B \log{\left(\tan{\left(c + d x \right)} \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{3 i B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{4 B}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{C d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 i C d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} + \frac{C d x}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{C \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} - \frac{2 i C}{4 b^{2} d \tan^{2}{\left(c + d x \right)} + 8 i b^{2} d \tan{\left(c + d x \right)} - 4 b^{2} d} & \text{for}\: a = i b \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{2}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{B a^{5} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a^{5} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{4 B a^{4} b d x}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{B a^{4} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a^{4} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{4 B a^{3} b^{2} d x \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{6 B a^{3} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{B a^{3} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{4 B a^{3} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a^{3} b^{2}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{6 B a^{2} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{B a^{2} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{4 B a^{2} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B a b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{4} \log{\left(\tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B a b^{4}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 B b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 B b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 C a^{5} d x}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{2 C a^{4} b d x \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{4 C a^{4} b \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 C a^{4} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 C a^{4} b}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 C a^{3} b^{2} d x}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} + \frac{4 C a^{3} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 C a^{3} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 C a^{2} b^{3} d x \tan{\left(c + d x \right)}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} - \frac{2 C a^{2} b^{3}}{2 a^{7} d + 2 a^{6} b d \tan{\left(c + d x \right)} + 4 a^{5} b^{2} d + 4 a^{4} b^{3} d \tan{\left(c + d x \right)} + 2 a^{3} b^{4} d + 2 a^{2} b^{5} d \tan{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(B*tan(c) + C*tan(c)**2)*cot(c)**2/tan(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-B*log(tan(c + d*x)**2 + 1)/(2*d) + B*log(tan(c + d*x))/d + C*x)/a**2, Eq(b, 0)), ((B*log(tan(c + d*x)**2 + 1)/(2*d) - B*log(tan(c + d*x))/d - B/(2*d*tan(c + d*x)**2) - C*x - C/(d*tan(c + d*x)))/b**2, Eq(a, 0)), (3*I*B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 6*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 3*I*B*d*x/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*B*log(tan(c + d*x)**2 + 1)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 4*B*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 8*I*B*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*B*log(tan(c + d*x))/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 3*I*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*B/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - C*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*I*C*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + C*d*x/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - C*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*I*C/(4*b**2*d*tan(c + d*x)**2 - 8*I*b**2*d*tan(c + d*x) - 4*b**2*d), Eq(a, -I*b)), (-3*I*B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 6*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 3*I*B*d*x/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 2*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*B*log(tan(c + d*x)**2 + 1)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 4*B*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 8*I*B*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*B*log(tan(c + d*x))/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 3*I*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + 4*B/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - C*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*I*C*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) + C*d*x/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - C*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d) - 2*I*C/(4*b**2*d*tan(c + d*x)**2 + 8*I*b**2*d*tan(c + d*x) - 4*b**2*d), Eq(a, I*b)), (x*(B*tan(c) + C*tan(c)**2)*cot(c)**2/(a + b*tan(c))**2, Eq(d, 0)), (-B*a**5*log(tan(c + d*x)**2 + 1)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*B*a**5*log(tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 4*B*a**4*b*d*x/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - B*a**4*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*B*a**4*b*log(tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 4*B*a**3*b**2*d*x*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 6*B*a**3*b**2*log(a/b + tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + B*a**3*b**2*log(tan(c + d*x)**2 + 1)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 4*B*a**3*b**2*log(tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*B*a**3*b**2/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 6*B*a**2*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + B*a**2*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 4*B*a**2*b**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*B*a*b**4*log(a/b + tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*B*a*b**4*log(tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*B*a*b**4/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*B*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*B*b**5*log(tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*C*a**5*d*x/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 2*C*a**4*b*d*x*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 4*C*a**4*b*log(a/b + tan(c + d*x))/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*C*a**4*b*log(tan(c + d*x)**2 + 1)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*C*a**4*b/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*C*a**3*b**2*d*x/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) + 4*C*a**3*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*C*a**3*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*C*a**2*b**3*d*x*tan(c + d*x)/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)) - 2*C*a**2*b**3/(2*a**7*d + 2*a**6*b*d*tan(c + d*x) + 4*a**5*b**2*d + 4*a**4*b**3*d*tan(c + d*x) + 2*a**3*b**4*d + 2*a**2*b**5*d*tan(c + d*x)), True))","A",0
37,1,8097,0,15.712239," ","integrate(cot(d*x+c)**3*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**2,x)","\begin{cases} \text{NaN} & \text{for}\: a = 0 \wedge b = 0 \wedge c = 0 \wedge d = 0 \\\frac{B x + \frac{B}{d \tan{\left(c + d x \right)}} - \frac{B}{3 d \tan^{3}{\left(c + d x \right)}} + \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} - \frac{C \log{\left(\tan{\left(c + d x \right)} \right)}}{d} - \frac{C}{2 d \tan^{2}{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{9 B d x \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{18 i B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{9 B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{16 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{9 B \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{14 i B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 B}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{3 i C d x \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{6 C d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{3 i C d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{8 i C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 C \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{3 i C \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 C \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} - 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} & \text{for}\: a = - i b \\\frac{9 B d x \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{18 i B d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{9 B d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 i B \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{16 B \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{8 i B \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{9 B \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{14 i B \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 B}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{3 i C d x \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{6 C d x \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{3 i C d x \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 i C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{2 C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{4 C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{3}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{8 i C \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 C \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} - \frac{3 i C \tan^{2}{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} + \frac{4 C \tan{\left(c + d x \right)}}{4 b^{2} d \tan^{3}{\left(c + d x \right)} + 8 i b^{2} d \tan^{2}{\left(c + d x \right)} - 4 b^{2} d \tan{\left(c + d x \right)}} & \text{for}\: a = i b \\\text{NaN} & \text{for}\: c = - d x \\\frac{x \left(B \tan{\left(c \right)} + C \tan^{2}{\left(c \right)}\right) \cot^{3}{\left(c \right)}}{\left(a + b \tan{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{- B x - \frac{B}{d \tan{\left(c + d x \right)}} - \frac{C \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} + \frac{C \log{\left(\tan{\left(c + d x \right)} \right)}}{d}}{a^{2}} & \text{for}\: b = 0 \\- \frac{2 B a^{6} d x \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{6}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{5} b d x \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{5} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 B a^{5} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{5} b \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{4} b^{2} d x \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{4} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 B a^{4} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 B a^{4} b^{2}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 B a^{3} b^{3} d x \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{8 B a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{8 B a^{3} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{6 B a^{3} b^{3} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{8 B a^{2} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{8 B a^{2} b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 B a^{2} b^{4}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 B a b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 B a b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 B a b^{5} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 B b^{6} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 B b^{6} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{C a^{6} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 C a^{6} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 C a^{5} b d x \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{C a^{5} b \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 C a^{5} b \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{4 C a^{4} b^{2} d x \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{6 C a^{4} b^{2} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{C a^{4} b^{2} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 C a^{4} b^{2} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 C a^{4} b^{2} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{6 C a^{3} b^{3} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{C a^{3} b^{3} \log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{4 C a^{3} b^{3} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 C a^{2} b^{4} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 C a^{2} b^{4} \log{\left(\tan{\left(c + d x \right)} \right)} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 C a^{2} b^{4} \tan{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} - \frac{2 C a b^{5} \log{\left(\frac{a}{b} + \tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} + \frac{2 C a b^{5} \log{\left(\tan{\left(c + d x \right)} \right)} \tan^{2}{\left(c + d x \right)}}{2 a^{8} d \tan{\left(c + d x \right)} + 2 a^{7} b d \tan^{2}{\left(c + d x \right)} + 4 a^{6} b^{2} d \tan{\left(c + d x \right)} + 4 a^{5} b^{3} d \tan^{2}{\left(c + d x \right)} + 2 a^{4} b^{4} d \tan{\left(c + d x \right)} + 2 a^{3} b^{5} d \tan^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((nan, Eq(a, 0) & Eq(b, 0) & Eq(c, 0) & Eq(d, 0)), ((B*x + B/(d*tan(c + d*x)) - B/(3*d*tan(c + d*x)**3) + C*log(tan(c + d*x)**2 + 1)/(2*d) - C*log(tan(c + d*x))/d - C/(2*d*tan(c + d*x)**2))/b**2, Eq(a, 0)), (9*B*d*x*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 18*I*B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 9*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 8*I*B*log(tan(c + d*x))*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 16*B*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*I*B*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 9*B*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 14*I*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*B/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 3*I*C*d*x*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 6*C*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 3*I*C*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 2*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 2*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*C*log(tan(c + d*x))*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 8*I*C*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*C*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 3*I*C*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*C*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 - 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)), Eq(a, -I*b)), (9*B*d*x*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 18*I*B*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 9*B*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*I*B*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*I*B*log(tan(c + d*x))*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 16*B*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 8*I*B*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 9*B*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 14*I*B*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*B/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 3*I*C*d*x*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 6*C*d*x*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 3*I*C*d*x*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 2*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*I*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 2*C*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 4*C*log(tan(c + d*x))*tan(c + d*x)**3/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 8*I*C*log(tan(c + d*x))*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*C*log(tan(c + d*x))*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) - 3*I*C*tan(c + d*x)**2/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)) + 4*C*tan(c + d*x)/(4*b**2*d*tan(c + d*x)**3 + 8*I*b**2*d*tan(c + d*x)**2 - 4*b**2*d*tan(c + d*x)), Eq(a, I*b)), (nan, Eq(c, -d*x)), (x*(B*tan(c) + C*tan(c)**2)*cot(c)**3/(a + b*tan(c))**2, Eq(d, 0)), ((-B*x - B/(d*tan(c + d*x)) - C*log(tan(c + d*x)**2 + 1)/(2*d) + C*log(tan(c + d*x))/d)/a**2, Eq(b, 0)), (-2*B*a**6*d*x*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*B*a**6/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*B*a**5*b*d*x*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**5*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*B*a**5*b*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*B*a**5*b*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**4*b**2*d*x*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**4*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*B*a**4*b**2*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*B*a**4*b**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*B*a**3*b**3*d*x*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 8*B*a**3*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 8*B*a**3*b**3*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 6*B*a**3*b**3*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 8*B*a**2*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 8*B*a**2*b**4*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*B*a**2*b**4/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 4*B*a*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*B*a*b**5*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*B*a*b**5*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 4*B*b**6*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*B*b**6*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - C*a**6*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*C*a**6*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*C*a**5*b*d*x*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - C*a**5*b*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*C*a**5*b*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 4*C*a**4*b**2*d*x*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 6*C*a**4*b**2*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + C*a**4*b**2*log(tan(c + d*x)**2 + 1)*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 4*C*a**4*b**2*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*C*a**4*b**2*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 6*C*a**3*b**3*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + C*a**3*b**3*log(tan(c + d*x)**2 + 1)*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 4*C*a**3*b**3*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*C*a**2*b**4*log(a/b + tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*C*a**2*b**4*log(tan(c + d*x))*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*C*a**2*b**4*tan(c + d*x)/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) - 2*C*a*b**5*log(a/b + tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2) + 2*C*a*b**5*log(tan(c + d*x))*tan(c + d*x)**2/(2*a**8*d*tan(c + d*x) + 2*a**7*b*d*tan(c + d*x)**2 + 4*a**6*b**2*d*tan(c + d*x) + 4*a**5*b**3*d*tan(c + d*x)**2 + 2*a**4*b**4*d*tan(c + d*x) + 2*a**3*b**5*d*tan(c + d*x)**2), True))","A",0
38,-2,0,0,0.000000," ","integrate(tan(d*x+c)**3*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
39,-2,0,0,0.000000," ","integrate(tan(d*x+c)**2*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
40,-2,0,0,0.000000," ","integrate(tan(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
41,-2,0,0,0.000000," ","integrate((B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
42,-2,0,0,0.000000," ","integrate(cot(d*x+c)*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
43,-2,0,0,0.000000," ","integrate(cot(d*x+c)**2*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
44,-2,0,0,0.000000," ","integrate(cot(d*x+c)**3*(B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
45,0,0,0,0.000000," ","integrate(tan(d*x+c)**2*(b*tan(d*x+c))**n*(A+B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\int \left(b \tan{\left(c + d x \right)}\right)^{n} \left(A + B \tan{\left(c + d x \right)} + C \tan^{2}{\left(c + d x \right)}\right) \tan^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((b*tan(c + d*x))**n*(A + B*tan(c + d*x) + C*tan(c + d*x)**2)*tan(c + d*x)**2, x)","F",0
46,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(b*tan(d*x+c))**n*(A+B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\int \left(b \tan{\left(c + d x \right)}\right)^{n} \left(A + B \tan{\left(c + d x \right)} + C \tan^{2}{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((b*tan(c + d*x))**n*(A + B*tan(c + d*x) + C*tan(c + d*x)**2)*tan(c + d*x)**m, x)","F",0
47,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(b*tan(d*x+c))**(1/2)*(A+B*tan(d*x+c)+C*tan(d*x+c)**2),x)","\int \sqrt{b \tan{\left(c + d x \right)}} \left(A + B \tan{\left(c + d x \right)} + C \tan^{2}{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(b*tan(c + d*x))*(A + B*tan(c + d*x) + C*tan(c + d*x)**2)*tan(c + d*x)**m, x)","F",0
48,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c)+C*tan(d*x+c)**2)/(b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)} + C \tan^{2}{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\sqrt{b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x) + C*tan(c + d*x)**2)*tan(c + d*x)**m/sqrt(b*tan(c + d*x)), x)","F",0
49,0,0,0,0.000000," ","integrate(tan(d*x+c)**m*(A+B*tan(d*x+c)+C*tan(d*x+c)**2)/(a+b*tan(d*x+c))**(1/2),x)","\int \frac{\left(A + B \tan{\left(c + d x \right)} + C \tan^{2}{\left(c + d x \right)}\right) \tan^{m}{\left(c + d x \right)}}{\sqrt{a + b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + B*tan(c + d*x) + C*tan(c + d*x)**2)*tan(c + d*x)**m/sqrt(a + b*tan(c + d*x)), x)","F",0
50,1,1001,0,1.648158," ","integrate((a+b*tan(f*x+e))**3*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A a^{3} c x + \frac{A a^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 A a^{2} b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 A a^{2} b d x + \frac{3 A a^{2} b d \tan{\left(e + f x \right)}}{f} - 3 A a b^{2} c x + \frac{3 A a b^{2} c \tan{\left(e + f x \right)}}{f} - \frac{3 A a b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 A a b^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{A b^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A b^{3} c \tan^{2}{\left(e + f x \right)}}{2 f} + A b^{3} d x + \frac{A b^{3} d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{A b^{3} d \tan{\left(e + f x \right)}}{f} + \frac{B a^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - B a^{3} d x + \frac{B a^{3} d \tan{\left(e + f x \right)}}{f} - 3 B a^{2} b c x + \frac{3 B a^{2} b c \tan{\left(e + f x \right)}}{f} - \frac{3 B a^{2} b d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B a^{2} b d \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{3 B a b^{2} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B a b^{2} c \tan^{2}{\left(e + f x \right)}}{2 f} + 3 B a b^{2} d x + \frac{B a b^{2} d \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 B a b^{2} d \tan{\left(e + f x \right)}}{f} + B b^{3} c x + \frac{B b^{3} c \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B b^{3} c \tan{\left(e + f x \right)}}{f} + \frac{B b^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B b^{3} d \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{B b^{3} d \tan^{2}{\left(e + f x \right)}}{2 f} - C a^{3} c x + \frac{C a^{3} c \tan{\left(e + f x \right)}}{f} - \frac{C a^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C a^{3} d \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{3 C a^{2} b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C a^{2} b c \tan^{2}{\left(e + f x \right)}}{2 f} + 3 C a^{2} b d x + \frac{C a^{2} b d \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C a^{2} b d \tan{\left(e + f x \right)}}{f} + 3 C a b^{2} c x + \frac{C a b^{2} c \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C a b^{2} c \tan{\left(e + f x \right)}}{f} + \frac{3 C a b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C a b^{2} d \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{3 C a b^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{C b^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b^{3} c \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C b^{3} c \tan^{2}{\left(e + f x \right)}}{2 f} - C b^{3} d x + \frac{C b^{3} d \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{C b^{3} d \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{C b^{3} d \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{3} \left(c + d \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*c*x + A*a**3*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*A*a**2*b*c*log(tan(e + f*x)**2 + 1)/(2*f) - 3*A*a**2*b*d*x + 3*A*a**2*b*d*tan(e + f*x)/f - 3*A*a*b**2*c*x + 3*A*a*b**2*c*tan(e + f*x)/f - 3*A*a*b**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*A*a*b**2*d*tan(e + f*x)**2/(2*f) - A*b**3*c*log(tan(e + f*x)**2 + 1)/(2*f) + A*b**3*c*tan(e + f*x)**2/(2*f) + A*b**3*d*x + A*b**3*d*tan(e + f*x)**3/(3*f) - A*b**3*d*tan(e + f*x)/f + B*a**3*c*log(tan(e + f*x)**2 + 1)/(2*f) - B*a**3*d*x + B*a**3*d*tan(e + f*x)/f - 3*B*a**2*b*c*x + 3*B*a**2*b*c*tan(e + f*x)/f - 3*B*a**2*b*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*a**2*b*d*tan(e + f*x)**2/(2*f) - 3*B*a*b**2*c*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*a*b**2*c*tan(e + f*x)**2/(2*f) + 3*B*a*b**2*d*x + B*a*b**2*d*tan(e + f*x)**3/f - 3*B*a*b**2*d*tan(e + f*x)/f + B*b**3*c*x + B*b**3*c*tan(e + f*x)**3/(3*f) - B*b**3*c*tan(e + f*x)/f + B*b**3*d*log(tan(e + f*x)**2 + 1)/(2*f) + B*b**3*d*tan(e + f*x)**4/(4*f) - B*b**3*d*tan(e + f*x)**2/(2*f) - C*a**3*c*x + C*a**3*c*tan(e + f*x)/f - C*a**3*d*log(tan(e + f*x)**2 + 1)/(2*f) + C*a**3*d*tan(e + f*x)**2/(2*f) - 3*C*a**2*b*c*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*a**2*b*c*tan(e + f*x)**2/(2*f) + 3*C*a**2*b*d*x + C*a**2*b*d*tan(e + f*x)**3/f - 3*C*a**2*b*d*tan(e + f*x)/f + 3*C*a*b**2*c*x + C*a*b**2*c*tan(e + f*x)**3/f - 3*C*a*b**2*c*tan(e + f*x)/f + 3*C*a*b**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*a*b**2*d*tan(e + f*x)**4/(4*f) - 3*C*a*b**2*d*tan(e + f*x)**2/(2*f) + C*b**3*c*log(tan(e + f*x)**2 + 1)/(2*f) + C*b**3*c*tan(e + f*x)**4/(4*f) - C*b**3*c*tan(e + f*x)**2/(2*f) - C*b**3*d*x + C*b**3*d*tan(e + f*x)**5/(5*f) - C*b**3*d*tan(e + f*x)**3/(3*f) + C*b**3*d*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))**3*(c + d*tan(e))*(A + B*tan(e) + C*tan(e)**2), True))","A",0
51,1,617,0,0.980860," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A a^{2} c x + \frac{A a^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A a b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - 2 A a b d x + \frac{2 A a b d \tan{\left(e + f x \right)}}{f} - A b^{2} c x + \frac{A b^{2} c \tan{\left(e + f x \right)}}{f} - \frac{A b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A b^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{B a^{2} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - B a^{2} d x + \frac{B a^{2} d \tan{\left(e + f x \right)}}{f} - 2 B a b c x + \frac{2 B a b c \tan{\left(e + f x \right)}}{f} - \frac{B a b d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{B a b d \tan^{2}{\left(e + f x \right)}}{f} - \frac{B b^{2} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B b^{2} c \tan^{2}{\left(e + f x \right)}}{2 f} + B b^{2} d x + \frac{B b^{2} d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B b^{2} d \tan{\left(e + f x \right)}}{f} - C a^{2} c x + \frac{C a^{2} c \tan{\left(e + f x \right)}}{f} - \frac{C a^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C a^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{C a b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C a b c \tan^{2}{\left(e + f x \right)}}{f} + 2 C a b d x + \frac{2 C a b d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 C a b d \tan{\left(e + f x \right)}}{f} + C b^{2} c x + \frac{C b^{2} c \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C b^{2} c \tan{\left(e + f x \right)}}{f} + \frac{C b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b^{2} d \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C b^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{2} \left(c + d \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*c*x + A*a**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + A*a*b*c*log(tan(e + f*x)**2 + 1)/f - 2*A*a*b*d*x + 2*A*a*b*d*tan(e + f*x)/f - A*b**2*c*x + A*b**2*c*tan(e + f*x)/f - A*b**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + A*b**2*d*tan(e + f*x)**2/(2*f) + B*a**2*c*log(tan(e + f*x)**2 + 1)/(2*f) - B*a**2*d*x + B*a**2*d*tan(e + f*x)/f - 2*B*a*b*c*x + 2*B*a*b*c*tan(e + f*x)/f - B*a*b*d*log(tan(e + f*x)**2 + 1)/f + B*a*b*d*tan(e + f*x)**2/f - B*b**2*c*log(tan(e + f*x)**2 + 1)/(2*f) + B*b**2*c*tan(e + f*x)**2/(2*f) + B*b**2*d*x + B*b**2*d*tan(e + f*x)**3/(3*f) - B*b**2*d*tan(e + f*x)/f - C*a**2*c*x + C*a**2*c*tan(e + f*x)/f - C*a**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + C*a**2*d*tan(e + f*x)**2/(2*f) - C*a*b*c*log(tan(e + f*x)**2 + 1)/f + C*a*b*c*tan(e + f*x)**2/f + 2*C*a*b*d*x + 2*C*a*b*d*tan(e + f*x)**3/(3*f) - 2*C*a*b*d*tan(e + f*x)/f + C*b**2*c*x + C*b**2*c*tan(e + f*x)**3/(3*f) - C*b**2*c*tan(e + f*x)/f + C*b**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + C*b**2*d*tan(e + f*x)**4/(4*f) - C*b**2*d*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e))**2*(c + d*tan(e))*(A + B*tan(e) + C*tan(e)**2), True))","A",0
52,1,326,0,0.499517," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A a c x + \frac{A a d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - A b d x + \frac{A b d \tan{\left(e + f x \right)}}{f} + \frac{B a c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - B a d x + \frac{B a d \tan{\left(e + f x \right)}}{f} - B b c x + \frac{B b c \tan{\left(e + f x \right)}}{f} - \frac{B b d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B b d \tan^{2}{\left(e + f x \right)}}{2 f} - C a c x + \frac{C a c \tan{\left(e + f x \right)}}{f} - \frac{C a d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C a d \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{C b c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b c \tan^{2}{\left(e + f x \right)}}{2 f} + C b d x + \frac{C b d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C b d \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right) \left(c + d \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*c*x + A*a*d*log(tan(e + f*x)**2 + 1)/(2*f) + A*b*c*log(tan(e + f*x)**2 + 1)/(2*f) - A*b*d*x + A*b*d*tan(e + f*x)/f + B*a*c*log(tan(e + f*x)**2 + 1)/(2*f) - B*a*d*x + B*a*d*tan(e + f*x)/f - B*b*c*x + B*b*c*tan(e + f*x)/f - B*b*d*log(tan(e + f*x)**2 + 1)/(2*f) + B*b*d*tan(e + f*x)**2/(2*f) - C*a*c*x + C*a*c*tan(e + f*x)/f - C*a*d*log(tan(e + f*x)**2 + 1)/(2*f) + C*a*d*tan(e + f*x)**2/(2*f) - C*b*c*log(tan(e + f*x)**2 + 1)/(2*f) + C*b*c*tan(e + f*x)**2/(2*f) + C*b*d*x + C*b*d*tan(e + f*x)**3/(3*f) - C*b*d*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))*(c + d*tan(e))*(A + B*tan(e) + C*tan(e)**2), True))","A",0
53,1,131,0,0.277624," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A c x + \frac{A d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - B d x + \frac{B d \tan{\left(e + f x \right)}}{f} - C c x + \frac{C c \tan{\left(e + f x \right)}}{f} - \frac{C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C d \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(c + d \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*c*x + A*d*log(tan(e + f*x)**2 + 1)/(2*f) + B*c*log(tan(e + f*x)**2 + 1)/(2*f) - B*d*x + B*d*tan(e + f*x)/f - C*c*x + C*c*tan(e + f*x)/f - C*d*log(tan(e + f*x)**2 + 1)/(2*f) + C*d*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(c + d*tan(e))*(A + B*tan(e) + C*tan(e)**2), True))","A",0
54,1,2429,0,2.370060," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\- \frac{i A c f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{A c f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i A c}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{A d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i A d f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{A d}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{B c f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i B c f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{B c}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i B d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{B d f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{B d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i B d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i B d}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i C c f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{C c f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{C c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i C c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i C c}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 C d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 i C d f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 C d \tan^{2}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 C d}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} & \text{for}\: a = - i b \\\frac{i A c f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{A c f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i A c}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{A d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i A d f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{A d}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{B c f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i B c f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{B c}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i B d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{B d f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{B d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i B d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i B d}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i C c f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{C c f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{C c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i C c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i C c}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 C d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 i C d f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 C d \tan^{2}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{3 C d}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} & \text{for}\: a = i b \\\frac{A c x + \frac{A d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - B d x + \frac{B d \tan{\left(e + f x \right)}}{f} - C c x + \frac{C c \tan{\left(e + f x \right)}}{f} - \frac{C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C d \tan^{2}{\left(e + f x \right)}}{2 f}}{a} & \text{for}\: b = 0 \\\frac{x \left(c + d \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{a + b \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 A a b^{2} c f x}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{2 A a b^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{A a b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 A b^{3} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{A b^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 A b^{3} d f x}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 B a^{2} b d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{2 B a b^{2} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{B a b^{2} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{2 B a b^{2} d f x}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 B b^{3} c f x}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{B b^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{2 C a^{3} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 C a^{2} b c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 C a^{2} b d \tan{\left(e + f x \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{2 C a b^{2} c f x}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{C a b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{C b^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} - \frac{2 C b^{3} d f x}{2 a^{2} b^{2} f + 2 b^{4} f} + \frac{2 C b^{3} d \tan{\left(e + f x \right)}}{2 a^{2} b^{2} f + 2 b^{4} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))*(A + B*tan(e) + C*tan(e)**2)/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (-I*A*c*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - A*c*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*A*c/(-2*b*f*tan(e + f*x) + 2*I*b*f) - A*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*A*d*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) + A*d/(-2*b*f*tan(e + f*x) + 2*I*b*f) - B*c*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*B*c*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) + B*c/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*B*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - B*d*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - B*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*B*d*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*B*d/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*C*c*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - C*c*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - C*c*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*C*c*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*C*c/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 3*C*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 3*I*C*d*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*C*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - C*d*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*C*d*tan(e + f*x)**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 3*C*d/(-2*b*f*tan(e + f*x) + 2*I*b*f), Eq(a, -I*b)), (I*A*c*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - A*c*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*A*c/(-2*b*f*tan(e + f*x) - 2*I*b*f) - A*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*A*d*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + A*d/(-2*b*f*tan(e + f*x) - 2*I*b*f) - B*c*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*B*c*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + B*c/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*B*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - B*d*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) - B*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*B*d*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*B*d/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*C*c*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - C*c*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) - C*c*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*C*c*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*C*c/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 3*C*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 3*I*C*d*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*C*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - C*d*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*C*d*tan(e + f*x)**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 3*C*d/(-2*b*f*tan(e + f*x) - 2*I*b*f), Eq(a, I*b)), ((A*c*x + A*d*log(tan(e + f*x)**2 + 1)/(2*f) + B*c*log(tan(e + f*x)**2 + 1)/(2*f) - B*d*x + B*d*tan(e + f*x)/f - C*c*x + C*c*tan(e + f*x)/f - C*d*log(tan(e + f*x)**2 + 1)/(2*f) + C*d*tan(e + f*x)**2/(2*f))/a, Eq(b, 0)), (x*(c + d*tan(e))*(A + B*tan(e) + C*tan(e)**2)/(a + b*tan(e)), Eq(f, 0)), (2*A*a*b**2*c*f*x/(2*a**2*b**2*f + 2*b**4*f) - 2*A*a*b**2*d*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) + A*a*b**2*d*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) + 2*A*b**3*c*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) - A*b**3*c*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) + 2*A*b**3*d*f*x/(2*a**2*b**2*f + 2*b**4*f) + 2*B*a**2*b*d*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) - 2*B*a*b**2*c*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) + B*a*b**2*c*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) - 2*B*a*b**2*d*f*x/(2*a**2*b**2*f + 2*b**4*f) + 2*B*b**3*c*f*x/(2*a**2*b**2*f + 2*b**4*f) + B*b**3*d*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) - 2*C*a**3*d*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) + 2*C*a**2*b*c*log(a/b + tan(e + f*x))/(2*a**2*b**2*f + 2*b**4*f) + 2*C*a**2*b*d*tan(e + f*x)/(2*a**2*b**2*f + 2*b**4*f) - 2*C*a*b**2*c*f*x/(2*a**2*b**2*f + 2*b**4*f) - C*a*b**2*d*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) + C*b**3*c*log(tan(e + f*x)**2 + 1)/(2*a**2*b**2*f + 2*b**4*f) - 2*C*b**3*d*f*x/(2*a**2*b**2*f + 2*b**4*f) + 2*C*b**3*d*tan(e + f*x)/(2*a**2*b**2*f + 2*b**4*f), True))","A",0
55,1,9721,0,3.951509," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan^{2}{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\\frac{A c f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i A c f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{A c f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{A c \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i A c}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i A d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 A d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i A d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i A d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i B c f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 B c f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i B c f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i B c \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{B d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i B d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{B d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 B d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i B d}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{C c f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i C c f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{C c f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 C c \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i C c}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 i C d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{6 C d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 i C d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{4 i C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{5 i C d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{4 C d}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} + 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = - i b \\\frac{A c f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i A c f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{A c f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{A c \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i A c}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i A d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 A d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i A d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i A d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i B c f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 B c f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{i B c f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{i B c \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{B d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i B d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{B d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 B d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i B d}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{C c f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 i C c f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{C c f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 C c \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 i C c}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{3 i C d f x \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{6 C d f x \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{3 i C d f x}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{2 C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{4 i C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{2 C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} - \frac{5 i C d \tan{\left(e + f x \right)}}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} + \frac{4 C d}{- 4 b^{2} f \tan^{2}{\left(e + f x \right)} - 8 i b^{2} f \tan{\left(e + f x \right)} + 4 b^{2} f} & \text{for}\: a = i b \\\frac{A c x + \frac{A d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - B d x + \frac{B d \tan{\left(e + f x \right)}}{f} - C c x + \frac{C c \tan{\left(e + f x \right)}}{f} - \frac{C d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C d \tan^{2}{\left(e + f x \right)}}{2 f}}{a^{2}} & \text{for}\: b = 0 \\\frac{x \left(c + d \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\left(a + b \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{2 A a^{3} b^{2} c f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a^{3} b^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{A a^{3} b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 A a^{3} b^{2} d}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 A a^{2} b^{3} c f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{4 A a^{2} b^{3} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a^{2} b^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a^{2} b^{3} c}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{4 A a^{2} b^{3} d f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a^{2} b^{3} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{A a^{2} b^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a b^{4} c f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{4 A a b^{4} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a b^{4} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{4 A a b^{4} d f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 A a b^{4} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{A a b^{4} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 A a b^{4} d}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 A b^{5} c f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 A b^{5} c}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 A b^{5} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{A b^{5} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 B a^{4} b d}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 B a^{3} b^{2} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{B a^{3} b^{2} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a^{3} b^{2} c}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 B a^{3} b^{2} d f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{4 B a^{2} b^{3} c f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 B a^{2} b^{3} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{B a^{2} b^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 B a^{2} b^{3} d f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{4 B a^{2} b^{3} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a^{2} b^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 B a^{2} b^{3} d}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{4 B a b^{4} c f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a b^{4} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{B a b^{4} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a b^{4} c}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a b^{4} d f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{4 B a b^{4} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a b^{4} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 B b^{5} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{B b^{5} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 B b^{5} d f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a^{5} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a^{5} d}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 C a^{4} b c}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a^{4} b d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 C a^{3} b^{2} c f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 C a^{3} b^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{C a^{3} b^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a^{3} b^{2} d}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 C a^{2} b^{3} c f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{4 C a^{2} b^{3} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a^{2} b^{3} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{2 C a^{2} b^{3} c}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{4 C a^{2} b^{3} d f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{6 C a^{2} b^{3} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{C a^{2} b^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a b^{4} c f x}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{4 C a b^{4} c \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a b^{4} c \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} - \frac{4 C a b^{4} d f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{C a b^{4} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{2 C b^{5} c f x \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} + \frac{C b^{5} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 a^{5} b^{2} f + 2 a^{4} b^{3} f \tan{\left(e + f x \right)} + 4 a^{3} b^{4} f + 4 a^{2} b^{5} f \tan{\left(e + f x \right)} + 2 a b^{6} f + 2 b^{7} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))*(A + B*tan(e) + C*tan(e)**2)/tan(e)**2, Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (A*c*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*A*c*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - A*c*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + A*c*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*A*c/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*A*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*A*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*A*d*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*A*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*B*c*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*B*c*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*B*c*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*B*c*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - B*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*B*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + B*d*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*B*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*B*d/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - C*c*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*C*c*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + C*c*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*C*c*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*C*c/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*I*C*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 6*C*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*I*C*d*f*x/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*C*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 4*I*C*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*C*d*log(tan(e + f*x)**2 + 1)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 5*I*C*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 4*C*d/(-4*b**2*f*tan(e + f*x)**2 + 8*I*b**2*f*tan(e + f*x) + 4*b**2*f), Eq(a, -I*b)), (A*c*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*A*c*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - A*c*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + A*c*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*A*c/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*A*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*A*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*A*d*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*A*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*B*c*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*B*c*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - I*B*c*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + I*B*c*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - B*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*B*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + B*d*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*B*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*B*d/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - C*c*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*I*C*c*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + C*c*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*C*c*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*I*C*c/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 3*I*C*d*f*x*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 6*C*d*f*x*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 3*I*C*d*f*x/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 2*C*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 4*I*C*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 2*C*d*log(tan(e + f*x)**2 + 1)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) - 5*I*C*d*tan(e + f*x)/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f) + 4*C*d/(-4*b**2*f*tan(e + f*x)**2 - 8*I*b**2*f*tan(e + f*x) + 4*b**2*f), Eq(a, I*b)), ((A*c*x + A*d*log(tan(e + f*x)**2 + 1)/(2*f) + B*c*log(tan(e + f*x)**2 + 1)/(2*f) - B*d*x + B*d*tan(e + f*x)/f - C*c*x + C*c*tan(e + f*x)/f - C*d*log(tan(e + f*x)**2 + 1)/(2*f) + C*d*tan(e + f*x)**2/(2*f))/a**2, Eq(b, 0)), (x*(c + d*tan(e))*(A + B*tan(e) + C*tan(e)**2)/(a + b*tan(e))**2, Eq(f, 0)), (2*A*a**3*b**2*c*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*A*a**3*b**2*d*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + A*a**3*b**2*d*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*A*a**3*b**2*d/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*A*a**2*b**3*c*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 4*A*a**2*b**3*c*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*A*a**2*b**3*c*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*A*a**2*b**3*c/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 4*A*a**2*b**3*d*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*A*a**2*b**3*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + A*a**2*b**3*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*A*a*b**4*c*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 4*A*a*b**4*c*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*A*a*b**4*c*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 4*A*a*b**4*d*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*A*a*b**4*d*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - A*a*b**4*d*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*A*a*b**4*d/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*A*b**5*c*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*A*b**5*c/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*A*b**5*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - A*b**5*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*B*a**4*b*d/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*B*a**3*b**2*c*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + B*a**3*b**2*c*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*B*a**3*b**2*c/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*B*a**3*b**2*d*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 4*B*a**2*b**3*c*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*B*a**2*b**3*c*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + B*a**2*b**3*c*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*B*a**2*b**3*d*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 4*B*a**2*b**3*d*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*B*a**2*b**3*d*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*B*a**2*b**3*d/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 4*B*a*b**4*c*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*B*a*b**4*c*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - B*a*b**4*c*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*B*a*b**4*c/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*B*a*b**4*d*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 4*B*a*b**4*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*B*a*b**4*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*B*b**5*c*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - B*b**5*c*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*B*b**5*d*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*C*a**5*d*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*C*a**5*d/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*C*a**4*b*c/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*C*a**4*b*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*C*a**3*b**2*c*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*C*a**3*b**2*d*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - C*a**3*b**2*d*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*C*a**3*b**2*d/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*C*a**2*b**3*c*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 4*C*a**2*b**3*c*log(a/b + tan(e + f*x))/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*C*a**2*b**3*c*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 2*C*a**2*b**3*c/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 4*C*a**2*b**3*d*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 6*C*a**2*b**3*d*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - C*a**2*b**3*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*C*a*b**4*c*f*x/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 4*C*a*b**4*c*log(a/b + tan(e + f*x))*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*C*a*b**4*c*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) - 4*C*a*b**4*d*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + C*a*b**4*d*log(tan(e + f*x)**2 + 1)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + 2*C*b**5*c*f*x*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)) + C*b**5*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*a**5*b**2*f + 2*a**4*b**3*f*tan(e + f*x) + 4*a**3*b**4*f + 4*a**2*b**5*f*tan(e + f*x) + 2*a*b**6*f + 2*b**7*f*tan(e + f*x)), True))","A",0
56,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
57,1,1819,0,3.184186," ","integrate((a+b*tan(f*x+e))**3*(c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A a^{3} c^{2} x + \frac{A a^{3} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - A a^{3} d^{2} x + \frac{A a^{3} d^{2} \tan{\left(e + f x \right)}}{f} + \frac{3 A a^{2} b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 6 A a^{2} b c d x + \frac{6 A a^{2} b c d \tan{\left(e + f x \right)}}{f} - \frac{3 A a^{2} b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 A a^{2} b d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - 3 A a b^{2} c^{2} x + \frac{3 A a b^{2} c^{2} \tan{\left(e + f x \right)}}{f} - \frac{3 A a b^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{3 A a b^{2} c d \tan^{2}{\left(e + f x \right)}}{f} + 3 A a b^{2} d^{2} x + \frac{A a b^{2} d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 A a b^{2} d^{2} \tan{\left(e + f x \right)}}{f} - \frac{A b^{3} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A b^{3} c^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + 2 A b^{3} c d x + \frac{2 A b^{3} c d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 A b^{3} c d \tan{\left(e + f x \right)}}{f} + \frac{A b^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A b^{3} d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{A b^{3} d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{B a^{3} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 2 B a^{3} c d x + \frac{2 B a^{3} c d \tan{\left(e + f x \right)}}{f} - \frac{B a^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B a^{3} d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - 3 B a^{2} b c^{2} x + \frac{3 B a^{2} b c^{2} \tan{\left(e + f x \right)}}{f} - \frac{3 B a^{2} b c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{3 B a^{2} b c d \tan^{2}{\left(e + f x \right)}}{f} + 3 B a^{2} b d^{2} x + \frac{B a^{2} b d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 B a^{2} b d^{2} \tan{\left(e + f x \right)}}{f} - \frac{3 B a b^{2} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B a b^{2} c^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + 6 B a b^{2} c d x + \frac{2 B a b^{2} c d \tan^{3}{\left(e + f x \right)}}{f} - \frac{6 B a b^{2} c d \tan{\left(e + f x \right)}}{f} + \frac{3 B a b^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B a b^{2} d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{3 B a b^{2} d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + B b^{3} c^{2} x + \frac{B b^{3} c^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B b^{3} c^{2} \tan{\left(e + f x \right)}}{f} + \frac{B b^{3} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{B b^{3} c d \tan^{4}{\left(e + f x \right)}}{2 f} - \frac{B b^{3} c d \tan^{2}{\left(e + f x \right)}}{f} - B b^{3} d^{2} x + \frac{B b^{3} d^{2} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{B b^{3} d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{B b^{3} d^{2} \tan{\left(e + f x \right)}}{f} - C a^{3} c^{2} x + \frac{C a^{3} c^{2} \tan{\left(e + f x \right)}}{f} - \frac{C a^{3} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C a^{3} c d \tan^{2}{\left(e + f x \right)}}{f} + C a^{3} d^{2} x + \frac{C a^{3} d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C a^{3} d^{2} \tan{\left(e + f x \right)}}{f} - \frac{3 C a^{2} b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C a^{2} b c^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + 6 C a^{2} b c d x + \frac{2 C a^{2} b c d \tan^{3}{\left(e + f x \right)}}{f} - \frac{6 C a^{2} b c d \tan{\left(e + f x \right)}}{f} + \frac{3 C a^{2} b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C a^{2} b d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{3 C a^{2} b d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + 3 C a b^{2} c^{2} x + \frac{C a b^{2} c^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C a b^{2} c^{2} \tan{\left(e + f x \right)}}{f} + \frac{3 C a b^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{3 C a b^{2} c d \tan^{4}{\left(e + f x \right)}}{2 f} - \frac{3 C a b^{2} c d \tan^{2}{\left(e + f x \right)}}{f} - 3 C a b^{2} d^{2} x + \frac{3 C a b^{2} d^{2} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{C a b^{2} d^{2} \tan^{3}{\left(e + f x \right)}}{f} + \frac{3 C a b^{2} d^{2} \tan{\left(e + f x \right)}}{f} + \frac{C b^{3} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b^{3} c^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C b^{3} c^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - 2 C b^{3} c d x + \frac{2 C b^{3} c d \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{2 C b^{3} c d \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{2 C b^{3} c d \tan{\left(e + f x \right)}}{f} - \frac{C b^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b^{3} d^{2} \tan^{6}{\left(e + f x \right)}}{6 f} - \frac{C b^{3} d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} + \frac{C b^{3} d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{3} \left(c + d \tan{\left(e \right)}\right)^{2} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*c**2*x + A*a**3*c*d*log(tan(e + f*x)**2 + 1)/f - A*a**3*d**2*x + A*a**3*d**2*tan(e + f*x)/f + 3*A*a**2*b*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 6*A*a**2*b*c*d*x + 6*A*a**2*b*c*d*tan(e + f*x)/f - 3*A*a**2*b*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*A*a**2*b*d**2*tan(e + f*x)**2/(2*f) - 3*A*a*b**2*c**2*x + 3*A*a*b**2*c**2*tan(e + f*x)/f - 3*A*a*b**2*c*d*log(tan(e + f*x)**2 + 1)/f + 3*A*a*b**2*c*d*tan(e + f*x)**2/f + 3*A*a*b**2*d**2*x + A*a*b**2*d**2*tan(e + f*x)**3/f - 3*A*a*b**2*d**2*tan(e + f*x)/f - A*b**3*c**2*log(tan(e + f*x)**2 + 1)/(2*f) + A*b**3*c**2*tan(e + f*x)**2/(2*f) + 2*A*b**3*c*d*x + 2*A*b**3*c*d*tan(e + f*x)**3/(3*f) - 2*A*b**3*c*d*tan(e + f*x)/f + A*b**3*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + A*b**3*d**2*tan(e + f*x)**4/(4*f) - A*b**3*d**2*tan(e + f*x)**2/(2*f) + B*a**3*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 2*B*a**3*c*d*x + 2*B*a**3*c*d*tan(e + f*x)/f - B*a**3*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + B*a**3*d**2*tan(e + f*x)**2/(2*f) - 3*B*a**2*b*c**2*x + 3*B*a**2*b*c**2*tan(e + f*x)/f - 3*B*a**2*b*c*d*log(tan(e + f*x)**2 + 1)/f + 3*B*a**2*b*c*d*tan(e + f*x)**2/f + 3*B*a**2*b*d**2*x + B*a**2*b*d**2*tan(e + f*x)**3/f - 3*B*a**2*b*d**2*tan(e + f*x)/f - 3*B*a*b**2*c**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*a*b**2*c**2*tan(e + f*x)**2/(2*f) + 6*B*a*b**2*c*d*x + 2*B*a*b**2*c*d*tan(e + f*x)**3/f - 6*B*a*b**2*c*d*tan(e + f*x)/f + 3*B*a*b**2*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*a*b**2*d**2*tan(e + f*x)**4/(4*f) - 3*B*a*b**2*d**2*tan(e + f*x)**2/(2*f) + B*b**3*c**2*x + B*b**3*c**2*tan(e + f*x)**3/(3*f) - B*b**3*c**2*tan(e + f*x)/f + B*b**3*c*d*log(tan(e + f*x)**2 + 1)/f + B*b**3*c*d*tan(e + f*x)**4/(2*f) - B*b**3*c*d*tan(e + f*x)**2/f - B*b**3*d**2*x + B*b**3*d**2*tan(e + f*x)**5/(5*f) - B*b**3*d**2*tan(e + f*x)**3/(3*f) + B*b**3*d**2*tan(e + f*x)/f - C*a**3*c**2*x + C*a**3*c**2*tan(e + f*x)/f - C*a**3*c*d*log(tan(e + f*x)**2 + 1)/f + C*a**3*c*d*tan(e + f*x)**2/f + C*a**3*d**2*x + C*a**3*d**2*tan(e + f*x)**3/(3*f) - C*a**3*d**2*tan(e + f*x)/f - 3*C*a**2*b*c**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*a**2*b*c**2*tan(e + f*x)**2/(2*f) + 6*C*a**2*b*c*d*x + 2*C*a**2*b*c*d*tan(e + f*x)**3/f - 6*C*a**2*b*c*d*tan(e + f*x)/f + 3*C*a**2*b*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*a**2*b*d**2*tan(e + f*x)**4/(4*f) - 3*C*a**2*b*d**2*tan(e + f*x)**2/(2*f) + 3*C*a*b**2*c**2*x + C*a*b**2*c**2*tan(e + f*x)**3/f - 3*C*a*b**2*c**2*tan(e + f*x)/f + 3*C*a*b**2*c*d*log(tan(e + f*x)**2 + 1)/f + 3*C*a*b**2*c*d*tan(e + f*x)**4/(2*f) - 3*C*a*b**2*c*d*tan(e + f*x)**2/f - 3*C*a*b**2*d**2*x + 3*C*a*b**2*d**2*tan(e + f*x)**5/(5*f) - C*a*b**2*d**2*tan(e + f*x)**3/f + 3*C*a*b**2*d**2*tan(e + f*x)/f + C*b**3*c**2*log(tan(e + f*x)**2 + 1)/(2*f) + C*b**3*c**2*tan(e + f*x)**4/(4*f) - C*b**3*c**2*tan(e + f*x)**2/(2*f) - 2*C*b**3*c*d*x + 2*C*b**3*c*d*tan(e + f*x)**5/(5*f) - 2*C*b**3*c*d*tan(e + f*x)**3/(3*f) + 2*C*b**3*c*d*tan(e + f*x)/f - C*b**3*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + C*b**3*d**2*tan(e + f*x)**6/(6*f) - C*b**3*d**2*tan(e + f*x)**4/(4*f) + C*b**3*d**2*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e))**3*(c + d*tan(e))**2*(A + B*tan(e) + C*tan(e)**2), True))","A",0
58,1,1134,0,1.912757," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A a^{2} c^{2} x + \frac{A a^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - A a^{2} d^{2} x + \frac{A a^{2} d^{2} \tan{\left(e + f x \right)}}{f} + \frac{A a b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - 4 A a b c d x + \frac{4 A a b c d \tan{\left(e + f x \right)}}{f} - \frac{A a b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{A a b d^{2} \tan^{2}{\left(e + f x \right)}}{f} - A b^{2} c^{2} x + \frac{A b^{2} c^{2} \tan{\left(e + f x \right)}}{f} - \frac{A b^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{A b^{2} c d \tan^{2}{\left(e + f x \right)}}{f} + A b^{2} d^{2} x + \frac{A b^{2} d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{A b^{2} d^{2} \tan{\left(e + f x \right)}}{f} + \frac{B a^{2} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 2 B a^{2} c d x + \frac{2 B a^{2} c d \tan{\left(e + f x \right)}}{f} - \frac{B a^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B a^{2} d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - 2 B a b c^{2} x + \frac{2 B a b c^{2} \tan{\left(e + f x \right)}}{f} - \frac{2 B a b c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{2 B a b c d \tan^{2}{\left(e + f x \right)}}{f} + 2 B a b d^{2} x + \frac{2 B a b d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 B a b d^{2} \tan{\left(e + f x \right)}}{f} - \frac{B b^{2} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B b^{2} c^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + 2 B b^{2} c d x + \frac{2 B b^{2} c d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 B b^{2} c d \tan{\left(e + f x \right)}}{f} + \frac{B b^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B b^{2} d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{B b^{2} d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - C a^{2} c^{2} x + \frac{C a^{2} c^{2} \tan{\left(e + f x \right)}}{f} - \frac{C a^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C a^{2} c d \tan^{2}{\left(e + f x \right)}}{f} + C a^{2} d^{2} x + \frac{C a^{2} d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C a^{2} d^{2} \tan{\left(e + f x \right)}}{f} - \frac{C a b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C a b c^{2} \tan^{2}{\left(e + f x \right)}}{f} + 4 C a b c d x + \frac{4 C a b c d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{4 C a b c d \tan{\left(e + f x \right)}}{f} + \frac{C a b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C a b d^{2} \tan^{4}{\left(e + f x \right)}}{2 f} - \frac{C a b d^{2} \tan^{2}{\left(e + f x \right)}}{f} + C b^{2} c^{2} x + \frac{C b^{2} c^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C b^{2} c^{2} \tan{\left(e + f x \right)}}{f} + \frac{C b^{2} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C b^{2} c d \tan^{4}{\left(e + f x \right)}}{2 f} - \frac{C b^{2} c d \tan^{2}{\left(e + f x \right)}}{f} - C b^{2} d^{2} x + \frac{C b^{2} d^{2} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{C b^{2} d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{C b^{2} d^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{2} \left(c + d \tan{\left(e \right)}\right)^{2} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*c**2*x + A*a**2*c*d*log(tan(e + f*x)**2 + 1)/f - A*a**2*d**2*x + A*a**2*d**2*tan(e + f*x)/f + A*a*b*c**2*log(tan(e + f*x)**2 + 1)/f - 4*A*a*b*c*d*x + 4*A*a*b*c*d*tan(e + f*x)/f - A*a*b*d**2*log(tan(e + f*x)**2 + 1)/f + A*a*b*d**2*tan(e + f*x)**2/f - A*b**2*c**2*x + A*b**2*c**2*tan(e + f*x)/f - A*b**2*c*d*log(tan(e + f*x)**2 + 1)/f + A*b**2*c*d*tan(e + f*x)**2/f + A*b**2*d**2*x + A*b**2*d**2*tan(e + f*x)**3/(3*f) - A*b**2*d**2*tan(e + f*x)/f + B*a**2*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 2*B*a**2*c*d*x + 2*B*a**2*c*d*tan(e + f*x)/f - B*a**2*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + B*a**2*d**2*tan(e + f*x)**2/(2*f) - 2*B*a*b*c**2*x + 2*B*a*b*c**2*tan(e + f*x)/f - 2*B*a*b*c*d*log(tan(e + f*x)**2 + 1)/f + 2*B*a*b*c*d*tan(e + f*x)**2/f + 2*B*a*b*d**2*x + 2*B*a*b*d**2*tan(e + f*x)**3/(3*f) - 2*B*a*b*d**2*tan(e + f*x)/f - B*b**2*c**2*log(tan(e + f*x)**2 + 1)/(2*f) + B*b**2*c**2*tan(e + f*x)**2/(2*f) + 2*B*b**2*c*d*x + 2*B*b**2*c*d*tan(e + f*x)**3/(3*f) - 2*B*b**2*c*d*tan(e + f*x)/f + B*b**2*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + B*b**2*d**2*tan(e + f*x)**4/(4*f) - B*b**2*d**2*tan(e + f*x)**2/(2*f) - C*a**2*c**2*x + C*a**2*c**2*tan(e + f*x)/f - C*a**2*c*d*log(tan(e + f*x)**2 + 1)/f + C*a**2*c*d*tan(e + f*x)**2/f + C*a**2*d**2*x + C*a**2*d**2*tan(e + f*x)**3/(3*f) - C*a**2*d**2*tan(e + f*x)/f - C*a*b*c**2*log(tan(e + f*x)**2 + 1)/f + C*a*b*c**2*tan(e + f*x)**2/f + 4*C*a*b*c*d*x + 4*C*a*b*c*d*tan(e + f*x)**3/(3*f) - 4*C*a*b*c*d*tan(e + f*x)/f + C*a*b*d**2*log(tan(e + f*x)**2 + 1)/f + C*a*b*d**2*tan(e + f*x)**4/(2*f) - C*a*b*d**2*tan(e + f*x)**2/f + C*b**2*c**2*x + C*b**2*c**2*tan(e + f*x)**3/(3*f) - C*b**2*c**2*tan(e + f*x)/f + C*b**2*c*d*log(tan(e + f*x)**2 + 1)/f + C*b**2*c*d*tan(e + f*x)**4/(2*f) - C*b**2*c*d*tan(e + f*x)**2/f - C*b**2*d**2*x + C*b**2*d**2*tan(e + f*x)**5/(5*f) - C*b**2*d**2*tan(e + f*x)**3/(3*f) + C*b**2*d**2*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))**2*(c + d*tan(e))**2*(A + B*tan(e) + C*tan(e)**2), True))","A",0
59,1,617,0,0.974913," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A a c^{2} x + \frac{A a c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - A a d^{2} x + \frac{A a d^{2} \tan{\left(e + f x \right)}}{f} + \frac{A b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 2 A b c d x + \frac{2 A b c d \tan{\left(e + f x \right)}}{f} - \frac{A b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A b d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{B a c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 2 B a c d x + \frac{2 B a c d \tan{\left(e + f x \right)}}{f} - \frac{B a d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B a d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - B b c^{2} x + \frac{B b c^{2} \tan{\left(e + f x \right)}}{f} - \frac{B b c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{B b c d \tan^{2}{\left(e + f x \right)}}{f} + B b d^{2} x + \frac{B b d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B b d^{2} \tan{\left(e + f x \right)}}{f} - C a c^{2} x + \frac{C a c^{2} \tan{\left(e + f x \right)}}{f} - \frac{C a c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C a c d \tan^{2}{\left(e + f x \right)}}{f} + C a d^{2} x + \frac{C a d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C a d^{2} \tan{\left(e + f x \right)}}{f} - \frac{C b c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b c^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + 2 C b c d x + \frac{2 C b c d \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 C b c d \tan{\left(e + f x \right)}}{f} + \frac{C b d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C b d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right) \left(c + d \tan{\left(e \right)}\right)^{2} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*c**2*x + A*a*c*d*log(tan(e + f*x)**2 + 1)/f - A*a*d**2*x + A*a*d**2*tan(e + f*x)/f + A*b*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 2*A*b*c*d*x + 2*A*b*c*d*tan(e + f*x)/f - A*b*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + A*b*d**2*tan(e + f*x)**2/(2*f) + B*a*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 2*B*a*c*d*x + 2*B*a*c*d*tan(e + f*x)/f - B*a*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + B*a*d**2*tan(e + f*x)**2/(2*f) - B*b*c**2*x + B*b*c**2*tan(e + f*x)/f - B*b*c*d*log(tan(e + f*x)**2 + 1)/f + B*b*c*d*tan(e + f*x)**2/f + B*b*d**2*x + B*b*d**2*tan(e + f*x)**3/(3*f) - B*b*d**2*tan(e + f*x)/f - C*a*c**2*x + C*a*c**2*tan(e + f*x)/f - C*a*c*d*log(tan(e + f*x)**2 + 1)/f + C*a*c*d*tan(e + f*x)**2/f + C*a*d**2*x + C*a*d**2*tan(e + f*x)**3/(3*f) - C*a*d**2*tan(e + f*x)/f - C*b*c**2*log(tan(e + f*x)**2 + 1)/(2*f) + C*b*c**2*tan(e + f*x)**2/(2*f) + 2*C*b*c*d*x + 2*C*b*c*d*tan(e + f*x)**3/(3*f) - 2*C*b*c*d*tan(e + f*x)/f + C*b*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + C*b*d**2*tan(e + f*x)**4/(4*f) - C*b*d**2*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e))*(c + d*tan(e))**2*(A + B*tan(e) + C*tan(e)**2), True))","A",0
60,1,241,0,0.467253," ","integrate((c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A c^{2} x + \frac{A c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - A d^{2} x + \frac{A d^{2} \tan{\left(e + f x \right)}}{f} + \frac{B c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 2 B c d x + \frac{2 B c d \tan{\left(e + f x \right)}}{f} - \frac{B d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - C c^{2} x + \frac{C c^{2} \tan{\left(e + f x \right)}}{f} - \frac{C c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C c d \tan^{2}{\left(e + f x \right)}}{f} + C d^{2} x + \frac{C d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C d^{2} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(c + d \tan{\left(e \right)}\right)^{2} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*c**2*x + A*c*d*log(tan(e + f*x)**2 + 1)/f - A*d**2*x + A*d**2*tan(e + f*x)/f + B*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 2*B*c*d*x + 2*B*c*d*tan(e + f*x)/f - B*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + B*d**2*tan(e + f*x)**2/(2*f) - C*c**2*x + C*c**2*tan(e + f*x)/f - C*c*d*log(tan(e + f*x)**2 + 1)/f + C*c*d*tan(e + f*x)**2/f + C*d**2*x + C*d**2*tan(e + f*x)**3/(3*f) - C*d**2*tan(e + f*x)/f, Ne(f, 0)), (x*(c + d*tan(e))**2*(A + B*tan(e) + C*tan(e)**2), True))","A",0
61,1,4517,0,8.059946," ","integrate((c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right)^{2} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\- \frac{i A c^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{A c^{2} f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i A c^{2}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 A c d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{2 i A c d f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{2 A c d}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i A d^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{A d^{2} f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{A d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i A d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i A d^{2}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{B c^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i B c^{2} f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{B c^{2}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 i B c d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 B c d f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 B c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{2 i B c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{2 i B c d}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 B d^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 i B d^{2} f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i B d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{B d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 B d^{2} \tan^{2}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 B d^{2}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i C c^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{C c^{2} f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{C c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i C c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{i C c^{2}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{6 C c d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{6 i C c d f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 i C c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 C c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{4 C c d \tan^{2}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{6 C c d}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 i C d^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{3 C d^{2} f x}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} + \frac{2 C d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{2 i C d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{C d^{2} \tan^{3}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{i C d^{2} \tan^{2}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} - \frac{3 i C d^{2}}{- 2 b f \tan{\left(e + f x \right)} + 2 i b f} & \text{for}\: a = - i b \\\frac{i A c^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{A c^{2} f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i A c^{2}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 A c d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 i A c d f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{2 A c d}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i A d^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{A d^{2} f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{A d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i A d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i A d^{2}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{B c^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i B c^{2} f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{B c^{2}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{2 i B c d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 B c d f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 B c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 i B c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 i B c d}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 B d^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 i B d^{2} f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i B d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{B d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 B d^{2} \tan^{2}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{3 B d^{2}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i C c^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{C c^{2} f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{C c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i C c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{i C c^{2}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{6 C c d f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{6 i C c d f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{2 i C c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{2 C c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{4 C c d \tan^{2}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{6 C c d}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{3 i C d^{2} f x \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 C d^{2} f x}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{2 C d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{2 i C d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} - \frac{C d^{2} \tan^{3}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{i C d^{2} \tan^{2}{\left(e + f x \right)}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} + \frac{3 i C d^{2}}{- 2 b f \tan{\left(e + f x \right)} - 2 i b f} & \text{for}\: a = i b \\\frac{A c^{2} x + \frac{A c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - A d^{2} x + \frac{A d^{2} \tan{\left(e + f x \right)}}{f} + \frac{B c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 2 B c d x + \frac{2 B c d \tan{\left(e + f x \right)}}{f} - \frac{B d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - C c^{2} x + \frac{C c^{2} \tan{\left(e + f x \right)}}{f} - \frac{C c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C c d \tan^{2}{\left(e + f x \right)}}{f} + C d^{2} x + \frac{C d^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C d^{2} \tan{\left(e + f x \right)}}{f}}{a} & \text{for}\: b = 0 \\\frac{x \left(c + d \tan{\left(e \right)}\right)^{2} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{a + b \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 A a^{2} b^{2} d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 A a b^{3} c^{2} f x}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{4 A a b^{3} c d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 A a b^{3} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{2 A a b^{3} d^{2} f x}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 A b^{4} c^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{A b^{4} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{4 A b^{4} c d f x}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{A b^{4} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{2 B a^{3} b d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{4 B a^{2} b^{2} c d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 B a^{2} b^{2} d^{2} \tan{\left(e + f x \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{2 B a b^{3} c^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{B a b^{3} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{4 B a b^{3} c d f x}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{B a b^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 B b^{4} c^{2} f x}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 B b^{4} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{2 B b^{4} d^{2} f x}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 B b^{4} d^{2} \tan{\left(e + f x \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 C a^{4} d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{4 C a^{3} b c d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{2 C a^{3} b d^{2} \tan{\left(e + f x \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 C a^{2} b^{2} c^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{4 C a^{2} b^{2} c d \tan{\left(e + f x \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{C a^{2} b^{2} d^{2} \tan^{2}{\left(e + f x \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{2 C a b^{3} c^{2} f x}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{2 C a b^{3} c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{2 C a b^{3} d^{2} f x}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{2 C a b^{3} d^{2} \tan{\left(e + f x \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{C b^{4} c^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{4 C b^{4} c d f x}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{4 C b^{4} c d \tan{\left(e + f x \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} - \frac{C b^{4} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} + \frac{C b^{4} d^{2} \tan^{2}{\left(e + f x \right)}}{2 a^{2} b^{3} f + 2 b^{5} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))**2*(A + B*tan(e) + C*tan(e)**2)/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (-I*A*c**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - A*c**2*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*A*c**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*A*c*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 2*I*A*c*d*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 2*A*c*d/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*A*d**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - A*d**2*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - A*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*A*d**2*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*A*d**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) - B*c**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*B*c**2*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) + B*c**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*I*B*c*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*B*c*d*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*B*c*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 2*I*B*c*d*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 2*I*B*c*d/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 3*B*d**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 3*I*B*d**2*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*B*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - B*d**2*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*B*d**2*tan(e + f*x)**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 3*B*d**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*C*c**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - C*c**2*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - C*c**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*C*c**2*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + I*C*c**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 6*C*c*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 6*I*C*c*d*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*I*C*c*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*C*c*d*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 4*C*c*d*tan(e + f*x)**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 6*C*c*d/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 3*I*C*d**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 3*C*d**2*f*x/(-2*b*f*tan(e + f*x) + 2*I*b*f) + 2*C*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 2*I*C*d**2*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) + 2*I*b*f) - C*d**2*tan(e + f*x)**3/(-2*b*f*tan(e + f*x) + 2*I*b*f) - I*C*d**2*tan(e + f*x)**2/(-2*b*f*tan(e + f*x) + 2*I*b*f) - 3*I*C*d**2/(-2*b*f*tan(e + f*x) + 2*I*b*f), Eq(a, -I*b)), (I*A*c**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - A*c**2*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*A*c**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*A*c*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*I*A*c*d*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 2*A*c*d/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*A*d**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - A*d**2*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) - A*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*A*d**2*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*A*d**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) - B*c**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*B*c**2*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + B*c**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 2*I*B*c*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*B*c*d*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*B*c*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*I*B*c*d*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*I*B*c*d/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 3*B*d**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 3*I*B*d**2*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*B*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - B*d**2*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*B*d**2*tan(e + f*x)**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 3*B*d**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*C*c**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - C*c**2*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) - C*c**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*C*c**2*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - I*C*c**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 6*C*c*d*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 6*I*C*c*d*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 2*I*C*c*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 2*C*c*d*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 4*C*c*d*tan(e + f*x)**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 6*C*c*d/(-2*b*f*tan(e + f*x) - 2*I*b*f) - 3*I*C*d**2*f*x*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 3*C*d**2*f*x/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 2*C*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 2*I*C*d**2*log(tan(e + f*x)**2 + 1)/(-2*b*f*tan(e + f*x) - 2*I*b*f) - C*d**2*tan(e + f*x)**3/(-2*b*f*tan(e + f*x) - 2*I*b*f) + I*C*d**2*tan(e + f*x)**2/(-2*b*f*tan(e + f*x) - 2*I*b*f) + 3*I*C*d**2/(-2*b*f*tan(e + f*x) - 2*I*b*f), Eq(a, I*b)), ((A*c**2*x + A*c*d*log(tan(e + f*x)**2 + 1)/f - A*d**2*x + A*d**2*tan(e + f*x)/f + B*c**2*log(tan(e + f*x)**2 + 1)/(2*f) - 2*B*c*d*x + 2*B*c*d*tan(e + f*x)/f - B*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + B*d**2*tan(e + f*x)**2/(2*f) - C*c**2*x + C*c**2*tan(e + f*x)/f - C*c*d*log(tan(e + f*x)**2 + 1)/f + C*c*d*tan(e + f*x)**2/f + C*d**2*x + C*d**2*tan(e + f*x)**3/(3*f) - C*d**2*tan(e + f*x)/f)/a, Eq(b, 0)), (x*(c + d*tan(e))**2*(A + B*tan(e) + C*tan(e)**2)/(a + b*tan(e)), Eq(f, 0)), (2*A*a**2*b**2*d**2*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) + 2*A*a*b**3*c**2*f*x/(2*a**2*b**3*f + 2*b**5*f) - 4*A*a*b**3*c*d*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) + 2*A*a*b**3*c*d*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) - 2*A*a*b**3*d**2*f*x/(2*a**2*b**3*f + 2*b**5*f) + 2*A*b**4*c**2*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) - A*b**4*c**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) + 4*A*b**4*c*d*f*x/(2*a**2*b**3*f + 2*b**5*f) + A*b**4*d**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) - 2*B*a**3*b*d**2*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) + 4*B*a**2*b**2*c*d*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) + 2*B*a**2*b**2*d**2*tan(e + f*x)/(2*a**2*b**3*f + 2*b**5*f) - 2*B*a*b**3*c**2*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) + B*a*b**3*c**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) - 4*B*a*b**3*c*d*f*x/(2*a**2*b**3*f + 2*b**5*f) - B*a*b**3*d**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) + 2*B*b**4*c**2*f*x/(2*a**2*b**3*f + 2*b**5*f) + 2*B*b**4*c*d*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) - 2*B*b**4*d**2*f*x/(2*a**2*b**3*f + 2*b**5*f) + 2*B*b**4*d**2*tan(e + f*x)/(2*a**2*b**3*f + 2*b**5*f) + 2*C*a**4*d**2*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) - 4*C*a**3*b*c*d*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) - 2*C*a**3*b*d**2*tan(e + f*x)/(2*a**2*b**3*f + 2*b**5*f) + 2*C*a**2*b**2*c**2*log(a/b + tan(e + f*x))/(2*a**2*b**3*f + 2*b**5*f) + 4*C*a**2*b**2*c*d*tan(e + f*x)/(2*a**2*b**3*f + 2*b**5*f) + C*a**2*b**2*d**2*tan(e + f*x)**2/(2*a**2*b**3*f + 2*b**5*f) - 2*C*a*b**3*c**2*f*x/(2*a**2*b**3*f + 2*b**5*f) - 2*C*a*b**3*c*d*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) + 2*C*a*b**3*d**2*f*x/(2*a**2*b**3*f + 2*b**5*f) - 2*C*a*b**3*d**2*tan(e + f*x)/(2*a**2*b**3*f + 2*b**5*f) + C*b**4*c**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) - 4*C*b**4*c*d*f*x/(2*a**2*b**3*f + 2*b**5*f) + 4*C*b**4*c*d*tan(e + f*x)/(2*a**2*b**3*f + 2*b**5*f) - C*b**4*d**2*log(tan(e + f*x)**2 + 1)/(2*a**2*b**3*f + 2*b**5*f) + C*b**4*d**2*tan(e + f*x)**2/(2*a**2*b**3*f + 2*b**5*f), True))","A",0
62,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
64,1,1819,0,3.220817," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A a^{2} c^{3} x + \frac{3 A a^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 A a^{2} c d^{2} x + \frac{3 A a^{2} c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{A a^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A a^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{A a b c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - 6 A a b c^{2} d x + \frac{6 A a b c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{3 A a b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{3 A a b c d^{2} \tan^{2}{\left(e + f x \right)}}{f} + 2 A a b d^{3} x + \frac{2 A a b d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{2 A a b d^{3} \tan{\left(e + f x \right)}}{f} - A b^{2} c^{3} x + \frac{A b^{2} c^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 A b^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 A b^{2} c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + 3 A b^{2} c d^{2} x + \frac{A b^{2} c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 A b^{2} c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{A b^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A b^{2} d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{A b^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{B a^{2} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 B a^{2} c^{2} d x + \frac{3 B a^{2} c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{3 B a^{2} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B a^{2} c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + B a^{2} d^{3} x + \frac{B a^{2} d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B a^{2} d^{3} \tan{\left(e + f x \right)}}{f} - 2 B a b c^{3} x + \frac{2 B a b c^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 B a b c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{3 B a b c^{2} d \tan^{2}{\left(e + f x \right)}}{f} + 6 B a b c d^{2} x + \frac{2 B a b c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{6 B a b c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{B a b d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{B a b d^{3} \tan^{4}{\left(e + f x \right)}}{2 f} - \frac{B a b d^{3} \tan^{2}{\left(e + f x \right)}}{f} - \frac{B b^{2} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B b^{2} c^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + 3 B b^{2} c^{2} d x + \frac{B b^{2} c^{2} d \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 B b^{2} c^{2} d \tan{\left(e + f x \right)}}{f} + \frac{3 B b^{2} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B b^{2} c d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{3 B b^{2} c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - B b^{2} d^{3} x + \frac{B b^{2} d^{3} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{B b^{2} d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{B b^{2} d^{3} \tan{\left(e + f x \right)}}{f} - C a^{2} c^{3} x + \frac{C a^{2} c^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 C a^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C a^{2} c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + 3 C a^{2} c d^{2} x + \frac{C a^{2} c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C a^{2} c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{C a^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C a^{2} d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C a^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{C a b c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C a b c^{3} \tan^{2}{\left(e + f x \right)}}{f} + 6 C a b c^{2} d x + \frac{2 C a b c^{2} d \tan^{3}{\left(e + f x \right)}}{f} - \frac{6 C a b c^{2} d \tan{\left(e + f x \right)}}{f} + \frac{3 C a b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{3 C a b c d^{2} \tan^{4}{\left(e + f x \right)}}{2 f} - \frac{3 C a b c d^{2} \tan^{2}{\left(e + f x \right)}}{f} - 2 C a b d^{3} x + \frac{2 C a b d^{3} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{2 C a b d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{2 C a b d^{3} \tan{\left(e + f x \right)}}{f} + C b^{2} c^{3} x + \frac{C b^{2} c^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C b^{2} c^{3} \tan{\left(e + f x \right)}}{f} + \frac{3 C b^{2} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C b^{2} c^{2} d \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{3 C b^{2} c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} - 3 C b^{2} c d^{2} x + \frac{3 C b^{2} c d^{2} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{C b^{2} c d^{2} \tan^{3}{\left(e + f x \right)}}{f} + \frac{3 C b^{2} c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{C b^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b^{2} d^{3} \tan^{6}{\left(e + f x \right)}}{6 f} - \frac{C b^{2} d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} + \frac{C b^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right)^{2} \left(c + d \tan{\left(e \right)}\right)^{3} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*c**3*x + 3*A*a**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*A*a**2*c*d**2*x + 3*A*a**2*c*d**2*tan(e + f*x)/f - A*a**2*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + A*a**2*d**3*tan(e + f*x)**2/(2*f) + A*a*b*c**3*log(tan(e + f*x)**2 + 1)/f - 6*A*a*b*c**2*d*x + 6*A*a*b*c**2*d*tan(e + f*x)/f - 3*A*a*b*c*d**2*log(tan(e + f*x)**2 + 1)/f + 3*A*a*b*c*d**2*tan(e + f*x)**2/f + 2*A*a*b*d**3*x + 2*A*a*b*d**3*tan(e + f*x)**3/(3*f) - 2*A*a*b*d**3*tan(e + f*x)/f - A*b**2*c**3*x + A*b**2*c**3*tan(e + f*x)/f - 3*A*b**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*A*b**2*c**2*d*tan(e + f*x)**2/(2*f) + 3*A*b**2*c*d**2*x + A*b**2*c*d**2*tan(e + f*x)**3/f - 3*A*b**2*c*d**2*tan(e + f*x)/f + A*b**2*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + A*b**2*d**3*tan(e + f*x)**4/(4*f) - A*b**2*d**3*tan(e + f*x)**2/(2*f) + B*a**2*c**3*log(tan(e + f*x)**2 + 1)/(2*f) - 3*B*a**2*c**2*d*x + 3*B*a**2*c**2*d*tan(e + f*x)/f - 3*B*a**2*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*a**2*c*d**2*tan(e + f*x)**2/(2*f) + B*a**2*d**3*x + B*a**2*d**3*tan(e + f*x)**3/(3*f) - B*a**2*d**3*tan(e + f*x)/f - 2*B*a*b*c**3*x + 2*B*a*b*c**3*tan(e + f*x)/f - 3*B*a*b*c**2*d*log(tan(e + f*x)**2 + 1)/f + 3*B*a*b*c**2*d*tan(e + f*x)**2/f + 6*B*a*b*c*d**2*x + 2*B*a*b*c*d**2*tan(e + f*x)**3/f - 6*B*a*b*c*d**2*tan(e + f*x)/f + B*a*b*d**3*log(tan(e + f*x)**2 + 1)/f + B*a*b*d**3*tan(e + f*x)**4/(2*f) - B*a*b*d**3*tan(e + f*x)**2/f - B*b**2*c**3*log(tan(e + f*x)**2 + 1)/(2*f) + B*b**2*c**3*tan(e + f*x)**2/(2*f) + 3*B*b**2*c**2*d*x + B*b**2*c**2*d*tan(e + f*x)**3/f - 3*B*b**2*c**2*d*tan(e + f*x)/f + 3*B*b**2*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*b**2*c*d**2*tan(e + f*x)**4/(4*f) - 3*B*b**2*c*d**2*tan(e + f*x)**2/(2*f) - B*b**2*d**3*x + B*b**2*d**3*tan(e + f*x)**5/(5*f) - B*b**2*d**3*tan(e + f*x)**3/(3*f) + B*b**2*d**3*tan(e + f*x)/f - C*a**2*c**3*x + C*a**2*c**3*tan(e + f*x)/f - 3*C*a**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*a**2*c**2*d*tan(e + f*x)**2/(2*f) + 3*C*a**2*c*d**2*x + C*a**2*c*d**2*tan(e + f*x)**3/f - 3*C*a**2*c*d**2*tan(e + f*x)/f + C*a**2*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + C*a**2*d**3*tan(e + f*x)**4/(4*f) - C*a**2*d**3*tan(e + f*x)**2/(2*f) - C*a*b*c**3*log(tan(e + f*x)**2 + 1)/f + C*a*b*c**3*tan(e + f*x)**2/f + 6*C*a*b*c**2*d*x + 2*C*a*b*c**2*d*tan(e + f*x)**3/f - 6*C*a*b*c**2*d*tan(e + f*x)/f + 3*C*a*b*c*d**2*log(tan(e + f*x)**2 + 1)/f + 3*C*a*b*c*d**2*tan(e + f*x)**4/(2*f) - 3*C*a*b*c*d**2*tan(e + f*x)**2/f - 2*C*a*b*d**3*x + 2*C*a*b*d**3*tan(e + f*x)**5/(5*f) - 2*C*a*b*d**3*tan(e + f*x)**3/(3*f) + 2*C*a*b*d**3*tan(e + f*x)/f + C*b**2*c**3*x + C*b**2*c**3*tan(e + f*x)**3/(3*f) - C*b**2*c**3*tan(e + f*x)/f + 3*C*b**2*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*b**2*c**2*d*tan(e + f*x)**4/(4*f) - 3*C*b**2*c**2*d*tan(e + f*x)**2/(2*f) - 3*C*b**2*c*d**2*x + 3*C*b**2*c*d**2*tan(e + f*x)**5/(5*f) - C*b**2*c*d**2*tan(e + f*x)**3/f + 3*C*b**2*c*d**2*tan(e + f*x)/f - C*b**2*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + C*b**2*d**3*tan(e + f*x)**6/(6*f) - C*b**2*d**3*tan(e + f*x)**4/(4*f) + C*b**2*d**3*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(a + b*tan(e))**2*(c + d*tan(e))**3*(A + B*tan(e) + C*tan(e)**2), True))","A",0
65,1,1001,0,1.653569," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A a c^{3} x + \frac{3 A a c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 A a c d^{2} x + \frac{3 A a c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{A a d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A a d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{A b c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 A b c^{2} d x + \frac{3 A b c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{3 A b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 A b c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + A b d^{3} x + \frac{A b d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{A b d^{3} \tan{\left(e + f x \right)}}{f} + \frac{B a c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 B a c^{2} d x + \frac{3 B a c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{3 B a c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B a c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + B a d^{3} x + \frac{B a d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B a d^{3} \tan{\left(e + f x \right)}}{f} - B b c^{3} x + \frac{B b c^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 B b c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B b c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + 3 B b c d^{2} x + \frac{B b c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 B b c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{B b d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B b d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{B b d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} - C a c^{3} x + \frac{C a c^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 C a c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C a c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + 3 C a c d^{2} x + \frac{C a c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C a c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{C a d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C a d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C a d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} - \frac{C b c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b c^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + 3 C b c^{2} d x + \frac{C b c^{2} d \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C b c^{2} d \tan{\left(e + f x \right)}}{f} + \frac{3 C b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C b c d^{2} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{3 C b c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - C b d^{3} x + \frac{C b d^{3} \tan^{5}{\left(e + f x \right)}}{5 f} - \frac{C b d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} + \frac{C b d^{3} \tan{\left(e + f x \right)}}{f} & \text{for}\: f \neq 0 \\x \left(a + b \tan{\left(e \right)}\right) \left(c + d \tan{\left(e \right)}\right)^{3} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*c**3*x + 3*A*a*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*A*a*c*d**2*x + 3*A*a*c*d**2*tan(e + f*x)/f - A*a*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + A*a*d**3*tan(e + f*x)**2/(2*f) + A*b*c**3*log(tan(e + f*x)**2 + 1)/(2*f) - 3*A*b*c**2*d*x + 3*A*b*c**2*d*tan(e + f*x)/f - 3*A*b*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*A*b*c*d**2*tan(e + f*x)**2/(2*f) + A*b*d**3*x + A*b*d**3*tan(e + f*x)**3/(3*f) - A*b*d**3*tan(e + f*x)/f + B*a*c**3*log(tan(e + f*x)**2 + 1)/(2*f) - 3*B*a*c**2*d*x + 3*B*a*c**2*d*tan(e + f*x)/f - 3*B*a*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*a*c*d**2*tan(e + f*x)**2/(2*f) + B*a*d**3*x + B*a*d**3*tan(e + f*x)**3/(3*f) - B*a*d**3*tan(e + f*x)/f - B*b*c**3*x + B*b*c**3*tan(e + f*x)/f - 3*B*b*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*b*c**2*d*tan(e + f*x)**2/(2*f) + 3*B*b*c*d**2*x + B*b*c*d**2*tan(e + f*x)**3/f - 3*B*b*c*d**2*tan(e + f*x)/f + B*b*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + B*b*d**3*tan(e + f*x)**4/(4*f) - B*b*d**3*tan(e + f*x)**2/(2*f) - C*a*c**3*x + C*a*c**3*tan(e + f*x)/f - 3*C*a*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*a*c**2*d*tan(e + f*x)**2/(2*f) + 3*C*a*c*d**2*x + C*a*c*d**2*tan(e + f*x)**3/f - 3*C*a*c*d**2*tan(e + f*x)/f + C*a*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + C*a*d**3*tan(e + f*x)**4/(4*f) - C*a*d**3*tan(e + f*x)**2/(2*f) - C*b*c**3*log(tan(e + f*x)**2 + 1)/(2*f) + C*b*c**3*tan(e + f*x)**2/(2*f) + 3*C*b*c**2*d*x + C*b*c**2*d*tan(e + f*x)**3/f - 3*C*b*c**2*d*tan(e + f*x)/f + 3*C*b*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*b*c*d**2*tan(e + f*x)**4/(4*f) - 3*C*b*c*d**2*tan(e + f*x)**2/(2*f) - C*b*d**3*x + C*b*d**3*tan(e + f*x)**5/(5*f) - C*b*d**3*tan(e + f*x)**3/(3*f) + C*b*d**3*tan(e + f*x)/f, Ne(f, 0)), (x*(a + b*tan(e))*(c + d*tan(e))**3*(A + B*tan(e) + C*tan(e)**2), True))","A",0
66,1,410,0,0.762363," ","integrate((c+d*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\begin{cases} A c^{3} x + \frac{3 A c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 A c d^{2} x + \frac{3 A c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{A d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{B c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 B c^{2} d x + \frac{3 B c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{3 B c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + B d^{3} x + \frac{B d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B d^{3} \tan{\left(e + f x \right)}}{f} - C c^{3} x + \frac{C c^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 C c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + 3 C c d^{2} x + \frac{C c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{C d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} & \text{for}\: f \neq 0 \\x \left(c + d \tan{\left(e \right)}\right)^{3} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right) & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*c**3*x + 3*A*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*A*c*d**2*x + 3*A*c*d**2*tan(e + f*x)/f - A*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + A*d**3*tan(e + f*x)**2/(2*f) + B*c**3*log(tan(e + f*x)**2 + 1)/(2*f) - 3*B*c**2*d*x + 3*B*c**2*d*tan(e + f*x)/f - 3*B*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*c*d**2*tan(e + f*x)**2/(2*f) + B*d**3*x + B*d**3*tan(e + f*x)**3/(3*f) - B*d**3*tan(e + f*x)/f - C*c**3*x + C*c**3*tan(e + f*x)/f - 3*C*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*c**2*d*tan(e + f*x)**2/(2*f) + 3*C*c*d**2*x + C*c*d**2*tan(e + f*x)**3/f - 3*C*c*d**2*tan(e + f*x)/f + C*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + C*d**3*tan(e + f*x)**4/(4*f) - C*d**3*tan(e + f*x)**2/(2*f), Ne(f, 0)), (x*(c + d*tan(e))**3*(A + B*tan(e) + C*tan(e)**2), True))","A",0
67,1,7205,0,113.329949," ","integrate((c+d*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(c + d \tan{\left(e \right)}\right)^{3} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge f = 0 \\- \frac{3 i A c^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 A c^{3} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 i A c^{3}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 A c^{2} d f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 i A c^{2} d f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 A c^{2} d}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 i A c d^{2} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 A c d^{2} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 A c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 i A c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 i A c d^{2}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 A d^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 i A d^{3} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 i A d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 A d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{6 A d^{3} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 A d^{3}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 B c^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{3 i B c^{3} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{3 B c^{3}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 i B c^{2} d f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 B c^{2} d f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 B c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 i B c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 i B c^{2} d}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{27 B c d^{2} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{27 i B c d^{2} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 i B c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 B c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{18 B c d^{2} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{27 B c d^{2}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 i B d^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 B d^{3} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{6 B d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{6 i B d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 B d^{3} \tan^{3}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 i B d^{3} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 i B d^{3}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 i C c^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 C c^{3} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{3 C c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{3 i C c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{3 i C c^{3}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{27 C c^{2} d f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{27 i C c^{2} d f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 i C c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 C c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{18 C c^{2} d \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{27 C c^{2} d}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{27 i C c d^{2} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{27 C c d^{2} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{18 C c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{18 i C c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 C c d^{2} \tan^{3}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{9 i C c d^{2} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{27 i C c d^{2}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{15 C d^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{15 i C d^{3} f x}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{6 i C d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{6 C d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{2 C d^{3} \tan^{4}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} - \frac{i C d^{3} \tan^{3}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{9 C d^{3} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} + \frac{15 C d^{3}}{- 6 b f \tan{\left(e + f x \right)} + 6 i b f} & \text{for}\: a = - i b \\\frac{3 i A c^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 A c^{3} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{3 i A c^{3}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 A c^{2} d f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 i A c^{2} d f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 A c^{2} d}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 i A c d^{2} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 A c d^{2} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 A c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 i A c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 i A c d^{2}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 A d^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 i A d^{3} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{3 i A d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 A d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{6 A d^{3} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 A d^{3}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 B c^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 i B c^{3} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{3 B c^{3}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 i B c^{2} d f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 B c^{2} d f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 B c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 i B c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 i B c^{2} d}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{27 B c d^{2} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{27 i B c d^{2} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 i B c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 B c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{18 B c d^{2} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{27 B c d^{2}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 i B d^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 B d^{3} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{6 B d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{6 i B d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 B d^{3} \tan^{3}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{3 i B d^{3} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 i B d^{3}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{3 i C c^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 C c^{3} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 C c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 i C c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{3 i C c^{3}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{27 C c^{2} d f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{27 i C c^{2} d f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 i C c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 C c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{18 C c^{2} d \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{27 C c^{2} d}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{27 i C c d^{2} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{27 C c d^{2} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{18 C c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{18 i C c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{9 C c d^{2} \tan^{3}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 i C c d^{2} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{27 i C c d^{2}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{15 C d^{3} f x \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{15 i C d^{3} f x}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{6 i C d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{6 C d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} - \frac{2 C d^{3} \tan^{4}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{i C d^{3} \tan^{3}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{9 C d^{3} \tan^{2}{\left(e + f x \right)}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} + \frac{15 C d^{3}}{- 6 b f \tan{\left(e + f x \right)} - 6 i b f} & \text{for}\: a = i b \\\frac{A c^{3} x + \frac{3 A c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 A c d^{2} x + \frac{3 A c d^{2} \tan{\left(e + f x \right)}}{f} - \frac{A d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A d^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{B c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 B c^{2} d x + \frac{3 B c^{2} d \tan{\left(e + f x \right)}}{f} - \frac{3 B c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B c d^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + B d^{3} x + \frac{B d^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B d^{3} \tan{\left(e + f x \right)}}{f} - C c^{3} x + \frac{C c^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 C c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C c^{2} d \tan^{2}{\left(e + f x \right)}}{2 f} + 3 C c d^{2} x + \frac{C c d^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C c d^{2} \tan{\left(e + f x \right)}}{f} + \frac{C d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C d^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C d^{3} \tan^{2}{\left(e + f x \right)}}{2 f}}{a} & \text{for}\: b = 0 \\\frac{x \left(c + d \tan{\left(e \right)}\right)^{3} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{a + b \tan{\left(e \right)}} & \text{for}\: f = 0 \\- \frac{6 A a^{3} b^{2} d^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 A a^{2} b^{3} c d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 A a^{2} b^{3} d^{3} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 A a b^{4} c^{3} f x}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 A a b^{4} c^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{9 A a b^{4} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 A a b^{4} c d^{2} f x}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{3 A a b^{4} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 A b^{5} c^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{3 A b^{5} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 A b^{5} c^{2} d f x}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{9 A b^{5} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{6 A b^{5} d^{3} f x}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 A b^{5} d^{3} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 B a^{4} b d^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 B a^{3} b^{2} c d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{6 B a^{3} b^{2} d^{3} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 B a^{2} b^{3} c^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 B a^{2} b^{3} c d^{2} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{3 B a^{2} b^{3} d^{3} \tan^{2}{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{6 B a b^{4} c^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{3 B a b^{4} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 B a b^{4} c^{2} d f x}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{9 B a b^{4} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 B a b^{4} d^{3} f x}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{6 B a b^{4} d^{3} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 B b^{5} c^{3} f x}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{9 B b^{5} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 B b^{5} c d^{2} f x}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 B b^{5} c d^{2} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{3 B b^{5} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{3 B b^{5} d^{3} \tan^{2}{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{6 C a^{5} d^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 C a^{4} b c d^{2} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 C a^{4} b d^{3} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 C a^{3} b^{2} c^{2} d \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 C a^{3} b^{2} c d^{2} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{3 C a^{3} b^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 C a^{2} b^{3} c^{3} \log{\left(\frac{a}{b} + \tan{\left(e + f x \right)} \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 C a^{2} b^{3} c^{2} d \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{9 C a^{2} b^{3} c d^{2} \tan^{2}{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{2 C a^{2} b^{3} d^{3} \tan^{3}{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{6 C a b^{4} c^{3} f x}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{9 C a b^{4} c^{2} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 C a b^{4} c d^{2} f x}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 C a b^{4} c d^{2} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{3 C a b^{4} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{3 C a b^{4} d^{3} \tan^{2}{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{3 C b^{5} c^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{18 C b^{5} c^{2} d f x}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{18 C b^{5} c^{2} d \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{9 C b^{5} c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{9 C b^{5} c d^{2} \tan^{2}{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{6 C b^{5} d^{3} f x}{6 a^{2} b^{4} f + 6 b^{6} f} + \frac{2 C b^{5} d^{3} \tan^{3}{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} - \frac{6 C b^{5} d^{3} \tan{\left(e + f x \right)}}{6 a^{2} b^{4} f + 6 b^{6} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(c + d*tan(e))**3*(A + B*tan(e) + C*tan(e)**2)/tan(e), Eq(a, 0) & Eq(b, 0) & Eq(f, 0)), (-3*I*A*c**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*A*c**3*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*I*A*c**3/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*A*c**2*d*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*I*A*c**2*d*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*A*c**2*d/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*I*A*c*d**2*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*A*c*d**2*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*A*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*I*A*c*d**2*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*I*A*c*d**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*A*d**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*I*A*d**3*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*I*A*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*A*d**3*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 6*A*d**3*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*A*d**3/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*B*c**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 3*I*B*c**3*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 3*B*c**3/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*I*B*c**2*d*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*B*c**2*d*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*B*c**2*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*I*B*c**2*d*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*I*B*c**2*d/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 27*B*c*d**2*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 27*I*B*c*d**2*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*I*B*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*B*c*d**2*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 18*B*c*d**2*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 27*B*c*d**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*I*B*d**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*B*d**3*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 6*B*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 6*I*B*d**3*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*B*d**3*tan(e + f*x)**3/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*I*B*d**3*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*I*B*d**3/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*I*C*c**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*C*c**3*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 3*C*c**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 3*I*C*c**3*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 3*I*C*c**3/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 27*C*c**2*d*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 27*I*C*c**2*d*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*I*C*c**2*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*C*c**2*d*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 18*C*c**2*d*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 27*C*c**2*d/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 27*I*C*c*d**2*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 27*C*c*d**2*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 18*C*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 18*I*C*c*d**2*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*C*c*d**2*tan(e + f*x)**3/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 9*I*C*c*d**2*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 27*I*C*c*d**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 15*C*d**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 15*I*C*d**3*f*x/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 6*I*C*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 6*C*d**3*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) + 6*I*b*f) - 2*C*d**3*tan(e + f*x)**4/(-6*b*f*tan(e + f*x) + 6*I*b*f) - I*C*d**3*tan(e + f*x)**3/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 9*C*d**3*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) + 6*I*b*f) + 15*C*d**3/(-6*b*f*tan(e + f*x) + 6*I*b*f), Eq(a, -I*b)), (3*I*A*c**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*A*c**3*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 3*I*A*c**3/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*A*c**2*d*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*I*A*c**2*d*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*A*c**2*d/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*I*A*c*d**2*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*A*c*d**2*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*A*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*I*A*c*d**2*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*I*A*c*d**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*A*d**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*I*A*d**3*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 3*I*A*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*A*d**3*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 6*A*d**3*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*A*d**3/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*B*c**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*I*B*c**3*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 3*B*c**3/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*I*B*c**2*d*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*B*c**2*d*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*B*c**2*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*I*B*c**2*d*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*I*B*c**2*d/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 27*B*c*d**2*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 27*I*B*c*d**2*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*I*B*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*B*c*d**2*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 18*B*c*d**2*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 27*B*c*d**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*I*B*d**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*B*d**3*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 6*B*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 6*I*B*d**3*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*B*d**3*tan(e + f*x)**3/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 3*I*B*d**3*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*I*B*d**3/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 3*I*C*c**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*C*c**3*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*C*c**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*I*C*c**3*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 3*I*C*c**3/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 27*C*c**2*d*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 27*I*C*c**2*d*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*I*C*c**2*d*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*C*c**2*d*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 18*C*c**2*d*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 27*C*c**2*d/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 27*I*C*c*d**2*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 27*C*c*d**2*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 18*C*c*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 18*I*C*c*d**2*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 9*C*c*d**2*tan(e + f*x)**3/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*I*C*c*d**2*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 27*I*C*c*d**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 15*C*d**3*f*x*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 15*I*C*d**3*f*x/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 6*I*C*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 6*C*d**3*log(tan(e + f*x)**2 + 1)/(-6*b*f*tan(e + f*x) - 6*I*b*f) - 2*C*d**3*tan(e + f*x)**4/(-6*b*f*tan(e + f*x) - 6*I*b*f) + I*C*d**3*tan(e + f*x)**3/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 9*C*d**3*tan(e + f*x)**2/(-6*b*f*tan(e + f*x) - 6*I*b*f) + 15*C*d**3/(-6*b*f*tan(e + f*x) - 6*I*b*f), Eq(a, I*b)), ((A*c**3*x + 3*A*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) - 3*A*c*d**2*x + 3*A*c*d**2*tan(e + f*x)/f - A*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + A*d**3*tan(e + f*x)**2/(2*f) + B*c**3*log(tan(e + f*x)**2 + 1)/(2*f) - 3*B*c**2*d*x + 3*B*c**2*d*tan(e + f*x)/f - 3*B*c*d**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*c*d**2*tan(e + f*x)**2/(2*f) + B*d**3*x + B*d**3*tan(e + f*x)**3/(3*f) - B*d**3*tan(e + f*x)/f - C*c**3*x + C*c**3*tan(e + f*x)/f - 3*C*c**2*d*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*c**2*d*tan(e + f*x)**2/(2*f) + 3*C*c*d**2*x + C*c*d**2*tan(e + f*x)**3/f - 3*C*c*d**2*tan(e + f*x)/f + C*d**3*log(tan(e + f*x)**2 + 1)/(2*f) + C*d**3*tan(e + f*x)**4/(4*f) - C*d**3*tan(e + f*x)**2/(2*f))/a, Eq(b, 0)), (x*(c + d*tan(e))**3*(A + B*tan(e) + C*tan(e)**2)/(a + b*tan(e)), Eq(f, 0)), (-6*A*a**3*b**2*d**3*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) + 18*A*a**2*b**3*c*d**2*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) + 6*A*a**2*b**3*d**3*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) + 6*A*a*b**4*c**3*f*x/(6*a**2*b**4*f + 6*b**6*f) - 18*A*a*b**4*c**2*d*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) + 9*A*a*b**4*c**2*d*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) - 18*A*a*b**4*c*d**2*f*x/(6*a**2*b**4*f + 6*b**6*f) - 3*A*a*b**4*d**3*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) + 6*A*b**5*c**3*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) - 3*A*b**5*c**3*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) + 18*A*b**5*c**2*d*f*x/(6*a**2*b**4*f + 6*b**6*f) + 9*A*b**5*c*d**2*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) - 6*A*b**5*d**3*f*x/(6*a**2*b**4*f + 6*b**6*f) + 6*A*b**5*d**3*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) + 6*B*a**4*b*d**3*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) - 18*B*a**3*b**2*c*d**2*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) - 6*B*a**3*b**2*d**3*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) + 18*B*a**2*b**3*c**2*d*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) + 18*B*a**2*b**3*c*d**2*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) + 3*B*a**2*b**3*d**3*tan(e + f*x)**2/(6*a**2*b**4*f + 6*b**6*f) - 6*B*a*b**4*c**3*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) + 3*B*a*b**4*c**3*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) - 18*B*a*b**4*c**2*d*f*x/(6*a**2*b**4*f + 6*b**6*f) - 9*B*a*b**4*c*d**2*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) + 6*B*a*b**4*d**3*f*x/(6*a**2*b**4*f + 6*b**6*f) - 6*B*a*b**4*d**3*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) + 6*B*b**5*c**3*f*x/(6*a**2*b**4*f + 6*b**6*f) + 9*B*b**5*c**2*d*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) - 18*B*b**5*c*d**2*f*x/(6*a**2*b**4*f + 6*b**6*f) + 18*B*b**5*c*d**2*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) - 3*B*b**5*d**3*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) + 3*B*b**5*d**3*tan(e + f*x)**2/(6*a**2*b**4*f + 6*b**6*f) - 6*C*a**5*d**3*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) + 18*C*a**4*b*c*d**2*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) + 6*C*a**4*b*d**3*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) - 18*C*a**3*b**2*c**2*d*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) - 18*C*a**3*b**2*c*d**2*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) - 3*C*a**3*b**2*d**3*tan(e + f*x)**2/(6*a**2*b**4*f + 6*b**6*f) + 6*C*a**2*b**3*c**3*log(a/b + tan(e + f*x))/(6*a**2*b**4*f + 6*b**6*f) + 18*C*a**2*b**3*c**2*d*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) + 9*C*a**2*b**3*c*d**2*tan(e + f*x)**2/(6*a**2*b**4*f + 6*b**6*f) + 2*C*a**2*b**3*d**3*tan(e + f*x)**3/(6*a**2*b**4*f + 6*b**6*f) - 6*C*a*b**4*c**3*f*x/(6*a**2*b**4*f + 6*b**6*f) - 9*C*a*b**4*c**2*d*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) + 18*C*a*b**4*c*d**2*f*x/(6*a**2*b**4*f + 6*b**6*f) - 18*C*a*b**4*c*d**2*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) + 3*C*a*b**4*d**3*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) - 3*C*a*b**4*d**3*tan(e + f*x)**2/(6*a**2*b**4*f + 6*b**6*f) + 3*C*b**5*c**3*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) - 18*C*b**5*c**2*d*f*x/(6*a**2*b**4*f + 6*b**6*f) + 18*C*b**5*c**2*d*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f) - 9*C*b**5*c*d**2*log(tan(e + f*x)**2 + 1)/(6*a**2*b**4*f + 6*b**6*f) + 9*C*b**5*c*d**2*tan(e + f*x)**2/(6*a**2*b**4*f + 6*b**6*f) + 6*C*b**5*d**3*f*x/(6*a**2*b**4*f + 6*b**6*f) + 2*C*b**5*d**3*tan(e + f*x)**3/(6*a**2*b**4*f + 6*b**6*f) - 6*C*b**5*d**3*tan(e + f*x)/(6*a**2*b**4*f + 6*b**6*f), True))","A",0
68,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-2,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
70,1,7205,0,115.151761," ","integrate((a+b*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)^{3} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\- \frac{3 i A a^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 A a^{3} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 i A a^{3}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 A a^{2} b f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 i A a^{2} b f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 A a^{2} b}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 i A a b^{2} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 A a b^{2} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 A a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 i A a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 i A a b^{2}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 A b^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 i A b^{3} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 i A b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 A b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{6 A b^{3} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 A b^{3}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 B a^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{3 i B a^{3} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{3 B a^{3}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 i B a^{2} b f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 B a^{2} b f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 B a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 i B a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 i B a^{2} b}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{27 B a b^{2} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{27 i B a b^{2} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 i B a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 B a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{18 B a b^{2} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{27 B a b^{2}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 i B b^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 B b^{3} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{6 B b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{6 i B b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 B b^{3} \tan^{3}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 i B b^{3} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 i B b^{3}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 i C a^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 C a^{3} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{3 C a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{3 i C a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{3 i C a^{3}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{27 C a^{2} b f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{27 i C a^{2} b f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 i C a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 C a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{18 C a^{2} b \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{27 C a^{2} b}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{27 i C a b^{2} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{27 C a b^{2} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{18 C a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{18 i C a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 C a b^{2} \tan^{3}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{9 i C a b^{2} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{27 i C a b^{2}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{15 C b^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{15 i C b^{3} f x}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{6 i C b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{6 C b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{2 C b^{3} \tan^{4}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} - \frac{i C b^{3} \tan^{3}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{9 C b^{3} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} + \frac{15 C b^{3}}{- 6 d f \tan{\left(e + f x \right)} + 6 i d f} & \text{for}\: c = - i d \\\frac{3 i A a^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 A a^{3} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{3 i A a^{3}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 A a^{2} b f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 i A a^{2} b f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 A a^{2} b}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 i A a b^{2} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 A a b^{2} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 A a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 i A a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 i A a b^{2}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 A b^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 i A b^{3} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{3 i A b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 A b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{6 A b^{3} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 A b^{3}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 B a^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 i B a^{3} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{3 B a^{3}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 i B a^{2} b f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 B a^{2} b f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 B a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 i B a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 i B a^{2} b}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{27 B a b^{2} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{27 i B a b^{2} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 i B a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 B a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{18 B a b^{2} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{27 B a b^{2}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 i B b^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 B b^{3} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{6 B b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{6 i B b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 B b^{3} \tan^{3}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{3 i B b^{3} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 i B b^{3}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{3 i C a^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 C a^{3} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 C a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 i C a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{3 i C a^{3}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{27 C a^{2} b f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{27 i C a^{2} b f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 i C a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 C a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{18 C a^{2} b \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{27 C a^{2} b}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{27 i C a b^{2} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{27 C a b^{2} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{18 C a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{18 i C a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{9 C a b^{2} \tan^{3}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 i C a b^{2} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{27 i C a b^{2}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{15 C b^{3} f x \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{15 i C b^{3} f x}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{6 i C b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{6 C b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} - \frac{2 C b^{3} \tan^{4}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{i C b^{3} \tan^{3}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{9 C b^{3} \tan^{2}{\left(e + f x \right)}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} + \frac{15 C b^{3}}{- 6 d f \tan{\left(e + f x \right)} - 6 i d f} & \text{for}\: c = i d \\\frac{A a^{3} x + \frac{3 A a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 A a b^{2} x + \frac{3 A a b^{2} \tan{\left(e + f x \right)}}{f} - \frac{A b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{A b^{3} \tan^{2}{\left(e + f x \right)}}{2 f} + \frac{B a^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 3 B a^{2} b x + \frac{3 B a^{2} b \tan{\left(e + f x \right)}}{f} - \frac{3 B a b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 B a b^{2} \tan^{2}{\left(e + f x \right)}}{2 f} + B b^{3} x + \frac{B b^{3} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{B b^{3} \tan{\left(e + f x \right)}}{f} - C a^{3} x + \frac{C a^{3} \tan{\left(e + f x \right)}}{f} - \frac{3 C a^{2} b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{3 C a^{2} b \tan^{2}{\left(e + f x \right)}}{2 f} + 3 C a b^{2} x + \frac{C a b^{2} \tan^{3}{\left(e + f x \right)}}{f} - \frac{3 C a b^{2} \tan{\left(e + f x \right)}}{f} + \frac{C b^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b^{3} \tan^{4}{\left(e + f x \right)}}{4 f} - \frac{C b^{3} \tan^{2}{\left(e + f x \right)}}{2 f}}{c} & \text{for}\: d = 0 \\\frac{x \left(a + b \tan{\left(e \right)}\right)^{3} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{c + d \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{6 A a^{3} c d^{4} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 A a^{3} d^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{3 A a^{3} d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 A a^{2} b c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{9 A a^{2} b c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 A a^{2} b d^{5} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 A a b^{2} c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 A a b^{2} c d^{4} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{9 A a b^{2} d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{6 A b^{3} c^{3} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 A b^{3} c^{2} d^{3} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{3 A b^{3} c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{6 A b^{3} d^{5} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 A b^{3} d^{5} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{6 B a^{3} c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{3 B a^{3} c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 B a^{3} d^{5} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 B a^{2} b c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 B a^{2} b c d^{4} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{9 B a^{2} b d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 B a b^{2} c^{3} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 B a b^{2} c^{2} d^{3} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{9 B a b^{2} c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 B a b^{2} d^{5} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 B a b^{2} d^{5} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 B b^{3} c^{4} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{6 B b^{3} c^{3} d^{2} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{3 B b^{3} c^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 B b^{3} c d^{4} f x}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{6 B b^{3} c d^{4} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{3 B b^{3} d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{3 B b^{3} d^{5} \tan^{2}{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 C a^{3} c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{6 C a^{3} c d^{4} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{3 C a^{3} d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 C a^{2} b c^{3} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 C a^{2} b c^{2} d^{3} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{9 C a^{2} b c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 C a^{2} b d^{5} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 C a^{2} b d^{5} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 C a b^{2} c^{4} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 C a b^{2} c^{3} d^{2} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{9 C a b^{2} c^{2} d^{3} \tan^{2}{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{18 C a b^{2} c d^{4} f x}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{18 C a b^{2} c d^{4} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{9 C a b^{2} d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{9 C a b^{2} d^{5} \tan^{2}{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{6 C b^{3} c^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 C b^{3} c^{4} d \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{3 C b^{3} c^{3} d^{2} \tan^{2}{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{2 C b^{3} c^{2} d^{3} \tan^{3}{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{3 C b^{3} c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{3 C b^{3} c d^{4} \tan^{2}{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{6 C b^{3} d^{5} f x}{6 c^{2} d^{4} f + 6 d^{6} f} + \frac{2 C b^{3} d^{5} \tan^{3}{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} - \frac{6 C b^{3} d^{5} \tan{\left(e + f x \right)}}{6 c^{2} d^{4} f + 6 d^{6} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))**3*(A + B*tan(e) + C*tan(e)**2)/tan(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (-3*I*A*a**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*A*a**3*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*I*A*a**3/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*A*a**2*b*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*I*A*a**2*b*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*A*a**2*b/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*I*A*a*b**2*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*A*a*b**2*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*A*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*I*A*a*b**2*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*I*A*a*b**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*A*b**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*I*A*b**3*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*I*A*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*A*b**3*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 6*A*b**3*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*A*b**3/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*B*a**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 3*I*B*a**3*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 3*B*a**3/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*I*B*a**2*b*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*B*a**2*b*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*B*a**2*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*I*B*a**2*b*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*I*B*a**2*b/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 27*B*a*b**2*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 27*I*B*a*b**2*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*I*B*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*B*a*b**2*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 18*B*a*b**2*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 27*B*a*b**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*I*B*b**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*B*b**3*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 6*B*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 6*I*B*b**3*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*B*b**3*tan(e + f*x)**3/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*I*B*b**3*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*I*B*b**3/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*I*C*a**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*C*a**3*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 3*C*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 3*I*C*a**3*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 3*I*C*a**3/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 27*C*a**2*b*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 27*I*C*a**2*b*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*I*C*a**2*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*C*a**2*b*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 18*C*a**2*b*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 27*C*a**2*b/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 27*I*C*a*b**2*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 27*C*a*b**2*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 18*C*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 18*I*C*a*b**2*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*C*a*b**2*tan(e + f*x)**3/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 9*I*C*a*b**2*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 27*I*C*a*b**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 15*C*b**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 15*I*C*b**3*f*x/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 6*I*C*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 6*C*b**3*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) + 6*I*d*f) - 2*C*b**3*tan(e + f*x)**4/(-6*d*f*tan(e + f*x) + 6*I*d*f) - I*C*b**3*tan(e + f*x)**3/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 9*C*b**3*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) + 6*I*d*f) + 15*C*b**3/(-6*d*f*tan(e + f*x) + 6*I*d*f), Eq(c, -I*d)), (3*I*A*a**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*A*a**3*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 3*I*A*a**3/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*A*a**2*b*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*I*A*a**2*b*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*A*a**2*b/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*I*A*a*b**2*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*A*a*b**2*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*A*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*I*A*a*b**2*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*I*A*a*b**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*A*b**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*I*A*b**3*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 3*I*A*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*A*b**3*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 6*A*b**3*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*A*b**3/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*B*a**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*I*B*a**3*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 3*B*a**3/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*I*B*a**2*b*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*B*a**2*b*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*B*a**2*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*I*B*a**2*b*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*I*B*a**2*b/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 27*B*a*b**2*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 27*I*B*a*b**2*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*I*B*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*B*a*b**2*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 18*B*a*b**2*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 27*B*a*b**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*I*B*b**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*B*b**3*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 6*B*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 6*I*B*b**3*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*B*b**3*tan(e + f*x)**3/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 3*I*B*b**3*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*I*B*b**3/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 3*I*C*a**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*C*a**3*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*C*a**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*I*C*a**3*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 3*I*C*a**3/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 27*C*a**2*b*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 27*I*C*a**2*b*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*I*C*a**2*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*C*a**2*b*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 18*C*a**2*b*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 27*C*a**2*b/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 27*I*C*a*b**2*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 27*C*a*b**2*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 18*C*a*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 18*I*C*a*b**2*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 9*C*a*b**2*tan(e + f*x)**3/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*I*C*a*b**2*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 27*I*C*a*b**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 15*C*b**3*f*x*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 15*I*C*b**3*f*x/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 6*I*C*b**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 6*C*b**3*log(tan(e + f*x)**2 + 1)/(-6*d*f*tan(e + f*x) - 6*I*d*f) - 2*C*b**3*tan(e + f*x)**4/(-6*d*f*tan(e + f*x) - 6*I*d*f) + I*C*b**3*tan(e + f*x)**3/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 9*C*b**3*tan(e + f*x)**2/(-6*d*f*tan(e + f*x) - 6*I*d*f) + 15*C*b**3/(-6*d*f*tan(e + f*x) - 6*I*d*f), Eq(c, I*d)), ((A*a**3*x + 3*A*a**2*b*log(tan(e + f*x)**2 + 1)/(2*f) - 3*A*a*b**2*x + 3*A*a*b**2*tan(e + f*x)/f - A*b**3*log(tan(e + f*x)**2 + 1)/(2*f) + A*b**3*tan(e + f*x)**2/(2*f) + B*a**3*log(tan(e + f*x)**2 + 1)/(2*f) - 3*B*a**2*b*x + 3*B*a**2*b*tan(e + f*x)/f - 3*B*a*b**2*log(tan(e + f*x)**2 + 1)/(2*f) + 3*B*a*b**2*tan(e + f*x)**2/(2*f) + B*b**3*x + B*b**3*tan(e + f*x)**3/(3*f) - B*b**3*tan(e + f*x)/f - C*a**3*x + C*a**3*tan(e + f*x)/f - 3*C*a**2*b*log(tan(e + f*x)**2 + 1)/(2*f) + 3*C*a**2*b*tan(e + f*x)**2/(2*f) + 3*C*a*b**2*x + C*a*b**2*tan(e + f*x)**3/f - 3*C*a*b**2*tan(e + f*x)/f + C*b**3*log(tan(e + f*x)**2 + 1)/(2*f) + C*b**3*tan(e + f*x)**4/(4*f) - C*b**3*tan(e + f*x)**2/(2*f))/c, Eq(d, 0)), (x*(a + b*tan(e))**3*(A + B*tan(e) + C*tan(e)**2)/(c + d*tan(e)), Eq(f, 0)), (6*A*a**3*c*d**4*f*x/(6*c**2*d**4*f + 6*d**6*f) + 6*A*a**3*d**5*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) - 3*A*a**3*d**5*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) - 18*A*a**2*b*c*d**4*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) + 9*A*a**2*b*c*d**4*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) + 18*A*a**2*b*d**5*f*x/(6*c**2*d**4*f + 6*d**6*f) + 18*A*a*b**2*c**2*d**3*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) - 18*A*a*b**2*c*d**4*f*x/(6*c**2*d**4*f + 6*d**6*f) + 9*A*a*b**2*d**5*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) - 6*A*b**3*c**3*d**2*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) + 6*A*b**3*c**2*d**3*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) - 3*A*b**3*c*d**4*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) - 6*A*b**3*d**5*f*x/(6*c**2*d**4*f + 6*d**6*f) + 6*A*b**3*d**5*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) - 6*B*a**3*c*d**4*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) + 3*B*a**3*c*d**4*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) + 6*B*a**3*d**5*f*x/(6*c**2*d**4*f + 6*d**6*f) + 18*B*a**2*b*c**2*d**3*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) - 18*B*a**2*b*c*d**4*f*x/(6*c**2*d**4*f + 6*d**6*f) + 9*B*a**2*b*d**5*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) - 18*B*a*b**2*c**3*d**2*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) + 18*B*a*b**2*c**2*d**3*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) - 9*B*a*b**2*c*d**4*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) - 18*B*a*b**2*d**5*f*x/(6*c**2*d**4*f + 6*d**6*f) + 18*B*a*b**2*d**5*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) + 6*B*b**3*c**4*d*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) - 6*B*b**3*c**3*d**2*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) + 3*B*b**3*c**2*d**3*tan(e + f*x)**2/(6*c**2*d**4*f + 6*d**6*f) + 6*B*b**3*c*d**4*f*x/(6*c**2*d**4*f + 6*d**6*f) - 6*B*b**3*c*d**4*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) - 3*B*b**3*d**5*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) + 3*B*b**3*d**5*tan(e + f*x)**2/(6*c**2*d**4*f + 6*d**6*f) + 6*C*a**3*c**2*d**3*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) - 6*C*a**3*c*d**4*f*x/(6*c**2*d**4*f + 6*d**6*f) + 3*C*a**3*d**5*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) - 18*C*a**2*b*c**3*d**2*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) + 18*C*a**2*b*c**2*d**3*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) - 9*C*a**2*b*c*d**4*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) - 18*C*a**2*b*d**5*f*x/(6*c**2*d**4*f + 6*d**6*f) + 18*C*a**2*b*d**5*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) + 18*C*a*b**2*c**4*d*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) - 18*C*a*b**2*c**3*d**2*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) + 9*C*a*b**2*c**2*d**3*tan(e + f*x)**2/(6*c**2*d**4*f + 6*d**6*f) + 18*C*a*b**2*c*d**4*f*x/(6*c**2*d**4*f + 6*d**6*f) - 18*C*a*b**2*c*d**4*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) - 9*C*a*b**2*d**5*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) + 9*C*a*b**2*d**5*tan(e + f*x)**2/(6*c**2*d**4*f + 6*d**6*f) - 6*C*b**3*c**5*log(c/d + tan(e + f*x))/(6*c**2*d**4*f + 6*d**6*f) + 6*C*b**3*c**4*d*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f) - 3*C*b**3*c**3*d**2*tan(e + f*x)**2/(6*c**2*d**4*f + 6*d**6*f) + 2*C*b**3*c**2*d**3*tan(e + f*x)**3/(6*c**2*d**4*f + 6*d**6*f) + 3*C*b**3*c*d**4*log(tan(e + f*x)**2 + 1)/(6*c**2*d**4*f + 6*d**6*f) - 3*C*b**3*c*d**4*tan(e + f*x)**2/(6*c**2*d**4*f + 6*d**6*f) + 6*C*b**3*d**5*f*x/(6*c**2*d**4*f + 6*d**6*f) + 2*C*b**3*d**5*tan(e + f*x)**3/(6*c**2*d**4*f + 6*d**6*f) - 6*C*b**3*d**5*tan(e + f*x)/(6*c**2*d**4*f + 6*d**6*f), True))","A",0
71,1,4517,0,8.128397," ","integrate((a+b*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right)^{2} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\- \frac{i A a^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{A a^{2} f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i A a^{2}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 A a b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{2 i A a b f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{2 A a b}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i A b^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{A b^{2} f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{A b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i A b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i A b^{2}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{B a^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i B a^{2} f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{B a^{2}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 i B a b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 B a b f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 B a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{2 i B a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{2 i B a b}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 B b^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 i B b^{2} f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i B b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{B b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 B b^{2} \tan^{2}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 B b^{2}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i C a^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{C a^{2} f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{C a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i C a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i C a^{2}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{6 C a b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{6 i C a b f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 i C a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 C a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{4 C a b \tan^{2}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{6 C a b}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 i C b^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 C b^{2} f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{2 C b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 i C b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{C b^{2} \tan^{3}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i C b^{2} \tan^{2}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 i C b^{2}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} & \text{for}\: c = - i d \\\frac{i A a^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{A a^{2} f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i A a^{2}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 A a b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 i A a b f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{2 A a b}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i A b^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{A b^{2} f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{A b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i A b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i A b^{2}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{B a^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i B a^{2} f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{B a^{2}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{2 i B a b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 B a b f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 B a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 i B a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 i B a b}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 B b^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 i B b^{2} f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i B b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{B b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 B b^{2} \tan^{2}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{3 B b^{2}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i C a^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{C a^{2} f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{C a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i C a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i C a^{2}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{6 C a b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{6 i C a b f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{2 i C a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 C a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{4 C a b \tan^{2}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{6 C a b}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{3 i C b^{2} f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 C b^{2} f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{2 C b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{2 i C b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{C b^{2} \tan^{3}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i C b^{2} \tan^{2}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 i C b^{2}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} & \text{for}\: c = i d \\\frac{A a^{2} x + \frac{A a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} - A b^{2} x + \frac{A b^{2} \tan{\left(e + f x \right)}}{f} + \frac{B a^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - 2 B a b x + \frac{2 B a b \tan{\left(e + f x \right)}}{f} - \frac{B b^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B b^{2} \tan^{2}{\left(e + f x \right)}}{2 f} - C a^{2} x + \frac{C a^{2} \tan{\left(e + f x \right)}}{f} - \frac{C a b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{f} + \frac{C a b \tan^{2}{\left(e + f x \right)}}{f} + C b^{2} x + \frac{C b^{2} \tan^{3}{\left(e + f x \right)}}{3 f} - \frac{C b^{2} \tan{\left(e + f x \right)}}{f}}{c} & \text{for}\: d = 0 \\\frac{x \left(a + b \tan{\left(e \right)}\right)^{2} \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{c + d \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 A a^{2} c d^{3} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 A a^{2} d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{A a^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{4 A a b c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 A a b c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{4 A a b d^{4} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 A b^{2} c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 A b^{2} c d^{3} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{A b^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 B a^{2} c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{B a^{2} c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 B a^{2} d^{4} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{4 B a b c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{4 B a b c d^{3} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 B a b d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 B b^{2} c^{3} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 B b^{2} c^{2} d^{2} \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{B b^{2} c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 B b^{2} d^{4} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 B b^{2} d^{4} \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 C a^{2} c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 C a^{2} c d^{3} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{C a^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{4 C a b c^{3} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{4 C a b c^{2} d^{2} \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 C a b c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{4 C a b d^{4} f x}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{4 C a b d^{4} \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 C b^{2} c^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 C b^{2} c^{3} d \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{C b^{2} c^{2} d^{2} \tan^{2}{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{2 C b^{2} c d^{3} f x}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{2 C b^{2} c d^{3} \tan{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} - \frac{C b^{2} d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} + \frac{C b^{2} d^{4} \tan^{2}{\left(e + f x \right)}}{2 c^{2} d^{3} f + 2 d^{5} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))**2*(A + B*tan(e) + C*tan(e)**2)/tan(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (-I*A*a**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - A*a**2*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*A*a**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*A*a*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 2*I*A*a*b*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 2*A*a*b/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*A*b**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - A*b**2*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - A*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*A*b**2*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*A*b**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) - B*a**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*B*a**2*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) + B*a**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*I*B*a*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*B*a*b*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*B*a*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 2*I*B*a*b*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 2*I*B*a*b/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 3*B*b**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 3*I*B*b**2*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*B*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - B*b**2*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*B*b**2*tan(e + f*x)**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 3*B*b**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*C*a**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - C*a**2*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - C*a**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*C*a**2*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*C*a**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 6*C*a*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 6*I*C*a*b*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*I*C*a*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*C*a*b*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 4*C*a*b*tan(e + f*x)**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 6*C*a*b/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 3*I*C*b**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 3*C*b**2*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 2*C*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*I*C*b**2*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - C*b**2*tan(e + f*x)**3/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*C*b**2*tan(e + f*x)**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 3*I*C*b**2/(-2*d*f*tan(e + f*x) + 2*I*d*f), Eq(c, -I*d)), (I*A*a**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - A*a**2*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*A*a**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*A*a*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*I*A*a*b*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 2*A*a*b/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*A*b**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - A*b**2*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) - A*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*A*b**2*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*A*b**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) - B*a**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*B*a**2*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + B*a**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 2*I*B*a*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*B*a*b*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*B*a*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*I*B*a*b*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*I*B*a*b/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 3*B*b**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 3*I*B*b**2*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*B*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - B*b**2*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*B*b**2*tan(e + f*x)**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 3*B*b**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*C*a**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - C*a**2*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) - C*a**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*C*a**2*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*C*a**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 6*C*a*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 6*I*C*a*b*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 2*I*C*a*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*C*a*b*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 4*C*a*b*tan(e + f*x)**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 6*C*a*b/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 3*I*C*b**2*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 3*C*b**2*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 2*C*b**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 2*I*C*b**2*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - C*b**2*tan(e + f*x)**3/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*C*b**2*tan(e + f*x)**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 3*I*C*b**2/(-2*d*f*tan(e + f*x) - 2*I*d*f), Eq(c, I*d)), ((A*a**2*x + A*a*b*log(tan(e + f*x)**2 + 1)/f - A*b**2*x + A*b**2*tan(e + f*x)/f + B*a**2*log(tan(e + f*x)**2 + 1)/(2*f) - 2*B*a*b*x + 2*B*a*b*tan(e + f*x)/f - B*b**2*log(tan(e + f*x)**2 + 1)/(2*f) + B*b**2*tan(e + f*x)**2/(2*f) - C*a**2*x + C*a**2*tan(e + f*x)/f - C*a*b*log(tan(e + f*x)**2 + 1)/f + C*a*b*tan(e + f*x)**2/f + C*b**2*x + C*b**2*tan(e + f*x)**3/(3*f) - C*b**2*tan(e + f*x)/f)/c, Eq(d, 0)), (x*(a + b*tan(e))**2*(A + B*tan(e) + C*tan(e)**2)/(c + d*tan(e)), Eq(f, 0)), (2*A*a**2*c*d**3*f*x/(2*c**2*d**3*f + 2*d**5*f) + 2*A*a**2*d**4*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) - A*a**2*d**4*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 4*A*a*b*c*d**3*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) + 2*A*a*b*c*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) + 4*A*a*b*d**4*f*x/(2*c**2*d**3*f + 2*d**5*f) + 2*A*b**2*c**2*d**2*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) - 2*A*b**2*c*d**3*f*x/(2*c**2*d**3*f + 2*d**5*f) + A*b**2*d**4*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 2*B*a**2*c*d**3*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) + B*a**2*c*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) + 2*B*a**2*d**4*f*x/(2*c**2*d**3*f + 2*d**5*f) + 4*B*a*b*c**2*d**2*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) - 4*B*a*b*c*d**3*f*x/(2*c**2*d**3*f + 2*d**5*f) + 2*B*a*b*d**4*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 2*B*b**2*c**3*d*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) + 2*B*b**2*c**2*d**2*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) - B*b**2*c*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 2*B*b**2*d**4*f*x/(2*c**2*d**3*f + 2*d**5*f) + 2*B*b**2*d**4*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) + 2*C*a**2*c**2*d**2*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) - 2*C*a**2*c*d**3*f*x/(2*c**2*d**3*f + 2*d**5*f) + C*a**2*d**4*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 4*C*a*b*c**3*d*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) + 4*C*a*b*c**2*d**2*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) - 2*C*a*b*c*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) - 4*C*a*b*d**4*f*x/(2*c**2*d**3*f + 2*d**5*f) + 4*C*a*b*d**4*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) + 2*C*b**2*c**4*log(c/d + tan(e + f*x))/(2*c**2*d**3*f + 2*d**5*f) - 2*C*b**2*c**3*d*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) + C*b**2*c**2*d**2*tan(e + f*x)**2/(2*c**2*d**3*f + 2*d**5*f) + 2*C*b**2*c*d**3*f*x/(2*c**2*d**3*f + 2*d**5*f) - 2*C*b**2*c*d**3*tan(e + f*x)/(2*c**2*d**3*f + 2*d**5*f) - C*b**2*d**4*log(tan(e + f*x)**2 + 1)/(2*c**2*d**3*f + 2*d**5*f) + C*b**2*d**4*tan(e + f*x)**2/(2*c**2*d**3*f + 2*d**5*f), True))","A",0
72,1,2429,0,2.412109," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{A a x + \frac{A b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - B b x + \frac{B b \tan{\left(e + f x \right)}}{f} - C a x + \frac{C a \tan{\left(e + f x \right)}}{f} - \frac{C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b \tan^{2}{\left(e + f x \right)}}{2 f}}{c} & \text{for}\: d = 0 \\- \frac{i A a f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{A a f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i A a}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{A b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i A b f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{A b}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{B a f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i B a f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{B a}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i B b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{B b f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{B b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i B b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i B b}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i C a f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{C a f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{C a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i C a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i C a}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{3 C b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 i C b f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{2 C b \tan^{2}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{3 C b}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} & \text{for}\: c = - i d \\\frac{i A a f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{A a f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i A a}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{A b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i A b f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{A b}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{B a f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i B a f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{B a}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i B b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{B b f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{B b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i B b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i B b}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i C a f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{C a f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{C a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i C a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i C a}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 C b f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{3 i C b f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{2 C b \tan^{2}{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{3 C b}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} & \text{for}\: c = i d \\\frac{x \left(a + b \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{c + d \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 A a c d^{2} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 A a d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{A a d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{2 A b c d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{A b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 A b d^{3} f x}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{2 B a c d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{B a c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 B a d^{3} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 B b c^{2} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{2 B b c d^{2} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{B b d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 C a c^{2} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{2 C a c d^{2} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{C a d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{2 C b c^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 C b c^{2} d \tan{\left(e + f x \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{C b c d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} - \frac{2 C b d^{3} f x}{2 c^{2} d^{2} f + 2 d^{4} f} + \frac{2 C b d^{3} \tan{\left(e + f x \right)}}{2 c^{2} d^{2} f + 2 d^{4} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))*(A + B*tan(e) + C*tan(e)**2)/tan(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), ((A*a*x + A*b*log(tan(e + f*x)**2 + 1)/(2*f) + B*a*log(tan(e + f*x)**2 + 1)/(2*f) - B*b*x + B*b*tan(e + f*x)/f - C*a*x + C*a*tan(e + f*x)/f - C*b*log(tan(e + f*x)**2 + 1)/(2*f) + C*b*tan(e + f*x)**2/(2*f))/c, Eq(d, 0)), (-I*A*a*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - A*a*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*A*a/(-2*d*f*tan(e + f*x) + 2*I*d*f) - A*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*A*b*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) + A*b/(-2*d*f*tan(e + f*x) + 2*I*d*f) - B*a*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*B*a*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) + B*a/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*B*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - B*b*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - B*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*B*b*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*B*b/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*C*a*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - C*a*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - C*a*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*C*a*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*C*a/(-2*d*f*tan(e + f*x) + 2*I*d*f) + 3*C*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 3*I*C*b*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*C*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - C*b*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 2*C*b*tan(e + f*x)**2/(-2*d*f*tan(e + f*x) + 2*I*d*f) - 3*C*b/(-2*d*f*tan(e + f*x) + 2*I*d*f), Eq(c, -I*d)), (I*A*a*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - A*a*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*A*a/(-2*d*f*tan(e + f*x) - 2*I*d*f) - A*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*A*b*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + A*b/(-2*d*f*tan(e + f*x) - 2*I*d*f) - B*a*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*B*a*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + B*a/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*B*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - B*b*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) - B*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*B*b*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*B*b/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*C*a*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - C*a*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) - C*a*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*C*a*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*C*a/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 3*C*b*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) + 3*I*C*b*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*C*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - C*b*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 2*C*b*tan(e + f*x)**2/(-2*d*f*tan(e + f*x) - 2*I*d*f) - 3*C*b/(-2*d*f*tan(e + f*x) - 2*I*d*f), Eq(c, I*d)), (x*(a + b*tan(e))*(A + B*tan(e) + C*tan(e)**2)/(c + d*tan(e)), Eq(f, 0)), (2*A*a*c*d**2*f*x/(2*c**2*d**2*f + 2*d**4*f) + 2*A*a*d**3*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) - A*a*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) - 2*A*b*c*d**2*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) + A*b*c*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) + 2*A*b*d**3*f*x/(2*c**2*d**2*f + 2*d**4*f) - 2*B*a*c*d**2*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) + B*a*c*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) + 2*B*a*d**3*f*x/(2*c**2*d**2*f + 2*d**4*f) + 2*B*b*c**2*d*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) - 2*B*b*c*d**2*f*x/(2*c**2*d**2*f + 2*d**4*f) + B*b*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) + 2*C*a*c**2*d*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) - 2*C*a*c*d**2*f*x/(2*c**2*d**2*f + 2*d**4*f) + C*a*d**3*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) - 2*C*b*c**3*log(c/d + tan(e + f*x))/(2*c**2*d**2*f + 2*d**4*f) + 2*C*b*c**2*d*tan(e + f*x)/(2*c**2*d**2*f + 2*d**4*f) - C*b*c*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d**2*f + 2*d**4*f) - 2*C*b*d**3*f*x/(2*c**2*d**2*f + 2*d**4*f) + 2*C*b*d**3*tan(e + f*x)/(2*c**2*d**2*f + 2*d**4*f), True))","A",0
73,1,984,0,1.305164," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e)),x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{A x + \frac{B \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - C x + \frac{C \tan{\left(e + f x \right)}}{f}}{c} & \text{for}\: d = 0 \\- \frac{i A f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{A f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i A}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{B f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i B f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{B}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{i C f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{C f x}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} - \frac{C \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i C \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} + \frac{i C}{- 2 d f \tan{\left(e + f x \right)} + 2 i d f} & \text{for}\: c = - i d \\\frac{i A f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{A f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i A}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{B f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i B f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{B}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} + \frac{i C f x \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{C f x}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{C \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i C \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} - \frac{i C}{- 2 d f \tan{\left(e + f x \right)} - 2 i d f} & \text{for}\: c = i d \\\frac{x \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{c + d \tan{\left(e \right)}} & \text{for}\: f = 0 \\\frac{2 A c d f x}{2 c^{2} d f + 2 d^{3} f} + \frac{2 A d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d f + 2 d^{3} f} - \frac{A d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d f + 2 d^{3} f} - \frac{2 B c d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d f + 2 d^{3} f} + \frac{B c d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d f + 2 d^{3} f} + \frac{2 B d^{2} f x}{2 c^{2} d f + 2 d^{3} f} + \frac{2 C c^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{2} d f + 2 d^{3} f} - \frac{2 C c d f x}{2 c^{2} d f + 2 d^{3} f} + \frac{C d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{2} d f + 2 d^{3} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(e) + C*tan(e)**2)/tan(e), Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), ((A*x + B*log(tan(e + f*x)**2 + 1)/(2*f) - C*x + C*tan(e + f*x)/f)/c, Eq(d, 0)), (-I*A*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - A*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*A/(-2*d*f*tan(e + f*x) + 2*I*d*f) - B*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*B*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) + B/(-2*d*f*tan(e + f*x) + 2*I*d*f) - I*C*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) - C*f*x/(-2*d*f*tan(e + f*x) + 2*I*d*f) - C*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*C*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) + 2*I*d*f) + I*C/(-2*d*f*tan(e + f*x) + 2*I*d*f), Eq(c, -I*d)), (I*A*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - A*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*A/(-2*d*f*tan(e + f*x) - 2*I*d*f) - B*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*B*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) + B/(-2*d*f*tan(e + f*x) - 2*I*d*f) + I*C*f*x*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - C*f*x/(-2*d*f*tan(e + f*x) - 2*I*d*f) - C*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*C*log(tan(e + f*x)**2 + 1)/(-2*d*f*tan(e + f*x) - 2*I*d*f) - I*C/(-2*d*f*tan(e + f*x) - 2*I*d*f), Eq(c, I*d)), (x*(A + B*tan(e) + C*tan(e)**2)/(c + d*tan(e)), Eq(f, 0)), (2*A*c*d*f*x/(2*c**2*d*f + 2*d**3*f) + 2*A*d**2*log(c/d + tan(e + f*x))/(2*c**2*d*f + 2*d**3*f) - A*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d*f + 2*d**3*f) - 2*B*c*d*log(c/d + tan(e + f*x))/(2*c**2*d*f + 2*d**3*f) + B*c*d*log(tan(e + f*x)**2 + 1)/(2*c**2*d*f + 2*d**3*f) + 2*B*d**2*f*x/(2*c**2*d*f + 2*d**3*f) + 2*C*c**2*log(c/d + tan(e + f*x))/(2*c**2*d*f + 2*d**3*f) - 2*C*c*d*f*x/(2*c**2*d*f + 2*d**3*f) + C*d**2*log(tan(e + f*x)**2 + 1)/(2*c**2*d*f + 2*d**3*f), True))","A",0
74,-1,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e)),x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
76,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3/(c+d*tan(f*x+e)),x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
77,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,1,9721,0,4.099049," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(a + b \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan^{2}{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\\frac{A a f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i A a f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{A a f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{A a \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i A a}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i A b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 A b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i A b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i A b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i B a f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 B a f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i B a f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i B a \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{B b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i B b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{B b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 B b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i B b}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{C a f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i C a f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{C a f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 C a \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i C a}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 i C b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 C b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 i C b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 i C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{5 i C b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 C b}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = - i d \\\frac{A a f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i A a f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{A a f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{A a \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i A a}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i A b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 A b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i A b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i A b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i B a f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 B a f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{i B a f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{i B a \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{B b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i B b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{B b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 B b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i B b}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{C a f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 i C a f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{C a f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 C a \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 i C a}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{3 i C b f x \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{6 C b f x \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{3 i C b f x}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{2 C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan^{2}{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{4 i C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{2 C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} - \frac{5 i C b \tan{\left(e + f x \right)}}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} + \frac{4 C b}{- 4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} + 4 d^{2} f} & \text{for}\: c = i d \\\frac{A a x + \frac{A b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{B a \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - B b x + \frac{B b \tan{\left(e + f x \right)}}{f} - C a x + \frac{C a \tan{\left(e + f x \right)}}{f} - \frac{C b \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} + \frac{C b \tan^{2}{\left(e + f x \right)}}{2 f}}{c^{2}} & \text{for}\: d = 0 \\\frac{x \left(a + b \tan{\left(e \right)}\right) \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\left(c + d \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{2 A a c^{3} d^{2} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 A a c^{2} d^{3} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{4 A a c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a c^{2} d^{3}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a c d^{4} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{4 A a c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a d^{5} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 A a d^{5}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 A b c^{3} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{A b c^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 A b c^{3} d^{2}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{4 A b c^{2} d^{3} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 A b c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{A b c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{4 A b c d^{4} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 A b c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{A b c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 A b c d^{4}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 A b d^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{A b d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 B a c^{3} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{B a c^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a c^{3} d^{2}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{4 B a c^{2} d^{3} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 B a c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{B a c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{4 B a c d^{4} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{B a c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a c d^{4}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 B a d^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{B a d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 B b c^{4} d}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 B b c^{3} d^{2} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 B b c^{2} d^{3} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{4 B b c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 B b c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 B b c^{2} d^{3}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 B b c d^{4} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{4 B b c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 B b c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 B b d^{5} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 C a c^{4} d}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 C a c^{3} d^{2} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 C a c^{2} d^{3} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{4 C a c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{2 C a c^{2} d^{3}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a c d^{4} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{4 C a c d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 C a d^{5} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 C b c^{5} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 C b c^{5}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 C b c^{4} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 C b c^{3} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{C b c^{3} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{2 C b c^{3} d^{2}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{4 C b c^{2} d^{3} f x}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{6 C b c^{2} d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{C b c^{2} d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} - \frac{4 C b c d^{4} f x \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{C b c d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} + \frac{C b d^{5} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d^{2} f + 2 c^{4} d^{3} f \tan{\left(e + f x \right)} + 4 c^{3} d^{4} f + 4 c^{2} d^{5} f \tan{\left(e + f x \right)} + 2 c d^{6} f + 2 d^{7} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(a + b*tan(e))*(A + B*tan(e) + C*tan(e)**2)/tan(e)**2, Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (A*a*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*A*a*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - A*a*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + A*a*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*A*a/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*A*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*A*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*A*b*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*A*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*B*a*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*B*a*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*B*a*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*B*a*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - B*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*B*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + B*b*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*B*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*B*b/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - C*a*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*C*a*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + C*a*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*C*a*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*C*a/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*I*C*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*C*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*I*C*b*f*x/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*C*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*I*C*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*C*b*log(tan(e + f*x)**2 + 1)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 5*I*C*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*C*b/(-4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, -I*d)), (A*a*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*A*a*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - A*a*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + A*a*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*A*a/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*A*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*A*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*A*b*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*A*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*B*a*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*B*a*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - I*B*a*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + I*B*a*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - B*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*B*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + B*b*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*B*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*B*b/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - C*a*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*I*C*a*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + C*a*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*C*a*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*I*C*a/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 3*I*C*b*f*x*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 6*C*b*f*x*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 3*I*C*b*f*x/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 2*C*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)**2/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 4*I*C*b*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 2*C*b*log(tan(e + f*x)**2 + 1)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) - 5*I*C*b*tan(e + f*x)/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f) + 4*C*b/(-4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) + 4*d**2*f), Eq(c, I*d)), ((A*a*x + A*b*log(tan(e + f*x)**2 + 1)/(2*f) + B*a*log(tan(e + f*x)**2 + 1)/(2*f) - B*b*x + B*b*tan(e + f*x)/f - C*a*x + C*a*tan(e + f*x)/f - C*b*log(tan(e + f*x)**2 + 1)/(2*f) + C*b*tan(e + f*x)**2/(2*f))/c**2, Eq(d, 0)), (x*(a + b*tan(e))*(A + B*tan(e) + C*tan(e)**2)/(c + d*tan(e))**2, Eq(f, 0)), (2*A*a*c**3*d**2*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*A*a*c**2*d**3*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 4*A*a*c**2*d**3*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*A*a*c**2*d**3*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*A*a*c**2*d**3/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*A*a*c*d**4*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 4*A*a*c*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*A*a*c*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*A*a*d**5*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*A*a*d**5/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*A*b*c**3*d**2*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + A*b*c**3*d**2*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*A*b*c**3*d**2/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 4*A*b*c**2*d**3*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*A*b*c**2*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + A*b*c**2*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 4*A*b*c*d**4*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*A*b*c*d**4*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - A*b*c*d**4*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*A*b*c*d**4/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*A*b*d**5*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - A*b*d**5*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*B*a*c**3*d**2*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + B*a*c**3*d**2*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*B*a*c**3*d**2/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 4*B*a*c**2*d**3*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*B*a*c**2*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + B*a*c**2*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 4*B*a*c*d**4*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*B*a*c*d**4*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - B*a*c*d**4*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*B*a*c*d**4/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*B*a*d**5*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - B*a*d**5*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*B*b*c**4*d/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*B*b*c**3*d**2*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*B*b*c**2*d**3*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 4*B*b*c**2*d**3*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*B*b*c**2*d**3*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*B*b*c**2*d**3/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*B*b*c*d**4*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 4*B*b*c*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*B*b*c*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*B*b*d**5*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*C*a*c**4*d/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*C*a*c**3*d**2*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*C*a*c**2*d**3*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 4*C*a*c**2*d**3*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*C*a*c**2*d**3*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 2*C*a*c**2*d**3/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*C*a*c*d**4*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 4*C*a*c*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*C*a*c*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*C*a*d**5*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*C*b*c**5*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*C*b*c**5/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*C*b*c**4*d*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*C*b*c**3*d**2*log(c/d + tan(e + f*x))/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - C*b*c**3*d**2*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 2*C*b*c**3*d**2/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 4*C*b*c**2*d**3*f*x/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + 6*C*b*c**2*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - C*b*c**2*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) - 4*C*b*c*d**4*f*x*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + C*b*c*d**4*log(tan(e + f*x)**2 + 1)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)) + C*b*d**5*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d**2*f + 2*c**4*d**3*f*tan(e + f*x) + 4*c**3*d**4*f + 4*c**2*d**5*f*tan(e + f*x) + 2*c*d**6*f + 2*d**7*f*tan(e + f*x)), True))","A",0
80,1,4396,0,2.131863," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**2,x)","\begin{cases} \frac{\tilde{\infty} x \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\tan^{2}{\left(e \right)}} & \text{for}\: c = 0 \wedge d = 0 \wedge f = 0 \\- \frac{A f x \tan^{2}{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{2 i A f x \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{A f x}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{A \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{2 i A}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{i B f x \tan^{2}{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{2 B f x \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{i B f x}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{i B \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{C f x \tan^{2}{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{2 i C f x \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{C f x}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{3 C \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{2 i C}{4 d^{2} f \tan^{2}{\left(e + f x \right)} - 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} & \text{for}\: c = - i d \\- \frac{A f x \tan^{2}{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{2 i A f x \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{A f x}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{A \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{2 i A}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{i B f x \tan^{2}{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{2 B f x \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{i B f x}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{i B \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{C f x \tan^{2}{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} + \frac{2 i C f x \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{C f x}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{3 C \tan{\left(e + f x \right)}}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} - \frac{2 i C}{4 d^{2} f \tan^{2}{\left(e + f x \right)} + 8 i d^{2} f \tan{\left(e + f x \right)} - 4 d^{2} f} & \text{for}\: c = i d \\\frac{A x + \frac{B \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 f} - C x + \frac{C \tan{\left(e + f x \right)}}{f}}{c^{2}} & \text{for}\: d = 0 \\\frac{x \left(A + B \tan{\left(e \right)} + C \tan^{2}{\left(e \right)}\right)}{\left(c + d \tan{\left(e \right)}\right)^{2}} & \text{for}\: f = 0 \\\frac{2 A c^{3} d f x}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 A c^{2} d^{2} f x \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{4 A c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 A c^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 A c^{2} d^{2}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 A c d^{3} f x}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{4 A c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 A c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 A d^{4} f x \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 A d^{4}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 B c^{3} d \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{B c^{3} d \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 B c^{3} d}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{4 B c^{2} d^{2} f x}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 B c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{B c^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{4 B c d^{3} f x \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 B c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{B c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 B c d^{3}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 B d^{4} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{B d^{4} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 C c^{4}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 C c^{3} d f x}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 C c^{2} d^{2} f x \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{4 C c^{2} d^{2} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 C c^{2} d^{2} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{2 C c^{2} d^{2}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 C c d^{3} f x}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} - \frac{4 C c d^{3} \log{\left(\frac{c}{d} + \tan{\left(e + f x \right)} \right)} \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 C c d^{3} \log{\left(\tan^{2}{\left(e + f x \right)} + 1 \right)} \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} + \frac{2 C d^{4} f x \tan{\left(e + f x \right)}}{2 c^{5} d f + 2 c^{4} d^{2} f \tan{\left(e + f x \right)} + 4 c^{3} d^{3} f + 4 c^{2} d^{4} f \tan{\left(e + f x \right)} + 2 c d^{5} f + 2 d^{6} f \tan{\left(e + f x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*(A + B*tan(e) + C*tan(e)**2)/tan(e)**2, Eq(c, 0) & Eq(d, 0) & Eq(f, 0)), (-A*f*x*tan(e + f*x)**2/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + 2*I*A*f*x*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + A*f*x/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - A*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + 2*I*A/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + I*B*f*x*tan(e + f*x)**2/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + 2*B*f*x*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - I*B*f*x/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + I*B*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + C*f*x*tan(e + f*x)**2/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - 2*I*C*f*x*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - C*f*x/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - 3*C*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + 2*I*C/(4*d**2*f*tan(e + f*x)**2 - 8*I*d**2*f*tan(e + f*x) - 4*d**2*f), Eq(c, -I*d)), (-A*f*x*tan(e + f*x)**2/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - 2*I*A*f*x*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + A*f*x/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - A*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - 2*I*A/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - I*B*f*x*tan(e + f*x)**2/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + 2*B*f*x*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + I*B*f*x/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - I*B*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + C*f*x*tan(e + f*x)**2/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) + 2*I*C*f*x*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - C*f*x/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - 3*C*tan(e + f*x)/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f) - 2*I*C/(4*d**2*f*tan(e + f*x)**2 + 8*I*d**2*f*tan(e + f*x) - 4*d**2*f), Eq(c, I*d)), ((A*x + B*log(tan(e + f*x)**2 + 1)/(2*f) - C*x + C*tan(e + f*x)/f)/c**2, Eq(d, 0)), (x*(A + B*tan(e) + C*tan(e)**2)/(c + d*tan(e))**2, Eq(f, 0)), (2*A*c**3*d*f*x/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*A*c**2*d**2*f*x*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 4*A*c**2*d**2*log(c/d + tan(e + f*x))/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*A*c**2*d**2*log(tan(e + f*x)**2 + 1)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*A*c**2*d**2/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*A*c*d**3*f*x/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 4*A*c*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*A*c*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*A*d**4*f*x*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*A*d**4/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*B*c**3*d*log(c/d + tan(e + f*x))/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + B*c**3*d*log(tan(e + f*x)**2 + 1)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*B*c**3*d/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 4*B*c**2*d**2*f*x/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*B*c**2*d**2*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + B*c**2*d**2*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 4*B*c*d**3*f*x*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*B*c*d**3*log(c/d + tan(e + f*x))/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - B*c*d**3*log(tan(e + f*x)**2 + 1)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*B*c*d**3/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*B*d**4*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - B*d**4*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*C*c**4/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*C*c**3*d*f*x/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*C*c**2*d**2*f*x*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 4*C*c**2*d**2*log(c/d + tan(e + f*x))/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*C*c**2*d**2*log(tan(e + f*x)**2 + 1)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 2*C*c**2*d**2/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*C*c*d**3*f*x/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) - 4*C*c*d**3*log(c/d + tan(e + f*x))*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*C*c*d**3*log(tan(e + f*x)**2 + 1)*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)) + 2*C*d**4*f*x*tan(e + f*x)/(2*c**5*d*f + 2*c**4*d**2*f*tan(e + f*x) + 4*c**3*d**3*f + 4*c**2*d**4*f*tan(e + f*x) + 2*c*d**5*f + 2*d**6*f*tan(e + f*x)), True))","A",0
81,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
82,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
83,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3/(c+d*tan(f*x+e))**2,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
84,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
85,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
86,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
87,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
88,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
89,-2,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**3,x)","\text{Exception raised: NotImplementedError}"," ",0,"Exception raised: NotImplementedError","F(-2)",0
90,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{3} \sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3*sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
91,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{2} \sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
92,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right) \sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))*sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
93,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
94,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e)),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{a + b \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x)), x)","F",0
95,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2,x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**2, x)","F",0
96,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3,x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**3, x)","F",0
97,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3*(c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{3} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3*(c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
98,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*(c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
99,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
100,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
101,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e)),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{a + b \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x)), x)","F",0
102,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2,x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{2}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**2, x)","F",0
103,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3,x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**3, x)","F",0
104,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*(c + d*tan(e + f*x))**(5/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
105,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(5/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
106,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
107,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{3} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(c + d*tan(e + f*x)), x)","F",0
111,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(c + d*tan(e + f*x)), x)","F",0
112,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right) \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(c + d*tan(e + f*x)), x)","F",0
113,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(c + d*tan(e + f*x)), x)","F",0
114,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e)),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right) \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))*sqrt(c + d*tan(e + f*x))), x)","F",0
115,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**2,x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))**2*sqrt(c + d*tan(e + f*x))), x)","F",0
116,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{3} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
117,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
118,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right) \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
119,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
120,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(3/2)), x)","F",0
121,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))**2*(c + d*tan(e + f*x))**(3/2)), x)","F",0
122,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{3} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**3*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
123,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**2*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
124,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right) \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
125,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
126,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right) \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(5/2)), x)","F",0
127,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**2/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right)^{2} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))**2*(c + d*tan(e + f*x))**(5/2)), x)","F",0
128,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(a+b*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)*sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
130,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \sqrt{a + b \tan{\left(e + f x \right)}} \sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))*sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
131,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{a + b \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(a + b*tan(e + f*x)), x)","F",0
132,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(3/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**(3/2), x)","F",0
133,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(5/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**(5/2), x)","F",0
134,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(7/2),x)","\int \frac{\sqrt{c + d \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**(7/2), x)","F",0
135,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)*(c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)*(c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
136,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \sqrt{a + b \tan{\left(e + f x \right)}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
137,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(1/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{a + b \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(a + b*tan(e + f*x)), x)","F",0
138,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(3/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**(3/2), x)","F",0
139,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(5/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**(5/2), x)","F",0
140,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(7/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**(7/2), x)","F",0
141,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(1/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{a + b \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(a + b*tan(e + f*x)), x)","F",0
143,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(3/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**(3/2), x)","F",0
144,0,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(5/2),x)","\int \frac{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*tan(e + f*x))**(5/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(a + b*tan(e + f*x))**(5/2), x)","F",0
145,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate((c+d*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(5/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(c + d*tan(e + f*x)), x)","F",0
148,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(c + d*tan(e + f*x)), x)","F",0
149,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{\sqrt{a + b \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/sqrt(c + d*tan(e + f*x)), x)","F",0
150,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(1/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\sqrt{a + b \tan{\left(e + f x \right)}} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(sqrt(a + b*tan(e + f*x))*sqrt(c + d*tan(e + f*x))), x)","F",0
151,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))**(3/2)*sqrt(c + d*tan(e + f*x))), x)","F",0
152,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(1/2)/(a+b*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \sqrt{c + d \tan{\left(e + f x \right)}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))**(5/2)*sqrt(c + d*tan(e + f*x))), x)","F",0
153,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(5/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
154,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
155,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{\sqrt{a + b \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(3/2), x)","F",0
156,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\sqrt{a + b \tan{\left(e + f x \right)}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(sqrt(a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(3/2)), x)","F",0
157,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))**(3/2)*(c + d*tan(e + f*x))**(3/2)), x)","F",0
158,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(5/2)/(c+d*tan(f*x+e))**(3/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{5}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))**(5/2)*(c + d*tan(e + f*x))**(3/2)), x)","F",0
159,-1,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(5/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(3/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**(3/2)*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
161,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**(1/2)*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{\sqrt{a + b \tan{\left(e + f x \right)}} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**(5/2), x)","F",0
162,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(1/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\sqrt{a + b \tan{\left(e + f x \right)}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(sqrt(a + b*tan(e + f*x))*(c + d*tan(e + f*x))**(5/2)), x)","F",0
163,0,0,0,0.000000," ","integrate((A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(a+b*tan(f*x+e))**(3/2)/(c+d*tan(f*x+e))**(5/2),x)","\int \frac{A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}}{\left(a + b \tan{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(c + d \tan{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((A + B*tan(e + f*x) + C*tan(e + f*x)**2)/((a + b*tan(e + f*x))**(3/2)*(c + d*tan(e + f*x))**(5/2)), x)","F",0
164,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e))**n*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
165,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e))**3*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{3} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(c + d*tan(e + f*x))**3*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
166,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e))**2*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right)^{2} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(c + d*tan(e + f*x))**2*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
167,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(c+d*tan(f*x+e))*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(c + d \tan{\left(e + f x \right)}\right) \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(c + d*tan(e + f*x))*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
168,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(A+B*tan(f*x+e)+C*tan(f*x+e)**2),x)","\int \left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(A + B*tan(e + f*x) + C*tan(e + f*x)**2), x)","F",0
169,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e)),x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{c + d \tan{\left(e + f x \right)}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x)), x)","F",0
170,-2,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
171,0,0,0,0.000000," ","integrate((a+b*tan(f*x+e))**m*(A+B*tan(f*x+e)+C*tan(f*x+e)**2)/(c+d*tan(f*x+e))**3,x)","\int \frac{\left(a + b \tan{\left(e + f x \right)}\right)^{m} \left(A + B \tan{\left(e + f x \right)} + C \tan^{2}{\left(e + f x \right)}\right)}{\left(c + d \tan{\left(e + f x \right)}\right)^{3}}\, dx"," ",0,"Integral((a + b*tan(e + f*x))**m*(A + B*tan(e + f*x) + C*tan(e + f*x)**2)/(c + d*tan(e + f*x))**3, x)","F",0
