1,0,0,0,0.000000," ","integrate((A+C*cot(d*x+c)**2)/(b*tan(d*x+c))**(1/2),x)","\int \frac{A + C \cot^{2}{\left(c + d x \right)}}{\sqrt{b \tan{\left(c + d x \right)}}}\, dx"," ",0,"Integral((A + C*cot(c + d*x)**2)/sqrt(b*tan(c + d*x)), x)","F",0
2,1,22,0,0.125542," ","integrate(a+b*cot(d*x+c)**2,x)","a x + b \left(\begin{cases} - x - \frac{\cot{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \cot^{2}{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*x + b*Piecewise((-x - cot(c + d*x)/d, Ne(d, 0)), (x*cot(c)**2, True))","A",0
3,1,68,0,0.263242," ","integrate((a+b*cot(d*x+c)**2)**2,x)","\begin{cases} a^{2} x - 2 a b x - \frac{2 a b \cot{\left(c + d x \right)}}{d} + b^{2} x - \frac{b^{2} \cot^{3}{\left(c + d x \right)}}{3 d} + \frac{b^{2} \cot{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cot^{2}{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x - 2*a*b*x - 2*a*b*cot(c + d*x)/d + b**2*x - b**2*cot(c + d*x)**3/(3*d) + b**2*cot(c + d*x)/d, Ne(d, 0)), (x*(a + b*cot(c)**2)**2, True))","A",0
4,1,126,0,0.552222," ","integrate((a+b*cot(d*x+c)**2)**3,x)","\begin{cases} a^{3} x - 3 a^{2} b x - \frac{3 a^{2} b \cot{\left(c + d x \right)}}{d} + 3 a b^{2} x - \frac{a b^{2} \cot^{3}{\left(c + d x \right)}}{d} + \frac{3 a b^{2} \cot{\left(c + d x \right)}}{d} - b^{3} x - \frac{b^{3} \cot^{5}{\left(c + d x \right)}}{5 d} + \frac{b^{3} \cot^{3}{\left(c + d x \right)}}{3 d} - \frac{b^{3} \cot{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(a + b \cot^{2}{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x - 3*a**2*b*x - 3*a**2*b*cot(c + d*x)/d + 3*a*b**2*x - a*b**2*cot(c + d*x)**3/d + 3*a*b**2*cot(c + d*x)/d - b**3*x - b**3*cot(c + d*x)**5/(5*d) + b**3*cot(c + d*x)**3/(3*d) - b**3*cot(c + d*x)/d, Ne(d, 0)), (x*(a + b*cot(c)**2)**3, True))","A",0
5,1,279,0,1.461432," ","integrate(1/(a+b*cot(d*x+c)**2),x)","\begin{cases} \frac{\tilde{\infty} x}{\cot^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- x + \frac{1}{d \cot{\left(c + d x \right)}}}{b} & \text{for}\: a = 0 \\\frac{d x \cot^{2}{\left(c + d x \right)}}{2 b d \cot^{2}{\left(c + d x \right)} + 2 b d} + \frac{d x}{2 b d \cot^{2}{\left(c + d x \right)} + 2 b d} - \frac{\cot{\left(c + d x \right)}}{2 b d \cot^{2}{\left(c + d x \right)} + 2 b d} & \text{for}\: a = b \\\frac{x}{a + b \cot^{2}{\left(c \right)}} & \text{for}\: d = 0 \\\frac{x}{a} & \text{for}\: b = 0 \\\frac{2 i \sqrt{a} d x \sqrt{\frac{1}{b}}}{2 i a^{\frac{3}{2}} d \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b d \sqrt{\frac{1}{b}}} + \frac{\log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{2 i a^{\frac{3}{2}} d \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b d \sqrt{\frac{1}{b}}} - \frac{\log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{2 i a^{\frac{3}{2}} d \sqrt{\frac{1}{b}} - 2 i \sqrt{a} b d \sqrt{\frac{1}{b}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/cot(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-x + 1/(d*cot(c + d*x)))/b, Eq(a, 0)), (d*x*cot(c + d*x)**2/(2*b*d*cot(c + d*x)**2 + 2*b*d) + d*x/(2*b*d*cot(c + d*x)**2 + 2*b*d) - cot(c + d*x)/(2*b*d*cot(c + d*x)**2 + 2*b*d), Eq(a, b)), (x/(a + b*cot(c)**2), Eq(d, 0)), (x/a, Eq(b, 0)), (2*I*sqrt(a)*d*x*sqrt(1/b)/(2*I*a**(3/2)*d*sqrt(1/b) - 2*I*sqrt(a)*b*d*sqrt(1/b)) + log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(2*I*a**(3/2)*d*sqrt(1/b) - 2*I*sqrt(a)*b*d*sqrt(1/b)) - log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(2*I*a**(3/2)*d*sqrt(1/b) - 2*I*sqrt(a)*b*d*sqrt(1/b)), True))","A",0
6,1,2322,0,18.674921," ","integrate(1/(a+b*cot(d*x+c)**2)**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\cot^{4}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{x - \frac{1}{d \cot{\left(c + d x \right)}} + \frac{1}{3 d \cot^{3}{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{3 d x \cot^{4}{\left(c + d x \right)}}{8 b^{2} d \cot^{4}{\left(c + d x \right)} + 16 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 b^{2} d} + \frac{6 d x \cot^{2}{\left(c + d x \right)}}{8 b^{2} d \cot^{4}{\left(c + d x \right)} + 16 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 b^{2} d} + \frac{3 d x}{8 b^{2} d \cot^{4}{\left(c + d x \right)} + 16 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 b^{2} d} - \frac{3 \cot^{3}{\left(c + d x \right)}}{8 b^{2} d \cot^{4}{\left(c + d x \right)} + 16 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 b^{2} d} - \frac{5 \cot{\left(c + d x \right)}}{8 b^{2} d \cot^{4}{\left(c + d x \right)} + 16 b^{2} d \cot^{2}{\left(c + d x \right)} + 8 b^{2} d} & \text{for}\: a = b \\\frac{x}{\left(a + b \cot^{2}{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{x}{a^{2}} & \text{for}\: b = 0 \\\frac{4 i a^{\frac{5}{2}} d x \sqrt{\frac{1}{b}}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} + \frac{4 i a^{\frac{3}{2}} b d x \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} + \frac{2 i a^{\frac{3}{2}} b \sqrt{\frac{1}{b}} \cot{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} - \frac{2 i \sqrt{a} b^{2} \sqrt{\frac{1}{b}} \cot{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} + \frac{3 a^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} - \frac{3 a^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} + \frac{3 a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} - \frac{a b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} - \frac{3 a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} + \frac{a b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} - \frac{b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} + \frac{b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{4 i a^{\frac{9}{2}} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 8 i a^{\frac{7}{2}} b d \sqrt{\frac{1}{b}} - 8 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 4 i a^{\frac{5}{2}} b^{2} d \sqrt{\frac{1}{b}} + 4 i a^{\frac{3}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/cot(c)**4, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((x - 1/(d*cot(c + d*x)) + 1/(3*d*cot(c + d*x)**3))/b**2, Eq(a, 0)), (3*d*x*cot(c + d*x)**4/(8*b**2*d*cot(c + d*x)**4 + 16*b**2*d*cot(c + d*x)**2 + 8*b**2*d) + 6*d*x*cot(c + d*x)**2/(8*b**2*d*cot(c + d*x)**4 + 16*b**2*d*cot(c + d*x)**2 + 8*b**2*d) + 3*d*x/(8*b**2*d*cot(c + d*x)**4 + 16*b**2*d*cot(c + d*x)**2 + 8*b**2*d) - 3*cot(c + d*x)**3/(8*b**2*d*cot(c + d*x)**4 + 16*b**2*d*cot(c + d*x)**2 + 8*b**2*d) - 5*cot(c + d*x)/(8*b**2*d*cot(c + d*x)**4 + 16*b**2*d*cot(c + d*x)**2 + 8*b**2*d), Eq(a, b)), (x/(a + b*cot(c)**2)**2, Eq(d, 0)), (x/a**2, Eq(b, 0)), (4*I*a**(5/2)*d*x*sqrt(1/b)/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) + 4*I*a**(3/2)*b*d*x*sqrt(1/b)*cot(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) + 2*I*a**(3/2)*b*sqrt(1/b)*cot(c + d*x)/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) - 2*I*sqrt(a)*b**2*sqrt(1/b)*cot(c + d*x)/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) + 3*a**2*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) - 3*a**2*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) + 3*a*b*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) - a*b*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) - 3*a*b*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) + a*b*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) - b**2*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2) + b**2*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(4*I*a**(9/2)*d*sqrt(1/b) + 4*I*a**(7/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 8*I*a**(7/2)*b*d*sqrt(1/b) - 8*I*a**(5/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 4*I*a**(5/2)*b**2*d*sqrt(1/b) + 4*I*a**(3/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2), True))","A",0
7,1,9629,0,93.928702," ","integrate(1/(a+b*cot(d*x+c)**2)**3,x)","\begin{cases} \frac{\tilde{\infty} x}{\cot^{6}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- x + \frac{1}{d \cot{\left(c + d x \right)}} - \frac{1}{3 d \cot^{3}{\left(c + d x \right)}} + \frac{1}{5 d \cot^{5}{\left(c + d x \right)}}}{b^{3}} & \text{for}\: a = 0 \\\frac{15 d x \cot^{6}{\left(c + d x \right)}}{48 b^{3} d \cot^{6}{\left(c + d x \right)} + 144 b^{3} d \cot^{4}{\left(c + d x \right)} + 144 b^{3} d \cot^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{45 d x \cot^{4}{\left(c + d x \right)}}{48 b^{3} d \cot^{6}{\left(c + d x \right)} + 144 b^{3} d \cot^{4}{\left(c + d x \right)} + 144 b^{3} d \cot^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{45 d x \cot^{2}{\left(c + d x \right)}}{48 b^{3} d \cot^{6}{\left(c + d x \right)} + 144 b^{3} d \cot^{4}{\left(c + d x \right)} + 144 b^{3} d \cot^{2}{\left(c + d x \right)} + 48 b^{3} d} + \frac{15 d x}{48 b^{3} d \cot^{6}{\left(c + d x \right)} + 144 b^{3} d \cot^{4}{\left(c + d x \right)} + 144 b^{3} d \cot^{2}{\left(c + d x \right)} + 48 b^{3} d} - \frac{15 \cot^{5}{\left(c + d x \right)}}{48 b^{3} d \cot^{6}{\left(c + d x \right)} + 144 b^{3} d \cot^{4}{\left(c + d x \right)} + 144 b^{3} d \cot^{2}{\left(c + d x \right)} + 48 b^{3} d} - \frac{40 \cot^{3}{\left(c + d x \right)}}{48 b^{3} d \cot^{6}{\left(c + d x \right)} + 144 b^{3} d \cot^{4}{\left(c + d x \right)} + 144 b^{3} d \cot^{2}{\left(c + d x \right)} + 48 b^{3} d} - \frac{33 \cot{\left(c + d x \right)}}{48 b^{3} d \cot^{6}{\left(c + d x \right)} + 144 b^{3} d \cot^{4}{\left(c + d x \right)} + 144 b^{3} d \cot^{2}{\left(c + d x \right)} + 48 b^{3} d} & \text{for}\: a = b \\\frac{x}{\left(a + b \cot^{2}{\left(c \right)}\right)^{3}} & \text{for}\: d = 0 \\\frac{x}{a^{3}} & \text{for}\: b = 0 \\\frac{16 i a^{\frac{9}{2}} d x \sqrt{\frac{1}{b}}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{32 i a^{\frac{7}{2}} b d x \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{18 i a^{\frac{7}{2}} b \sqrt{\frac{1}{b}} \cot{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{16 i a^{\frac{5}{2}} b^{2} d x \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{14 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \cot^{3}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{28 i a^{\frac{5}{2}} b^{2} \sqrt{\frac{1}{b}} \cot{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{20 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \cot^{3}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{10 i a^{\frac{3}{2}} b^{3} \sqrt{\frac{1}{b}} \cot{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{6 i \sqrt{a} b^{4} \sqrt{\frac{1}{b}} \cot^{3}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{15 a^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{15 a^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{30 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{10 a^{3} b \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{30 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{10 a^{3} b \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{15 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{20 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{3 a^{2} b^{2} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{15 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{20 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{3 a^{2} b^{2} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{10 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{6 a b^{3} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{10 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{6 a b^{3} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{2}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} + \frac{3 b^{4} \log{\left(- i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} - \frac{3 b^{4} \log{\left(i \sqrt{a} \sqrt{\frac{1}{b}} + \cot{\left(c + d x \right)} \right)} \cot^{4}{\left(c + d x \right)}}{16 i a^{\frac{15}{2}} d \sqrt{\frac{1}{b}} + 32 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 48 i a^{\frac{13}{2}} b d \sqrt{\frac{1}{b}} + 16 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 96 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} + 48 i a^{\frac{11}{2}} b^{2} d \sqrt{\frac{1}{b}} - 48 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} + 96 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{9}{2}} b^{3} d \sqrt{\frac{1}{b}} + 48 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)} - 32 i a^{\frac{7}{2}} b^{4} d \sqrt{\frac{1}{b}} \cot^{2}{\left(c + d x \right)} - 16 i a^{\frac{5}{2}} b^{5} d \sqrt{\frac{1}{b}} \cot^{4}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/cot(c)**6, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-x + 1/(d*cot(c + d*x)) - 1/(3*d*cot(c + d*x)**3) + 1/(5*d*cot(c + d*x)**5))/b**3, Eq(a, 0)), (15*d*x*cot(c + d*x)**6/(48*b**3*d*cot(c + d*x)**6 + 144*b**3*d*cot(c + d*x)**4 + 144*b**3*d*cot(c + d*x)**2 + 48*b**3*d) + 45*d*x*cot(c + d*x)**4/(48*b**3*d*cot(c + d*x)**6 + 144*b**3*d*cot(c + d*x)**4 + 144*b**3*d*cot(c + d*x)**2 + 48*b**3*d) + 45*d*x*cot(c + d*x)**2/(48*b**3*d*cot(c + d*x)**6 + 144*b**3*d*cot(c + d*x)**4 + 144*b**3*d*cot(c + d*x)**2 + 48*b**3*d) + 15*d*x/(48*b**3*d*cot(c + d*x)**6 + 144*b**3*d*cot(c + d*x)**4 + 144*b**3*d*cot(c + d*x)**2 + 48*b**3*d) - 15*cot(c + d*x)**5/(48*b**3*d*cot(c + d*x)**6 + 144*b**3*d*cot(c + d*x)**4 + 144*b**3*d*cot(c + d*x)**2 + 48*b**3*d) - 40*cot(c + d*x)**3/(48*b**3*d*cot(c + d*x)**6 + 144*b**3*d*cot(c + d*x)**4 + 144*b**3*d*cot(c + d*x)**2 + 48*b**3*d) - 33*cot(c + d*x)/(48*b**3*d*cot(c + d*x)**6 + 144*b**3*d*cot(c + d*x)**4 + 144*b**3*d*cot(c + d*x)**2 + 48*b**3*d), Eq(a, b)), (x/(a + b*cot(c)**2)**3, Eq(d, 0)), (x/a**3, Eq(b, 0)), (16*I*a**(9/2)*d*x*sqrt(1/b)/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 32*I*a**(7/2)*b*d*x*sqrt(1/b)*cot(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 18*I*a**(7/2)*b*sqrt(1/b)*cot(c + d*x)/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 16*I*a**(5/2)*b**2*d*x*sqrt(1/b)*cot(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 14*I*a**(5/2)*b**2*sqrt(1/b)*cot(c + d*x)**3/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 28*I*a**(5/2)*b**2*sqrt(1/b)*cot(c + d*x)/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 20*I*a**(3/2)*b**3*sqrt(1/b)*cot(c + d*x)**3/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 10*I*a**(3/2)*b**3*sqrt(1/b)*cot(c + d*x)/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 6*I*sqrt(a)*b**4*sqrt(1/b)*cot(c + d*x)**3/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 15*a**4*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 15*a**4*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 30*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 10*a**3*b*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 30*a**3*b*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 10*a**3*b*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 15*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 20*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 3*a**2*b**2*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 15*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 20*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 3*a**2*b**2*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 10*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 6*a*b**3*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 10*a*b**3*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 6*a*b**3*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**2/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) + 3*b**4*log(-I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4) - 3*b**4*log(I*sqrt(a)*sqrt(1/b) + cot(c + d*x))*cot(c + d*x)**4/(16*I*a**(15/2)*d*sqrt(1/b) + 32*I*a**(13/2)*b*d*sqrt(1/b)*cot(c + d*x)**2 - 48*I*a**(13/2)*b*d*sqrt(1/b) + 16*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**4 - 96*I*a**(11/2)*b**2*d*sqrt(1/b)*cot(c + d*x)**2 + 48*I*a**(11/2)*b**2*d*sqrt(1/b) - 48*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**4 + 96*I*a**(9/2)*b**3*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(9/2)*b**3*d*sqrt(1/b) + 48*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**4 - 32*I*a**(7/2)*b**4*d*sqrt(1/b)*cot(c + d*x)**2 - 16*I*a**(5/2)*b**5*d*sqrt(1/b)*cot(c + d*x)**4), True))","A",0
8,0,0,0,0.000000," ","integrate((1+cot(x)**2)**(3/2),x)","\int \left(\cot^{2}{\left(x \right)} + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((cot(x)**2 + 1)**(3/2), x)","F",0
9,0,0,0,0.000000," ","integrate((1+cot(x)**2)**(1/2),x)","\int \sqrt{\cot^{2}{\left(x \right)} + 1}\, dx"," ",0,"Integral(sqrt(cot(x)**2 + 1), x)","F",0
10,1,14,0,0.341681," ","integrate(1/(1+cot(x)**2)**(1/2),x)","- \frac{\cot{\left(x \right)}}{\sqrt{\cot^{2}{\left(x \right)} + 1}}"," ",0,"-cot(x)/sqrt(cot(x)**2 + 1)","A",0
11,0,0,0,0.000000," ","integrate((-1-cot(x)**2)**(3/2),x)","\int \left(- \cot^{2}{\left(x \right)} - 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((-cot(x)**2 - 1)**(3/2), x)","F",0
12,0,0,0,0.000000," ","integrate((-1-cot(x)**2)**(1/2),x)","\int \sqrt{- \cot^{2}{\left(x \right)} - 1}\, dx"," ",0,"Integral(sqrt(-cot(x)**2 - 1), x)","F",0
13,1,15,0,0.337694," ","integrate(1/(-1-cot(x)**2)**(1/2),x)","- \frac{\cot{\left(x \right)}}{\sqrt{- \cot^{2}{\left(x \right)} - 1}}"," ",0,"-cot(x)/sqrt(-cot(x)**2 - 1)","A",0
14,0,0,0,0.000000," ","integrate(cot(x)**3/(a+a*cot(x)**2)**(1/2),x)","\int \frac{\cot^{3}{\left(x \right)}}{\sqrt{a \left(\cot^{2}{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(x)**3/sqrt(a*(cot(x)**2 + 1)), x)","F",0
15,0,0,0,0.000000," ","integrate(cot(x)**2/(a+a*cot(x)**2)**(1/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\sqrt{a \left(\cot^{2}{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(cot(x)**2/sqrt(a*(cot(x)**2 + 1)), x)","F",0
16,1,12,0,1.195674," ","integrate(cot(x)/(a+a*cot(x)**2)**(1/2),x)","\frac{1}{\sqrt{a \cot^{2}{\left(x \right)} + a}}"," ",0,"1/sqrt(a*cot(x)**2 + a)","A",0
17,0,0,0,0.000000," ","integrate(tan(x)/(a+a*cot(x)**2)**(1/2),x)","\int \frac{\tan{\left(x \right)}}{\sqrt{a \left(\cot^{2}{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(x)/sqrt(a*(cot(x)**2 + 1)), x)","F",0
18,0,0,0,0.000000," ","integrate(tan(x)**2/(a+a*cot(x)**2)**(1/2),x)","\int \frac{\tan^{2}{\left(x \right)}}{\sqrt{a \left(\cot^{2}{\left(x \right)} + 1\right)}}\, dx"," ",0,"Integral(tan(x)**2/sqrt(a*(cot(x)**2 + 1)), x)","F",0
19,0,0,0,0.000000," ","integrate(cot(x)**3*(a+b*cot(x)**2)**(1/2),x)","\int \sqrt{a + b \cot^{2}{\left(x \right)}} \cot^{3}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cot(x)**2)*cot(x)**3, x)","F",0
20,0,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)**2)**(1/2),x)","\int \sqrt{a + b \cot^{2}{\left(x \right)}} \cot{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cot(x)**2)*cot(x), x)","F",0
21,0,0,0,0.000000," ","integrate((a+b*cot(x)**2)**(1/2)*tan(x),x)","\int \sqrt{a + b \cot^{2}{\left(x \right)}} \tan{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cot(x)**2)*tan(x), x)","F",0
22,0,0,0,0.000000," ","integrate(cot(x)**2*(a+b*cot(x)**2)**(1/2),x)","\int \sqrt{a + b \cot^{2}{\left(x \right)}} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cot(x)**2)*cot(x)**2, x)","F",0
23,0,0,0,0.000000," ","integrate((a+b*cot(x)**2)**(1/2),x)","\int \sqrt{a + b \cot^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cot(x)**2), x)","F",0
24,0,0,0,0.000000," ","integrate((a+b*cot(x)**2)**(1/2)*tan(x)**2,x)","\int \sqrt{a + b \cot^{2}{\left(x \right)}} \tan^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cot(x)**2)*tan(x)**2, x)","F",0
25,0,0,0,0.000000," ","integrate((a+b*cot(x)**2)**(1/2)*tan(x)**4,x)","\int \sqrt{a + b \cot^{2}{\left(x \right)}} \tan^{4}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cot(x)**2)*tan(x)**4, x)","F",0
26,0,0,0,0.000000," ","integrate(cot(x)**3*(a+b*cot(x)**2)**(3/2),x)","\int \left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}} \cot^{3}{\left(x \right)}\, dx"," ",0,"Integral((a + b*cot(x)**2)**(3/2)*cot(x)**3, x)","F",0
27,0,0,0,0.000000," ","integrate(cot(x)**2*(a+b*cot(x)**2)**(3/2),x)","\int \left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}} \cot^{2}{\left(x \right)}\, dx"," ",0,"Integral((a + b*cot(x)**2)**(3/2)*cot(x)**2, x)","F",0
28,0,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)**2)**(3/2),x)","\int \left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}} \cot{\left(x \right)}\, dx"," ",0,"Integral((a + b*cot(x)**2)**(3/2)*cot(x), x)","F",0
29,0,0,0,0.000000," ","integrate((a+b*cot(x)**2)**(3/2)*tan(x),x)","\int \left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}} \tan{\left(x \right)}\, dx"," ",0,"Integral((a + b*cot(x)**2)**(3/2)*tan(x), x)","F",0
30,0,0,0,0.000000," ","integrate((a+b*cot(x)**2)**(3/2)*tan(x)**2,x)","\int \left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}} \tan^{2}{\left(x \right)}\, dx"," ",0,"Integral((a + b*cot(x)**2)**(3/2)*tan(x)**2, x)","F",0
31,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c)**2)**(5/2),x)","\int \left(a + b \cot^{2}{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((a + b*cot(c + d*x)**2)**(5/2), x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c)**2)**(3/2),x)","\int \left(a + b \cot^{2}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*cot(c + d*x)**2)**(3/2), x)","F",0
33,0,0,0,0.000000," ","integrate((a+b*cot(d*x+c)**2)**(1/2),x)","\int \sqrt{a + b \cot^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*cot(c + d*x)**2), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(a+b*cot(d*x+c)**2)**(1/2),x)","\int \frac{1}{\sqrt{a + b \cot^{2}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*cot(c + d*x)**2), x)","F",0
35,0,0,0,0.000000," ","integrate(1/(a+b*cot(d*x+c)**2)**(3/2),x)","\int \frac{1}{\left(a + b \cot^{2}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x)**2)**(-3/2), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(a+b*cot(d*x+c)**2)**(5/2),x)","\int \frac{1}{\left(a + b \cot^{2}{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x)**2)**(-5/2), x)","F",0
37,0,0,0,0.000000," ","integrate(1/(a+b*cot(d*x+c)**2)**(7/2),x)","\int \frac{1}{\left(a + b \cot^{2}{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((a + b*cot(c + d*x)**2)**(-7/2), x)","F",0
38,0,0,0,0.000000," ","integrate((1-cot(x)**2)**(3/2),x)","\int \left(1 - \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((1 - cot(x)**2)**(3/2), x)","F",0
39,0,0,0,0.000000," ","integrate((1-cot(x)**2)**(1/2),x)","\int \sqrt{1 - \cot^{2}{\left(x \right)}}\, dx"," ",0,"Integral(sqrt(1 - cot(x)**2), x)","F",0
40,0,0,0,0.000000," ","integrate(1/(1-cot(x)**2)**(1/2),x)","\int \frac{1}{\sqrt{1 - \cot^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(1/sqrt(1 - cot(x)**2), x)","F",0
41,0,0,0,0.000000," ","integrate((-1+cot(x)**2)**(3/2),x)","\int \left(\cot^{2}{\left(x \right)} - 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((cot(x)**2 - 1)**(3/2), x)","F",0
42,0,0,0,0.000000," ","integrate((-1+cot(x)**2)**(1/2),x)","\int \sqrt{\cot^{2}{\left(x \right)} - 1}\, dx"," ",0,"Integral(sqrt(cot(x)**2 - 1), x)","F",0
43,0,0,0,0.000000," ","integrate(1/(-1+cot(x)**2)**(1/2),x)","\int \frac{1}{\sqrt{\cot^{2}{\left(x \right)} - 1}}\, dx"," ",0,"Integral(1/sqrt(cot(x)**2 - 1), x)","F",0
44,0,0,0,0.000000," ","integrate(cot(x)**3/(a+b*cot(x)**2)**(1/2),x)","\int \frac{\cot^{3}{\left(x \right)}}{\sqrt{a + b \cot^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(cot(x)**3/sqrt(a + b*cot(x)**2), x)","F",0
45,0,0,0,0.000000," ","integrate(cot(x)**2/(a+b*cot(x)**2)**(1/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\sqrt{a + b \cot^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(cot(x)**2/sqrt(a + b*cot(x)**2), x)","F",0
46,0,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)**2)**(1/2),x)","\int \frac{\cot{\left(x \right)}}{\sqrt{a + b \cot^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(cot(x)/sqrt(a + b*cot(x)**2), x)","F",0
47,0,0,0,0.000000," ","integrate(tan(x)/(a+b*cot(x)**2)**(1/2),x)","\int \frac{\tan{\left(x \right)}}{\sqrt{a + b \cot^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(tan(x)/sqrt(a + b*cot(x)**2), x)","F",0
48,0,0,0,0.000000," ","integrate(tan(x)**2/(a+b*cot(x)**2)**(1/2),x)","\int \frac{\tan^{2}{\left(x \right)}}{\sqrt{a + b \cot^{2}{\left(x \right)}}}\, dx"," ",0,"Integral(tan(x)**2/sqrt(a + b*cot(x)**2), x)","F",0
49,0,0,0,0.000000," ","integrate(cot(x)**3/(a+b*cot(x)**2)**(3/2),x)","\int \frac{\cot^{3}{\left(x \right)}}{\left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(x)**3/(a + b*cot(x)**2)**(3/2), x)","F",0
50,0,0,0,0.000000," ","integrate(cot(x)**2/(a+b*cot(x)**2)**(3/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(x)**2/(a + b*cot(x)**2)**(3/2), x)","F",0
51,1,48,0,10.367423," ","integrate(cot(x)/(a+b*cot(x)**2)**(3/2),x)","- \frac{1}{\left(a - b\right) \sqrt{a + b \cot^{2}{\left(x \right)}}} - \frac{\operatorname{atan}{\left(\frac{\sqrt{a + b \cot^{2}{\left(x \right)}}}{\sqrt{- a + b}} \right)}}{\sqrt{- a + b} \left(a - b\right)}"," ",0,"-1/((a - b)*sqrt(a + b*cot(x)**2)) - atan(sqrt(a + b*cot(x)**2)/sqrt(-a + b))/(sqrt(-a + b)*(a - b))","A",0
52,0,0,0,0.000000," ","integrate(tan(x)/(a+b*cot(x)**2)**(3/2),x)","\int \frac{\tan{\left(x \right)}}{\left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(x)/(a + b*cot(x)**2)**(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate(tan(x)**2/(a+b*cot(x)**2)**(3/2),x)","\int \frac{\tan^{2}{\left(x \right)}}{\left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(tan(x)**2/(a + b*cot(x)**2)**(3/2), x)","F",0
54,0,0,0,0.000000," ","integrate(cot(x)**3/(a+b*cot(x)**2)**(5/2),x)","\int \frac{\cot^{3}{\left(x \right)}}{\left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(x)**3/(a + b*cot(x)**2)**(5/2), x)","F",0
55,0,0,0,0.000000," ","integrate(cot(x)**2/(a+b*cot(x)**2)**(5/2),x)","\int \frac{\cot^{2}{\left(x \right)}}{\left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(x)**2/(a + b*cot(x)**2)**(5/2), x)","F",0
56,1,70,0,16.769955," ","integrate(cot(x)/(a+b*cot(x)**2)**(5/2),x)","- \frac{1}{3 \left(a - b\right) \left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{3}{2}}} - \frac{1}{\left(a - b\right)^{2} \sqrt{a + b \cot^{2}{\left(x \right)}}} - \frac{\operatorname{atan}{\left(\frac{\sqrt{a + b \cot^{2}{\left(x \right)}}}{\sqrt{- a + b}} \right)}}{\sqrt{- a + b} \left(a - b\right)^{2}}"," ",0,"-1/(3*(a - b)*(a + b*cot(x)**2)**(3/2)) - 1/((a - b)**2*sqrt(a + b*cot(x)**2)) - atan(sqrt(a + b*cot(x)**2)/sqrt(-a + b))/(sqrt(-a + b)*(a - b)**2)","A",0
57,0,0,0,0.000000," ","integrate(tan(x)/(a+b*cot(x)**2)**(5/2),x)","\int \frac{\tan{\left(x \right)}}{\left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(x)/(a + b*cot(x)**2)**(5/2), x)","F",0
58,0,0,0,0.000000," ","integrate(tan(x)**2/(a+b*cot(x)**2)**(5/2),x)","\int \frac{\tan^{2}{\left(x \right)}}{\left(a + b \cot^{2}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(tan(x)**2/(a + b*cot(x)**2)**(5/2), x)","F",0
59,1,34,0,0.285610," ","integrate(1/(1+cot(x)**3),x)","\frac{x}{2} - \frac{\log{\left(\tan{\left(x \right)} + 1 \right)}}{6} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{4} + \frac{\log{\left(\tan^{2}{\left(x \right)} - \tan{\left(x \right)} + 1 \right)}}{3}"," ",0,"x/2 - log(tan(x) + 1)/6 - log(tan(x)**2 + 1)/4 + log(tan(x)**2 - tan(x) + 1)/3","A",0
60,0,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)**4)**(1/2),x)","\int \sqrt{a + b \cot^{4}{\left(x \right)}} \cot{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*cot(x)**4)*cot(x), x)","F",0
61,0,0,0,0.000000," ","integrate(cot(x)*(a+b*cot(x)**4)**(3/2),x)","\int \left(a + b \cot^{4}{\left(x \right)}\right)^{\frac{3}{2}} \cot{\left(x \right)}\, dx"," ",0,"Integral((a + b*cot(x)**4)**(3/2)*cot(x), x)","F",0
62,0,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)**4)**(1/2),x)","\int \frac{\cot{\left(x \right)}}{\sqrt{a + b \cot^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(cot(x)/sqrt(a + b*cot(x)**4), x)","F",0
63,0,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)**4)**(3/2),x)","\int \frac{\cot{\left(x \right)}}{\left(a + b \cot^{4}{\left(x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(x)/(a + b*cot(x)**4)**(3/2), x)","F",0
64,0,0,0,0.000000," ","integrate(cot(x)/(a+b*cot(x)**4)**(5/2),x)","\int \frac{\cot{\left(x \right)}}{\left(a + b \cot^{4}{\left(x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(x)/(a + b*cot(x)**4)**(5/2), x)","F",0
