1,0,0,0,0.000000," ","integrate((b*coth(d*x+c))**(7/2),x)","\int \left(b \coth{\left(c + d x \right)}\right)^{\frac{7}{2}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(7/2), x)","F",0
2,0,0,0,0.000000," ","integrate((b*coth(d*x+c))**(5/2),x)","\int \left(b \coth{\left(c + d x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(5/2), x)","F",0
3,0,0,0,0.000000," ","integrate((b*coth(d*x+c))**(3/2),x)","\int \left(b \coth{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(3/2), x)","F",0
4,0,0,0,0.000000," ","integrate((b*coth(d*x+c))**(1/2),x)","\int \sqrt{b \coth{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(b*coth(c + d*x)), x)","F",0
5,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{b \coth{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*coth(c + d*x)), x)","F",0
6,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c))**(3/2),x)","\int \frac{1}{\left(b \coth{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(-3/2), x)","F",0
7,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c))**(5/2),x)","\int \frac{1}{\left(b \coth{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(-5/2), x)","F",0
8,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c))**(7/2),x)","\int \frac{1}{\left(b \coth{\left(c + d x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(-7/2), x)","F",0
9,0,0,0,0.000000," ","integrate((b*coth(d*x+c))**(4/3),x)","\int \left(b \coth{\left(c + d x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(4/3), x)","F",0
10,0,0,0,0.000000," ","integrate((b*coth(d*x+c))**(2/3),x)","\int \left(b \coth{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(2/3), x)","F",0
11,0,0,0,0.000000," ","integrate((b*coth(d*x+c))**(1/3),x)","\int \sqrt[3]{b \coth{\left(c + d x \right)}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(1/3), x)","F",0
12,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c))**(1/3),x)","\int \frac{1}{\sqrt[3]{b \coth{\left(c + d x \right)}}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(-1/3), x)","F",0
13,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c))**(2/3),x)","\int \frac{1}{\left(b \coth{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(-2/3), x)","F",0
14,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c))**(4/3),x)","\int \frac{1}{\left(b \coth{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x))**(-4/3), x)","F",0
15,0,0,0,0.000000," ","integrate(coth(b*x+a)**n,x)","\int \coth^{n}{\left(a + b x \right)}\, dx"," ",0,"Integral(coth(a + b*x)**n, x)","F",0
16,0,0,0,0.000000," ","integrate((b*coth(d*x+c))**n,x)","\int \left(b \coth{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((b*coth(c + d*x))**n, x)","F",0
17,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**2)**n,x)","\int \left(b \coth^{2}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**n, x)","F",0
18,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**2)**(3/2),x)","\int \left(b \coth^{2}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**(3/2), x)","F",0
19,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**2)**(1/2),x)","\int \sqrt{b \coth^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(b*coth(c + d*x)**2), x)","F",0
20,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**2)**(1/2),x)","\int \frac{1}{\sqrt{b \coth^{2}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*coth(c + d*x)**2), x)","F",0
21,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**2)**(3/2),x)","\int \frac{1}{\left(b \coth^{2}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**(-3/2), x)","F",0
22,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**2)**(4/3),x)","\int \left(b \coth^{2}{\left(c + d x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**(4/3), x)","F",0
23,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**2)**(2/3),x)","\int \left(b \coth^{2}{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**(2/3), x)","F",0
24,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**2)**(1/3),x)","\int \sqrt[3]{b \coth^{2}{\left(c + d x \right)}}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**(1/3), x)","F",0
25,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**2)**(1/3),x)","\int \frac{1}{\sqrt[3]{b \coth^{2}{\left(c + d x \right)}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**(-1/3), x)","F",0
26,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**2)**(2/3),x)","\int \frac{1}{\left(b \coth^{2}{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**(-2/3), x)","F",0
27,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**2)**(4/3),x)","\int \frac{1}{\left(b \coth^{2}{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**2)**(-4/3), x)","F",0
28,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**3)**n,x)","\int \left(b \coth^{3}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((b*coth(c + d*x)**3)**n, x)","F",0
29,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**3)**(3/2),x)","\int \left(b \coth^{3}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*coth(c + d*x)**3)**(3/2), x)","F",0
30,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**3)**(1/2),x)","\int \sqrt{b \coth^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(b*coth(c + d*x)**3), x)","F",0
31,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**3)**(1/2),x)","\int \frac{1}{\sqrt{b \coth^{3}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*coth(c + d*x)**3), x)","F",0
32,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**3)**(3/2),x)","\int \frac{1}{\left(b \coth^{3}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**3)**(-3/2), x)","F",0
33,-1,0,0,0.000000," ","integrate((b*coth(d*x+c)**3)**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,1,90,0,23.763767," ","integrate((b*coth(d*x+c)**3)**(2/3),x)","\begin{cases} \tilde{\infty} b^{\frac{2}{3}} x & \text{for}\: c = \log{\left(- e^{- d x} \right)} \vee c = \log{\left(e^{- d x} \right)} \\x \left(b \coth^{3}{\left(c \right)}\right)^{\frac{2}{3}} & \text{for}\: d = 0 \\b^{\frac{2}{3}} x \left(\frac{1}{\tanh^{3}{\left(c + d x \right)}}\right)^{\frac{2}{3}} \tanh^{2}{\left(c + d x \right)} - \frac{b^{\frac{2}{3}} \left(\frac{1}{\tanh^{3}{\left(c + d x \right)}}\right)^{\frac{2}{3}} \tanh{\left(c + d x \right)}}{d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*b**(2/3)*x, Eq(c, log(exp(-d*x))) | Eq(c, log(-exp(-d*x)))), (x*(b*coth(c)**3)**(2/3), Eq(d, 0)), (b**(2/3)*x*(tanh(c + d*x)**(-3))**(2/3)*tanh(c + d*x)**2 - b**(2/3)*(tanh(c + d*x)**(-3))**(2/3)*tanh(c + d*x)/d, True))","A",0
35,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**3)**(1/3),x)","\int \sqrt[3]{b \coth^{3}{\left(c + d x \right)}}\, dx"," ",0,"Integral((b*coth(c + d*x)**3)**(1/3), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**3)**(1/3),x)","\int \frac{1}{\sqrt[3]{b \coth^{3}{\left(c + d x \right)}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**3)**(-1/3), x)","F",0
37,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**3)**(2/3),x)","\int \frac{1}{\left(b \coth^{3}{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**3)**(-2/3), x)","F",0
38,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**3)**(4/3),x)","\int \frac{1}{\left(b \coth^{3}{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**3)**(-4/3), x)","F",0
39,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**4)**n,x)","\int \left(b \coth^{4}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**n, x)","F",0
40,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**4)**(3/2),x)","\int \left(b \coth^{4}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**(3/2), x)","F",0
41,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**4)**(1/2),x)","\int \sqrt{b \coth^{4}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(b*coth(c + d*x)**4), x)","F",0
42,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**4)**(1/2),x)","\int \frac{1}{\sqrt{b \coth^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*coth(c + d*x)**4), x)","F",0
43,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**4)**(3/2),x)","\int \frac{1}{\left(b \coth^{4}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**(-3/2), x)","F",0
44,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**4)**(4/3),x)","\int \left(b \coth^{4}{\left(c + d x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**(4/3), x)","F",0
45,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**4)**(2/3),x)","\int \left(b \coth^{4}{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**(2/3), x)","F",0
46,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**4)**(1/3),x)","\int \sqrt[3]{b \coth^{4}{\left(c + d x \right)}}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**(1/3), x)","F",0
47,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**4)**(1/3),x)","\int \frac{1}{\sqrt[3]{b \coth^{4}{\left(c + d x \right)}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**(-1/3), x)","F",0
48,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**4)**(2/3),x)","\int \frac{1}{\left(b \coth^{4}{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**(-2/3), x)","F",0
49,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**4)**(4/3),x)","\int \frac{1}{\left(b \coth^{4}{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**4)**(-4/3), x)","F",0
50,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**m)**n,x)","\int \left(b \coth^{m}{\left(c + d x \right)}\right)^{n}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**n, x)","F",0
51,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**m)**(3/2),x)","\int \left(b \coth^{m}{\left(c + d x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**(3/2), x)","F",0
52,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**m)**(1/2),x)","\int \sqrt{b \coth^{m}{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(b*coth(c + d*x)**m), x)","F",0
53,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**m)**(1/2),x)","\int \frac{1}{\sqrt{b \coth^{m}{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*coth(c + d*x)**m), x)","F",0
54,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**m)**(3/2),x)","\int \frac{1}{\left(b \coth^{m}{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**(-3/2), x)","F",0
55,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**m)**(4/3),x)","\int \left(b \coth^{m}{\left(c + d x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**(4/3), x)","F",0
56,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**m)**(2/3),x)","\int \left(b \coth^{m}{\left(c + d x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**(2/3), x)","F",0
57,0,0,0,0.000000," ","integrate((b*coth(d*x+c)**m)**(1/3),x)","\int \sqrt[3]{b \coth^{m}{\left(c + d x \right)}}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**(1/3), x)","F",0
58,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**m)**(1/3),x)","\int \frac{1}{\sqrt[3]{b \coth^{m}{\left(c + d x \right)}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**(-1/3), x)","F",0
59,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**m)**(2/3),x)","\int \frac{1}{\left(b \coth^{m}{\left(c + d x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**(-2/3), x)","F",0
60,0,0,0,0.000000," ","integrate(1/(b*coth(d*x+c)**m)**(4/3),x)","\int \frac{1}{\left(b \coth^{m}{\left(c + d x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((b*coth(c + d*x)**m)**(-4/3), x)","F",0
61,1,48,0,1.222785," ","integrate((1+coth(x))**5,x)","32 x - 16 \log{\left(\tanh{\left(x \right)} + 1 \right)} + 16 \log{\left(\tanh{\left(x \right)} \right)} - \frac{15}{\tanh{\left(x \right)}} - \frac{11}{2 \tanh^{2}{\left(x \right)}} - \frac{5}{3 \tanh^{3}{\left(x \right)}} - \frac{1}{4 \tanh^{4}{\left(x \right)}}"," ",0,"32*x - 16*log(tanh(x) + 1) + 16*log(tanh(x)) - 15/tanh(x) - 11/(2*tanh(x)**2) - 5/(3*tanh(x)**3) - 1/(4*tanh(x)**4)","A",0
62,1,37,0,0.915218," ","integrate((1+coth(x))**4,x)","16 x - 8 \log{\left(\tanh{\left(x \right)} + 1 \right)} + 8 \log{\left(\tanh{\left(x \right)} \right)} - \frac{7}{\tanh{\left(x \right)}} - \frac{2}{\tanh^{2}{\left(x \right)}} - \frac{1}{3 \tanh^{3}{\left(x \right)}}"," ",0,"16*x - 8*log(tanh(x) + 1) + 8*log(tanh(x)) - 7/tanh(x) - 2/tanh(x)**2 - 1/(3*tanh(x)**3)","A",0
63,1,31,0,0.681604," ","integrate((1+coth(x))**3,x)","8 x - 4 \log{\left(\tanh{\left(x \right)} + 1 \right)} + 4 \log{\left(\tanh{\left(x \right)} \right)} - \frac{3}{\tanh{\left(x \right)}} - \frac{1}{2 \tanh^{2}{\left(x \right)}}"," ",0,"8*x - 4*log(tanh(x) + 1) + 4*log(tanh(x)) - 3/tanh(x) - 1/(2*tanh(x)**2)","A",0
64,1,22,0,0.368955," ","integrate((1+coth(x))**2,x)","4 x - 2 \log{\left(\tanh{\left(x \right)} + 1 \right)} + 2 \log{\left(\tanh{\left(x \right)} \right)} - \frac{1}{\tanh{\left(x \right)}}"," ",0,"4*x - 2*log(tanh(x) + 1) + 2*log(tanh(x)) - 1/tanh(x)","A",0
65,1,27,0,0.444114," ","integrate(1/(1+coth(x)),x)","\frac{x \tanh{\left(x \right)}}{2 \tanh{\left(x \right)} + 2} + \frac{x}{2 \tanh{\left(x \right)} + 2} + \frac{1}{2 \tanh{\left(x \right)} + 2}"," ",0,"x*tanh(x)/(2*tanh(x) + 2) + x/(2*tanh(x) + 2) + 1/(2*tanh(x) + 2)","B",0
66,1,88,0,0.809249," ","integrate(1/(1+coth(x))**2,x)","\frac{x \tanh^{2}{\left(x \right)}}{4 \tanh^{2}{\left(x \right)} + 8 \tanh{\left(x \right)} + 4} + \frac{2 x \tanh{\left(x \right)}}{4 \tanh^{2}{\left(x \right)} + 8 \tanh{\left(x \right)} + 4} + \frac{x}{4 \tanh^{2}{\left(x \right)} + 8 \tanh{\left(x \right)} + 4} + \frac{3 \tanh{\left(x \right)}}{4 \tanh^{2}{\left(x \right)} + 8 \tanh{\left(x \right)} + 4} + \frac{2}{4 \tanh^{2}{\left(x \right)} + 8 \tanh{\left(x \right)} + 4}"," ",0,"x*tanh(x)**2/(4*tanh(x)**2 + 8*tanh(x) + 4) + 2*x*tanh(x)/(4*tanh(x)**2 + 8*tanh(x) + 4) + x/(4*tanh(x)**2 + 8*tanh(x) + 4) + 3*tanh(x)/(4*tanh(x)**2 + 8*tanh(x) + 4) + 2/(4*tanh(x)**2 + 8*tanh(x) + 4)","B",0
67,1,182,0,1.054441," ","integrate(1/(1+coth(x))**3,x)","\frac{3 x \tanh^{3}{\left(x \right)}}{24 \tanh^{3}{\left(x \right)} + 72 \tanh^{2}{\left(x \right)} + 72 \tanh{\left(x \right)} + 24} + \frac{9 x \tanh^{2}{\left(x \right)}}{24 \tanh^{3}{\left(x \right)} + 72 \tanh^{2}{\left(x \right)} + 72 \tanh{\left(x \right)} + 24} + \frac{9 x \tanh{\left(x \right)}}{24 \tanh^{3}{\left(x \right)} + 72 \tanh^{2}{\left(x \right)} + 72 \tanh{\left(x \right)} + 24} + \frac{3 x}{24 \tanh^{3}{\left(x \right)} + 72 \tanh^{2}{\left(x \right)} + 72 \tanh{\left(x \right)} + 24} + \frac{21 \tanh^{2}{\left(x \right)}}{24 \tanh^{3}{\left(x \right)} + 72 \tanh^{2}{\left(x \right)} + 72 \tanh{\left(x \right)} + 24} + \frac{27 \tanh{\left(x \right)}}{24 \tanh^{3}{\left(x \right)} + 72 \tanh^{2}{\left(x \right)} + 72 \tanh{\left(x \right)} + 24} + \frac{10}{24 \tanh^{3}{\left(x \right)} + 72 \tanh^{2}{\left(x \right)} + 72 \tanh{\left(x \right)} + 24}"," ",0,"3*x*tanh(x)**3/(24*tanh(x)**3 + 72*tanh(x)**2 + 72*tanh(x) + 24) + 9*x*tanh(x)**2/(24*tanh(x)**3 + 72*tanh(x)**2 + 72*tanh(x) + 24) + 9*x*tanh(x)/(24*tanh(x)**3 + 72*tanh(x)**2 + 72*tanh(x) + 24) + 3*x/(24*tanh(x)**3 + 72*tanh(x)**2 + 72*tanh(x) + 24) + 21*tanh(x)**2/(24*tanh(x)**3 + 72*tanh(x)**2 + 72*tanh(x) + 24) + 27*tanh(x)/(24*tanh(x)**3 + 72*tanh(x)**2 + 72*tanh(x) + 24) + 10/(24*tanh(x)**3 + 72*tanh(x)**2 + 72*tanh(x) + 24)","B",0
68,1,299,0,1.419278," ","integrate(1/(1+coth(x))**4,x)","\frac{3 x \tanh^{4}{\left(x \right)}}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48} + \frac{12 x \tanh^{3}{\left(x \right)}}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48} + \frac{18 x \tanh^{2}{\left(x \right)}}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48} + \frac{12 x \tanh{\left(x \right)}}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48} + \frac{3 x}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48} + \frac{45 \tanh^{3}{\left(x \right)}}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48} + \frac{84 \tanh^{2}{\left(x \right)}}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48} + \frac{61 \tanh{\left(x \right)}}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48} + \frac{16}{48 \tanh^{4}{\left(x \right)} + 192 \tanh^{3}{\left(x \right)} + 288 \tanh^{2}{\left(x \right)} + 192 \tanh{\left(x \right)} + 48}"," ",0,"3*x*tanh(x)**4/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48) + 12*x*tanh(x)**3/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48) + 18*x*tanh(x)**2/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48) + 12*x*tanh(x)/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48) + 3*x/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48) + 45*tanh(x)**3/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48) + 84*tanh(x)**2/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48) + 61*tanh(x)/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48) + 16/(48*tanh(x)**4 + 192*tanh(x)**3 + 288*tanh(x)**2 + 192*tanh(x) + 48)","B",0
69,1,444,0,1.802542," ","integrate(1/(1+coth(x))**5,x)","\frac{15 x \tanh^{5}{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{75 x \tanh^{4}{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{150 x \tanh^{3}{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{150 x \tanh^{2}{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{75 x \tanh{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{15 x}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{465 \tanh^{4}{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{1125 \tanh^{3}{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{1205 \tanh^{2}{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{625 \tanh{\left(x \right)}}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480} + \frac{128}{480 \tanh^{5}{\left(x \right)} + 2400 \tanh^{4}{\left(x \right)} + 4800 \tanh^{3}{\left(x \right)} + 4800 \tanh^{2}{\left(x \right)} + 2400 \tanh{\left(x \right)} + 480}"," ",0,"15*x*tanh(x)**5/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 75*x*tanh(x)**4/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 150*x*tanh(x)**3/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 150*x*tanh(x)**2/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 75*x*tanh(x)/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 15*x/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 465*tanh(x)**4/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 1125*tanh(x)**3/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 1205*tanh(x)**2/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 625*tanh(x)/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480) + 128/(480*tanh(x)**5 + 2400*tanh(x)**4 + 4800*tanh(x)**3 + 4800*tanh(x)**2 + 2400*tanh(x) + 480)","B",0
70,0,0,0,0.000000," ","integrate((1+coth(x))**(7/2),x)","\int \left(\coth{\left(x \right)} + 1\right)^{\frac{7}{2}}\, dx"," ",0,"Integral((coth(x) + 1)**(7/2), x)","F",0
71,0,0,0,0.000000," ","integrate((1+coth(x))**(5/2),x)","\int \left(\coth{\left(x \right)} + 1\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((coth(x) + 1)**(5/2), x)","F",0
72,0,0,0,0.000000," ","integrate((1+coth(x))**(3/2),x)","\int \left(\coth{\left(x \right)} + 1\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((coth(x) + 1)**(3/2), x)","F",0
73,0,0,0,0.000000," ","integrate((1+coth(x))**(1/2),x)","\int \sqrt{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sqrt(coth(x) + 1), x)","F",0
74,0,0,0,0.000000," ","integrate(1/(1+coth(x))**(1/2),x)","\int \frac{1}{\sqrt{\coth{\left(x \right)} + 1}}\, dx"," ",0,"Integral(1/sqrt(coth(x) + 1), x)","F",0
75,0,0,0,0.000000," ","integrate(1/(1+coth(x))**(3/2),x)","\int \frac{1}{\left(\coth{\left(x \right)} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((coth(x) + 1)**(-3/2), x)","F",0
76,0,0,0,0.000000," ","integrate(1/(1+coth(x))**(5/2),x)","\int \frac{1}{\left(\coth{\left(x \right)} + 1\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((coth(x) + 1)**(-5/2), x)","F",0
77,1,325,0,13.420055," ","integrate((a+b*coth(d*x+c))**5,x)","\begin{cases} a^{5} x + \tilde{\infty} a^{4} b x + \tilde{\infty} a^{3} b^{2} x + \tilde{\infty} a^{2} b^{3} x + \tilde{\infty} a b^{4} x + \tilde{\infty} b^{5} x & \text{for}\: c = \log{\left(- e^{- d x} \right)} \vee c = \log{\left(e^{- d x} \right)} \\x \left(a + b \coth{\left(c \right)}\right)^{5} & \text{for}\: d = 0 \\a^{5} x + 5 a^{4} b x - \frac{5 a^{4} b \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d} + \frac{5 a^{4} b \log{\left(\tanh{\left(c + d x \right)} \right)}}{d} + 10 a^{3} b^{2} x - \frac{10 a^{3} b^{2}}{d \tanh{\left(c + d x \right)}} + 10 a^{2} b^{3} x - \frac{10 a^{2} b^{3} \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d} + \frac{10 a^{2} b^{3} \log{\left(\tanh{\left(c + d x \right)} \right)}}{d} - \frac{5 a^{2} b^{3}}{d \tanh^{2}{\left(c + d x \right)}} + 5 a b^{4} x - \frac{5 a b^{4}}{d \tanh{\left(c + d x \right)}} - \frac{5 a b^{4}}{3 d \tanh^{3}{\left(c + d x \right)}} + b^{5} x - \frac{b^{5} \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d} + \frac{b^{5} \log{\left(\tanh{\left(c + d x \right)} \right)}}{d} - \frac{b^{5}}{2 d \tanh^{2}{\left(c + d x \right)}} - \frac{b^{5}}{4 d \tanh^{4}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**5*x + zoo*a**4*b*x + zoo*a**3*b**2*x + zoo*a**2*b**3*x + zoo*a*b**4*x + zoo*b**5*x, Eq(c, log(exp(-d*x))) | Eq(c, log(-exp(-d*x)))), (x*(a + b*coth(c))**5, Eq(d, 0)), (a**5*x + 5*a**4*b*x - 5*a**4*b*log(tanh(c + d*x) + 1)/d + 5*a**4*b*log(tanh(c + d*x))/d + 10*a**3*b**2*x - 10*a**3*b**2/(d*tanh(c + d*x)) + 10*a**2*b**3*x - 10*a**2*b**3*log(tanh(c + d*x) + 1)/d + 10*a**2*b**3*log(tanh(c + d*x))/d - 5*a**2*b**3/(d*tanh(c + d*x)**2) + 5*a*b**4*x - 5*a*b**4/(d*tanh(c + d*x)) - 5*a*b**4/(3*d*tanh(c + d*x)**3) + b**5*x - b**5*log(tanh(c + d*x) + 1)/d + b**5*log(tanh(c + d*x))/d - b**5/(2*d*tanh(c + d*x)**2) - b**5/(4*d*tanh(c + d*x)**4), True))","A",0
78,1,233,0,6.234685," ","integrate((a+b*coth(d*x+c))**4,x)","\begin{cases} a^{4} x + \tilde{\infty} a^{3} b x + \tilde{\infty} a^{2} b^{2} x + \tilde{\infty} a b^{3} x + \tilde{\infty} b^{4} x & \text{for}\: c = \log{\left(- e^{- d x} \right)} \vee c = \log{\left(e^{- d x} \right)} \\x \left(a + b \coth{\left(c \right)}\right)^{4} & \text{for}\: d = 0 \\a^{4} x + 4 a^{3} b x - \frac{4 a^{3} b \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 a^{3} b \log{\left(\tanh{\left(c + d x \right)} \right)}}{d} + 6 a^{2} b^{2} x - \frac{6 a^{2} b^{2}}{d \tanh{\left(c + d x \right)}} + 4 a b^{3} x - \frac{4 a b^{3} \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d} + \frac{4 a b^{3} \log{\left(\tanh{\left(c + d x \right)} \right)}}{d} - \frac{2 a b^{3}}{d \tanh^{2}{\left(c + d x \right)}} + b^{4} x - \frac{b^{4}}{d \tanh{\left(c + d x \right)}} - \frac{b^{4}}{3 d \tanh^{3}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x + zoo*a**3*b*x + zoo*a**2*b**2*x + zoo*a*b**3*x + zoo*b**4*x, Eq(c, log(exp(-d*x))) | Eq(c, log(-exp(-d*x)))), (x*(a + b*coth(c))**4, Eq(d, 0)), (a**4*x + 4*a**3*b*x - 4*a**3*b*log(tanh(c + d*x) + 1)/d + 4*a**3*b*log(tanh(c + d*x))/d + 6*a**2*b**2*x - 6*a**2*b**2/(d*tanh(c + d*x)) + 4*a*b**3*x - 4*a*b**3*log(tanh(c + d*x) + 1)/d + 4*a*b**3*log(tanh(c + d*x))/d - 2*a*b**3/(d*tanh(c + d*x)**2) + b**4*x - b**4/(d*tanh(c + d*x)) - b**4/(3*d*tanh(c + d*x)**3), True))","A",0
79,1,175,0,2.850328," ","integrate((a+b*coth(d*x+c))**3,x)","\begin{cases} a^{3} x + \tilde{\infty} a^{2} b x + \tilde{\infty} a b^{2} x + \tilde{\infty} b^{3} x & \text{for}\: c = \log{\left(- e^{- d x} \right)} \vee c = \log{\left(e^{- d x} \right)} \\x \left(a + b \coth{\left(c \right)}\right)^{3} & \text{for}\: d = 0 \\a^{3} x + 3 a^{2} b x - \frac{3 a^{2} b \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d} + \frac{3 a^{2} b \log{\left(\tanh{\left(c + d x \right)} \right)}}{d} + 3 a b^{2} x - \frac{3 a b^{2}}{d \tanh{\left(c + d x \right)}} + b^{3} x - \frac{b^{3} \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d} + \frac{b^{3} \log{\left(\tanh{\left(c + d x \right)} \right)}}{d} - \frac{b^{3}}{2 d \tanh^{2}{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x + zoo*a**2*b*x + zoo*a*b**2*x + zoo*b**3*x, Eq(c, log(exp(-d*x))) | Eq(c, log(-exp(-d*x)))), (x*(a + b*coth(c))**3, Eq(d, 0)), (a**3*x + 3*a**2*b*x - 3*a**2*b*log(tanh(c + d*x) + 1)/d + 3*a**2*b*log(tanh(c + d*x))/d + 3*a*b**2*x - 3*a*b**2/(d*tanh(c + d*x)) + b**3*x - b**3*log(tanh(c + d*x) + 1)/d + b**3*log(tanh(c + d*x))/d - b**3/(2*d*tanh(c + d*x)**2), True))","A",0
80,1,104,0,1.355291," ","integrate((a+b*coth(d*x+c))**2,x)","\begin{cases} a^{2} x + \tilde{\infty} a b x + \tilde{\infty} b^{2} x & \text{for}\: c = \log{\left(- e^{- d x} \right)} \vee c = \log{\left(e^{- d x} \right)} \\x \left(a + b \coth{\left(c \right)}\right)^{2} & \text{for}\: d = 0 \\a^{2} x + 2 a b x - \frac{2 a b \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d} + \frac{2 a b \log{\left(\tanh{\left(c + d x \right)} \right)}}{d} + b^{2} x - \frac{b^{2}}{d \tanh{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x + zoo*a*b*x + zoo*b**2*x, Eq(c, log(exp(-d*x))) | Eq(c, log(-exp(-d*x)))), (x*(a + b*coth(c))**2, Eq(d, 0)), (a**2*x + 2*a*b*x - 2*a*b*log(tanh(c + d*x) + 1)/d + 2*a*b*log(tanh(c + d*x))/d + b**2*x - b**2/(d*tanh(c + d*x)), True))","A",0
81,1,236,0,2.556708," ","integrate(1/(a+b*coth(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x}{\coth{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{d x \tanh{\left(c + d x \right)}}{2 b d \tanh{\left(c + d x \right)} - 2 b d} + \frac{d x}{2 b d \tanh{\left(c + d x \right)} - 2 b d} - \frac{1}{2 b d \tanh{\left(c + d x \right)} - 2 b d} & \text{for}\: a = - b \\\frac{d x \tanh{\left(c + d x \right)}}{2 b d \tanh{\left(c + d x \right)} + 2 b d} + \frac{d x}{2 b d \tanh{\left(c + d x \right)} + 2 b d} + \frac{1}{2 b d \tanh{\left(c + d x \right)} + 2 b d} & \text{for}\: a = b \\\frac{x}{a + b \coth{\left(c \right)}} & \text{for}\: d = 0 \\\frac{x - \frac{\log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{d}}{b} & \text{for}\: a = 0 \\\frac{a d x}{a^{2} d - b^{2} d} - \frac{b d x}{a^{2} d - b^{2} d} + \frac{b \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{a^{2} d - b^{2} d} - \frac{b \log{\left(\tanh{\left(c + d x \right)} + \frac{b}{a} \right)}}{a^{2} d - b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/coth(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-d*x*tanh(c + d*x)/(2*b*d*tanh(c + d*x) - 2*b*d) + d*x/(2*b*d*tanh(c + d*x) - 2*b*d) - 1/(2*b*d*tanh(c + d*x) - 2*b*d), Eq(a, -b)), (d*x*tanh(c + d*x)/(2*b*d*tanh(c + d*x) + 2*b*d) + d*x/(2*b*d*tanh(c + d*x) + 2*b*d) + 1/(2*b*d*tanh(c + d*x) + 2*b*d), Eq(a, b)), (x/(a + b*coth(c)), Eq(d, 0)), ((x - log(tanh(c + d*x) + 1)/d)/b, Eq(a, 0)), (a*d*x/(a**2*d - b**2*d) - b*d*x/(a**2*d - b**2*d) + b*log(tanh(c + d*x) + 1)/(a**2*d - b**2*d) - b*log(tanh(c + d*x) + b/a)/(a**2*d - b**2*d), True))","A",0
82,0,0,0,0.000000," ","integrate(1/(a+b*coth(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x}{\coth^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{x - \frac{\tanh{\left(c + d x \right)}}{d}}{b^{2}} & \text{for}\: a = 0 \\\frac{d x \tanh^{2}{\left(c + d x \right)}}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} - 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} - \frac{2 d x \tanh{\left(c + d x \right)}}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} - 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} + \frac{d x}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} - 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 \tanh{\left(c + d x \right)}}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} - 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} - \frac{2}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} - 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = - b \\\frac{d x \tanh^{2}{\left(c + d x \right)}}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} + 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} + \frac{2 d x \tanh{\left(c + d x \right)}}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} + 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} + \frac{d x}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} + 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} + \frac{3 \tanh{\left(c + d x \right)}}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} + 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} + \frac{2}{4 b^{2} d \tanh^{2}{\left(c + d x \right)} + 8 b^{2} d \tanh{\left(c + d x \right)} + 4 b^{2} d} & \text{for}\: a = b \\\frac{\int \left(- \frac{2 e^{2 c} e^{2 d x}}{e^{4 c} e^{4 d x} \coth^{2}{\left(c + d x \right)} - 2 e^{4 c} e^{4 d x} \coth{\left(c + d x \right)} + e^{4 c} e^{4 d x} - 2 e^{2 c} e^{2 d x} \coth^{2}{\left(c + d x \right)} + 2 e^{2 c} e^{2 d x} + \coth^{2}{\left(c + d x \right)} + 2 \coth{\left(c + d x \right)} + 1}\right)\, dx + \int \frac{e^{4 c} e^{4 d x}}{e^{4 c} e^{4 d x} \coth^{2}{\left(c + d x \right)} - 2 e^{4 c} e^{4 d x} \coth{\left(c + d x \right)} + e^{4 c} e^{4 d x} - 2 e^{2 c} e^{2 d x} \coth^{2}{\left(c + d x \right)} + 2 e^{2 c} e^{2 d x} + \coth^{2}{\left(c + d x \right)} + 2 \coth{\left(c + d x \right)} + 1}\, dx + \int \frac{1}{e^{4 c} e^{4 d x} \coth^{2}{\left(c + d x \right)} - 2 e^{4 c} e^{4 d x} \coth{\left(c + d x \right)} + e^{4 c} e^{4 d x} - 2 e^{2 c} e^{2 d x} \coth^{2}{\left(c + d x \right)} + 2 e^{2 c} e^{2 d x} + \coth^{2}{\left(c + d x \right)} + 2 \coth{\left(c + d x \right)} + 1}\, dx}{b^{2}} & \text{for}\: a = \frac{- b e^{2 c} e^{2 d x} - b}{e^{2 c} e^{2 d x} - 1} \\\frac{x}{\left(a + b \coth{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{a^{4} d x \tanh{\left(c + d x \right)}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} - \frac{2 a^{3} b d x \tanh{\left(c + d x \right)}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} + \frac{a^{3} b d x}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} + \frac{2 a^{3} b \log{\left(\tanh{\left(c + d x \right)} + 1 \right)} \tanh{\left(c + d x \right)}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} - \frac{2 a^{3} b \log{\left(\tanh{\left(c + d x \right)} + \frac{b}{a} \right)} \tanh{\left(c + d x \right)}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} + \frac{a^{2} b^{2} d x \tanh{\left(c + d x \right)}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} - \frac{2 a^{2} b^{2} d x}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} + \frac{2 a^{2} b^{2} \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} - \frac{2 a^{2} b^{2} \log{\left(\tanh{\left(c + d x \right)} + \frac{b}{a} \right)}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} - \frac{a^{2} b^{2}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} + \frac{a b^{3} d x}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} + \frac{b^{4}}{a^{6} d \tanh{\left(c + d x \right)} + a^{5} b d - 2 a^{4} b^{2} d \tanh{\left(c + d x \right)} - 2 a^{3} b^{3} d + a^{2} b^{4} d \tanh{\left(c + d x \right)} + a b^{5} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x/coth(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((x - tanh(c + d*x)/d)/b**2, Eq(a, 0)), (d*x*tanh(c + d*x)**2/(4*b**2*d*tanh(c + d*x)**2 - 8*b**2*d*tanh(c + d*x) + 4*b**2*d) - 2*d*x*tanh(c + d*x)/(4*b**2*d*tanh(c + d*x)**2 - 8*b**2*d*tanh(c + d*x) + 4*b**2*d) + d*x/(4*b**2*d*tanh(c + d*x)**2 - 8*b**2*d*tanh(c + d*x) + 4*b**2*d) + 3*tanh(c + d*x)/(4*b**2*d*tanh(c + d*x)**2 - 8*b**2*d*tanh(c + d*x) + 4*b**2*d) - 2/(4*b**2*d*tanh(c + d*x)**2 - 8*b**2*d*tanh(c + d*x) + 4*b**2*d), Eq(a, -b)), (d*x*tanh(c + d*x)**2/(4*b**2*d*tanh(c + d*x)**2 + 8*b**2*d*tanh(c + d*x) + 4*b**2*d) + 2*d*x*tanh(c + d*x)/(4*b**2*d*tanh(c + d*x)**2 + 8*b**2*d*tanh(c + d*x) + 4*b**2*d) + d*x/(4*b**2*d*tanh(c + d*x)**2 + 8*b**2*d*tanh(c + d*x) + 4*b**2*d) + 3*tanh(c + d*x)/(4*b**2*d*tanh(c + d*x)**2 + 8*b**2*d*tanh(c + d*x) + 4*b**2*d) + 2/(4*b**2*d*tanh(c + d*x)**2 + 8*b**2*d*tanh(c + d*x) + 4*b**2*d), Eq(a, b)), ((Integral(-2*exp(2*c)*exp(2*d*x)/(exp(4*c)*exp(4*d*x)*coth(c + d*x)**2 - 2*exp(4*c)*exp(4*d*x)*coth(c + d*x) + exp(4*c)*exp(4*d*x) - 2*exp(2*c)*exp(2*d*x)*coth(c + d*x)**2 + 2*exp(2*c)*exp(2*d*x) + coth(c + d*x)**2 + 2*coth(c + d*x) + 1), x) + Integral(exp(4*c)*exp(4*d*x)/(exp(4*c)*exp(4*d*x)*coth(c + d*x)**2 - 2*exp(4*c)*exp(4*d*x)*coth(c + d*x) + exp(4*c)*exp(4*d*x) - 2*exp(2*c)*exp(2*d*x)*coth(c + d*x)**2 + 2*exp(2*c)*exp(2*d*x) + coth(c + d*x)**2 + 2*coth(c + d*x) + 1), x) + Integral(1/(exp(4*c)*exp(4*d*x)*coth(c + d*x)**2 - 2*exp(4*c)*exp(4*d*x)*coth(c + d*x) + exp(4*c)*exp(4*d*x) - 2*exp(2*c)*exp(2*d*x)*coth(c + d*x)**2 + 2*exp(2*c)*exp(2*d*x) + coth(c + d*x)**2 + 2*coth(c + d*x) + 1), x))/b**2, Eq(a, (-b*exp(2*c)*exp(2*d*x) - b)/(exp(2*c)*exp(2*d*x) - 1))), (x/(a + b*coth(c))**2, Eq(d, 0)), (a**4*d*x*tanh(c + d*x)/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) - 2*a**3*b*d*x*tanh(c + d*x)/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) + a**3*b*d*x/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) + 2*a**3*b*log(tanh(c + d*x) + 1)*tanh(c + d*x)/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) - 2*a**3*b*log(tanh(c + d*x) + b/a)*tanh(c + d*x)/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) + a**2*b**2*d*x*tanh(c + d*x)/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) - 2*a**2*b**2*d*x/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) + 2*a**2*b**2*log(tanh(c + d*x) + 1)/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) - 2*a**2*b**2*log(tanh(c + d*x) + b/a)/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) - a**2*b**2/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) + a*b**3*d*x/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d) + b**4/(a**6*d*tanh(c + d*x) + a**5*b*d - 2*a**4*b**2*d*tanh(c + d*x) - 2*a**3*b**3*d + a**2*b**4*d*tanh(c + d*x) + a*b**5*d), True))","F",0
83,-1,0,0,0.000000," ","integrate(1/(a+b*coth(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(1/(a+b*coth(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,1,42,0,0.811366," ","integrate(1/(4+6*coth(d*x+c)),x)","\begin{cases} \frac{x}{10} - \frac{3 \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{10 d} + \frac{3 \log{\left(\tanh{\left(c + d x \right)} + \frac{3}{2} \right)}}{10 d} & \text{for}\: d \neq 0 \\\frac{x}{6 \coth{\left(c \right)} + 4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x/10 - 3*log(tanh(c + d*x) + 1)/(10*d) + 3*log(tanh(c + d*x) + 3/2)/(10*d), Ne(d, 0)), (x/(6*coth(c) + 4), True))","A",0
86,1,42,0,0.805080," ","integrate(1/(4-6*coth(d*x+c)),x)","\begin{cases} - \frac{x}{2} - \frac{3 \log{\left(\tanh{\left(c + d x \right)} - \frac{3}{2} \right)}}{10 d} + \frac{3 \log{\left(\tanh{\left(c + d x \right)} + 1 \right)}}{10 d} & \text{for}\: d \neq 0 \\\frac{x}{4 - 6 \coth{\left(c \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x/2 - 3*log(tanh(c + d*x) - 3/2)/(10*d) + 3*log(tanh(c + d*x) + 1)/(10*d), Ne(d, 0)), (x/(4 - 6*coth(c)), True))","A",0
87,0,0,0,0.000000," ","integrate((a+b*coth(d*x+c))**(1/2),x)","\int \sqrt{a + b \coth{\left(c + d x \right)}}\, dx"," ",0,"Integral(sqrt(a + b*coth(c + d*x)), x)","F",0
88,0,0,0,0.000000," ","integrate(1/(a+b*coth(d*x+c))**(1/2),x)","\int \frac{1}{\sqrt{a + b \coth{\left(c + d x \right)}}}\, dx"," ",0,"Integral(1/sqrt(a + b*coth(c + d*x)), x)","F",0
89,0,0,0,0.000000," ","integrate(sinh(x)**4/(1+coth(x)),x)","\int \frac{\sinh^{4}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sinh(x)**4/(coth(x) + 1), x)","F",0
90,0,0,0,0.000000," ","integrate(sinh(x)**3/(1+coth(x)),x)","\int \frac{\sinh^{3}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sinh(x)**3/(coth(x) + 1), x)","F",0
91,0,0,0,0.000000," ","integrate(sinh(x)**2/(1+coth(x)),x)","\int \frac{\sinh^{2}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sinh(x)**2/(coth(x) + 1), x)","F",0
92,0,0,0,0.000000," ","integrate(sinh(x)/(1+coth(x)),x)","\int \frac{\sinh{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sinh(x)/(coth(x) + 1), x)","F",0
93,0,0,0,0.000000," ","integrate(csch(x)/(1+coth(x)),x)","\int \frac{\operatorname{csch}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(csch(x)/(coth(x) + 1), x)","F",0
94,0,0,0,0.000000," ","integrate(csch(x)**2/(1+coth(x)),x)","\int \frac{\operatorname{csch}^{2}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(csch(x)**2/(coth(x) + 1), x)","F",0
95,0,0,0,0.000000," ","integrate(csch(x)**3/(1+coth(x)),x)","\int \frac{\operatorname{csch}^{3}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(csch(x)**3/(coth(x) + 1), x)","F",0
96,0,0,0,0.000000," ","integrate(csch(x)**4/(1+coth(x)),x)","\int \frac{\operatorname{csch}^{4}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(csch(x)**4/(coth(x) + 1), x)","F",0
97,0,0,0,0.000000," ","integrate(sinh(x)**4/(a+b*coth(x)),x)","\int \frac{\sinh^{4}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(sinh(x)**4/(a + b*coth(x)), x)","F",0
98,0,0,0,0.000000," ","integrate(sinh(x)**3/(a+b*coth(x)),x)","\int \frac{\sinh^{3}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(sinh(x)**3/(a + b*coth(x)), x)","F",0
99,0,0,0,0.000000," ","integrate(sinh(x)**2/(a+b*coth(x)),x)","\int \frac{\sinh^{2}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(sinh(x)**2/(a + b*coth(x)), x)","F",0
100,0,0,0,0.000000," ","integrate(sinh(x)/(a+b*coth(x)),x)","\int \frac{\sinh{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(sinh(x)/(a + b*coth(x)), x)","F",0
101,0,0,0,0.000000," ","integrate(csch(x)/(a+b*coth(x)),x)","\int \frac{\operatorname{csch}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(csch(x)/(a + b*coth(x)), x)","F",0
102,0,0,0,0.000000," ","integrate(csch(x)**2/(a+b*coth(x)),x)","\int \frac{\operatorname{csch}^{2}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(csch(x)**2/(a + b*coth(x)), x)","F",0
103,0,0,0,0.000000," ","integrate(csch(x)**3/(a+b*coth(x)),x)","\int \frac{\operatorname{csch}^{3}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(csch(x)**3/(a + b*coth(x)), x)","F",0
104,0,0,0,0.000000," ","integrate(csch(x)**4/(a+b*coth(x)),x)","\int \frac{\operatorname{csch}^{4}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(csch(x)**4/(a + b*coth(x)), x)","F",0
105,0,0,0,0.000000," ","integrate(cosh(x)**4/(1+coth(x)),x)","\int \frac{\cosh^{4}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(cosh(x)**4/(coth(x) + 1), x)","F",0
106,0,0,0,0.000000," ","integrate(cosh(x)**3/(1+coth(x)),x)","\int \frac{\cosh^{3}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(cosh(x)**3/(coth(x) + 1), x)","F",0
107,0,0,0,0.000000," ","integrate(cosh(x)**2/(1+coth(x)),x)","\int \frac{\cosh^{2}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(cosh(x)**2/(coth(x) + 1), x)","F",0
108,0,0,0,0.000000," ","integrate(cosh(x)/(1+coth(x)),x)","\int \frac{\cosh{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(cosh(x)/(coth(x) + 1), x)","F",0
109,0,0,0,0.000000," ","integrate(sech(x)/(1+coth(x)),x)","\int \frac{\operatorname{sech}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sech(x)/(coth(x) + 1), x)","F",0
110,0,0,0,0.000000," ","integrate(sech(x)**2/(1+coth(x)),x)","\int \frac{\operatorname{sech}^{2}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sech(x)**2/(coth(x) + 1), x)","F",0
111,0,0,0,0.000000," ","integrate(sech(x)**3/(1+coth(x)),x)","\int \frac{\operatorname{sech}^{3}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sech(x)**3/(coth(x) + 1), x)","F",0
112,0,0,0,0.000000," ","integrate(sech(x)**4/(1+coth(x)),x)","\int \frac{\operatorname{sech}^{4}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(sech(x)**4/(coth(x) + 1), x)","F",0
113,0,0,0,0.000000," ","integrate(sech(x)**2*(1+coth(x))**(1/2),x)","\int \sqrt{\coth{\left(x \right)} + 1} \operatorname{sech}^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(coth(x) + 1)*sech(x)**2, x)","F",0
114,0,0,0,0.000000," ","integrate(cosh(x)**4/(a+b*coth(x)),x)","\int \frac{\cosh^{4}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(cosh(x)**4/(a + b*coth(x)), x)","F",0
115,0,0,0,0.000000," ","integrate(cosh(x)**3/(a+b*coth(x)),x)","\int \frac{\cosh^{3}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(cosh(x)**3/(a + b*coth(x)), x)","F",0
116,0,0,0,0.000000," ","integrate(cosh(x)**2/(a+b*coth(x)),x)","\int \frac{\cosh^{2}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(cosh(x)**2/(a + b*coth(x)), x)","F",0
117,0,0,0,0.000000," ","integrate(cosh(x)/(a+b*coth(x)),x)","\int \frac{\cosh{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(cosh(x)/(a + b*coth(x)), x)","F",0
118,0,0,0,0.000000," ","integrate(sech(x)/(a+b*coth(x)),x)","\int \frac{\operatorname{sech}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(sech(x)/(a + b*coth(x)), x)","F",0
119,0,0,0,0.000000," ","integrate(sech(x)**2/(a+b*coth(x)),x)","\int \frac{\operatorname{sech}^{2}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(sech(x)**2/(a + b*coth(x)), x)","F",0
120,0,0,0,0.000000," ","integrate(sech(x)**3/(a+b*coth(x)),x)","\int \frac{\operatorname{sech}^{3}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(sech(x)**3/(a + b*coth(x)), x)","F",0
121,0,0,0,0.000000," ","integrate(sech(x)**4/(a+b*coth(x)),x)","\int \frac{\operatorname{sech}^{4}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(sech(x)**4/(a + b*coth(x)), x)","F",0
122,0,0,0,0.000000," ","integrate(sech(x)/(I+2*coth(x)),x)","\int \frac{\operatorname{sech}{\left(x \right)}}{2 \coth{\left(x \right)} + i}\, dx"," ",0,"Integral(sech(x)/(2*coth(x) + I), x)","F",0
123,0,0,0,0.000000," ","integrate(tanh(x)**4/(1+coth(x)),x)","\int \frac{\tanh^{4}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(tanh(x)**4/(coth(x) + 1), x)","F",0
124,0,0,0,0.000000," ","integrate(tanh(x)**3/(1+coth(x)),x)","\int \frac{\tanh^{3}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(tanh(x)**3/(coth(x) + 1), x)","F",0
125,0,0,0,0.000000," ","integrate(tanh(x)**2/(1+coth(x)),x)","\int \frac{\tanh^{2}{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(tanh(x)**2/(coth(x) + 1), x)","F",0
126,0,0,0,0.000000," ","integrate(tanh(x)/(1+coth(x)),x)","\int \frac{\tanh{\left(x \right)}}{\coth{\left(x \right)} + 1}\, dx"," ",0,"Integral(tanh(x)/(coth(x) + 1), x)","F",0
127,1,27,0,0.445438," ","integrate(1/(1+coth(x)),x)","\frac{x \tanh{\left(x \right)}}{2 \tanh{\left(x \right)} + 2} + \frac{x}{2 \tanh{\left(x \right)} + 2} + \frac{1}{2 \tanh{\left(x \right)} + 2}"," ",0,"x*tanh(x)/(2*tanh(x) + 2) + x/(2*tanh(x) + 2) + 1/(2*tanh(x) + 2)","B",0
128,1,27,0,0.479257," ","integrate(coth(x)/(1+coth(x)),x)","\frac{x \tanh{\left(x \right)}}{2 \tanh{\left(x \right)} + 2} + \frac{x}{2 \tanh{\left(x \right)} + 2} - \frac{1}{2 \tanh{\left(x \right)} + 2}"," ",0,"x*tanh(x)/(2*tanh(x) + 2) + x/(2*tanh(x) + 2) - 1/(2*tanh(x) + 2)","B",0
129,1,92,0,0.620942," ","integrate(coth(x)**2/(1+coth(x)),x)","\frac{x \tanh{\left(x \right)}}{2 \tanh{\left(x \right)} + 2} + \frac{x}{2 \tanh{\left(x \right)} + 2} - \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh{\left(x \right)}}{2 \tanh{\left(x \right)} + 2} - \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)}}{2 \tanh{\left(x \right)} + 2} + \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{2 \tanh{\left(x \right)} + 2} + \frac{2 \log{\left(\tanh{\left(x \right)} \right)}}{2 \tanh{\left(x \right)} + 2} + \frac{1}{2 \tanh{\left(x \right)} + 2}"," ",0,"x*tanh(x)/(2*tanh(x) + 2) + x/(2*tanh(x) + 2) - 2*log(tanh(x) + 1)*tanh(x)/(2*tanh(x) + 2) - 2*log(tanh(x) + 1)/(2*tanh(x) + 2) + 2*log(tanh(x))*tanh(x)/(2*tanh(x) + 2) + 2*log(tanh(x))/(2*tanh(x) + 2) + 1/(2*tanh(x) + 2)","B",0
130,1,160,0,0.933976," ","integrate(coth(x)**3/(1+coth(x)),x)","\frac{x \tanh^{2}{\left(x \right)}}{2 \tanh^{2}{\left(x \right)} + 2 \tanh{\left(x \right)}} + \frac{x \tanh{\left(x \right)}}{2 \tanh^{2}{\left(x \right)} + 2 \tanh{\left(x \right)}} + \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{2}{\left(x \right)}}{2 \tanh^{2}{\left(x \right)} + 2 \tanh{\left(x \right)}} + \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh{\left(x \right)}}{2 \tanh^{2}{\left(x \right)} + 2 \tanh{\left(x \right)}} - \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{2 \tanh^{2}{\left(x \right)} + 2 \tanh{\left(x \right)}} - \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{2 \tanh^{2}{\left(x \right)} + 2 \tanh{\left(x \right)}} - \frac{3 \tanh{\left(x \right)}}{2 \tanh^{2}{\left(x \right)} + 2 \tanh{\left(x \right)}} - \frac{2}{2 \tanh^{2}{\left(x \right)} + 2 \tanh{\left(x \right)}}"," ",0,"x*tanh(x)**2/(2*tanh(x)**2 + 2*tanh(x)) + x*tanh(x)/(2*tanh(x)**2 + 2*tanh(x)) + 2*log(tanh(x) + 1)*tanh(x)**2/(2*tanh(x)**2 + 2*tanh(x)) + 2*log(tanh(x) + 1)*tanh(x)/(2*tanh(x)**2 + 2*tanh(x)) - 2*log(tanh(x))*tanh(x)**2/(2*tanh(x)**2 + 2*tanh(x)) - 2*log(tanh(x))*tanh(x)/(2*tanh(x)**2 + 2*tanh(x)) - 3*tanh(x)/(2*tanh(x)**2 + 2*tanh(x)) - 2/(2*tanh(x)**2 + 2*tanh(x))","B",0
131,1,197,0,1.183097," ","integrate(coth(x)**4/(1+coth(x)),x)","\frac{x \tanh^{3}{\left(x \right)}}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}} + \frac{x \tanh^{2}{\left(x \right)}}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}} - \frac{4 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{3}{\left(x \right)}}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}} - \frac{4 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{2}{\left(x \right)}}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}} + \frac{4 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{3}{\left(x \right)}}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}} + \frac{4 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}} + \frac{3 \tanh^{2}{\left(x \right)}}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}} + \frac{\tanh{\left(x \right)}}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}} - \frac{1}{2 \tanh^{3}{\left(x \right)} + 2 \tanh^{2}{\left(x \right)}}"," ",0,"x*tanh(x)**3/(2*tanh(x)**3 + 2*tanh(x)**2) + x*tanh(x)**2/(2*tanh(x)**3 + 2*tanh(x)**2) - 4*log(tanh(x) + 1)*tanh(x)**3/(2*tanh(x)**3 + 2*tanh(x)**2) - 4*log(tanh(x) + 1)*tanh(x)**2/(2*tanh(x)**3 + 2*tanh(x)**2) + 4*log(tanh(x))*tanh(x)**3/(2*tanh(x)**3 + 2*tanh(x)**2) + 4*log(tanh(x))*tanh(x)**2/(2*tanh(x)**3 + 2*tanh(x)**2) + 3*tanh(x)**2/(2*tanh(x)**3 + 2*tanh(x)**2) + tanh(x)/(2*tanh(x)**3 + 2*tanh(x)**2) - 1/(2*tanh(x)**3 + 2*tanh(x)**2)","B",0
132,0,0,0,0.000000," ","integrate(coth(x)*(1+coth(x))**(3/2),x)","\int \left(\coth{\left(x \right)} + 1\right)^{\frac{3}{2}} \coth{\left(x \right)}\, dx"," ",0,"Integral((coth(x) + 1)**(3/2)*coth(x), x)","F",0
133,0,0,0,0.000000," ","integrate(coth(x)*(1+coth(x))**(1/2),x)","\int \sqrt{\coth{\left(x \right)} + 1} \coth{\left(x \right)}\, dx"," ",0,"Integral(sqrt(coth(x) + 1)*coth(x), x)","F",0
134,0,0,0,0.000000," ","integrate(coth(x)/(1+coth(x))**(1/2),x)","\int \frac{\coth{\left(x \right)}}{\sqrt{\coth{\left(x \right)} + 1}}\, dx"," ",0,"Integral(coth(x)/sqrt(coth(x) + 1), x)","F",0
135,0,0,0,0.000000," ","integrate(coth(x)/(1+coth(x))**(3/2),x)","\int \frac{\coth{\left(x \right)}}{\left(\coth{\left(x \right)} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(coth(x)/(coth(x) + 1)**(3/2), x)","F",0
136,0,0,0,0.000000," ","integrate(coth(x)**2*(1+coth(x))**(3/2),x)","\int \left(\coth{\left(x \right)} + 1\right)^{\frac{3}{2}} \coth^{2}{\left(x \right)}\, dx"," ",0,"Integral((coth(x) + 1)**(3/2)*coth(x)**2, x)","F",0
137,0,0,0,0.000000," ","integrate(coth(x)**2*(1+coth(x))**(1/2),x)","\int \sqrt{\coth{\left(x \right)} + 1} \coth^{2}{\left(x \right)}\, dx"," ",0,"Integral(sqrt(coth(x) + 1)*coth(x)**2, x)","F",0
138,0,0,0,0.000000," ","integrate(coth(x)**2/(1+coth(x))**(1/2),x)","\int \frac{\coth^{2}{\left(x \right)}}{\sqrt{\coth{\left(x \right)} + 1}}\, dx"," ",0,"Integral(coth(x)**2/sqrt(coth(x) + 1), x)","F",0
139,0,0,0,0.000000," ","integrate(coth(x)**2/(1+coth(x))**(3/2),x)","\int \frac{\coth^{2}{\left(x \right)}}{\left(\coth{\left(x \right)} + 1\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(coth(x)**2/(coth(x) + 1)**(3/2), x)","F",0
140,0,0,0,0.000000," ","integrate(tanh(x)**4/(a+b*coth(x)),x)","\int \frac{\tanh^{4}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(tanh(x)**4/(a + b*coth(x)), x)","F",0
141,0,0,0,0.000000," ","integrate(tanh(x)**3/(a+b*coth(x)),x)","\int \frac{\tanh^{3}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(tanh(x)**3/(a + b*coth(x)), x)","F",0
142,0,0,0,0.000000," ","integrate(tanh(x)**2/(a+b*coth(x)),x)","\int \frac{\tanh^{2}{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(tanh(x)**2/(a + b*coth(x)), x)","F",0
143,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(x)),x)","\int \frac{\tanh{\left(x \right)}}{a + b \coth{\left(x \right)}}\, dx"," ",0,"Integral(tanh(x)/(a + b*coth(x)), x)","F",0
144,1,148,0,0.910939," ","integrate(1/(a+b*coth(x)),x)","\begin{cases} \tilde{\infty} \left(x - \log{\left(\tanh{\left(x \right)} + 1 \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \\- \frac{x \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} - 2 b} + \frac{x}{2 b \tanh{\left(x \right)} - 2 b} - \frac{1}{2 b \tanh{\left(x \right)} - 2 b} & \text{for}\: a = - b \\\frac{x \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} + 2 b} + \frac{x}{2 b \tanh{\left(x \right)} + 2 b} + \frac{1}{2 b \tanh{\left(x \right)} + 2 b} & \text{for}\: a = b \\\frac{x - \log{\left(\tanh{\left(x \right)} + 1 \right)}}{b} & \text{for}\: a = 0 \\\frac{a x}{a^{2} - b^{2}} - \frac{b x}{a^{2} - b^{2}} + \frac{b \log{\left(\tanh{\left(x \right)} + 1 \right)}}{a^{2} - b^{2}} - \frac{b \log{\left(\tanh{\left(x \right)} + \frac{b}{a} \right)}}{a^{2} - b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(x - log(tanh(x) + 1)), Eq(a, 0) & Eq(b, 0)), (-x*tanh(x)/(2*b*tanh(x) - 2*b) + x/(2*b*tanh(x) - 2*b) - 1/(2*b*tanh(x) - 2*b), Eq(a, -b)), (x*tanh(x)/(2*b*tanh(x) + 2*b) + x/(2*b*tanh(x) + 2*b) + 1/(2*b*tanh(x) + 2*b), Eq(a, b)), ((x - log(tanh(x) + 1))/b, Eq(a, 0)), (a*x/(a**2 - b**2) - b*x/(a**2 - b**2) + b*log(tanh(x) + 1)/(a**2 - b**2) - b*log(tanh(x) + b/a)/(a**2 - b**2), True))","A",0
145,1,134,0,0.926521," ","integrate(coth(x)/(a+b*coth(x)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\\frac{x \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} - 2 b} - \frac{x}{2 b \tanh{\left(x \right)} - 2 b} - \frac{1}{2 b \tanh{\left(x \right)} - 2 b} & \text{for}\: a = - b \\\frac{x \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} + 2 b} + \frac{x}{2 b \tanh{\left(x \right)} + 2 b} - \frac{1}{2 b \tanh{\left(x \right)} + 2 b} & \text{for}\: a = b \\\frac{x}{b} & \text{for}\: a = 0 \\\frac{a x}{a^{2} - b^{2}} - \frac{a \log{\left(\tanh{\left(x \right)} + 1 \right)}}{a^{2} - b^{2}} + \frac{a \log{\left(\tanh{\left(x \right)} + \frac{b}{a} \right)}}{a^{2} - b^{2}} - \frac{b x}{a^{2} - b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (x*tanh(x)/(2*b*tanh(x) - 2*b) - x/(2*b*tanh(x) - 2*b) - 1/(2*b*tanh(x) - 2*b), Eq(a, -b)), (x*tanh(x)/(2*b*tanh(x) + 2*b) + x/(2*b*tanh(x) + 2*b) - 1/(2*b*tanh(x) + 2*b), Eq(a, b)), (x/b, Eq(a, 0)), (a*x/(a**2 - b**2) - a*log(tanh(x) + 1)/(a**2 - b**2) + a*log(tanh(x) + b/a)/(a**2 - b**2) - b*x/(a**2 - b**2), True))","A",0
146,1,372,0,1.630180," ","integrate(coth(x)**2/(a+b*coth(x)),x)","\begin{cases} \tilde{\infty} \left(x - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{x - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)}}{b} & \text{for}\: a = 0 \\\frac{3 x \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} - 2 b} - \frac{3 x}{2 b \tanh{\left(x \right)} - 2 b} - \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} - 2 b} + \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)}}{2 b \tanh{\left(x \right)} - 2 b} + \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} - 2 b} - \frac{2 \log{\left(\tanh{\left(x \right)} \right)}}{2 b \tanh{\left(x \right)} - 2 b} - \frac{1}{2 b \tanh{\left(x \right)} - 2 b} & \text{for}\: a = - b \\\frac{x \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} + 2 b} + \frac{x}{2 b \tanh{\left(x \right)} + 2 b} - \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} + 2 b} - \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)}}{2 b \tanh{\left(x \right)} + 2 b} + \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{2 b \tanh{\left(x \right)} + 2 b} + \frac{2 \log{\left(\tanh{\left(x \right)} \right)}}{2 b \tanh{\left(x \right)} + 2 b} + \frac{1}{2 b \tanh{\left(x \right)} + 2 b} & \text{for}\: a = b \\\frac{x - \frac{1}{\tanh{\left(x \right)}}}{a} & \text{for}\: b = 0 \\- \frac{a^{2} \log{\left(\tanh{\left(x \right)} + \frac{b}{a} \right)}}{a^{2} b - b^{3}} + \frac{a^{2} \log{\left(\tanh{\left(x \right)} \right)}}{a^{2} b - b^{3}} + \frac{a b x}{a^{2} b - b^{3}} - \frac{b^{2} x}{a^{2} b - b^{3}} + \frac{b^{2} \log{\left(\tanh{\left(x \right)} + 1 \right)}}{a^{2} b - b^{3}} - \frac{b^{2} \log{\left(\tanh{\left(x \right)} \right)}}{a^{2} b - b^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(x - log(tanh(x) + 1) + log(tanh(x))), Eq(a, 0) & Eq(b, 0)), ((x - log(tanh(x) + 1) + log(tanh(x)))/b, Eq(a, 0)), (3*x*tanh(x)/(2*b*tanh(x) - 2*b) - 3*x/(2*b*tanh(x) - 2*b) - 2*log(tanh(x) + 1)*tanh(x)/(2*b*tanh(x) - 2*b) + 2*log(tanh(x) + 1)/(2*b*tanh(x) - 2*b) + 2*log(tanh(x))*tanh(x)/(2*b*tanh(x) - 2*b) - 2*log(tanh(x))/(2*b*tanh(x) - 2*b) - 1/(2*b*tanh(x) - 2*b), Eq(a, -b)), (x*tanh(x)/(2*b*tanh(x) + 2*b) + x/(2*b*tanh(x) + 2*b) - 2*log(tanh(x) + 1)*tanh(x)/(2*b*tanh(x) + 2*b) - 2*log(tanh(x) + 1)/(2*b*tanh(x) + 2*b) + 2*log(tanh(x))*tanh(x)/(2*b*tanh(x) + 2*b) + 2*log(tanh(x))/(2*b*tanh(x) + 2*b) + 1/(2*b*tanh(x) + 2*b), Eq(a, b)), ((x - 1/tanh(x))/a, Eq(b, 0)), (-a**2*log(tanh(x) + b/a)/(a**2*b - b**3) + a**2*log(tanh(x))/(a**2*b - b**3) + a*b*x/(a**2*b - b**3) - b**2*x/(a**2*b - b**3) + b**2*log(tanh(x) + 1)/(a**2*b - b**3) - b**2*log(tanh(x))/(a**2*b - b**3), True))","A",0
147,1,636,0,2.397712," ","integrate(coth(x)**3/(a+b*coth(x)),x)","\begin{cases} \tilde{\infty} \left(x - \frac{1}{\tanh{\left(x \right)}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{x - \frac{1}{\tanh{\left(x \right)}}}{b} & \text{for}\: a = 0 \\\frac{5 x \tanh^{2}{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} - 2 b \tanh{\left(x \right)}} - \frac{5 x \tanh{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} - 2 b \tanh{\left(x \right)}} - \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{2}{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} - 2 b \tanh{\left(x \right)}} + \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} - 2 b \tanh{\left(x \right)}} + \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} - 2 b \tanh{\left(x \right)}} - \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} - 2 b \tanh{\left(x \right)}} - \frac{3 \tanh{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} - 2 b \tanh{\left(x \right)}} + \frac{2}{2 b \tanh^{2}{\left(x \right)} - 2 b \tanh{\left(x \right)}} & \text{for}\: a = - b \\\frac{x \tanh^{2}{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} + 2 b \tanh{\left(x \right)}} + \frac{x \tanh{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} + 2 b \tanh{\left(x \right)}} + \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{2}{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} + 2 b \tanh{\left(x \right)}} + \frac{2 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} + 2 b \tanh{\left(x \right)}} - \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} + 2 b \tanh{\left(x \right)}} - \frac{2 \log{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} + 2 b \tanh{\left(x \right)}} - \frac{3 \tanh{\left(x \right)}}{2 b \tanh^{2}{\left(x \right)} + 2 b \tanh{\left(x \right)}} - \frac{2}{2 b \tanh^{2}{\left(x \right)} + 2 b \tanh{\left(x \right)}} & \text{for}\: a = b \\\frac{x - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)} - \frac{1}{2 \tanh^{2}{\left(x \right)}}}{a} & \text{for}\: b = 0 \\\frac{a^{3} \log{\left(\tanh{\left(x \right)} + \frac{b}{a} \right)} \tanh{\left(x \right)}}{a^{2} b^{2} \tanh{\left(x \right)} - b^{4} \tanh{\left(x \right)}} - \frac{a^{3} \log{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{a^{2} b^{2} \tanh{\left(x \right)} - b^{4} \tanh{\left(x \right)}} - \frac{a^{2} b}{a^{2} b^{2} \tanh{\left(x \right)} - b^{4} \tanh{\left(x \right)}} + \frac{a b^{2} x \tanh{\left(x \right)}}{a^{2} b^{2} \tanh{\left(x \right)} - b^{4} \tanh{\left(x \right)}} - \frac{a b^{2} \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh{\left(x \right)}}{a^{2} b^{2} \tanh{\left(x \right)} - b^{4} \tanh{\left(x \right)}} + \frac{a b^{2} \log{\left(\tanh{\left(x \right)} \right)} \tanh{\left(x \right)}}{a^{2} b^{2} \tanh{\left(x \right)} - b^{4} \tanh{\left(x \right)}} - \frac{b^{3} x \tanh{\left(x \right)}}{a^{2} b^{2} \tanh{\left(x \right)} - b^{4} \tanh{\left(x \right)}} + \frac{b^{3}}{a^{2} b^{2} \tanh{\left(x \right)} - b^{4} \tanh{\left(x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(x - 1/tanh(x)), Eq(a, 0) & Eq(b, 0)), ((x - 1/tanh(x))/b, Eq(a, 0)), (5*x*tanh(x)**2/(2*b*tanh(x)**2 - 2*b*tanh(x)) - 5*x*tanh(x)/(2*b*tanh(x)**2 - 2*b*tanh(x)) - 2*log(tanh(x) + 1)*tanh(x)**2/(2*b*tanh(x)**2 - 2*b*tanh(x)) + 2*log(tanh(x) + 1)*tanh(x)/(2*b*tanh(x)**2 - 2*b*tanh(x)) + 2*log(tanh(x))*tanh(x)**2/(2*b*tanh(x)**2 - 2*b*tanh(x)) - 2*log(tanh(x))*tanh(x)/(2*b*tanh(x)**2 - 2*b*tanh(x)) - 3*tanh(x)/(2*b*tanh(x)**2 - 2*b*tanh(x)) + 2/(2*b*tanh(x)**2 - 2*b*tanh(x)), Eq(a, -b)), (x*tanh(x)**2/(2*b*tanh(x)**2 + 2*b*tanh(x)) + x*tanh(x)/(2*b*tanh(x)**2 + 2*b*tanh(x)) + 2*log(tanh(x) + 1)*tanh(x)**2/(2*b*tanh(x)**2 + 2*b*tanh(x)) + 2*log(tanh(x) + 1)*tanh(x)/(2*b*tanh(x)**2 + 2*b*tanh(x)) - 2*log(tanh(x))*tanh(x)**2/(2*b*tanh(x)**2 + 2*b*tanh(x)) - 2*log(tanh(x))*tanh(x)/(2*b*tanh(x)**2 + 2*b*tanh(x)) - 3*tanh(x)/(2*b*tanh(x)**2 + 2*b*tanh(x)) - 2/(2*b*tanh(x)**2 + 2*b*tanh(x)), Eq(a, b)), ((x - log(tanh(x) + 1) + log(tanh(x)) - 1/(2*tanh(x)**2))/a, Eq(b, 0)), (a**3*log(tanh(x) + b/a)*tanh(x)/(a**2*b**2*tanh(x) - b**4*tanh(x)) - a**3*log(tanh(x))*tanh(x)/(a**2*b**2*tanh(x) - b**4*tanh(x)) - a**2*b/(a**2*b**2*tanh(x) - b**4*tanh(x)) + a*b**2*x*tanh(x)/(a**2*b**2*tanh(x) - b**4*tanh(x)) - a*b**2*log(tanh(x) + 1)*tanh(x)/(a**2*b**2*tanh(x) - b**4*tanh(x)) + a*b**2*log(tanh(x))*tanh(x)/(a**2*b**2*tanh(x) - b**4*tanh(x)) - b**3*x*tanh(x)/(a**2*b**2*tanh(x) - b**4*tanh(x)) + b**3/(a**2*b**2*tanh(x) - b**4*tanh(x)), True))","A",0
148,1,882,0,3.398707," ","integrate(coth(x)**4/(a+b*coth(x)),x)","\begin{cases} \tilde{\infty} \left(x - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)} - \frac{1}{2 \tanh^{2}{\left(x \right)}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{x - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)} - \frac{1}{2 \tanh^{2}{\left(x \right)}}}{b} & \text{for}\: a = 0 \\\frac{7 x \tanh^{3}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} - \frac{7 x \tanh^{2}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} - \frac{4 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{3}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} + \frac{4 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{2}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} + \frac{4 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{3}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} - \frac{4 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} - \frac{3 \tanh^{2}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} + \frac{\tanh{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} + \frac{1}{2 b \tanh^{3}{\left(x \right)} - 2 b \tanh^{2}{\left(x \right)}} & \text{for}\: a = - b \\\frac{x \tanh^{3}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} + \frac{x \tanh^{2}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} - \frac{4 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{3}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} - \frac{4 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{2}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} + \frac{4 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{3}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} + \frac{4 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} + \frac{3 \tanh^{2}{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} + \frac{\tanh{\left(x \right)}}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} - \frac{1}{2 b \tanh^{3}{\left(x \right)} + 2 b \tanh^{2}{\left(x \right)}} & \text{for}\: a = b \\\frac{x - \frac{1}{\tanh{\left(x \right)}} - \frac{1}{3 \tanh^{3}{\left(x \right)}}}{a} & \text{for}\: b = 0 \\- \frac{2 a^{4} \log{\left(\tanh{\left(x \right)} + \frac{b}{a} \right)} \tanh^{2}{\left(x \right)}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} + \frac{2 a^{4} \log{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} + \frac{2 a^{3} b \tanh{\left(x \right)}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} - \frac{a^{2} b^{2}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} + \frac{2 a b^{3} x \tanh^{2}{\left(x \right)}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} - \frac{2 a b^{3} \tanh{\left(x \right)}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} - \frac{2 b^{4} x \tanh^{2}{\left(x \right)}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} + \frac{2 b^{4} \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{2}{\left(x \right)}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} - \frac{2 b^{4} \log{\left(\tanh{\left(x \right)} \right)} \tanh^{2}{\left(x \right)}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} + \frac{b^{4}}{2 a^{2} b^{3} \tanh^{2}{\left(x \right)} - 2 b^{5} \tanh^{2}{\left(x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(x - log(tanh(x) + 1) + log(tanh(x)) - 1/(2*tanh(x)**2)), Eq(a, 0) & Eq(b, 0)), ((x - log(tanh(x) + 1) + log(tanh(x)) - 1/(2*tanh(x)**2))/b, Eq(a, 0)), (7*x*tanh(x)**3/(2*b*tanh(x)**3 - 2*b*tanh(x)**2) - 7*x*tanh(x)**2/(2*b*tanh(x)**3 - 2*b*tanh(x)**2) - 4*log(tanh(x) + 1)*tanh(x)**3/(2*b*tanh(x)**3 - 2*b*tanh(x)**2) + 4*log(tanh(x) + 1)*tanh(x)**2/(2*b*tanh(x)**3 - 2*b*tanh(x)**2) + 4*log(tanh(x))*tanh(x)**3/(2*b*tanh(x)**3 - 2*b*tanh(x)**2) - 4*log(tanh(x))*tanh(x)**2/(2*b*tanh(x)**3 - 2*b*tanh(x)**2) - 3*tanh(x)**2/(2*b*tanh(x)**3 - 2*b*tanh(x)**2) + tanh(x)/(2*b*tanh(x)**3 - 2*b*tanh(x)**2) + 1/(2*b*tanh(x)**3 - 2*b*tanh(x)**2), Eq(a, -b)), (x*tanh(x)**3/(2*b*tanh(x)**3 + 2*b*tanh(x)**2) + x*tanh(x)**2/(2*b*tanh(x)**3 + 2*b*tanh(x)**2) - 4*log(tanh(x) + 1)*tanh(x)**3/(2*b*tanh(x)**3 + 2*b*tanh(x)**2) - 4*log(tanh(x) + 1)*tanh(x)**2/(2*b*tanh(x)**3 + 2*b*tanh(x)**2) + 4*log(tanh(x))*tanh(x)**3/(2*b*tanh(x)**3 + 2*b*tanh(x)**2) + 4*log(tanh(x))*tanh(x)**2/(2*b*tanh(x)**3 + 2*b*tanh(x)**2) + 3*tanh(x)**2/(2*b*tanh(x)**3 + 2*b*tanh(x)**2) + tanh(x)/(2*b*tanh(x)**3 + 2*b*tanh(x)**2) - 1/(2*b*tanh(x)**3 + 2*b*tanh(x)**2), Eq(a, b)), ((x - 1/tanh(x) - 1/(3*tanh(x)**3))/a, Eq(b, 0)), (-2*a**4*log(tanh(x) + b/a)*tanh(x)**2/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) + 2*a**4*log(tanh(x))*tanh(x)**2/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) + 2*a**3*b*tanh(x)/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) - a**2*b**2/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) + 2*a*b**3*x*tanh(x)**2/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) - 2*a*b**3*tanh(x)/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) - 2*b**4*x*tanh(x)**2/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) + 2*b**4*log(tanh(x) + 1)*tanh(x)**2/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) - 2*b**4*log(tanh(x))*tanh(x)**2/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2) + b**4/(2*a**2*b**3*tanh(x)**2 - 2*b**5*tanh(x)**2), True))","A",0
149,1,1013,0,5.019591," ","integrate(coth(x)**5/(a+b*coth(x)),x)","\begin{cases} \tilde{\infty} \left(x - \frac{1}{\tanh{\left(x \right)}} - \frac{1}{3 \tanh^{3}{\left(x \right)}}\right) & \text{for}\: a = 0 \wedge b = 0 \\\frac{x - \frac{1}{\tanh{\left(x \right)}} - \frac{1}{3 \tanh^{3}{\left(x \right)}}}{b} & \text{for}\: a = 0 \\\frac{27 x \tanh^{4}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} - \frac{27 x \tanh^{3}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} - \frac{12 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{4}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} + \frac{12 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{3}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} + \frac{12 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{4}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} - \frac{12 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{3}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} - \frac{15 \tanh^{3}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} + \frac{9 \tanh^{2}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} + \frac{\tanh{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} + \frac{2}{6 b \tanh^{4}{\left(x \right)} - 6 b \tanh^{3}{\left(x \right)}} & \text{for}\: a = - b \\\frac{3 x \tanh^{4}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} + \frac{3 x \tanh^{3}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} + \frac{12 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{4}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} + \frac{12 \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{3}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} - \frac{12 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{4}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} - \frac{12 \log{\left(\tanh{\left(x \right)} \right)} \tanh^{3}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} - \frac{15 \tanh^{3}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} - \frac{9 \tanh^{2}{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} + \frac{\tanh{\left(x \right)}}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} - \frac{2}{6 b \tanh^{4}{\left(x \right)} + 6 b \tanh^{3}{\left(x \right)}} & \text{for}\: a = b \\\frac{x - \log{\left(\tanh{\left(x \right)} + 1 \right)} + \log{\left(\tanh{\left(x \right)} \right)} - \frac{1}{2 \tanh^{2}{\left(x \right)}} - \frac{1}{4 \tanh^{4}{\left(x \right)}}}{a} & \text{for}\: b = 0 \\\frac{6 a^{5} \log{\left(\tanh{\left(x \right)} + \frac{b}{a} \right)} \tanh^{3}{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} - \frac{6 a^{5} \log{\left(\tanh{\left(x \right)} \right)} \tanh^{3}{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} - \frac{6 a^{4} b \tanh^{2}{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} + \frac{3 a^{3} b^{2} \tanh{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} - \frac{2 a^{2} b^{3}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} + \frac{6 a b^{4} x \tanh^{3}{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} - \frac{6 a b^{4} \log{\left(\tanh{\left(x \right)} + 1 \right)} \tanh^{3}{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} + \frac{6 a b^{4} \log{\left(\tanh{\left(x \right)} \right)} \tanh^{3}{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} - \frac{3 a b^{4} \tanh{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} - \frac{6 b^{5} x \tanh^{3}{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} + \frac{6 b^{5} \tanh^{2}{\left(x \right)}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} + \frac{2 b^{5}}{6 a^{2} b^{4} \tanh^{3}{\left(x \right)} - 6 b^{6} \tanh^{3}{\left(x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*(x - 1/tanh(x) - 1/(3*tanh(x)**3)), Eq(a, 0) & Eq(b, 0)), ((x - 1/tanh(x) - 1/(3*tanh(x)**3))/b, Eq(a, 0)), (27*x*tanh(x)**4/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) - 27*x*tanh(x)**3/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) - 12*log(tanh(x) + 1)*tanh(x)**4/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) + 12*log(tanh(x) + 1)*tanh(x)**3/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) + 12*log(tanh(x))*tanh(x)**4/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) - 12*log(tanh(x))*tanh(x)**3/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) - 15*tanh(x)**3/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) + 9*tanh(x)**2/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) + tanh(x)/(6*b*tanh(x)**4 - 6*b*tanh(x)**3) + 2/(6*b*tanh(x)**4 - 6*b*tanh(x)**3), Eq(a, -b)), (3*x*tanh(x)**4/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) + 3*x*tanh(x)**3/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) + 12*log(tanh(x) + 1)*tanh(x)**4/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) + 12*log(tanh(x) + 1)*tanh(x)**3/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) - 12*log(tanh(x))*tanh(x)**4/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) - 12*log(tanh(x))*tanh(x)**3/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) - 15*tanh(x)**3/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) - 9*tanh(x)**2/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) + tanh(x)/(6*b*tanh(x)**4 + 6*b*tanh(x)**3) - 2/(6*b*tanh(x)**4 + 6*b*tanh(x)**3), Eq(a, b)), ((x - log(tanh(x) + 1) + log(tanh(x)) - 1/(2*tanh(x)**2) - 1/(4*tanh(x)**4))/a, Eq(b, 0)), (6*a**5*log(tanh(x) + b/a)*tanh(x)**3/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) - 6*a**5*log(tanh(x))*tanh(x)**3/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) - 6*a**4*b*tanh(x)**2/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) + 3*a**3*b**2*tanh(x)/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) - 2*a**2*b**3/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) + 6*a*b**4*x*tanh(x)**3/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) - 6*a*b**4*log(tanh(x) + 1)*tanh(x)**3/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) + 6*a*b**4*log(tanh(x))*tanh(x)**3/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) - 3*a*b**4*tanh(x)/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) - 6*b**5*x*tanh(x)**3/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) + 6*b**5*tanh(x)**2/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3) + 2*b**5/(6*a**2*b**4*tanh(x)**3 - 6*b**6*tanh(x)**3), True))","A",0
150,0,0,0,0.000000," ","integrate(x*csch(x)**2/(a+b*coth(x))**2,x)","\int \frac{x \operatorname{csch}^{2}{\left(x \right)}}{\left(a + b \coth{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(x*csch(x)**2/(a + b*coth(x))**2, x)","F",0
151,0,0,0,0.000000," ","integrate(x**3*coth(a+2*ln(x)),x)","\int x^{3} \coth{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(x**3*coth(a + 2*log(x)), x)","F",0
152,0,0,0,0.000000," ","integrate(x**2*coth(a+2*ln(x)),x)","\int x^{2} \coth{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(x**2*coth(a + 2*log(x)), x)","F",0
153,0,0,0,0.000000," ","integrate(x*coth(a+2*ln(x)),x)","\int x \coth{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(x*coth(a + 2*log(x)), x)","F",0
154,0,0,0,0.000000," ","integrate(coth(a+2*ln(x)),x)","\int \coth{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(coth(a + 2*log(x)), x)","F",0
155,1,27,0,0.975702," ","integrate(coth(a+2*ln(x))/x,x)","\log{\left(x \right)} - \frac{\log{\left(\tanh{\left(a + 2 \log{\left(x \right)} \right)} + 1 \right)}}{2} + \frac{\log{\left(\tanh{\left(a + 2 \log{\left(x \right)} \right)} \right)}}{2}"," ",0,"log(x) - log(tanh(a + 2*log(x)) + 1)/2 + log(tanh(a + 2*log(x)))/2","B",0
156,0,0,0,0.000000," ","integrate(coth(a+2*ln(x))/x**2,x)","\int \frac{\coth{\left(a + 2 \log{\left(x \right)} \right)}}{x^{2}}\, dx"," ",0,"Integral(coth(a + 2*log(x))/x**2, x)","F",0
157,0,0,0,0.000000," ","integrate(coth(a+2*ln(x))/x**3,x)","\int \frac{\coth{\left(a + 2 \log{\left(x \right)} \right)}}{x^{3}}\, dx"," ",0,"Integral(coth(a + 2*log(x))/x**3, x)","F",0
158,0,0,0,0.000000," ","integrate(x**3*coth(a+2*ln(x))**2,x)","\int x^{3} \coth^{2}{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(x**3*coth(a + 2*log(x))**2, x)","F",0
159,0,0,0,0.000000," ","integrate(x**2*coth(a+2*ln(x))**2,x)","\int x^{2} \coth^{2}{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(x**2*coth(a + 2*log(x))**2, x)","F",0
160,0,0,0,0.000000," ","integrate(x*coth(a+2*ln(x))**2,x)","\int x \coth^{2}{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(x*coth(a + 2*log(x))**2, x)","F",0
161,0,0,0,0.000000," ","integrate(coth(a+2*ln(x))**2,x)","\int \coth^{2}{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(coth(a + 2*log(x))**2, x)","F",0
162,1,32,0,7.362065," ","integrate(coth(a+2*ln(x))**2/x,x)","\begin{cases} \tilde{\infty} \log{\left(x \right)} & \text{for}\: a = \log{\left(- \frac{1}{x^{2}} \right)} \vee a = \log{\left(\frac{1}{x^{2}} \right)} \\\log{\left(x \right)} - \frac{1}{2 \tanh{\left(a + 2 \log{\left(x \right)} \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(x), Eq(a, log(x**(-2))) | Eq(a, log(-1/x**2))), (log(x) - 1/(2*tanh(a + 2*log(x))), True))","A",0
163,0,0,0,0.000000," ","integrate(coth(a+2*ln(x))**2/x**2,x)","\int \frac{\coth^{2}{\left(a + 2 \log{\left(x \right)} \right)}}{x^{2}}\, dx"," ",0,"Integral(coth(a + 2*log(x))**2/x**2, x)","F",0
164,0,0,0,0.000000," ","integrate(coth(a+2*ln(x))**2/x**3,x)","\int \frac{\coth^{2}{\left(a + 2 \log{\left(x \right)} \right)}}{x^{3}}\, dx"," ",0,"Integral(coth(a + 2*log(x))**2/x**3, x)","F",0
165,0,0,0,0.000000," ","integrate((e*x)**m*coth(a+2*ln(x)),x)","\int \left(e x\right)^{m} \coth{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral((e*x)**m*coth(a + 2*log(x)), x)","F",0
166,0,0,0,0.000000," ","integrate((e*x)**m*coth(a+2*ln(x))**2,x)","\int \left(e x\right)^{m} \coth^{2}{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral((e*x)**m*coth(a + 2*log(x))**2, x)","F",0
167,0,0,0,0.000000," ","integrate((e*x)**m*coth(a+2*ln(x))**3,x)","\int \left(e x\right)^{m} \coth^{3}{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral((e*x)**m*coth(a + 2*log(x))**3, x)","F",0
168,0,0,0,0.000000," ","integrate(coth(a+b*ln(x))**p,x)","\int \coth^{p}{\left(a + b \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(coth(a + b*log(x))**p, x)","F",0
169,0,0,0,0.000000," ","integrate((e*x)**m*coth(a+b*ln(x))**p,x)","\int \left(e x\right)^{m} \coth^{p}{\left(a + b \log{\left(x \right)} \right)}\, dx"," ",0,"Integral((e*x)**m*coth(a + b*log(x))**p, x)","F",0
170,0,0,0,0.000000," ","integrate(coth(a+1/2*ln(x))**p,x)","\int \coth^{p}{\left(a + \frac{\log{\left(x \right)}}{2} \right)}\, dx"," ",0,"Integral(coth(a + log(x)/2)**p, x)","F",0
171,0,0,0,0.000000," ","integrate(coth(a+1/4*ln(x))**p,x)","\int \coth^{p}{\left(a + \frac{\log{\left(x \right)}}{4} \right)}\, dx"," ",0,"Integral(coth(a + log(x)/4)**p, x)","F",0
172,0,0,0,0.000000," ","integrate(coth(a+1/6*ln(x))**p,x)","\int \coth^{p}{\left(a + \frac{\log{\left(x \right)}}{6} \right)}\, dx"," ",0,"Integral(coth(a + log(x)/6)**p, x)","F",0
173,0,0,0,0.000000," ","integrate(coth(a+1/8*ln(x))**p,x)","\int \coth^{p}{\left(a + \frac{\log{\left(x \right)}}{8} \right)}\, dx"," ",0,"Integral(coth(a + log(x)/8)**p, x)","F",0
174,0,0,0,0.000000," ","integrate(coth(a+ln(x))**p,x)","\int \coth^{p}{\left(a + \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(coth(a + log(x))**p, x)","F",0
175,0,0,0,0.000000," ","integrate(coth(a+2*ln(x))**p,x)","\int \coth^{p}{\left(a + 2 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(coth(a + 2*log(x))**p, x)","F",0
176,0,0,0,0.000000," ","integrate(coth(a+3*ln(x))**p,x)","\int \coth^{p}{\left(a + 3 \log{\left(x \right)} \right)}\, dx"," ",0,"Integral(coth(a + 3*log(x))**p, x)","F",0
177,0,0,0,0.000000," ","integrate(x**3*coth(d*(a+b*ln(c*x**n))),x)","\int x^{3} \coth{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral(x**3*coth(a*d + b*d*log(c*x**n)), x)","F",0
178,0,0,0,0.000000," ","integrate(x**2*coth(d*(a+b*ln(c*x**n))),x)","\int x^{2} \coth{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral(x**2*coth(a*d + b*d*log(c*x**n)), x)","F",0
179,0,0,0,0.000000," ","integrate(x*coth(d*(a+b*ln(c*x**n))),x)","\int x \coth{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral(x*coth(a*d + b*d*log(c*x**n)), x)","F",0
180,0,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n))),x)","\int \coth{\left(d \left(a + b \log{\left(c x^{n} \right)}\right) \right)}\, dx"," ",0,"Integral(coth(d*(a + b*log(c*x**n))), x)","F",0
181,0,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n)))/x,x)","\int \frac{\coth{\left(a d + b d \log{\left(c x^{n} \right)} \right)}}{x}\, dx"," ",0,"Integral(coth(a*d + b*d*log(c*x**n))/x, x)","F",0
182,0,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n)))/x**2,x)","\int \frac{\coth{\left(a d + b d \log{\left(c x^{n} \right)} \right)}}{x^{2}}\, dx"," ",0,"Integral(coth(a*d + b*d*log(c*x**n))/x**2, x)","F",0
183,0,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n)))/x**3,x)","\int \frac{\coth{\left(a d + b d \log{\left(c x^{n} \right)} \right)}}{x^{3}}\, dx"," ",0,"Integral(coth(a*d + b*d*log(c*x**n))/x**3, x)","F",0
184,0,0,0,0.000000," ","integrate(x**3*coth(d*(a+b*ln(c*x**n)))**2,x)","\int x^{3} \coth^{2}{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral(x**3*coth(a*d + b*d*log(c*x**n))**2, x)","F",0
185,0,0,0,0.000000," ","integrate(x**2*coth(d*(a+b*ln(c*x**n)))**2,x)","\int x^{2} \coth^{2}{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral(x**2*coth(a*d + b*d*log(c*x**n))**2, x)","F",0
186,0,0,0,0.000000," ","integrate(x*coth(d*(a+b*ln(c*x**n)))**2,x)","\int x \coth^{2}{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral(x*coth(a*d + b*d*log(c*x**n))**2, x)","F",0
187,0,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n)))**2,x)","\int \coth^{2}{\left(d \left(a + b \log{\left(c x^{n} \right)}\right) \right)}\, dx"," ",0,"Integral(coth(d*(a + b*log(c*x**n)))**2, x)","F",0
188,0,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n)))**2/x,x)","\int \frac{\coth^{2}{\left(a d + b d \log{\left(c x^{n} \right)} \right)}}{x}\, dx"," ",0,"Integral(coth(a*d + b*d*log(c*x**n))**2/x, x)","F",0
189,0,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n)))**2/x**2,x)","\int \frac{\coth^{2}{\left(a d + b d \log{\left(c x^{n} \right)} \right)}}{x^{2}}\, dx"," ",0,"Integral(coth(a*d + b*d*log(c*x**n))**2/x**2, x)","F",0
190,-1,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n)))**2/x**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate(coth(a+b*ln(c*x**n))**3/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,-1,0,0,0.000000," ","integrate(coth(a+b*ln(c*x**n))**4/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate(coth(a+b*ln(c*x**n))**5/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,0,0,0,0.000000," ","integrate((e*x)**m*coth(d*(a+b*ln(c*x**n))),x)","\int \left(e x\right)^{m} \coth{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral((e*x)**m*coth(a*d + b*d*log(c*x**n)), x)","F",0
195,0,0,0,0.000000," ","integrate((e*x)**m*coth(d*(a+b*ln(c*x**n)))**2,x)","\int \left(e x\right)^{m} \coth^{2}{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral((e*x)**m*coth(a*d + b*d*log(c*x**n))**2, x)","F",0
196,0,0,0,0.000000," ","integrate((e*x)**m*coth(d*(a+b*ln(c*x**n)))**3,x)","\int \left(e x\right)^{m} \coth^{3}{\left(a d + b d \log{\left(c x^{n} \right)} \right)}\, dx"," ",0,"Integral((e*x)**m*coth(a*d + b*d*log(c*x**n))**3, x)","F",0
197,0,0,0,0.000000," ","integrate(coth(d*(a+b*ln(c*x**n)))**p,x)","\int \coth^{p}{\left(d \left(a + b \log{\left(c x^{n} \right)}\right) \right)}\, dx"," ",0,"Integral(coth(d*(a + b*log(c*x**n)))**p, x)","F",0
198,-1,0,0,0.000000," ","integrate((e*x)**m*coth(d*(a+b*ln(c*x**n)))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate(coth(a+b*ln(c*x**n))**(5/2)/x,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,0,0,0,0.000000," ","integrate(coth(a+b*ln(c*x**n))**(3/2)/x,x)","\int \frac{\coth^{\frac{3}{2}}{\left(a + b \log{\left(c x^{n} \right)} \right)}}{x}\, dx"," ",0,"Integral(coth(a + b*log(c*x**n))**(3/2)/x, x)","F",0
201,0,0,0,0.000000," ","integrate(coth(a+b*ln(c*x**n))**(1/2)/x,x)","\int \frac{\sqrt{\coth{\left(a + b \log{\left(c x^{n} \right)} \right)}}}{x}\, dx"," ",0,"Integral(sqrt(coth(a + b*log(c*x**n)))/x, x)","F",0
202,0,0,0,0.000000," ","integrate(1/x/coth(a+b*ln(c*x**n))**(1/2),x)","\int \frac{1}{x \sqrt{\coth{\left(a + b \log{\left(c x^{n} \right)} \right)}}}\, dx"," ",0,"Integral(1/(x*sqrt(coth(a + b*log(c*x**n)))), x)","F",0
203,0,0,0,0.000000," ","integrate(1/x/coth(a+b*ln(c*x**n))**(3/2),x)","\int \frac{1}{x \coth^{\frac{3}{2}}{\left(a + b \log{\left(c x^{n} \right)} \right)}}\, dx"," ",0,"Integral(1/(x*coth(a + b*log(c*x**n))**(3/2)), x)","F",0
204,-1,0,0,0.000000," ","integrate(1/x/coth(a+b*ln(c*x**n))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,0,0,0,0.000000," ","integrate(coth(x)**5/(a+b*coth(x)**2+c*coth(x)**4)**(1/2),x)","\int \frac{\coth^{5}{\left(x \right)}}{\sqrt{a + b \coth^{2}{\left(x \right)} + c \coth^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(coth(x)**5/sqrt(a + b*coth(x)**2 + c*coth(x)**4), x)","F",0
206,0,0,0,0.000000," ","integrate(coth(x)**3/(a+b*coth(x)**2+c*coth(x)**4)**(1/2),x)","\int \frac{\coth^{3}{\left(x \right)}}{\sqrt{a + b \coth^{2}{\left(x \right)} + c \coth^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(coth(x)**3/sqrt(a + b*coth(x)**2 + c*coth(x)**4), x)","F",0
207,0,0,0,0.000000," ","integrate(coth(x)/(a+b*coth(x)**2+c*coth(x)**4)**(1/2),x)","\int \frac{\coth{\left(x \right)}}{\sqrt{a + b \coth^{2}{\left(x \right)} + c \coth^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(coth(x)/sqrt(a + b*coth(x)**2 + c*coth(x)**4), x)","F",0
208,0,0,0,0.000000," ","integrate(tanh(x)/(a+b*coth(x)**2+c*coth(x)**4)**(1/2),x)","\int \frac{\tanh{\left(x \right)}}{\sqrt{a + b \coth^{2}{\left(x \right)} + c \coth^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(tanh(x)/sqrt(a + b*coth(x)**2 + c*coth(x)**4), x)","F",0
209,0,0,0,0.000000," ","integrate(tanh(x)**3/(a+b*coth(x)**2+c*coth(x)**4)**(1/2),x)","\int \frac{\tanh^{3}{\left(x \right)}}{\sqrt{a + b \coth^{2}{\left(x \right)} + c \coth^{4}{\left(x \right)}}}\, dx"," ",0,"Integral(tanh(x)**3/sqrt(a + b*coth(x)**2 + c*coth(x)**4), x)","F",0
210,0,0,0,0.000000," ","integrate(coth(x)*(a+b*coth(x)**2+c*coth(x)**4)**(1/2),x)","\int \sqrt{a + b \coth^{2}{\left(x \right)} + c \coth^{4}{\left(x \right)}} \coth{\left(x \right)}\, dx"," ",0,"Integral(sqrt(a + b*coth(x)**2 + c*coth(x)**4)*coth(x), x)","F",0
211,-1,0,0,0.000000," ","integrate(exp(c*(b*x+a))*(coth(b*c*x+a*c)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate(exp(c*(b*x+a))*(coth(b*c*x+a*c)**2)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))*(coth(b*c*x+a*c)**2)**(1/2),x)","e^{a c} \int \sqrt{\coth^{2}{\left(a c + b c x \right)}} e^{b c x}\, dx"," ",0,"exp(a*c)*Integral(sqrt(coth(a*c + b*c*x)**2)*exp(b*c*x), x)","F",0
214,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))/(coth(b*c*x+a*c)**2)**(1/2),x)","e^{a c} \int \frac{e^{b c x}}{\sqrt{\coth^{2}{\left(a c + b c x \right)}}}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)/sqrt(coth(a*c + b*c*x)**2), x)","F",0
215,0,0,0,0.000000," ","integrate(exp(c*(b*x+a))/(coth(b*c*x+a*c)**2)**(3/2),x)","e^{a c} \int \frac{e^{b c x}}{\left(\coth^{2}{\left(a c + b c x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"exp(a*c)*Integral(exp(b*c*x)/(coth(a*c + b*c*x)**2)**(3/2), x)","F",0
216,-1,0,0,0.000000," ","integrate(exp(c*(b*x+a))/(coth(b*c*x+a*c)**2)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,0,0,0,0.000000," ","integrate(sin(coth(b*x+a))**3,x)","\int \sin^{3}{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(sin(coth(a + b*x))**3, x)","F",0
218,0,0,0,0.000000," ","integrate(sin(coth(b*x+a))**2,x)","\int \sin^{2}{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(sin(coth(a + b*x))**2, x)","F",0
219,0,0,0,0.000000," ","integrate(sin(coth(b*x+a)),x)","\int \sin{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(sin(coth(a + b*x)), x)","F",0
220,0,0,0,0.000000," ","integrate(csc(coth(b*x+a)),x)","\int \csc{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(csc(coth(a + b*x)), x)","F",0
221,0,0,0,0.000000," ","integrate(cos(coth(b*x+a))**3,x)","\int \cos^{3}{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(cos(coth(a + b*x))**3, x)","F",0
222,0,0,0,0.000000," ","integrate(cos(coth(b*x+a))**2,x)","\int \cos^{2}{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(cos(coth(a + b*x))**2, x)","F",0
223,0,0,0,0.000000," ","integrate(cos(coth(b*x+a)),x)","\int \cos{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(cos(coth(a + b*x)), x)","F",0
224,0,0,0,0.000000," ","integrate(sec(coth(b*x+a)),x)","\int \sec{\left(\coth{\left(a + b x \right)} \right)}\, dx"," ",0,"Integral(sec(coth(a + b*x)), x)","F",0
