1,1,14,0,0.174077," ","integrate(sin(b*x+a),x)","\begin{cases} - \frac{\cos{\left(a + b x \right)}}{b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-cos(a + b*x)/b, Ne(b, 0)), (x*sin(a), True))","A",0
2,1,46,0,0.222532," ","integrate(sin(b*x+a)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(a + b x \right)}}{2} + \frac{x \cos^{2}{\left(a + b x \right)}}{2} - \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b), Ne(b, 0)), (x*sin(a)**2, True))","A",0
3,1,37,0,0.475417," ","integrate(sin(b*x+a)**3,x)","\begin{cases} - \frac{\sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 \cos^{3}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**2*cos(a + b*x)/b - 2*cos(a + b*x)**3/(3*b), Ne(b, 0)), (x*sin(a)**3, True))","A",0
4,1,95,0,1.075492," ","integrate(sin(b*x+a)**4,x)","\begin{cases} \frac{3 x \sin^{4}{\left(a + b x \right)}}{8} + \frac{3 x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{3 x \cos^{4}{\left(a + b x \right)}}{8} - \frac{5 \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{3 \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x*sin(a + b*x)**4/8 + 3*x*sin(a + b*x)**2*cos(a + b*x)**2/4 + 3*x*cos(a + b*x)**4/8 - 5*sin(a + b*x)**3*cos(a + b*x)/(8*b) - 3*sin(a + b*x)*cos(a + b*x)**3/(8*b), Ne(b, 0)), (x*sin(a)**4, True))","A",0
5,1,60,0,1.878890," ","integrate(sin(b*x+a)**5,x)","\begin{cases} - \frac{\sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{4 \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{8 \cos^{5}{\left(a + b x \right)}}{15 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**4*cos(a + b*x)/b - 4*sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 8*cos(a + b*x)**5/(15*b), Ne(b, 0)), (x*sin(a)**5, True))","A",0
6,1,139,0,3.494268," ","integrate(sin(b*x+a)**6,x)","\begin{cases} \frac{5 x \sin^{6}{\left(a + b x \right)}}{16} + \frac{15 x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16} + \frac{15 x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{16} + \frac{5 x \cos^{6}{\left(a + b x \right)}}{16} - \frac{11 \sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b} - \frac{5 \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{6 b} - \frac{5 \sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{16 b} & \text{for}\: b \neq 0 \\x \sin^{6}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*x*sin(a + b*x)**6/16 + 15*x*sin(a + b*x)**4*cos(a + b*x)**2/16 + 15*x*sin(a + b*x)**2*cos(a + b*x)**4/16 + 5*x*cos(a + b*x)**6/16 - 11*sin(a + b*x)**5*cos(a + b*x)/(16*b) - 5*sin(a + b*x)**3*cos(a + b*x)**3/(6*b) - 5*sin(a + b*x)*cos(a + b*x)**5/(16*b), Ne(b, 0)), (x*sin(a)**6, True))","A",0
7,1,80,0,6.079044," ","integrate(sin(b*x+a)**7,x)","\begin{cases} - \frac{\sin^{6}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{b} - \frac{2 \sin^{4}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{b} - \frac{8 \sin^{2}{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{5 b} - \frac{16 \cos^{7}{\left(a + b x \right)}}{35 b} & \text{for}\: b \neq 0 \\x \sin^{7}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**6*cos(a + b*x)/b - 2*sin(a + b*x)**4*cos(a + b*x)**3/b - 8*sin(a + b*x)**2*cos(a + b*x)**5/(5*b) - 16*cos(a + b*x)**7/(35*b), Ne(b, 0)), (x*sin(a)**7, True))","A",0
8,1,184,0,10.279044," ","integrate(sin(b*x+a)**8,x)","\begin{cases} \frac{35 x \sin^{8}{\left(a + b x \right)}}{128} + \frac{35 x \sin^{6}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{32} + \frac{105 x \sin^{4}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{64} + \frac{35 x \sin^{2}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{32} + \frac{35 x \cos^{8}{\left(a + b x \right)}}{128} - \frac{93 \sin^{7}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{128 b} - \frac{511 \sin^{5}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{384 b} - \frac{385 \sin^{3}{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{384 b} - \frac{35 \sin{\left(a + b x \right)} \cos^{7}{\left(a + b x \right)}}{128 b} & \text{for}\: b \neq 0 \\x \sin^{8}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((35*x*sin(a + b*x)**8/128 + 35*x*sin(a + b*x)**6*cos(a + b*x)**2/32 + 105*x*sin(a + b*x)**4*cos(a + b*x)**4/64 + 35*x*sin(a + b*x)**2*cos(a + b*x)**6/32 + 35*x*cos(a + b*x)**8/128 - 93*sin(a + b*x)**7*cos(a + b*x)/(128*b) - 511*sin(a + b*x)**5*cos(a + b*x)**3/(384*b) - 385*sin(a + b*x)**3*cos(a + b*x)**5/(384*b) - 35*sin(a + b*x)*cos(a + b*x)**7/(128*b), Ne(b, 0)), (x*sin(a)**8, True))","A",0
9,-1,0,0,0.000000," ","integrate(sin(b*x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,0,0,0,0.000000," ","integrate(sin(b*x)**(5/2),x)","\int \sin^{\frac{5}{2}}{\left(b x \right)}\, dx"," ",0,"Integral(sin(b*x)**(5/2), x)","F",0
11,0,0,0,0.000000," ","integrate(sin(b*x)**(3/2),x)","\int \sin^{\frac{3}{2}}{\left(b x \right)}\, dx"," ",0,"Integral(sin(b*x)**(3/2), x)","F",0
12,0,0,0,0.000000," ","integrate(sin(b*x)**(1/2),x)","\int \sqrt{\sin{\left(b x \right)}}\, dx"," ",0,"Integral(sqrt(sin(b*x)), x)","F",0
13,0,0,0,0.000000," ","integrate(1/sin(b*x)**(1/2),x)","\int \frac{1}{\sqrt{\sin{\left(b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(sin(b*x)), x)","F",0
14,0,0,0,0.000000," ","integrate(1/sin(b*x)**(3/2),x)","\int \frac{1}{\sin^{\frac{3}{2}}{\left(b x \right)}}\, dx"," ",0,"Integral(sin(b*x)**(-3/2), x)","F",0
15,0,0,0,0.000000," ","integrate(1/sin(b*x)**(5/2),x)","\int \frac{1}{\sin^{\frac{5}{2}}{\left(b x \right)}}\, dx"," ",0,"Integral(sin(b*x)**(-5/2), x)","F",0
16,0,0,0,0.000000," ","integrate(1/sin(b*x)**(7/2),x)","\int \frac{1}{\sin^{\frac{7}{2}}{\left(b x \right)}}\, dx"," ",0,"Integral(sin(b*x)**(-7/2), x)","F",0
17,-1,0,0,0.000000," ","integrate(sin(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,0,0,0,0.000000," ","integrate(sin(b*x+a)**(5/2),x)","\int \sin^{\frac{5}{2}}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**(5/2), x)","F",0
19,0,0,0,0.000000," ","integrate(sin(b*x+a)**(3/2),x)","\int \sin^{\frac{3}{2}}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**(3/2), x)","F",0
20,0,0,0,0.000000," ","integrate(sin(b*x+a)**(1/2),x)","\int \sqrt{\sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(sin(a + b*x)), x)","F",0
21,0,0,0,0.000000," ","integrate(1/sin(b*x+a)**(1/2),x)","\int \frac{1}{\sqrt{\sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(sin(a + b*x)), x)","F",0
22,0,0,0,0.000000," ","integrate(1/sin(b*x+a)**(3/2),x)","\int \frac{1}{\sin^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sin(a + b*x)**(-3/2), x)","F",0
23,0,0,0,0.000000," ","integrate(1/sin(b*x+a)**(5/2),x)","\int \frac{1}{\sin^{\frac{5}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sin(a + b*x)**(-5/2), x)","F",0
24,0,0,0,0.000000," ","integrate(1/sin(b*x+a)**(7/2),x)","\int \frac{1}{\sin^{\frac{7}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sin(a + b*x)**(-7/2), x)","F",0
25,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2),x)","\int \left(c \sin{\left(a + b x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(5/2), x)","F",0
27,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(3/2),x)","\int \left(c \sin{\left(a + b x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(3/2), x)","F",0
28,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(1/2),x)","\int \sqrt{c \sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(c*sin(a + b*x)), x)","F",0
29,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{c \sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/sqrt(c*sin(a + b*x)), x)","F",0
30,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a))**(3/2),x)","\int \frac{1}{\left(c \sin{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(-3/2), x)","F",0
31,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a))**(5/2),x)","\int \frac{1}{\left(c \sin{\left(a + b x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(-5/2), x)","F",0
32,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a))**(7/2),x)","\int \frac{1}{\left(c \sin{\left(a + b x \right)}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(-7/2), x)","F",0
33,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(4/3),x)","\int \left(c \sin{\left(a + b x \right)}\right)^{\frac{4}{3}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(4/3), x)","F",0
34,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(2/3),x)","\int \left(c \sin{\left(a + b x \right)}\right)^{\frac{2}{3}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(2/3), x)","F",0
35,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(1/3),x)","\int \sqrt[3]{c \sin{\left(a + b x \right)}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(1/3), x)","F",0
36,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a))**(1/3),x)","\int \frac{1}{\sqrt[3]{c \sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(-1/3), x)","F",0
37,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a))**(2/3),x)","\int \frac{1}{\left(c \sin{\left(a + b x \right)}\right)^{\frac{2}{3}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(-2/3), x)","F",0
38,0,0,0,0.000000," ","integrate(1/(c*sin(b*x+a))**(4/3),x)","\int \frac{1}{\left(c \sin{\left(a + b x \right)}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(-4/3), x)","F",0
39,0,0,0,0.000000," ","integrate(sin(b*x+a)**n,x)","\int \sin^{n}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**n, x)","F",0
40,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**n,x)","\int \left(c \sin{\left(a + b x \right)}\right)^{n}\, dx"," ",0,"Integral((c*sin(a + b*x))**n, x)","F",0
41,0,0,0,0.000000," ","integrate((a*sin(f*x+e))**m*(b*sin(f*x+e))**n,x)","\int \left(a \sin{\left(e + f x \right)}\right)^{m} \left(b \sin{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*sin(e + f*x))**m*(b*sin(e + f*x))**n, x)","F",0
42,1,22,0,1.374634," ","integrate(cos(b*x+a)**3*sin(b*x+a),x)","\begin{cases} - \frac{\cos^{4}{\left(a + b x \right)}}{4 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-cos(a + b*x)**4/(4*b), Ne(b, 0)), (x*sin(a)*cos(a)**3, True))","A",0
43,1,22,0,0.685529," ","integrate(cos(b*x+a)**2*sin(b*x+a),x)","\begin{cases} - \frac{\cos^{3}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-cos(a + b*x)**3/(3*b), Ne(b, 0)), (x*sin(a)*cos(a)**2, True))","A",0
44,1,19,0,0.309346," ","integrate(cos(b*x+a)*sin(b*x+a),x)","\begin{cases} \frac{\sin^{2}{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sin(a + b*x)**2/(2*b), Ne(b, 0)), (x*sin(a)*cos(a), True))","A",0
45,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a),x)","\int \sin{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)*sec(a + b*x), x)","F",0
46,0,0,0,0.000000," ","integrate(sec(b*x+a)**2*sin(b*x+a),x)","\int \sin{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)*sec(a + b*x)**2, x)","F",0
47,0,0,0,0.000000," ","integrate(sec(b*x+a)**3*sin(b*x+a),x)","\int \sin{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)*sec(a + b*x)**3, x)","F",0
48,0,0,0,0.000000," ","integrate(sec(b*x+a)**4*sin(b*x+a),x)","\int \sin{\left(a + b x \right)} \sec^{4}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)*sec(a + b*x)**4, x)","F",0
49,1,88,0,19.099708," ","integrate(cos(b*x+a)**7*sin(b*x+a)**2,x)","\begin{cases} \frac{16 \sin^{9}{\left(a + b x \right)}}{315 b} + \frac{8 \sin^{7}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{35 b} + \frac{2 \sin^{5}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{5 b} + \frac{\sin^{3}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \cos^{7}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*sin(a + b*x)**9/(315*b) + 8*sin(a + b*x)**7*cos(a + b*x)**2/(35*b) + 2*sin(a + b*x)**5*cos(a + b*x)**4/(5*b) + sin(a + b*x)**3*cos(a + b*x)**6/(3*b), Ne(b, 0)), (x*sin(a)**2*cos(a)**7, True))","A",0
50,1,66,0,8.515468," ","integrate(cos(b*x+a)**5*sin(b*x+a)**2,x)","\begin{cases} \frac{8 \sin^{7}{\left(a + b x \right)}}{105 b} + \frac{4 \sin^{5}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{15 b} + \frac{\sin^{3}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \cos^{5}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*sin(a + b*x)**7/(105*b) + 4*sin(a + b*x)**5*cos(a + b*x)**2/(15*b) + sin(a + b*x)**3*cos(a + b*x)**4/(3*b), Ne(b, 0)), (x*sin(a)**2*cos(a)**5, True))","A",0
51,1,44,0,3.020491," ","integrate(cos(b*x+a)**3*sin(b*x+a)**2,x)","\begin{cases} \frac{2 \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{\sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sin(a + b*x)**5/(15*b) + sin(a + b*x)**3*cos(a + b*x)**2/(3*b), Ne(b, 0)), (x*sin(a)**2*cos(a)**3, True))","A",0
52,1,20,0,0.710101," ","integrate(cos(b*x+a)*sin(b*x+a)**2,x)","\begin{cases} \frac{\sin^{3}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sin(a + b*x)**3/(3*b), Ne(b, 0)), (x*sin(a)**2*cos(a), True))","A",0
53,0,0,0,0.000000," ","integrate(sec(b*x+a)**2*sin(b*x+a)**2,x)","\int \sin^{2}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**2*sec(a + b*x)**2, x)","F",0
54,0,0,0,0.000000," ","integrate(sec(b*x+a)**4*sin(b*x+a)**2,x)","\int \sin^{2}{\left(a + b x \right)} \sec^{4}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**2*sec(a + b*x)**4, x)","F",0
55,-1,0,0,0.000000," ","integrate(sec(b*x+a)**6*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate(sec(b*x+a)**8*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate(sec(b*x+a)**10*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,1,189,0,15.098537," ","integrate(cos(b*x+a)**6*sin(b*x+a)**2,x)","\begin{cases} \frac{5 x \sin^{8}{\left(a + b x \right)}}{128} + \frac{5 x \sin^{6}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{32} + \frac{15 x \sin^{4}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{64} + \frac{5 x \sin^{2}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{32} + \frac{5 x \cos^{8}{\left(a + b x \right)}}{128} + \frac{5 \sin^{7}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{128 b} + \frac{55 \sin^{5}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{384 b} + \frac{73 \sin^{3}{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{384 b} - \frac{5 \sin{\left(a + b x \right)} \cos^{7}{\left(a + b x \right)}}{128 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \cos^{6}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*x*sin(a + b*x)**8/128 + 5*x*sin(a + b*x)**6*cos(a + b*x)**2/32 + 15*x*sin(a + b*x)**4*cos(a + b*x)**4/64 + 5*x*sin(a + b*x)**2*cos(a + b*x)**6/32 + 5*x*cos(a + b*x)**8/128 + 5*sin(a + b*x)**7*cos(a + b*x)/(128*b) + 55*sin(a + b*x)**5*cos(a + b*x)**3/(384*b) + 73*sin(a + b*x)**3*cos(a + b*x)**5/(384*b) - 5*sin(a + b*x)*cos(a + b*x)**7/(128*b), Ne(b, 0)), (x*sin(a)**2*cos(a)**6, True))","A",0
59,1,136,0,5.055072," ","integrate(cos(b*x+a)**4*sin(b*x+a)**2,x)","\begin{cases} \frac{x \sin^{6}{\left(a + b x \right)}}{16} + \frac{3 x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{16} + \frac{x \cos^{6}{\left(a + b x \right)}}{16} + \frac{\sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b} + \frac{\sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{6 b} - \frac{\sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{16 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \cos^{4}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**6/16 + 3*x*sin(a + b*x)**4*cos(a + b*x)**2/16 + 3*x*sin(a + b*x)**2*cos(a + b*x)**4/16 + x*cos(a + b*x)**6/16 + sin(a + b*x)**5*cos(a + b*x)/(16*b) + sin(a + b*x)**3*cos(a + b*x)**3/(6*b) - sin(a + b*x)*cos(a + b*x)**5/(16*b), Ne(b, 0)), (x*sin(a)**2*cos(a)**4, True))","A",0
60,1,92,0,1.454381," ","integrate(cos(b*x+a)**2*sin(b*x+a)**2,x)","\begin{cases} \frac{x \sin^{4}{\left(a + b x \right)}}{8} + \frac{x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{x \cos^{4}{\left(a + b x \right)}}{8} + \frac{\sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{\sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**4/8 + x*sin(a + b*x)**2*cos(a + b*x)**2/4 + x*cos(a + b*x)**4/8 + sin(a + b*x)**3*cos(a + b*x)/(8*b) - sin(a + b*x)*cos(a + b*x)**3/(8*b), Ne(b, 0)), (x*sin(a)**2*cos(a)**2, True))","A",0
61,1,46,0,0.348659," ","integrate(sin(b*x+a)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(a + b x \right)}}{2} + \frac{x \cos^{2}{\left(a + b x \right)}}{2} - \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b), Ne(b, 0)), (x*sin(a)**2, True))","A",0
62,1,3160,0,55.345666," ","integrate(sec(b*x+a)*sin(b*x+a)**2,x)","\frac{\begin{cases} \frac{\log{\left(\tan{\left(a + b x \right)} + \sec{\left(a + b x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x \left(\tan{\left(a \right)} \sec{\left(a \right)} + \sec^{2}{\left(a \right)}\right)}{\tan{\left(a \right)} + \sec{\left(a \right)}} & \text{otherwise} \end{cases}}{2} + 2 \left(\begin{cases} 0 & \text{for}\: b = 0 \\\frac{\sin{\left(b x \right)}}{b} & \text{for}\: a = - \frac{\pi}{2} \\- \frac{\sin{\left(b x \right)}}{b} & \text{for}\: a = \frac{\pi}{2} \\- \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)} \tan^{3}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)} \tan^{3}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)} \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)} \tan{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)} \tan^{3}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)} \tan^{3}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)} \tan{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)} \tan{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2 \tan^{4}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan^{3}{\left(\frac{a}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan{\left(\frac{a}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)} \cos{\left(a \right)} + \left(\begin{cases} \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: a = - \frac{\pi}{2} \\- \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: a = \frac{\pi}{2} \\\frac{x}{\cos{\left(a \right)}} & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}}{b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}}{b} & \text{otherwise} \end{cases}\right) \cos^{2}{\left(a \right)} - \frac{\begin{cases} \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: a = - \frac{\pi}{2} \\- \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: a = \frac{\pi}{2} \\\frac{x}{\cos{\left(a \right)}} & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)}}{b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)}}{b} & \text{otherwise} \end{cases}}{2} - 2 \left(\begin{cases} \frac{x}{\cos{\left(a \right)}} & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{for}\: a = - \frac{\pi}{2} \\- \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{for}\: a = \frac{\pi}{2} \\\frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2 \tan^{4}{\left(\frac{a}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan^{3}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2 \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \cos^{2}{\left(a \right)} + \begin{cases} \frac{x}{\cos{\left(a \right)}} & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{for}\: a = - \frac{\pi}{2} \\- \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2}{b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{for}\: a = \frac{\pi}{2} \\\frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{a}{2} \right)}}{\tan{\left(\frac{a}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{a}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2 \tan^{4}{\left(\frac{a}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan^{3}{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan{\left(\frac{a}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2 \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{a}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(a + b*x) + sec(a + b*x))/b, Ne(b, 0)), (x*(tan(a)*sec(a) + sec(a)**2)/(tan(a) + sec(a)), True))/2 + 2*Piecewise((0, Eq(b, 0)), (sin(b*x)/b, Eq(a, -pi/2)), (-sin(b*x)/b, Eq(a, pi/2)), (-2*log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))*tan(a/2)**3*tan(b*x/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))*tan(a/2)**3/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))*tan(a/2)*tan(b*x/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))*tan(a/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))*tan(a/2)**3*tan(b*x/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))*tan(a/2)**3/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))*tan(a/2)*tan(b*x/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))*tan(a/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 2*tan(a/2)**4/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*tan(a/2)**3*tan(b*x/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*tan(a/2)*tan(b*x/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b), True))*sin(a)*cos(a) + Piecewise((log(tan(b*x/2))/b, Eq(a, -pi/2)), (-log(tan(b*x/2))/b, Eq(a, pi/2)), (x/cos(a), Eq(b, 0)), (log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))/b - log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))/b, True))*cos(a)**2 - Piecewise((log(tan(b*x/2))/b, Eq(a, -pi/2)), (-log(tan(b*x/2))/b, Eq(a, pi/2)), (x/cos(a), Eq(b, 0)), (log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))/b - log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))/b, True))/2 - 2*Piecewise((x/cos(a), Eq(b, 0)), (log(tan(b*x/2))*tan(b*x/2)**2/(b*tan(b*x/2)**2 + b) + log(tan(b*x/2))/(b*tan(b*x/2)**2 + b) + 2/(b*tan(b*x/2)**2 + b), Eq(a, -pi/2)), (-log(tan(b*x/2))*tan(b*x/2)**2/(b*tan(b*x/2)**2 + b) - log(tan(b*x/2))/(b*tan(b*x/2)**2 + b) - 2/(b*tan(b*x/2)**2 + b), Eq(a, pi/2)), (4*log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))*tan(a/2)**2*tan(b*x/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 4*log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))*tan(a/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))*tan(a/2)**2*tan(b*x/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))*tan(a/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 2*tan(a/2)**4*tan(b*x/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*tan(a/2)**3/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*tan(a/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 2*tan(b*x/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b), True))*cos(a)**2 + Piecewise((x/cos(a), Eq(b, 0)), (log(tan(b*x/2))*tan(b*x/2)**2/(b*tan(b*x/2)**2 + b) + log(tan(b*x/2))/(b*tan(b*x/2)**2 + b) + 2/(b*tan(b*x/2)**2 + b), Eq(a, -pi/2)), (-log(tan(b*x/2))*tan(b*x/2)**2/(b*tan(b*x/2)**2 + b) - log(tan(b*x/2))/(b*tan(b*x/2)**2 + b) - 2/(b*tan(b*x/2)**2 + b), Eq(a, pi/2)), (4*log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))*tan(a/2)**2*tan(b*x/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 4*log(tan(b*x/2) - tan(a/2)/(tan(a/2) - 1) - 1/(tan(a/2) - 1))*tan(a/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))*tan(a/2)**2*tan(b*x/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*log(tan(b*x/2) + tan(a/2)/(tan(a/2) + 1) - 1/(tan(a/2) + 1))*tan(a/2)**2/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 2*tan(a/2)**4*tan(b*x/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*tan(a/2)**3/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) - 4*tan(a/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b) + 2*tan(b*x/2)/(b*tan(a/2)**4*tan(b*x/2)**2 + b*tan(a/2)**4 + 2*b*tan(a/2)**2*tan(b*x/2)**2 + 2*b*tan(a/2)**2 + b*tan(b*x/2)**2 + b), True))","B",0
63,0,0,0,0.000000," ","integrate(sec(b*x+a)**3*sin(b*x+a)**2,x)","\int \sin^{2}{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**2*sec(a + b*x)**3, x)","F",0
64,0,0,0,0.000000," ","integrate(sec(b*x+a)**5*sin(b*x+a)**2,x)","\int \sin^{2}{\left(a + b x \right)} \sec^{5}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**2*sec(a + b*x)**5, x)","F",0
65,-1,0,0,0.000000," ","integrate(sec(b*x+a)**7*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,1,44,0,14.210750," ","integrate(cos(b*x+a)**5*sin(b*x+a)**3,x)","\begin{cases} - \frac{\sin^{2}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{6 b} - \frac{\cos^{8}{\left(a + b x \right)}}{24 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} \cos^{5}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**2*cos(a + b*x)**6/(6*b) - cos(a + b*x)**8/(24*b), Ne(b, 0)), (x*sin(a)**3*cos(a)**5, True))","A",0
67,1,46,0,8.873896," ","integrate(cos(b*x+a)**4*sin(b*x+a)**3,x)","\begin{cases} - \frac{\sin^{2}{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{5 b} - \frac{2 \cos^{7}{\left(a + b x \right)}}{35 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} \cos^{4}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**2*cos(a + b*x)**5/(5*b) - 2*cos(a + b*x)**7/(35*b), Ne(b, 0)), (x*sin(a)**3*cos(a)**4, True))","A",0
68,1,44,0,4.327026," ","integrate(cos(b*x+a)**3*sin(b*x+a)**3,x)","\begin{cases} - \frac{\sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{4 b} - \frac{\cos^{6}{\left(a + b x \right)}}{12 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**2*cos(a + b*x)**4/(4*b) - cos(a + b*x)**6/(12*b), Ne(b, 0)), (x*sin(a)**3*cos(a)**3, True))","A",0
69,1,46,0,2.455281," ","integrate(cos(b*x+a)**2*sin(b*x+a)**3,x)","\begin{cases} - \frac{\sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{2 \cos^{5}{\left(a + b x \right)}}{15 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**2*cos(a + b*x)**3/(3*b) - 2*cos(a + b*x)**5/(15*b), Ne(b, 0)), (x*sin(a)**3*cos(a)**2, True))","A",0
70,1,20,0,1.318727," ","integrate(cos(b*x+a)*sin(b*x+a)**3,x)","\begin{cases} \frac{\sin^{4}{\left(a + b x \right)}}{4 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sin(a + b*x)**4/(4*b), Ne(b, 0)), (x*sin(a)**3*cos(a), True))","A",0
71,0,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)**3,x)","\int \sin^{3}{\left(a + b x \right)} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**3*sec(a + b*x), x)","F",0
72,-2,0,0,0.000000," ","integrate(sec(b*x+a)**2*sin(b*x+a)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
73,-1,0,0,0.000000," ","integrate(sec(b*x+a)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(sec(b*x+a)**4*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate(sec(b*x+a)**5*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate(sec(b*x+a)**6*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(sec(b*x+a)**7*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(sec(b*x+a)**8*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(sec(b*x+a)**9*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,1,88,0,49.837712," ","integrate(cos(b*x+a)**7*sin(b*x+a)**4,x)","\begin{cases} \frac{16 \sin^{11}{\left(a + b x \right)}}{1155 b} + \frac{8 \sin^{9}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{105 b} + \frac{6 \sin^{7}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{35 b} + \frac{\sin^{5}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{5 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} \cos^{7}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*sin(a + b*x)**11/(1155*b) + 8*sin(a + b*x)**9*cos(a + b*x)**2/(105*b) + 6*sin(a + b*x)**7*cos(a + b*x)**4/(35*b) + sin(a + b*x)**5*cos(a + b*x)**6/(5*b), Ne(b, 0)), (x*sin(a)**4*cos(a)**7, True))","A",0
81,1,66,0,20.520443," ","integrate(cos(b*x+a)**5*sin(b*x+a)**4,x)","\begin{cases} \frac{8 \sin^{9}{\left(a + b x \right)}}{315 b} + \frac{4 \sin^{7}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{35 b} + \frac{\sin^{5}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{5 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} \cos^{5}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*sin(a + b*x)**9/(315*b) + 4*sin(a + b*x)**7*cos(a + b*x)**2/(35*b) + sin(a + b*x)**5*cos(a + b*x)**4/(5*b), Ne(b, 0)), (x*sin(a)**4*cos(a)**5, True))","A",0
82,1,44,0,7.362782," ","integrate(cos(b*x+a)**3*sin(b*x+a)**4,x)","\begin{cases} \frac{2 \sin^{7}{\left(a + b x \right)}}{35 b} + \frac{\sin^{5}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{5 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sin(a + b*x)**7/(35*b) + sin(a + b*x)**5*cos(a + b*x)**2/(5*b), Ne(b, 0)), (x*sin(a)**4*cos(a)**3, True))","A",0
83,1,20,0,2.247457," ","integrate(cos(b*x+a)*sin(b*x+a)**4,x)","\begin{cases} \frac{\sin^{5}{\left(a + b x \right)}}{5 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sin(a + b*x)**5/(5*b), Ne(b, 0)), (x*sin(a)**4*cos(a), True))","A",0
84,0,0,0,0.000000," ","integrate(sec(b*x+a)**2*sin(b*x+a)**4,x)","\int \sin^{4}{\left(a + b x \right)} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**4*sec(a + b*x)**2, x)","F",0
85,-1,0,0,0.000000," ","integrate(sec(b*x+a)**4*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(sec(b*x+a)**6*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(sec(b*x+a)**8*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate(sec(b*x+a)**10*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,1,231,0,32.100824," ","integrate(cos(b*x+a)**6*sin(b*x+a)**4,x)","\begin{cases} \frac{3 x \sin^{10}{\left(a + b x \right)}}{256} + \frac{15 x \sin^{8}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{256} + \frac{15 x \sin^{6}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{128} + \frac{15 x \sin^{4}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{128} + \frac{15 x \sin^{2}{\left(a + b x \right)} \cos^{8}{\left(a + b x \right)}}{256} + \frac{3 x \cos^{10}{\left(a + b x \right)}}{256} + \frac{3 \sin^{9}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{256 b} + \frac{7 \sin^{7}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{128 b} + \frac{\sin^{5}{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{10 b} - \frac{7 \sin^{3}{\left(a + b x \right)} \cos^{7}{\left(a + b x \right)}}{128 b} - \frac{3 \sin{\left(a + b x \right)} \cos^{9}{\left(a + b x \right)}}{256 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} \cos^{6}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x*sin(a + b*x)**10/256 + 15*x*sin(a + b*x)**8*cos(a + b*x)**2/256 + 15*x*sin(a + b*x)**6*cos(a + b*x)**4/128 + 15*x*sin(a + b*x)**4*cos(a + b*x)**6/128 + 15*x*sin(a + b*x)**2*cos(a + b*x)**8/256 + 3*x*cos(a + b*x)**10/256 + 3*sin(a + b*x)**9*cos(a + b*x)/(256*b) + 7*sin(a + b*x)**7*cos(a + b*x)**3/(128*b) + sin(a + b*x)**5*cos(a + b*x)**5/(10*b) - 7*sin(a + b*x)**3*cos(a + b*x)**7/(128*b) - 3*sin(a + b*x)*cos(a + b*x)**9/(256*b), Ne(b, 0)), (x*sin(a)**4*cos(a)**6, True))","A",0
90,1,189,0,13.086854," ","integrate(cos(b*x+a)**4*sin(b*x+a)**4,x)","\begin{cases} \frac{3 x \sin^{8}{\left(a + b x \right)}}{128} + \frac{3 x \sin^{6}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{32} + \frac{9 x \sin^{4}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{64} + \frac{3 x \sin^{2}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{32} + \frac{3 x \cos^{8}{\left(a + b x \right)}}{128} + \frac{3 \sin^{7}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{128 b} + \frac{11 \sin^{5}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{128 b} - \frac{11 \sin^{3}{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{128 b} - \frac{3 \sin{\left(a + b x \right)} \cos^{7}{\left(a + b x \right)}}{128 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} \cos^{4}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x*sin(a + b*x)**8/128 + 3*x*sin(a + b*x)**6*cos(a + b*x)**2/32 + 9*x*sin(a + b*x)**4*cos(a + b*x)**4/64 + 3*x*sin(a + b*x)**2*cos(a + b*x)**6/32 + 3*x*cos(a + b*x)**8/128 + 3*sin(a + b*x)**7*cos(a + b*x)/(128*b) + 11*sin(a + b*x)**5*cos(a + b*x)**3/(128*b) - 11*sin(a + b*x)**3*cos(a + b*x)**5/(128*b) - 3*sin(a + b*x)*cos(a + b*x)**7/(128*b), Ne(b, 0)), (x*sin(a)**4*cos(a)**4, True))","A",0
91,1,136,0,4.564745," ","integrate(cos(b*x+a)**2*sin(b*x+a)**4,x)","\begin{cases} \frac{x \sin^{6}{\left(a + b x \right)}}{16} + \frac{3 x \sin^{4}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{16} + \frac{x \cos^{6}{\left(a + b x \right)}}{16} + \frac{\sin^{5}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{16 b} - \frac{\sin^{3}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{6 b} - \frac{\sin{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{16 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**6/16 + 3*x*sin(a + b*x)**4*cos(a + b*x)**2/16 + 3*x*sin(a + b*x)**2*cos(a + b*x)**4/16 + x*cos(a + b*x)**6/16 + sin(a + b*x)**5*cos(a + b*x)/(16*b) - sin(a + b*x)**3*cos(a + b*x)**3/(6*b) - sin(a + b*x)*cos(a + b*x)**5/(16*b), Ne(b, 0)), (x*sin(a)**4*cos(a)**2, True))","A",0
92,1,95,0,1.240374," ","integrate(sin(b*x+a)**4,x)","\begin{cases} \frac{3 x \sin^{4}{\left(a + b x \right)}}{8} + \frac{3 x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{3 x \cos^{4}{\left(a + b x \right)}}{8} - \frac{5 \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{3 \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x*sin(a + b*x)**4/8 + 3*x*sin(a + b*x)**2*cos(a + b*x)**2/4 + 3*x*cos(a + b*x)**4/8 - 5*sin(a + b*x)**3*cos(a + b*x)/(8*b) - 3*sin(a + b*x)*cos(a + b*x)**3/(8*b), Ne(b, 0)), (x*sin(a)**4, True))","A",0
93,-1,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,0,0,0,0.000000," ","integrate(sec(b*x+a)**3*sin(b*x+a)**4,x)","\int \sin^{4}{\left(a + b x \right)} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(a + b*x)**4*sec(a + b*x)**3, x)","F",0
95,-1,0,0,0.000000," ","integrate(sec(b*x+a)**5*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(sec(b*x+a)**7*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(sec(b*x+a)**9*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,1,65,0,71.135435," ","integrate(cos(b*x+a)**7*sin(b*x+a)**5,x)","\begin{cases} - \frac{\sin^{4}{\left(a + b x \right)} \cos^{8}{\left(a + b x \right)}}{8 b} - \frac{\sin^{2}{\left(a + b x \right)} \cos^{10}{\left(a + b x \right)}}{20 b} - \frac{\cos^{12}{\left(a + b x \right)}}{120 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(a \right)} \cos^{7}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**4*cos(a + b*x)**8/(8*b) - sin(a + b*x)**2*cos(a + b*x)**10/(20*b) - cos(a + b*x)**12/(120*b), Ne(b, 0)), (x*sin(a)**5*cos(a)**7, True))","A",0
99,1,68,0,47.179471," ","integrate(cos(b*x+a)**6*sin(b*x+a)**5,x)","\begin{cases} - \frac{\sin^{4}{\left(a + b x \right)} \cos^{7}{\left(a + b x \right)}}{7 b} - \frac{4 \sin^{2}{\left(a + b x \right)} \cos^{9}{\left(a + b x \right)}}{63 b} - \frac{8 \cos^{11}{\left(a + b x \right)}}{693 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(a \right)} \cos^{6}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**4*cos(a + b*x)**7/(7*b) - 4*sin(a + b*x)**2*cos(a + b*x)**9/(63*b) - 8*cos(a + b*x)**11/(693*b), Ne(b, 0)), (x*sin(a)**5*cos(a)**6, True))","A",0
100,1,65,0,30.080465," ","integrate(cos(b*x+a)**5*sin(b*x+a)**5,x)","\begin{cases} - \frac{\sin^{4}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{6 b} - \frac{\sin^{2}{\left(a + b x \right)} \cos^{8}{\left(a + b x \right)}}{12 b} - \frac{\cos^{10}{\left(a + b x \right)}}{60 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(a \right)} \cos^{5}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**4*cos(a + b*x)**6/(6*b) - sin(a + b*x)**2*cos(a + b*x)**8/(12*b) - cos(a + b*x)**10/(60*b), Ne(b, 0)), (x*sin(a)**5*cos(a)**5, True))","A",0
101,1,68,0,20.093285," ","integrate(cos(b*x+a)**4*sin(b*x+a)**5,x)","\begin{cases} - \frac{\sin^{4}{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{5 b} - \frac{4 \sin^{2}{\left(a + b x \right)} \cos^{7}{\left(a + b x \right)}}{35 b} - \frac{8 \cos^{9}{\left(a + b x \right)}}{315 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(a \right)} \cos^{4}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**4*cos(a + b*x)**5/(5*b) - 4*sin(a + b*x)**2*cos(a + b*x)**7/(35*b) - 8*cos(a + b*x)**9/(315*b), Ne(b, 0)), (x*sin(a)**5*cos(a)**4, True))","A",0
102,1,65,0,12.763341," ","integrate(cos(b*x+a)**3*sin(b*x+a)**5,x)","\begin{cases} - \frac{\sin^{4}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{4 b} - \frac{\sin^{2}{\left(a + b x \right)} \cos^{6}{\left(a + b x \right)}}{6 b} - \frac{\cos^{8}{\left(a + b x \right)}}{24 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**4*cos(a + b*x)**4/(4*b) - sin(a + b*x)**2*cos(a + b*x)**6/(6*b) - cos(a + b*x)**8/(24*b), Ne(b, 0)), (x*sin(a)**5*cos(a)**3, True))","A",0
103,1,68,0,7.502225," ","integrate(cos(b*x+a)**2*sin(b*x+a)**5,x)","\begin{cases} - \frac{\sin^{4}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{3 b} - \frac{4 \sin^{2}{\left(a + b x \right)} \cos^{5}{\left(a + b x \right)}}{15 b} - \frac{8 \cos^{7}{\left(a + b x \right)}}{105 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)**4*cos(a + b*x)**3/(3*b) - 4*sin(a + b*x)**2*cos(a + b*x)**5/(15*b) - 8*cos(a + b*x)**7/(105*b), Ne(b, 0)), (x*sin(a)**5*cos(a)**2, True))","A",0
104,1,20,0,4.044981," ","integrate(cos(b*x+a)*sin(b*x+a)**5,x)","\begin{cases} \frac{\sin^{6}{\left(a + b x \right)}}{6 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((sin(a + b*x)**6/(6*b), Ne(b, 0)), (x*sin(a)**5*cos(a), True))","A",0
105,-1,0,0,0.000000," ","integrate(sec(b*x+a)*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(sec(b*x+a)**2*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(sec(b*x+a)**3*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(sec(b*x+a)**4*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(sec(b*x+a)**5*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate(sec(b*x+a)**6*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(sec(b*x+a)**7*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(sec(b*x+a)**8*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(sec(b*x+a)**9*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(sec(b*x+a)**10*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate(sec(b*x+a)**11*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(sec(b*x+a)**12*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate(sec(b*x+a)**13*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate(sec(b*x+a)**3*sin(b*x+a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate(sec(b*x+a)**6*sin(b*x+a)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,1,1085,0,8.156260," ","integrate(cos(b*x+a)**6/sin(b*x+a),x)","\begin{cases} \frac{15 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{75 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{150 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{150 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{75 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{15 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{90 \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{180 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{280 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{140 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} + \frac{46}{15 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 150 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 75 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 15 b} & \text{for}\: b \neq 0 \\\frac{x \cos^{6}{\left(a \right)}}{\sin{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**10/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 75*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**8/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 150*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 150*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 75*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 15*log(tan(a/2 + b*x/2))/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 90*tan(a/2 + b*x/2)**8/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 180*tan(a/2 + b*x/2)**6/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 280*tan(a/2 + b*x/2)**4/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 140*tan(a/2 + b*x/2)**2/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b) + 46/(15*b*tan(a/2 + b*x/2)**10 + 75*b*tan(a/2 + b*x/2)**8 + 150*b*tan(a/2 + b*x/2)**6 + 150*b*tan(a/2 + b*x/2)**4 + 75*b*tan(a/2 + b*x/2)**2 + 15*b), Ne(b, 0)), (x*cos(a)**6/sin(a), True))","A",0
121,1,1086,0,6.542551," ","integrate(cos(b*x+a)**5/sin(b*x+a),x)","\begin{cases} - \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{6 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{6 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} & \text{for}\: b \neq 0 \\\frac{x \cos^{5}{\left(a \right)}}{\sin{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 6*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2)**2 + 1)/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 4*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 6*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 4*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b), Ne(b, 0)), (x*cos(a)**5/sin(a), True))","A",0
122,1,473,0,2.998968," ","integrate(cos(b*x+a)**4/sin(b*x+a),x)","\begin{cases} \frac{3 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{3 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 3 b} + \frac{9 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{3 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 3 b} + \frac{9 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{3 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 3 b} + \frac{3 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{3 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 3 b} + \frac{12 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{3 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 3 b} + \frac{12 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{3 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 3 b} + \frac{8}{3 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 9 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 3 b} & \text{for}\: b \neq 0 \\\frac{x \cos^{4}{\left(a \right)}}{\sin{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(3*b*tan(a/2 + b*x/2)**6 + 9*b*tan(a/2 + b*x/2)**4 + 9*b*tan(a/2 + b*x/2)**2 + 3*b) + 9*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(3*b*tan(a/2 + b*x/2)**6 + 9*b*tan(a/2 + b*x/2)**4 + 9*b*tan(a/2 + b*x/2)**2 + 3*b) + 9*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(3*b*tan(a/2 + b*x/2)**6 + 9*b*tan(a/2 + b*x/2)**4 + 9*b*tan(a/2 + b*x/2)**2 + 3*b) + 3*log(tan(a/2 + b*x/2))/(3*b*tan(a/2 + b*x/2)**6 + 9*b*tan(a/2 + b*x/2)**4 + 9*b*tan(a/2 + b*x/2)**2 + 3*b) + 12*tan(a/2 + b*x/2)**4/(3*b*tan(a/2 + b*x/2)**6 + 9*b*tan(a/2 + b*x/2)**4 + 9*b*tan(a/2 + b*x/2)**2 + 3*b) + 12*tan(a/2 + b*x/2)**2/(3*b*tan(a/2 + b*x/2)**6 + 9*b*tan(a/2 + b*x/2)**4 + 9*b*tan(a/2 + b*x/2)**2 + 3*b) + 8/(3*b*tan(a/2 + b*x/2)**6 + 9*b*tan(a/2 + b*x/2)**4 + 9*b*tan(a/2 + b*x/2)**2 + 3*b), Ne(b, 0)), (x*cos(a)**4/sin(a), True))","A",0
123,1,369,0,2.345116," ","integrate(cos(b*x+a)**3/sin(b*x+a),x)","\begin{cases} - \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} & \text{for}\: b \neq 0 \\\frac{x \cos^{3}{\left(a \right)}}{\sin{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - 2*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2)**2 + 1)/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + 2*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - 2*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b), Ne(b, 0)), (x*cos(a)**3/sin(a), True))","A",0
124,1,92,0,1.307721," ","integrate(cos(b*x+a)**2/sin(b*x+a),x)","\begin{cases} \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{2}{b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} & \text{for}\: b \neq 0 \\\frac{x \cos^{2}{\left(a \right)}}{\sin{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))/(b*tan(a/2 + b*x/2)**2 + b) + 2/(b*tan(a/2 + b*x/2)**2 + b), Ne(b, 0)), (x*cos(a)**2/sin(a), True))","A",0
125,1,17,0,0.606464," ","integrate(cos(b*x+a)/sin(b*x+a),x)","\begin{cases} \frac{\log{\left(\sin{\left(a + b x \right)} \right)}}{b} & \text{for}\: b \neq 0 \\\frac{x \cos{\left(a \right)}}{\sin{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(a + b*x))/b, Ne(b, 0)), (x*cos(a)/sin(a), True))","A",0
126,0,0,0,0.000000," ","integrate(sec(b*x+a)/sin(b*x+a),x)","\int \frac{\sec{\left(a + b x \right)}}{\sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)/sin(a + b*x), x)","F",0
127,0,0,0,0.000000," ","integrate(sec(b*x+a)**2/sin(b*x+a),x)","\int \frac{\sec^{2}{\left(a + b x \right)}}{\sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**2/sin(a + b*x), x)","F",0
128,0,0,0,0.000000," ","integrate(sec(b*x+a)**3/sin(b*x+a),x)","\int \frac{\sec^{3}{\left(a + b x \right)}}{\sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**3/sin(a + b*x), x)","F",0
129,0,0,0,0.000000," ","integrate(sec(b*x+a)**4/sin(b*x+a),x)","\int \frac{\sec^{4}{\left(a + b x \right)}}{\sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**4/sin(a + b*x), x)","F",0
130,0,0,0,0.000000," ","integrate(sec(b*x+a)**5/sin(b*x+a),x)","\int \frac{\sec^{5}{\left(a + b x \right)}}{\sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**5/sin(a + b*x), x)","F",0
131,0,0,0,0.000000," ","integrate(sec(b*x+a)**6/sin(b*x+a),x)","\int \frac{\sec^{6}{\left(a + b x \right)}}{\sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**6/sin(a + b*x), x)","F",0
132,0,0,0,0.000000," ","integrate(sec(b*x+a)**7/sin(b*x+a),x)","\int \frac{\sec^{7}{\left(a + b x \right)}}{\sin{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**7/sin(a + b*x), x)","F",0
133,1,82,0,8.666653," ","integrate(cos(b*x+a)**7/sin(b*x+a)**2,x)","\begin{cases} - \frac{16 \sin^{5}{\left(a + b x \right)}}{5 b} - \frac{8 \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} - \frac{6 \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{b} - \frac{\cos^{6}{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{7}{\left(a \right)}}{\sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-16*sin(a + b*x)**5/(5*b) - 8*sin(a + b*x)**3*cos(a + b*x)**2/b - 6*sin(a + b*x)*cos(a + b*x)**4/b - cos(a + b*x)**6/(b*sin(a + b*x)), Ne(b, 0)), (x*cos(a)**7/sin(a)**2, True))","A",0
134,1,119,0,5.336121," ","integrate(cos(b*x+a)**6/sin(b*x+a)**2,x)","\begin{cases} - \frac{15 x \sin^{4}{\left(a + b x \right)}}{8} - \frac{15 x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} - \frac{15 x \cos^{4}{\left(a + b x \right)}}{8} - \frac{15 \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} - \frac{25 \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{8 b} - \frac{\cos^{5}{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{6}{\left(a \right)}}{\sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*x*sin(a + b*x)**4/8 - 15*x*sin(a + b*x)**2*cos(a + b*x)**2/4 - 15*x*cos(a + b*x)**4/8 - 15*sin(a + b*x)**3*cos(a + b*x)/(8*b) - 25*sin(a + b*x)*cos(a + b*x)**3/(8*b) - cos(a + b*x)**5/(b*sin(a + b*x)), Ne(b, 0)), (x*cos(a)**6/sin(a)**2, True))","A",0
135,1,61,0,3.248839," ","integrate(cos(b*x+a)**5/sin(b*x+a)**2,x)","\begin{cases} - \frac{8 \sin^{3}{\left(a + b x \right)}}{3 b} - \frac{4 \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} - \frac{\cos^{4}{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{5}{\left(a \right)}}{\sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-8*sin(a + b*x)**3/(3*b) - 4*sin(a + b*x)*cos(a + b*x)**2/b - cos(a + b*x)**4/(b*sin(a + b*x)), Ne(b, 0)), (x*cos(a)**5/sin(a)**2, True))","A",0
136,1,75,0,1.771077," ","integrate(cos(b*x+a)**4/sin(b*x+a)**2,x)","\begin{cases} - \frac{3 x \sin^{2}{\left(a + b x \right)}}{2} - \frac{3 x \cos^{2}{\left(a + b x \right)}}{2} - \frac{3 \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} - \frac{\cos^{3}{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{4}{\left(a \right)}}{\sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*x*sin(a + b*x)**2/2 - 3*x*cos(a + b*x)**2/2 - 3*sin(a + b*x)*cos(a + b*x)/(2*b) - cos(a + b*x)**3/(b*sin(a + b*x)), Ne(b, 0)), (x*cos(a)**4/sin(a)**2, True))","A",0
137,1,39,0,1.399338," ","integrate(cos(b*x+a)**3/sin(b*x+a)**2,x)","\begin{cases} - \frac{2 \sin{\left(a + b x \right)}}{b} - \frac{\cos^{2}{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{3}{\left(a \right)}}{\sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sin(a + b*x)/b - cos(a + b*x)**2/(b*sin(a + b*x)), Ne(b, 0)), (x*cos(a)**3/sin(a)**2, True))","A",0
138,1,29,0,1.082496," ","integrate(cos(b*x+a)**2/sin(b*x+a)**2,x)","\begin{cases} - x - \frac{\cos{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{2}{\left(a \right)}}{\sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x - cos(a + b*x)/(b*sin(a + b*x)), Ne(b, 0)), (x*cos(a)**2/sin(a)**2, True))","A",0
139,1,20,0,1.021696," ","integrate(cos(b*x+a)/sin(b*x+a)**2,x)","\begin{cases} - \frac{1}{b \sin{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos{\left(a \right)}}{\sin^{2}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(b*sin(a + b*x)), Ne(b, 0)), (x*cos(a)/sin(a)**2, True))","A",0
140,0,0,0,0.000000," ","integrate(sec(b*x+a)/sin(b*x+a)**2,x)","\int \frac{\sec{\left(a + b x \right)}}{\sin^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)/sin(a + b*x)**2, x)","F",0
141,0,0,0,0.000000," ","integrate(sec(b*x+a)**2/sin(b*x+a)**2,x)","\int \frac{\sec^{2}{\left(a + b x \right)}}{\sin^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**2/sin(a + b*x)**2, x)","F",0
142,0,0,0,0.000000," ","integrate(sec(b*x+a)**3/sin(b*x+a)**2,x)","\int \frac{\sec^{3}{\left(a + b x \right)}}{\sin^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**3/sin(a + b*x)**2, x)","F",0
143,0,0,0,0.000000," ","integrate(sec(b*x+a)**4/sin(b*x+a)**2,x)","\int \frac{\sec^{4}{\left(a + b x \right)}}{\sin^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**4/sin(a + b*x)**2, x)","F",0
144,0,0,0,0.000000," ","integrate(sec(b*x+a)**5/sin(b*x+a)**2,x)","\int \frac{\sec^{5}{\left(a + b x \right)}}{\sin^{2}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**5/sin(a + b*x)**2, x)","F",0
145,1,1484,0,12.973058," ","integrate(cos(b*x+a)**7/sin(b*x+a)**3,x)","\begin{cases} \frac{24 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{96 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{144 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{96 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{24 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{24 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{96 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{144 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{96 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{24 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{\tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{57 \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{80 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{57 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{8 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 48 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 32 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{7}{\left(a \right)}}{\sin^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((24*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**10/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 96*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**8/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 144*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**6/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 96*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 24*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 24*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**10/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 96*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**8/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 144*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 96*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 24*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - tan(a/2 + b*x/2)**12/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 57*tan(a/2 + b*x/2)**8/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 80*tan(a/2 + b*x/2)**6/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 57*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 1/(8*b*tan(a/2 + b*x/2)**10 + 32*b*tan(a/2 + b*x/2)**8 + 48*b*tan(a/2 + b*x/2)**6 + 32*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2), Ne(b, 0)), (x*cos(a)**7/sin(a)**3, True))","A",0
146,1,719,0,11.079206," ","integrate(cos(b*x+a)**6/sin(b*x+a)**3,x)","\begin{cases} - \frac{60 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{180 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{180 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{60 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{3 \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{165 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{225 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{130 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{3}{24 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 72 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 24 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{6}{\left(a \right)}}{\sin^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-60*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**8/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2) - 180*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2) - 180*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2) - 60*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2) + 3*tan(a/2 + b*x/2)**10/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2) - 165*tan(a/2 + b*x/2)**6/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2) - 225*tan(a/2 + b*x/2)**4/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2) - 130*tan(a/2 + b*x/2)**2/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2) - 3/(24*b*tan(a/2 + b*x/2)**8 + 72*b*tan(a/2 + b*x/2)**6 + 72*b*tan(a/2 + b*x/2)**4 + 24*b*tan(a/2 + b*x/2)**2), Ne(b, 0)), (x*cos(a)**6/sin(a)**3, True))","A",0
147,1,614,0,4.831426," ","integrate(cos(b*x+a)**5/sin(b*x+a)**3,x)","\begin{cases} \frac{16 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{32 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{16 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{16 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{32 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{16 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{\tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{18 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{5}{\left(a \right)}}{\sin^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**6/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 32*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 16*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 16*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 32*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 16*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - tan(a/2 + b*x/2)**8/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 18*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 1/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2), Ne(b, 0)), (x*cos(a)**5/sin(a)**3, True))","A",0
148,1,241,0,3.924928," ","integrate(cos(b*x+a)**4/sin(b*x+a)**3,x)","\begin{cases} - \frac{12 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{12 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{\tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{18 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{8 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{4}{\left(a \right)}}{\sin^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 12*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(8*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + tan(a/2 + b*x/2)**6/(8*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 18*tan(a/2 + b*x/2)**2/(8*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 1/(8*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2), Ne(b, 0)), (x*cos(a)**4/sin(a)**3, True))","A",0
149,1,42,0,1.497379," ","integrate(cos(b*x+a)**3/sin(b*x+a)**3,x)","\begin{cases} - \frac{\log{\left(\sin{\left(a + b x \right)} \right)}}{b} - \frac{\cos^{2}{\left(a + b x \right)}}{2 b \sin^{2}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{3}{\left(a \right)}}{\sin^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(sin(a + b*x))/b - cos(a + b*x)**2/(2*b*sin(a + b*x)**2), Ne(b, 0)), (x*cos(a)**3/sin(a)**3, True))","A",0
150,1,58,0,1.607159," ","integrate(cos(b*x+a)**2/sin(b*x+a)**3,x)","\begin{cases} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{2 b} + \frac{\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b} - \frac{1}{8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{2}{\left(a \right)}}{\sin^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(a/2 + b*x/2))/(2*b) + tan(a/2 + b*x/2)**2/(8*b) - 1/(8*b*tan(a/2 + b*x/2)**2), Ne(b, 0)), (x*cos(a)**2/sin(a)**3, True))","A",0
151,1,24,0,1.460470," ","integrate(cos(b*x+a)/sin(b*x+a)**3,x)","\begin{cases} - \frac{1}{2 b \sin^{2}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos{\left(a \right)}}{\sin^{3}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(2*b*sin(a + b*x)**2), Ne(b, 0)), (x*cos(a)/sin(a)**3, True))","A",0
152,0,0,0,0.000000," ","integrate(sec(b*x+a)/sin(b*x+a)**3,x)","\int \frac{\sec{\left(a + b x \right)}}{\sin^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)/sin(a + b*x)**3, x)","F",0
153,0,0,0,0.000000," ","integrate(sec(b*x+a)**2/sin(b*x+a)**3,x)","\int \frac{\sec^{2}{\left(a + b x \right)}}{\sin^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**2/sin(a + b*x)**3, x)","F",0
154,0,0,0,0.000000," ","integrate(sec(b*x+a)**3/sin(b*x+a)**3,x)","\int \frac{\sec^{3}{\left(a + b x \right)}}{\sin^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**3/sin(a + b*x)**3, x)","F",0
155,0,0,0,0.000000," ","integrate(sec(b*x+a)**4/sin(b*x+a)**3,x)","\int \frac{\sec^{4}{\left(a + b x \right)}}{\sin^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**4/sin(a + b*x)**3, x)","F",0
156,0,0,0,0.000000," ","integrate(sec(b*x+a)**5/sin(b*x+a)**3,x)","\int \frac{\sec^{5}{\left(a + b x \right)}}{\sin^{3}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**5/sin(a + b*x)**3, x)","F",0
157,1,105,0,22.232731," ","integrate(cos(b*x+a)**9/sin(b*x+a)**4,x)","\begin{cases} \frac{128 \sin^{5}{\left(a + b x \right)}}{15 b} + \frac{64 \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{3 b} + \frac{16 \sin{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{b} + \frac{8 \cos^{6}{\left(a + b x \right)}}{3 b \sin{\left(a + b x \right)}} - \frac{\cos^{8}{\left(a + b x \right)}}{3 b \sin^{3}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{9}{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((128*sin(a + b*x)**5/(15*b) + 64*sin(a + b*x)**3*cos(a + b*x)**2/(3*b) + 16*sin(a + b*x)*cos(a + b*x)**4/b + 8*cos(a + b*x)**6/(3*b*sin(a + b*x)) - cos(a + b*x)**8/(3*b*sin(a + b*x)**3), Ne(b, 0)), (x*cos(a)**9/sin(a)**4, True))","A",0
158,1,141,0,14.833828," ","integrate(cos(b*x+a)**8/sin(b*x+a)**4,x)","\begin{cases} \frac{35 x \sin^{4}{\left(a + b x \right)}}{8} + \frac{35 x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{35 x \cos^{4}{\left(a + b x \right)}}{8} + \frac{35 \sin^{3}{\left(a + b x \right)} \cos{\left(a + b x \right)}}{8 b} + \frac{175 \sin{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)}}{24 b} + \frac{7 \cos^{5}{\left(a + b x \right)}}{3 b \sin{\left(a + b x \right)}} - \frac{\cos^{7}{\left(a + b x \right)}}{3 b \sin^{3}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{8}{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((35*x*sin(a + b*x)**4/8 + 35*x*sin(a + b*x)**2*cos(a + b*x)**2/4 + 35*x*cos(a + b*x)**4/8 + 35*sin(a + b*x)**3*cos(a + b*x)/(8*b) + 175*sin(a + b*x)*cos(a + b*x)**3/(24*b) + 7*cos(a + b*x)**5/(3*b*sin(a + b*x)) - cos(a + b*x)**7/(3*b*sin(a + b*x)**3), Ne(b, 0)), (x*cos(a)**8/sin(a)**4, True))","A",0
159,1,82,0,9.587653," ","integrate(cos(b*x+a)**7/sin(b*x+a)**4,x)","\begin{cases} \frac{16 \sin^{3}{\left(a + b x \right)}}{3 b} + \frac{8 \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b} + \frac{2 \cos^{4}{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} - \frac{\cos^{6}{\left(a + b x \right)}}{3 b \sin^{3}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{7}{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*sin(a + b*x)**3/(3*b) + 8*sin(a + b*x)*cos(a + b*x)**2/b + 2*cos(a + b*x)**4/(b*sin(a + b*x)) - cos(a + b*x)**6/(3*b*sin(a + b*x)**3), Ne(b, 0)), (x*cos(a)**7/sin(a)**4, True))","A",0
160,1,97,0,6.722381," ","integrate(cos(b*x+a)**6/sin(b*x+a)**4,x)","\begin{cases} \frac{5 x \sin^{2}{\left(a + b x \right)}}{2} + \frac{5 x \cos^{2}{\left(a + b x \right)}}{2} + \frac{5 \sin{\left(a + b x \right)} \cos{\left(a + b x \right)}}{2 b} + \frac{5 \cos^{3}{\left(a + b x \right)}}{3 b \sin{\left(a + b x \right)}} - \frac{\cos^{5}{\left(a + b x \right)}}{3 b \sin^{3}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{6}{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*x*sin(a + b*x)**2/2 + 5*x*cos(a + b*x)**2/2 + 5*sin(a + b*x)*cos(a + b*x)/(2*b) + 5*cos(a + b*x)**3/(3*b*sin(a + b*x)) - cos(a + b*x)**5/(3*b*sin(a + b*x)**3), Ne(b, 0)), (x*cos(a)**6/sin(a)**4, True))","A",0
161,1,63,0,3.761682," ","integrate(cos(b*x+a)**5/sin(b*x+a)**4,x)","\begin{cases} \frac{8 \sin{\left(a + b x \right)}}{3 b} + \frac{4 \cos^{2}{\left(a + b x \right)}}{3 b \sin{\left(a + b x \right)}} - \frac{\cos^{4}{\left(a + b x \right)}}{3 b \sin^{3}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{5}{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*sin(a + b*x)/(3*b) + 4*cos(a + b*x)**2/(3*b*sin(a + b*x)) - cos(a + b*x)**4/(3*b*sin(a + b*x)**3), Ne(b, 0)), (x*cos(a)**5/sin(a)**4, True))","A",0
162,1,48,0,2.536783," ","integrate(cos(b*x+a)**4/sin(b*x+a)**4,x)","\begin{cases} x + \frac{\cos{\left(a + b x \right)}}{b \sin{\left(a + b x \right)}} - \frac{\cos^{3}{\left(a + b x \right)}}{3 b \sin^{3}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{4}{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x + cos(a + b*x)/(b*sin(a + b*x)) - cos(a + b*x)**3/(3*b*sin(a + b*x)**3), Ne(b, 0)), (x*cos(a)**4/sin(a)**4, True))","A",0
163,1,42,0,2.263266," ","integrate(cos(b*x+a)**3/sin(b*x+a)**4,x)","\begin{cases} \frac{2}{3 b \sin{\left(a + b x \right)}} - \frac{\cos^{2}{\left(a + b x \right)}}{3 b \sin^{3}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{3}{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2/(3*b*sin(a + b*x)) - cos(a + b*x)**2/(3*b*sin(a + b*x)**3), Ne(b, 0)), (x*cos(a)**3/sin(a)**4, True))","A",0
164,1,71,0,2.614208," ","integrate(cos(b*x+a)**2/sin(b*x+a)**4,x)","\begin{cases} \frac{\tan^{3}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{24 b} - \frac{\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b} + \frac{1}{8 b \tan{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{24 b \tan^{3}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{2}{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((tan(a/2 + b*x/2)**3/(24*b) - tan(a/2 + b*x/2)/(8*b) + 1/(8*b*tan(a/2 + b*x/2)) - 1/(24*b*tan(a/2 + b*x/2)**3), Ne(b, 0)), (x*cos(a)**2/sin(a)**4, True))","A",0
165,1,24,0,1.572742," ","integrate(cos(b*x+a)/sin(b*x+a)**4,x)","\begin{cases} - \frac{1}{3 b \sin^{3}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos{\left(a \right)}}{\sin^{4}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(3*b*sin(a + b*x)**3), Ne(b, 0)), (x*cos(a)/sin(a)**4, True))","A",0
166,0,0,0,0.000000," ","integrate(sec(b*x+a)/sin(b*x+a)**4,x)","\int \frac{\sec{\left(a + b x \right)}}{\sin^{4}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)/sin(a + b*x)**4, x)","F",0
167,0,0,0,0.000000," ","integrate(sec(b*x+a)**2/sin(b*x+a)**4,x)","\int \frac{\sec^{2}{\left(a + b x \right)}}{\sin^{4}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**2/sin(a + b*x)**4, x)","F",0
168,0,0,0,0.000000," ","integrate(sec(b*x+a)**3/sin(b*x+a)**4,x)","\int \frac{\sec^{3}{\left(a + b x \right)}}{\sin^{4}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**3/sin(a + b*x)**4, x)","F",0
169,0,0,0,0.000000," ","integrate(sec(b*x+a)**4/sin(b*x+a)**4,x)","\int \frac{\sec^{4}{\left(a + b x \right)}}{\sin^{4}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**4/sin(a + b*x)**4, x)","F",0
170,0,0,0,0.000000," ","integrate(sec(b*x+a)**5/sin(b*x+a)**4,x)","\int \frac{\sec^{5}{\left(a + b x \right)}}{\sin^{4}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**5/sin(a + b*x)**4, x)","F",0
171,1,1664,0,27.693431," ","integrate(cos(b*x+a)**9/sin(b*x+a)**5,x)","\begin{cases} - \frac{384 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1536 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{2304 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1536 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{384 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{384 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{1536 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{2304 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{1536 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{384 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{\tan^{16}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{24 \tan^{14}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{744 \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1182 \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{744 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{24 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{64 b \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 384 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 256 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{9}{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-384*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**12/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 1536*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**10/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 2304*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**8/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 1536*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**6/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 384*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 384*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**12/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 1536*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**10/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 2304*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**8/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 1536*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 384*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - tan(a/2 + b*x/2)**16/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 24*tan(a/2 + b*x/2)**14/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 744*tan(a/2 + b*x/2)**10/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 1182*tan(a/2 + b*x/2)**8/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 744*tan(a/2 + b*x/2)**6/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 24*tan(a/2 + b*x/2)**2/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 1/(64*b*tan(a/2 + b*x/2)**12 + 256*b*tan(a/2 + b*x/2)**10 + 384*b*tan(a/2 + b*x/2)**8 + 256*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4), Ne(b, 0)), (x*cos(a)**9/sin(a)**5, True))","A",0
172,1,869,0,18.449574," ","integrate(cos(b*x+a)**8/sin(b*x+a)**5,x)","\begin{cases} \frac{840 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{2520 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{2520 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{840 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{3 \tan^{14}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{63 \tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{2016 \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{3066 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{1694 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{63 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{3}{192 b \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 576 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 192 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{8}{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((840*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**10/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) + 2520*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**8/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) + 2520*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) + 840*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) + 3*tan(a/2 + b*x/2)**14/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) - 63*tan(a/2 + b*x/2)**12/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) + 2016*tan(a/2 + b*x/2)**8/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) + 3066*tan(a/2 + b*x/2)**6/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) + 1694*tan(a/2 + b*x/2)**4/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) + 63*tan(a/2 + b*x/2)**2/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4) - 3/(192*b*tan(a/2 + b*x/2)**10 + 576*b*tan(a/2 + b*x/2)**8 + 576*b*tan(a/2 + b*x/2)**6 + 192*b*tan(a/2 + b*x/2)**4), Ne(b, 0)), (x*cos(a)**8/sin(a)**5, True))","A",0
173,1,733,0,11.567928," ","integrate(cos(b*x+a)**7/sin(b*x+a)**5,x)","\begin{cases} - \frac{192 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{384 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{192 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{192 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{384 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{192 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{\tan^{12}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{18 \tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{166 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{18 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{64 b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 128 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{7}{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-192*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**8/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 384*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**6/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 192*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 192*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**8/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 384*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 192*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - tan(a/2 + b*x/2)**12/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 18*tan(a/2 + b*x/2)**10/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 166*tan(a/2 + b*x/2)**6/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 18*tan(a/2 + b*x/2)**2/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 1/(64*b*tan(a/2 + b*x/2)**8 + 128*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4), Ne(b, 0)), (x*cos(a)**7/sin(a)**5, True))","A",0
174,1,330,0,6.829056," ","integrate(cos(b*x+a)**6/sin(b*x+a)**5,x)","\begin{cases} \frac{120 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{120 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{\tan^{10}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{15 \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{160 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{15 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{64 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{6}{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((120*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(64*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 120*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(64*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + tan(a/2 + b*x/2)**10/(64*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 15*tan(a/2 + b*x/2)**8/(64*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 160*tan(a/2 + b*x/2)**4/(64*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) + 15*tan(a/2 + b*x/2)**2/(64*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4) - 1/(64*b*tan(a/2 + b*x/2)**6 + 64*b*tan(a/2 + b*x/2)**4), Ne(b, 0)), (x*cos(a)**6/sin(a)**5, True))","A",0
175,1,61,0,3.044716," ","integrate(cos(b*x+a)**5/sin(b*x+a)**5,x)","\begin{cases} \frac{\log{\left(\sin{\left(a + b x \right)} \right)}}{b} + \frac{\cos^{2}{\left(a + b x \right)}}{2 b \sin^{2}{\left(a + b x \right)}} - \frac{\cos^{4}{\left(a + b x \right)}}{4 b \sin^{4}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{5}{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(a + b*x))/b + cos(a + b*x)**2/(2*b*sin(a + b*x)**2) - cos(a + b*x)**4/(4*b*sin(a + b*x)**4), Ne(b, 0)), (x*cos(a)**5/sin(a)**5, True))","A",0
176,1,92,0,4.161185," ","integrate(cos(b*x+a)**4/sin(b*x+a)**5,x)","\begin{cases} \frac{3 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{8 b} + \frac{\tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b} - \frac{\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b} + \frac{1}{8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{4}{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*log(tan(a/2 + b*x/2))/(8*b) + tan(a/2 + b*x/2)**4/(64*b) - tan(a/2 + b*x/2)**2/(8*b) + 1/(8*b*tan(a/2 + b*x/2)**2) - 1/(64*b*tan(a/2 + b*x/2)**4), Ne(b, 0)), (x*cos(a)**4/sin(a)**5, True))","A",0
177,1,44,0,2.898034," ","integrate(cos(b*x+a)**3/sin(b*x+a)**5,x)","\begin{cases} \frac{1}{4 b \sin^{2}{\left(a + b x \right)}} - \frac{\cos^{2}{\left(a + b x \right)}}{4 b \sin^{4}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{3}{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1/(4*b*sin(a + b*x)**2) - cos(a + b*x)**2/(4*b*sin(a + b*x)**4), Ne(b, 0)), (x*cos(a)**3/sin(a)**5, True))","A",0
178,1,58,0,3.952459," ","integrate(cos(b*x+a)**2/sin(b*x+a)**5,x)","\begin{cases} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{8 b} + \frac{\tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{64 b} - \frac{1}{64 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos^{2}{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(tan(a/2 + b*x/2))/(8*b) + tan(a/2 + b*x/2)**4/(64*b) - 1/(64*b*tan(a/2 + b*x/2)**4), Ne(b, 0)), (x*cos(a)**2/sin(a)**5, True))","A",0
179,1,24,0,2.679320," ","integrate(cos(b*x+a)/sin(b*x+a)**5,x)","\begin{cases} - \frac{1}{4 b \sin^{4}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \cos{\left(a \right)}}{\sin^{5}{\left(a \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-1/(4*b*sin(a + b*x)**4), Ne(b, 0)), (x*cos(a)/sin(a)**5, True))","A",0
180,0,0,0,0.000000," ","integrate(sec(b*x+a)/sin(b*x+a)**5,x)","\int \frac{\sec{\left(a + b x \right)}}{\sin^{5}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)/sin(a + b*x)**5, x)","F",0
181,0,0,0,0.000000," ","integrate(sec(b*x+a)**2/sin(b*x+a)**5,x)","\int \frac{\sec^{2}{\left(a + b x \right)}}{\sin^{5}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**2/sin(a + b*x)**5, x)","F",0
182,0,0,0,0.000000," ","integrate(sec(b*x+a)**3/sin(b*x+a)**5,x)","\int \frac{\sec^{3}{\left(a + b x \right)}}{\sin^{5}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**3/sin(a + b*x)**5, x)","F",0
183,0,0,0,0.000000," ","integrate(sec(b*x+a)**4/sin(b*x+a)**5,x)","\int \frac{\sec^{4}{\left(a + b x \right)}}{\sin^{5}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**4/sin(a + b*x)**5, x)","F",0
184,0,0,0,0.000000," ","integrate(sec(b*x+a)**5/sin(b*x+a)**5,x)","\int \frac{\sec^{5}{\left(a + b x \right)}}{\sin^{5}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sec(a + b*x)**5/sin(a + b*x)**5, x)","F",0
185,1,29,0,0.070117," ","integrate(cos(x)**2/sin(x)**6,x)","\frac{2 \cos{\left(x \right)}}{15 \sin{\left(x \right)}} + \frac{\cos{\left(x \right)}}{15 \sin^{3}{\left(x \right)}} - \frac{\cos{\left(x \right)}}{5 \sin^{5}{\left(x \right)}}"," ",0,"2*cos(x)/(15*sin(x)) + cos(x)/(15*sin(x)**3) - cos(x)/(5*sin(x)**5)","B",0
186,1,15,0,0.112989," ","integrate(cos(x)**3/sin(x)**7,x)","- \frac{2 - 3 \sin^{2}{\left(x \right)}}{12 \sin^{6}{\left(x \right)}}"," ",0,"-(2 - 3*sin(x)**2)/(12*sin(x)**6)","A",0
187,1,34,0,52.071599," ","integrate((d*cos(b*x+a))**(3/2)*sin(b*x+a),x)","\begin{cases} - \frac{2 d^{\frac{3}{2}} \cos^{\frac{5}{2}}{\left(a + b x \right)}}{5 b} & \text{for}\: b \neq 0 \\x \left(d \cos{\left(a \right)}\right)^{\frac{3}{2}} \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*d**(3/2)*cos(a + b*x)**(5/2)/(5*b), Ne(b, 0)), (x*(d*cos(a))**(3/2)*sin(a), True))","A",0
188,1,34,0,1.667081," ","integrate((d*cos(b*x+a))**(1/2)*sin(b*x+a),x)","\begin{cases} - \frac{2 \sqrt{d} \cos^{\frac{3}{2}}{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sqrt{d \cos{\left(a \right)}} \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(d)*cos(a + b*x)**(3/2)/(3*b), Ne(b, 0)), (x*sqrt(d*cos(a))*sin(a), True))","A",0
189,1,32,0,1.547376," ","integrate(sin(b*x+a)/(d*cos(b*x+a))**(1/2),x)","\begin{cases} - \frac{2 \sqrt{\cos{\left(a + b x \right)}}}{b \sqrt{d}} & \text{for}\: b \neq 0 \\\frac{x \sin{\left(a \right)}}{\sqrt{d \cos{\left(a \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(cos(a + b*x))/(b*sqrt(d)), Ne(b, 0)), (x*sin(a)/sqrt(d*cos(a)), True))","A",0
190,1,31,0,5.956300," ","integrate(sin(b*x+a)/(d*cos(b*x+a))**(3/2),x)","\begin{cases} \frac{2}{b d^{\frac{3}{2}} \sqrt{\cos{\left(a + b x \right)}}} & \text{for}\: b \neq 0 \\\frac{x \sin{\left(a \right)}}{\left(d \cos{\left(a \right)}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2/(b*d**(3/2)*sqrt(cos(a + b*x))), Ne(b, 0)), (x*sin(a)/(d*cos(a))**(3/2), True))","A",0
191,1,32,0,56.234892," ","integrate(sin(b*x+a)/(d*cos(b*x+a))**(5/2),x)","\begin{cases} \frac{2}{3 b d^{\frac{5}{2}} \cos^{\frac{3}{2}}{\left(a + b x \right)}} & \text{for}\: b \neq 0 \\\frac{x \sin{\left(a \right)}}{\left(d \cos{\left(a \right)}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2/(3*b*d**(5/2)*cos(a + b*x)**(3/2)), Ne(b, 0)), (x*sin(a)/(d*cos(a))**(5/2), True))","A",0
192,-1,0,0,0.000000," ","integrate(sin(b*x+a)/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
193,-1,0,0,0.000000," ","integrate(sin(b*x+a)/(d*cos(b*x+a))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
194,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(9/2)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
195,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(7/2)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
196,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(5/2)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*sin(b*x+a)**2,x)","\int \sqrt{d \cos{\left(a + b x \right)}} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(d*cos(a + b*x))*sin(a + b*x)**2, x)","F",0
199,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*cos(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*cos(b*x+a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/(d*cos(b*x+a))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,1,65,0,12.455664," ","integrate((d*cos(b*x+a))**(1/2)*sin(b*x+a)**3,x)","\begin{cases} - \frac{2 \sqrt{d} \sin^{2}{\left(a + b x \right)} \cos^{\frac{3}{2}}{\left(a + b x \right)}}{3 b} - \frac{8 \sqrt{d} \cos^{\frac{7}{2}}{\left(a + b x \right)}}{21 b} & \text{for}\: b \neq 0 \\x \sqrt{d \cos{\left(a \right)}} \sin^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sqrt(d)*sin(a + b*x)**2*cos(a + b*x)**(3/2)/(3*b) - 8*sqrt(d)*cos(a + b*x)**(7/2)/(21*b), Ne(b, 0)), (x*sqrt(d*cos(a))*sin(a)**3, True))","A",0
205,1,63,0,6.172101," ","integrate(sin(b*x+a)**3/(d*cos(b*x+a))**(1/2),x)","\begin{cases} - \frac{2 \sin^{2}{\left(a + b x \right)} \sqrt{\cos{\left(a + b x \right)}}}{b \sqrt{d}} - \frac{8 \cos^{\frac{5}{2}}{\left(a + b x \right)}}{5 b \sqrt{d}} & \text{for}\: b \neq 0 \\\frac{x \sin^{3}{\left(a \right)}}{\sqrt{d \cos{\left(a \right)}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sin(a + b*x)**2*sqrt(cos(a + b*x))/(b*sqrt(d)) - 8*cos(a + b*x)**(5/2)/(5*b*sqrt(d)), Ne(b, 0)), (x*sin(a)**3/sqrt(d*cos(a)), True))","A",0
206,1,61,0,6.509788," ","integrate(sin(b*x+a)**3/(d*cos(b*x+a))**(3/2),x)","\begin{cases} \frac{2 \sin^{2}{\left(a + b x \right)}}{b d^{\frac{3}{2}} \sqrt{\cos{\left(a + b x \right)}}} + \frac{8 \cos^{\frac{3}{2}}{\left(a + b x \right)}}{3 b d^{\frac{3}{2}}} & \text{for}\: b \neq 0 \\\frac{x \sin^{3}{\left(a \right)}}{\left(d \cos{\left(a \right)}\right)^{\frac{3}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sin(a + b*x)**2/(b*d**(3/2)*sqrt(cos(a + b*x))) + 8*cos(a + b*x)**(3/2)/(3*b*d**(3/2)), Ne(b, 0)), (x*sin(a)**3/(d*cos(a))**(3/2), True))","A",0
207,1,63,0,55.338151," ","integrate(sin(b*x+a)**3/(d*cos(b*x+a))**(5/2),x)","\begin{cases} \frac{2 \sin^{2}{\left(a + b x \right)}}{3 b d^{\frac{5}{2}} \cos^{\frac{3}{2}}{\left(a + b x \right)}} + \frac{8 \sqrt{\cos{\left(a + b x \right)}}}{3 b d^{\frac{5}{2}}} & \text{for}\: b \neq 0 \\\frac{x \sin^{3}{\left(a \right)}}{\left(d \cos{\left(a \right)}\right)^{\frac{5}{2}}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*sin(a + b*x)**2/(3*b*d**(5/2)*cos(a + b*x)**(3/2)) + 8*sqrt(cos(a + b*x))/(3*b*d**(5/2)), Ne(b, 0)), (x*sin(a)**3/(d*cos(a))**(5/2), True))","A",0
208,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*cos(b*x+a))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/(d*cos(b*x+a))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
211,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(9/2)*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(7/2)*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(5/2)*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate(sin(b*x+a)**4/(d*cos(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate(sin(b*x+a)**4/(d*cos(b*x+a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate(sin(b*x+a)**4/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate(sin(b*x+a)**4/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,-1,0,0,0.000000," ","integrate(sin(b*x+a)**4/(d*cos(b*x+a))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,-1,0,0,0.000000," ","integrate(cos(b*x+a)**(3/2)*sin(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
222,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(9/2)*csc(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(7/2)*csc(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(5/2)*csc(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
225,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)*csc(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
226,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*csc(b*x+a),x)","\int \sqrt{d \cos{\left(a + b x \right)}} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(d*cos(a + b*x))*csc(a + b*x), x)","F",0
227,0,0,0,0.000000," ","integrate(csc(b*x+a)/(d*cos(b*x+a))**(1/2),x)","\int \frac{\csc{\left(a + b x \right)}}{\sqrt{d \cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(csc(a + b*x)/sqrt(d*cos(a + b*x)), x)","F",0
228,0,0,0,0.000000," ","integrate(csc(b*x+a)/(d*cos(b*x+a))**(3/2),x)","\int \frac{\csc{\left(a + b x \right)}}{\left(d \cos{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(a + b*x)/(d*cos(a + b*x))**(3/2), x)","F",0
229,-1,0,0,0.000000," ","integrate(csc(b*x+a)/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,-1,0,0,0.000000," ","integrate(csc(b*x+a)/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
231,-1,0,0,0.000000," ","integrate(csc(b*x+a)/(d*cos(b*x+a))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
232,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(11/2)*csc(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
233,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(9/2)*csc(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
234,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(7/2)*csc(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
235,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(5/2)*csc(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
236,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)*csc(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
237,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*csc(b*x+a)**2,x)","\int \sqrt{d \cos{\left(a + b x \right)}} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(d*cos(a + b*x))*csc(a + b*x)**2, x)","F",0
238,0,0,0,0.000000," ","integrate(csc(b*x+a)**2/(d*cos(b*x+a))**(1/2),x)","\int \frac{\csc^{2}{\left(a + b x \right)}}{\sqrt{d \cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(csc(a + b*x)**2/sqrt(d*cos(a + b*x)), x)","F",0
239,0,0,0,0.000000," ","integrate(csc(b*x+a)**2/(d*cos(b*x+a))**(3/2),x)","\int \frac{\csc^{2}{\left(a + b x \right)}}{\left(d \cos{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(a + b*x)**2/(d*cos(a + b*x))**(3/2), x)","F",0
240,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
241,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
242,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(11/2)*csc(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
243,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(9/2)*csc(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
244,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(7/2)*csc(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
245,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(5/2)*csc(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
246,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)*csc(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*csc(b*x+a)**3,x)","\int \sqrt{d \cos{\left(a + b x \right)}} \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sqrt(d*cos(a + b*x))*csc(a + b*x)**3, x)","F",0
248,0,0,0,0.000000," ","integrate(csc(b*x+a)**3/(d*cos(b*x+a))**(1/2),x)","\int \frac{\csc^{3}{\left(a + b x \right)}}{\sqrt{d \cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(csc(a + b*x)**3/sqrt(d*cos(a + b*x)), x)","F",0
249,0,0,0,0.000000," ","integrate(csc(b*x+a)**3/(d*cos(b*x+a))**(3/2),x)","\int \frac{\csc^{3}{\left(a + b x \right)}}{\left(d \cos{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(a + b*x)**3/(d*cos(a + b*x))**(3/2), x)","F",0
250,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
252,1,34,0,28.388417," ","integrate((d*cos(b*x+a))**(1/5)*sin(b*x+a),x)","\begin{cases} - \frac{5 \sqrt[5]{d} \cos^{\frac{6}{5}}{\left(a + b x \right)}}{6 b} & \text{for}\: b \neq 0 \\x \sqrt[5]{d \cos{\left(a \right)}} \sin{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*d**(1/5)*cos(a + b*x)**(6/5)/(6*b), Ne(b, 0)), (x*(d*cos(a))**(1/5)*sin(a), True))","A",0
253,1,167,0,37.159860," ","integrate(cos(x)**3*sin(x)**(1/2),x)","\frac{28 \sqrt{2} \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{11}{2}}{\left(\frac{x}{2} \right)}}{21 \tan^{6}{\left(\frac{x}{2} \right)} + 63 \tan^{4}{\left(\frac{x}{2} \right)} + 63 \tan^{2}{\left(\frac{x}{2} \right)} + 21} + \frac{8 \sqrt{2} \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{7}{2}}{\left(\frac{x}{2} \right)}}{21 \tan^{6}{\left(\frac{x}{2} \right)} + 63 \tan^{4}{\left(\frac{x}{2} \right)} + 63 \tan^{2}{\left(\frac{x}{2} \right)} + 21} + \frac{28 \sqrt{2} \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{3}{2}}{\left(\frac{x}{2} \right)}}{21 \tan^{6}{\left(\frac{x}{2} \right)} + 63 \tan^{4}{\left(\frac{x}{2} \right)} + 63 \tan^{2}{\left(\frac{x}{2} \right)} + 21}"," ",0,"28*sqrt(2)*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(11/2)/(21*tan(x/2)**6 + 63*tan(x/2)**4 + 63*tan(x/2)**2 + 21) + 8*sqrt(2)*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(7/2)/(21*tan(x/2)**6 + 63*tan(x/2)**4 + 63*tan(x/2)**2 + 21) + 28*sqrt(2)*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(3/2)/(21*tan(x/2)**6 + 63*tan(x/2)**4 + 63*tan(x/2)**2 + 21)","B",0
254,1,24,0,66.229573," ","integrate(cos(x)**3*sin(x)**(3/2),x)","\frac{8 \sin^{\frac{9}{2}}{\left(x \right)}}{45} + \frac{2 \sin^{\frac{5}{2}}{\left(x \right)} \cos^{2}{\left(x \right)}}{5}"," ",0,"8*sin(x)**(9/2)/45 + 2*sin(x)**(5/2)*cos(x)**2/5","A",0
255,-1,0,0,0.000000," ","integrate(cos(x)**3*sin(x)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,1,323,0,32.713743," ","integrate(cos(x)**3/sin(x)**(1/2),x)","\frac{10 \sqrt{2} \tan^{5}{\left(\frac{x}{2} \right)}}{5 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{13}{2}}{\left(\frac{x}{2} \right)} + 15 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{9}{2}}{\left(\frac{x}{2} \right)} + 15 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{5}{2}}{\left(\frac{x}{2} \right)} + 5 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \sqrt{\tan{\left(\frac{x}{2} \right)}}} + \frac{12 \sqrt{2} \tan^{3}{\left(\frac{x}{2} \right)}}{5 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{13}{2}}{\left(\frac{x}{2} \right)} + 15 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{9}{2}}{\left(\frac{x}{2} \right)} + 15 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{5}{2}}{\left(\frac{x}{2} \right)} + 5 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \sqrt{\tan{\left(\frac{x}{2} \right)}}} + \frac{10 \sqrt{2} \tan{\left(\frac{x}{2} \right)}}{5 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{13}{2}}{\left(\frac{x}{2} \right)} + 15 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{9}{2}}{\left(\frac{x}{2} \right)} + 15 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \tan^{\frac{5}{2}}{\left(\frac{x}{2} \right)} + 5 \sqrt{\frac{1}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}} \sqrt{\tan{\left(\frac{x}{2} \right)}}}"," ",0,"10*sqrt(2)*tan(x/2)**5/(5*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(13/2) + 15*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(9/2) + 15*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(5/2) + 5*sqrt(1/(tan(x/2)**2 + 1))*sqrt(tan(x/2))) + 12*sqrt(2)*tan(x/2)**3/(5*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(13/2) + 15*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(9/2) + 15*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(5/2) + 5*sqrt(1/(tan(x/2)**2 + 1))*sqrt(tan(x/2))) + 10*sqrt(2)*tan(x/2)/(5*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(13/2) + 15*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(9/2) + 15*sqrt(1/(tan(x/2)**2 + 1))*tan(x/2)**(5/2) + 5*sqrt(1/(tan(x/2)**2 + 1))*sqrt(tan(x/2)))","B",0
257,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(9/2)*(c*sin(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(5/2)*(c*sin(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*(c*sin(b*x+a))**(1/2),x)","\int \sqrt{c \sin{\left(a + b x \right)}} \sqrt{d \cos{\left(a + b x \right)}}\, dx"," ",0,"Integral(sqrt(c*sin(a + b*x))*sqrt(d*cos(a + b*x)), x)","F",0
260,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(1/2)/(d*cos(b*x+a))**(3/2),x)","\int \frac{\sqrt{c \sin{\left(a + b x \right)}}}{\left(d \cos{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(c*sin(a + b*x))/(d*cos(a + b*x))**(3/2), x)","F",0
261,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(1/2)/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
262,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)*(c*sin(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(1/2)/(d*cos(b*x+a))**(1/2),x)","\int \frac{\sqrt{c \sin{\left(a + b x \right)}}}{\sqrt{d \cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(sqrt(c*sin(a + b*x))/sqrt(d*cos(a + b*x)), x)","F",0
264,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(1/2)/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(1/2)/(d*cos(b*x+a))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(1/2)/(d*cos(b*x+a))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
267,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)*(c*sin(b*x+a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
268,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(3/2)/(d*cos(b*x+a))**(1/2),x)","\int \frac{\left(c \sin{\left(a + b x \right)}\right)^{\frac{3}{2}}}{\sqrt{d \cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(3/2)/sqrt(d*cos(a + b*x)), x)","F",0
269,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(3/2)/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(3/2)/(d*cos(b*x+a))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
271,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*(c*sin(b*x+a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
272,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**(3/2)/(d*cos(b*x+a))**(3/2),x)","\int \frac{\left(c \sin{\left(a + b x \right)}\right)^{\frac{3}{2}}}{\left(d \cos{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**(3/2)/(d*cos(a + b*x))**(3/2), x)","F",0
273,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(3/2)/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(3/2)/(d*cos(b*x+a))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(3/2)/(d*cos(b*x+a))**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(9/2)*(c*sin(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(5/2)*(c*sin(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*(c*sin(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2)/(d*cos(b*x+a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2)/(d*cos(b*x+a))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2)/(d*cos(b*x+a))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2)/(d*cos(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2)/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2)/(d*cos(b*x+a))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2)/(d*cos(b*x+a))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**(5/2)/(d*cos(b*x+a))**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate(sin(b*x+a)**(7/2)/cos(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate(sin(x)**(3/2)/cos(x)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,0,0,0,0.000000," ","integrate(sin(x)**(1/2)/cos(x)**(1/2),x)","\int \frac{\sqrt{\sin{\left(x \right)}}}{\sqrt{\cos{\left(x \right)}}}\, dx"," ",0,"Integral(sqrt(sin(x))/sqrt(cos(x)), x)","F",0
290,-1,0,0,0.000000," ","integrate(sin(x)**(5/2)/cos(x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(7/2)/(c*sin(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)/(c*sin(b*x+a))**(1/2),x)","\int \frac{\left(d \cos{\left(a + b x \right)}\right)^{\frac{3}{2}}}{\sqrt{c \sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral((d*cos(a + b*x))**(3/2)/sqrt(c*sin(a + b*x)), x)","F",0
293,0,0,0,0.000000," ","integrate(1/(d*cos(b*x+a))**(1/2)/(c*sin(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{c \sin{\left(a + b x \right)}} \sqrt{d \cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(c*sin(a + b*x))*sqrt(d*cos(a + b*x))), x)","F",0
294,-1,0,0,0.000000," ","integrate(1/(d*cos(b*x+a))**(5/2)/(c*sin(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
295,-1,0,0,0.000000," ","integrate(1/(d*cos(b*x+a))**(9/2)/(c*sin(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)/(c*sin(b*x+a))**(1/2),x)","\int \frac{\sqrt{d \cos{\left(a + b x \right)}}}{\sqrt{c \sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral(sqrt(d*cos(a + b*x))/sqrt(c*sin(a + b*x)), x)","F",0
297,0,0,0,0.000000," ","integrate(1/(d*cos(b*x+a))**(3/2)/(c*sin(b*x+a))**(1/2),x)","\int \frac{1}{\sqrt{c \sin{\left(a + b x \right)}} \left(d \cos{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(c*sin(a + b*x))*(d*cos(a + b*x))**(3/2)), x)","F",0
298,-1,0,0,0.000000," ","integrate(1/(d*cos(b*x+a))**(7/2)/(c*sin(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
299,-1,0,0,0.000000," ","integrate(1/(d*cos(b*x+a))**(11/2)/(c*sin(b*x+a))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
300,0,0,0,0.000000," ","integrate(cos(b*x+a)**(1/2)/sin(b*x+a)**(1/2),x)","\int \frac{\sqrt{\cos{\left(a + b x \right)}}}{\sqrt{\sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral(sqrt(cos(a + b*x))/sqrt(sin(a + b*x)), x)","F",0
301,0,0,0,0.000000," ","integrate(cos(b*x+a)**(3/2)/sin(b*x+a)**(3/2),x)","\int \frac{\cos^{\frac{3}{2}}{\left(a + b x \right)}}{\sin^{\frac{3}{2}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(cos(a + b*x)**(3/2)/sin(a + b*x)**(3/2), x)","F",0
302,-1,0,0,0.000000," ","integrate(cos(b*x+a)**(5/2)/sin(b*x+a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
303,-1,0,0,0.000000," ","integrate(cos(b*x+a)**(7/2)/sin(b*x+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
304,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(b*sin(f*x+e))**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
305,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(b*sin(f*x+e))**(1/3),x)","\int \sqrt[3]{b \sin{\left(e + f x \right)}} \cos^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sin(e + f*x))**(1/3)*cos(e + f*x)**2, x)","F",0
306,0,0,0,0.000000," ","integrate((b*sin(f*x+e))**(1/3),x)","\int \sqrt[3]{b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral((b*sin(e + f*x))**(1/3), x)","F",0
307,0,0,0,0.000000," ","integrate(sec(f*x+e)**2*(b*sin(f*x+e))**(1/3),x)","\int \sqrt[3]{b \sin{\left(e + f x \right)}} \sec^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sin(e + f*x))**(1/3)*sec(e + f*x)**2, x)","F",0
308,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(b*sin(f*x+e))**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
309,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(b*sin(f*x+e))**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
310,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(b*sin(f*x+e))**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
311,0,0,0,0.000000," ","integrate((b*sin(f*x+e))**(5/3),x)","\int \left(b \sin{\left(e + f x \right)}\right)^{\frac{5}{3}}\, dx"," ",0,"Integral((b*sin(e + f*x))**(5/3), x)","F",0
312,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2*(b*sin(f*x+e))**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
313,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(b*sin(f*x+e))**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
314,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4/(b*sin(f*x+e))**(1/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
315,0,0,0,0.000000," ","integrate(cos(f*x+e)**2/(b*sin(f*x+e))**(1/3),x)","\int \frac{\cos^{2}{\left(e + f x \right)}}{\sqrt[3]{b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cos(e + f*x)**2/(b*sin(e + f*x))**(1/3), x)","F",0
316,0,0,0,0.000000," ","integrate(1/(b*sin(f*x+e))**(1/3),x)","\int \frac{1}{\sqrt[3]{b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral((b*sin(e + f*x))**(-1/3), x)","F",0
317,0,0,0,0.000000," ","integrate(sec(f*x+e)**2/(b*sin(f*x+e))**(1/3),x)","\int \frac{\sec^{2}{\left(e + f x \right)}}{\sqrt[3]{b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sec(e + f*x)**2/(b*sin(e + f*x))**(1/3), x)","F",0
318,0,0,0,0.000000," ","integrate(sec(f*x+e)**4/(b*sin(f*x+e))**(1/3),x)","\int \frac{\sec^{4}{\left(e + f x \right)}}{\sqrt[3]{b \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sec(e + f*x)**4/(b*sin(e + f*x))**(1/3), x)","F",0
319,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4/(b*sin(f*x+e))**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
320,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(b*sin(f*x+e))**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
321,0,0,0,0.000000," ","integrate(1/(b*sin(f*x+e))**(5/3),x)","\int \frac{1}{\left(b \sin{\left(e + f x \right)}\right)^{\frac{5}{3}}}\, dx"," ",0,"Integral((b*sin(e + f*x))**(-5/3), x)","F",0
322,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2/(b*sin(f*x+e))**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4/(b*sin(f*x+e))**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
324,0,0,0,0.000000," ","integrate(sin(b*x+a)**(1/3)/cos(b*x+a)**(1/3),x)","\int \frac{\sqrt[3]{\sin{\left(a + b x \right)}}}{\sqrt[3]{\cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral(sin(a + b*x)**(1/3)/cos(a + b*x)**(1/3), x)","F",0
325,0,0,0,0.000000," ","integrate(sin(b*x+a)**(2/3)/cos(b*x+a)**(2/3),x)","\int \frac{\sin^{\frac{2}{3}}{\left(a + b x \right)}}{\cos^{\frac{2}{3}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(sin(a + b*x)**(2/3)/cos(a + b*x)**(2/3), x)","F",0
326,-1,0,0,0.000000," ","integrate(sin(b*x+a)**(4/3)/cos(b*x+a)**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
327,-1,0,0,0.000000," ","integrate(sin(b*x+a)**(5/3)/cos(b*x+a)**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
328,-1,0,0,0.000000," ","integrate(sin(b*x+a)**(7/3)/cos(b*x+a)**(7/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,0,0,0,0.000000," ","integrate(cos(b*x+a)**(1/3)/sin(b*x+a)**(1/3),x)","\int \frac{\sqrt[3]{\cos{\left(a + b x \right)}}}{\sqrt[3]{\sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral(cos(a + b*x)**(1/3)/sin(a + b*x)**(1/3), x)","F",0
330,0,0,0,0.000000," ","integrate(cos(b*x+a)**(2/3)/sin(b*x+a)**(2/3),x)","\int \frac{\cos^{\frac{2}{3}}{\left(a + b x \right)}}{\sin^{\frac{2}{3}}{\left(a + b x \right)}}\, dx"," ",0,"Integral(cos(a + b*x)**(2/3)/sin(a + b*x)**(2/3), x)","F",0
331,-1,0,0,0.000000," ","integrate(cos(b*x+a)**(4/3)/sin(b*x+a)**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
332,-1,0,0,0.000000," ","integrate(cos(b*x+a)**(5/3)/sin(b*x+a)**(5/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate(cos(b*x+a)**(7/3)/sin(b*x+a)**(7/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate(cos(x)**(2/3)/sin(x)**(8/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(sin(x)**(2/3)/cos(x)**(8/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,0,0,0,0.000000," ","integrate(cos(f*x+e)**n*sin(f*x+e)**m,x)","\int \sin^{m}{\left(e + f x \right)} \cos^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral(sin(e + f*x)**m*cos(e + f*x)**n, x)","F",0
337,0,0,0,0.000000," ","integrate((d*cos(f*x+e))**n*sin(f*x+e)**m,x)","\int \left(d \cos{\left(e + f x \right)}\right)^{n} \sin^{m}{\left(e + f x \right)}\, dx"," ",0,"Integral((d*cos(e + f*x))**n*sin(e + f*x)**m, x)","F",0
338,0,0,0,0.000000," ","integrate(cos(f*x+e)**n*(b*sin(f*x+e))**m,x)","\int \left(b \sin{\left(e + f x \right)}\right)^{m} \cos^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sin(e + f*x))**m*cos(e + f*x)**n, x)","F",0
339,0,0,0,0.000000," ","integrate((d*cos(f*x+e))**n*(b*sin(f*x+e))**m,x)","\int \left(b \sin{\left(e + f x \right)}\right)^{m} \left(d \cos{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((b*sin(e + f*x))**m*(d*cos(e + f*x))**n, x)","F",0
340,1,2050,0,66.309685," ","integrate(cos(b*x+a)**5*(c*sin(b*x+a))**m,x)","\begin{cases} x \left(c \sin{\left(a \right)}\right)^{m} \cos^{5}{\left(a \right)} & \text{for}\: b = 0 \\\frac{\frac{\log{\left(\sin{\left(a + b x \right)} \right)}}{b} + \frac{\cos^{2}{\left(a + b x \right)}}{2 b \sin^{2}{\left(a + b x \right)}} - \frac{\cos^{4}{\left(a + b x \right)}}{4 b \sin^{4}{\left(a + b x \right)}}}{c^{5}} & \text{for}\: m = -5 \\\frac{\frac{16 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{32 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{16 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{16 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{32 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{16 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{\tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} + \frac{18 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}} - \frac{1}{8 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 16 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 8 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}}{c^{3}} & \text{for}\: m = -3 \\\frac{- \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{6 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{6 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b}}{c} & \text{for}\: m = -1 \\\frac{c^{m} m^{2} \sin{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{b m^{3} + 9 b m^{2} + 23 b m + 15 b} + \frac{4 c^{m} m \sin^{3}{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b m^{3} + 9 b m^{2} + 23 b m + 15 b} + \frac{8 c^{m} m \sin{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{b m^{3} + 9 b m^{2} + 23 b m + 15 b} + \frac{8 c^{m} \sin^{5}{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)}}{b m^{3} + 9 b m^{2} + 23 b m + 15 b} + \frac{20 c^{m} \sin^{3}{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b m^{3} + 9 b m^{2} + 23 b m + 15 b} + \frac{15 c^{m} \sin{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)} \cos^{4}{\left(a + b x \right)}}{b m^{3} + 9 b m^{2} + 23 b m + 15 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(c*sin(a))**m*cos(a)**5, Eq(b, 0)), ((log(sin(a + b*x))/b + cos(a + b*x)**2/(2*b*sin(a + b*x)**2) - cos(a + b*x)**4/(4*b*sin(a + b*x)**4))/c**5, Eq(m, -5)), ((16*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**6/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 32*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 16*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 16*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 32*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 16*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - tan(a/2 + b*x/2)**8/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) + 18*tan(a/2 + b*x/2)**4/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2) - 1/(8*b*tan(a/2 + b*x/2)**6 + 16*b*tan(a/2 + b*x/2)**4 + 8*b*tan(a/2 + b*x/2)**2))/c**3, Eq(m, -3)), ((-log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 6*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2)**2 + 1)/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 4*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 6*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 4*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b))/c, Eq(m, -1)), (c**m*m**2*sin(a + b*x)*sin(a + b*x)**m*cos(a + b*x)**4/(b*m**3 + 9*b*m**2 + 23*b*m + 15*b) + 4*c**m*m*sin(a + b*x)**3*sin(a + b*x)**m*cos(a + b*x)**2/(b*m**3 + 9*b*m**2 + 23*b*m + 15*b) + 8*c**m*m*sin(a + b*x)*sin(a + b*x)**m*cos(a + b*x)**4/(b*m**3 + 9*b*m**2 + 23*b*m + 15*b) + 8*c**m*sin(a + b*x)**5*sin(a + b*x)**m/(b*m**3 + 9*b*m**2 + 23*b*m + 15*b) + 20*c**m*sin(a + b*x)**3*sin(a + b*x)**m*cos(a + b*x)**2/(b*m**3 + 9*b*m**2 + 23*b*m + 15*b) + 15*c**m*sin(a + b*x)*sin(a + b*x)**m*cos(a + b*x)**4/(b*m**3 + 9*b*m**2 + 23*b*m + 15*b), True))","A",0
341,1,530,0,13.278370," ","integrate(cos(b*x+a)**3*(c*sin(b*x+a))**m,x)","\begin{cases} x \left(c \sin{\left(a \right)}\right)^{m} \cos^{3}{\left(a \right)} & \text{for}\: b = 0 \\\frac{- \frac{\log{\left(\sin{\left(a + b x \right)} \right)}}{b} - \frac{\cos^{2}{\left(a + b x \right)}}{2 b \sin^{2}{\left(a + b x \right)}}}{c^{3}} & \text{for}\: m = -3 \\\frac{- \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b}}{c} & \text{for}\: m = -1 \\\frac{c^{m} m \sin{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b m^{2} + 4 b m + 3 b} + \frac{2 c^{m} \sin^{3}{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)}}{b m^{2} + 4 b m + 3 b} + \frac{3 c^{m} \sin{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)}}{b m^{2} + 4 b m + 3 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(c*sin(a))**m*cos(a)**3, Eq(b, 0)), ((-log(sin(a + b*x))/b - cos(a + b*x)**2/(2*b*sin(a + b*x)**2))/c**3, Eq(m, -3)), ((-log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - 2*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2)**2 + 1)/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + 2*log(tan(a/2 + b*x/2))*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2))/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - 2*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b))/c, Eq(m, -1)), (c**m*m*sin(a + b*x)*sin(a + b*x)**m*cos(a + b*x)**2/(b*m**2 + 4*b*m + 3*b) + 2*c**m*sin(a + b*x)**3*sin(a + b*x)**m/(b*m**2 + 4*b*m + 3*b) + 3*c**m*sin(a + b*x)*sin(a + b*x)**m*cos(a + b*x)**2/(b*m**2 + 4*b*m + 3*b), True))","A",0
342,1,58,0,2.043034," ","integrate(cos(b*x+a)*(c*sin(b*x+a))**m,x)","\begin{cases} \frac{x \cos{\left(a \right)}}{c \sin{\left(a \right)}} & \text{for}\: b = 0 \wedge m = -1 \\x \left(c \sin{\left(a \right)}\right)^{m} \cos{\left(a \right)} & \text{for}\: b = 0 \\\frac{\log{\left(\sin{\left(a + b x \right)} \right)}}{b c} & \text{for}\: m = -1 \\\frac{c^{m} \sin{\left(a + b x \right)} \sin^{m}{\left(a + b x \right)}}{b m + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(a)/(c*sin(a)), Eq(b, 0) & Eq(m, -1)), (x*(c*sin(a))**m*cos(a), Eq(b, 0)), (log(sin(a + b*x))/(b*c), Eq(m, -1)), (c**m*sin(a + b*x)*sin(a + b*x)**m/(b*m + b), True))","A",0
343,0,0,0,0.000000," ","integrate(sec(b*x+a)*(c*sin(b*x+a))**m,x)","\int \left(c \sin{\left(a + b x \right)}\right)^{m} \sec{\left(a + b x \right)}\, dx"," ",0,"Integral((c*sin(a + b*x))**m*sec(a + b*x), x)","F",0
344,0,0,0,0.000000," ","integrate(sec(b*x+a)**3*(c*sin(b*x+a))**m,x)","\int \left(c \sin{\left(a + b x \right)}\right)^{m} \sec^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((c*sin(a + b*x))**m*sec(a + b*x)**3, x)","F",0
345,-1,0,0,0.000000," ","integrate(cos(b*x+a)**4*(c*sin(b*x+a))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
346,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2*(c*sin(b*x+a))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**m,x)","\int \left(c \sin{\left(a + b x \right)}\right)^{m}\, dx"," ",0,"Integral((c*sin(a + b*x))**m, x)","F",0
348,0,0,0,0.000000," ","integrate(sec(b*x+a)**2*(c*sin(b*x+a))**m,x)","\int \left(c \sin{\left(a + b x \right)}\right)^{m} \sec^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((c*sin(a + b*x))**m*sec(a + b*x)**2, x)","F",0
349,-1,0,0,0.000000," ","integrate(sec(b*x+a)**4*(c*sin(b*x+a))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**(3/2)*(c*sin(b*x+a))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
351,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**(1/2)*(c*sin(b*x+a))**m,x)","\int \left(c \sin{\left(a + b x \right)}\right)^{m} \sqrt{d \cos{\left(a + b x \right)}}\, dx"," ",0,"Integral((c*sin(a + b*x))**m*sqrt(d*cos(a + b*x)), x)","F",0
352,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**m/(d*cos(b*x+a))**(1/2),x)","\int \frac{\left(c \sin{\left(a + b x \right)}\right)^{m}}{\sqrt{d \cos{\left(a + b x \right)}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**m/sqrt(d*cos(a + b*x)), x)","F",0
353,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**m/(d*cos(b*x+a))**(3/2),x)","\int \frac{\left(c \sin{\left(a + b x \right)}\right)^{m}}{\left(d \cos{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**m/(d*cos(a + b*x))**(3/2), x)","F",0
354,-1,0,0,0.000000," ","integrate((c*sin(b*x+a))**m/(d*cos(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
355,1,2462,0,75.791090," ","integrate((d*cos(b*x+a))**n*sin(b*x+a)**5,x)","\begin{cases} x \left(d \cos{\left(a \right)}\right)^{n} \sin^{5}{\left(a \right)} & \text{for}\: b = 0 \\\frac{- \frac{\log{\left(\cos{\left(a + b x \right)} \right)}}{b} + \frac{\sin^{4}{\left(a + b x \right)}}{4 b \cos^{4}{\left(a + b x \right)}} - \frac{\sin^{2}{\left(a + b x \right)}}{2 b \cos^{2}{\left(a + b x \right)}}}{d^{5}} & \text{for}\: n = -5 \\\frac{\frac{2 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b}}{d^{3}} & \text{for}\: n = -3 \\\frac{- \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{6 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{6 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{4 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{6 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{4 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{8 \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{8}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{6}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 6 b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 4 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b}}{d} & \text{for}\: n = -1 \\- \frac{d^{n} n^{2} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{3} + 9 b n^{2} + 23 b n + 15 b} - \frac{8 d^{n} n \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{3} + 9 b n^{2} + 23 b n + 15 b} - \frac{4 d^{n} n \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{3} + 9 b n^{2} + 23 b n + 15 b} - \frac{15 d^{n} \sin^{4}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{3} + 9 b n^{2} + 23 b n + 15 b} - \frac{20 d^{n} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{3} + 9 b n^{2} + 23 b n + 15 b} - \frac{8 d^{n} \cos^{5}{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{3} + 9 b n^{2} + 23 b n + 15 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(d*cos(a))**n*sin(a)**5, Eq(b, 0)), ((-log(cos(a + b*x))/b + sin(a + b*x)**4/(4*b*cos(a + b*x)**4) - sin(a + b*x)**2/(2*b*cos(a + b*x)**2))/d**5, Eq(n, -5)), ((2*log(tan(a/2 + b*x/2) - 1)*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) - 4*log(tan(a/2 + b*x/2) - 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) + 2*log(tan(a/2 + b*x/2) - 1)/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) + 2*log(tan(a/2 + b*x/2) + 1)*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) - 4*log(tan(a/2 + b*x/2) + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) + 2*log(tan(a/2 + b*x/2) + 1)/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) - 2*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) + 4*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) - 2*log(tan(a/2 + b*x/2)**2 + 1)/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) + 4*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b) + 4*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 - 2*b*tan(a/2 + b*x/2)**4 + b))/d**3, Eq(n, -3)), ((-log(tan(a/2 + b*x/2) - 1)*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*log(tan(a/2 + b*x/2) - 1)*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 6*log(tan(a/2 + b*x/2) - 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*log(tan(a/2 + b*x/2) - 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2) - 1)/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2) + 1)*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*log(tan(a/2 + b*x/2) + 1)*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 6*log(tan(a/2 + b*x/2) + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 4*log(tan(a/2 + b*x/2) + 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2) + 1)/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**8/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 4*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 6*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + 4*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2)**2 + 1)/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 2*tan(a/2 + b*x/2)**6/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 8*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b) - 2*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**8 + 4*b*tan(a/2 + b*x/2)**6 + 6*b*tan(a/2 + b*x/2)**4 + 4*b*tan(a/2 + b*x/2)**2 + b))/d, Eq(n, -1)), (-d**n*n**2*sin(a + b*x)**4*cos(a + b*x)*cos(a + b*x)**n/(b*n**3 + 9*b*n**2 + 23*b*n + 15*b) - 8*d**n*n*sin(a + b*x)**4*cos(a + b*x)*cos(a + b*x)**n/(b*n**3 + 9*b*n**2 + 23*b*n + 15*b) - 4*d**n*n*sin(a + b*x)**2*cos(a + b*x)**3*cos(a + b*x)**n/(b*n**3 + 9*b*n**2 + 23*b*n + 15*b) - 15*d**n*sin(a + b*x)**4*cos(a + b*x)*cos(a + b*x)**n/(b*n**3 + 9*b*n**2 + 23*b*n + 15*b) - 20*d**n*sin(a + b*x)**2*cos(a + b*x)**3*cos(a + b*x)**n/(b*n**3 + 9*b*n**2 + 23*b*n + 15*b) - 8*d**n*cos(a + b*x)**5*cos(a + b*x)**n/(b*n**3 + 9*b*n**2 + 23*b*n + 15*b), True))","A",0
356,1,694,0,12.777533," ","integrate((d*cos(b*x+a))**n*sin(b*x+a)**3,x)","\begin{cases} x \left(d \cos{\left(a \right)}\right)^{n} \sin^{3}{\left(a \right)} & \text{for}\: b = 0 \\\frac{\frac{\log{\left(\cos{\left(a + b x \right)} \right)}}{b} + \frac{\sin^{2}{\left(a + b x \right)}}{2 b \cos^{2}{\left(a + b x \right)}}}{d^{3}} & \text{for}\: n = -3 \\\frac{- \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} - 1 \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{2 \log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} + \frac{\log{\left(\tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 1 \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b} - \frac{2 \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + 2 b \tan^{2}{\left(\frac{a}{2} + \frac{b x}{2} \right)} + b}}{d} & \text{for}\: n = -1 \\- \frac{d^{n} n \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{2} + 4 b n + 3 b} - \frac{3 d^{n} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{2} + 4 b n + 3 b} - \frac{2 d^{n} \cos^{3}{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n^{2} + 4 b n + 3 b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(d*cos(a))**n*sin(a)**3, Eq(b, 0)), ((log(cos(a + b*x))/b + sin(a + b*x)**2/(2*b*cos(a + b*x)**2))/d**3, Eq(n, -3)), ((-log(tan(a/2 + b*x/2) - 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - 2*log(tan(a/2 + b*x/2) - 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2) - 1)/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2) + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - 2*log(tan(a/2 + b*x/2) + 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - log(tan(a/2 + b*x/2) + 1)/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**4/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + 2*log(tan(a/2 + b*x/2)**2 + 1)*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) + log(tan(a/2 + b*x/2)**2 + 1)/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b) - 2*tan(a/2 + b*x/2)**2/(b*tan(a/2 + b*x/2)**4 + 2*b*tan(a/2 + b*x/2)**2 + b))/d, Eq(n, -1)), (-d**n*n*sin(a + b*x)**2*cos(a + b*x)*cos(a + b*x)**n/(b*n**2 + 4*b*n + 3*b) - 3*d**n*sin(a + b*x)**2*cos(a + b*x)*cos(a + b*x)**n/(b*n**2 + 4*b*n + 3*b) - 2*d**n*cos(a + b*x)**3*cos(a + b*x)**n/(b*n**2 + 4*b*n + 3*b), True))","A",0
357,1,61,0,1.918525," ","integrate((d*cos(b*x+a))**n*sin(b*x+a),x)","\begin{cases} \frac{x \sin{\left(a \right)}}{d \cos{\left(a \right)}} & \text{for}\: b = 0 \wedge n = -1 \\x \left(d \cos{\left(a \right)}\right)^{n} \sin{\left(a \right)} & \text{for}\: b = 0 \\- \frac{\log{\left(\cos{\left(a + b x \right)} \right)}}{b d} & \text{for}\: n = -1 \\- \frac{d^{n} \cos{\left(a + b x \right)} \cos^{n}{\left(a + b x \right)}}{b n + b} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)/(d*cos(a)), Eq(b, 0) & Eq(n, -1)), (x*(d*cos(a))**n*sin(a), Eq(b, 0)), (-log(cos(a + b*x))/(b*d), Eq(n, -1)), (-d**n*cos(a + b*x)*cos(a + b*x)**n/(b*n + b), True))","A",0
358,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*csc(b*x+a),x)","\int \left(d \cos{\left(a + b x \right)}\right)^{n} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral((d*cos(a + b*x))**n*csc(a + b*x), x)","F",0
359,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*csc(b*x+a)**3,x)","\int \left(d \cos{\left(a + b x \right)}\right)^{n} \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral((d*cos(a + b*x))**n*csc(a + b*x)**3, x)","F",0
360,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*csc(b*x+a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*sin(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*sin(b*x+a)**2,x)","\int \left(d \cos{\left(a + b x \right)}\right)^{n} \sin^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((d*cos(a + b*x))**n*sin(a + b*x)**2, x)","F",0
363,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**n,x)","\int \left(d \cos{\left(a + b x \right)}\right)^{n}\, dx"," ",0,"Integral((d*cos(a + b*x))**n, x)","F",0
364,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*csc(b*x+a)**2,x)","\int \left(d \cos{\left(a + b x \right)}\right)^{n} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral((d*cos(a + b*x))**n*csc(a + b*x)**2, x)","F",0
365,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*csc(b*x+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
366,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*(c*sin(b*x+a))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
367,-1,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*(c*sin(b*x+a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
368,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**n*(c*sin(b*x+a))**(1/2),x)","\int \sqrt{c \sin{\left(a + b x \right)}} \left(d \cos{\left(a + b x \right)}\right)^{n}\, dx"," ",0,"Integral(sqrt(c*sin(a + b*x))*(d*cos(a + b*x))**n, x)","F",0
369,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**n/(c*sin(b*x+a))**(1/2),x)","\int \frac{\left(d \cos{\left(a + b x \right)}\right)^{n}}{\sqrt{c \sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral((d*cos(a + b*x))**n/sqrt(c*sin(a + b*x)), x)","F",0
370,0,0,0,0.000000," ","integrate((d*cos(b*x+a))**n/(c*sin(b*x+a))**(3/2),x)","\int \frac{\left(d \cos{\left(a + b x \right)}\right)^{n}}{\left(c \sin{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*cos(a + b*x))**n/(c*sin(a + b*x))**(3/2), x)","F",0
371,-1,0,0,0.000000," ","integrate(sin(f*x+e)**7*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,0,0,0,0.000000," ","integrate(sin(f*x+e)*(b*sec(f*x+e))**(1/2),x)","\int \sqrt{b \sec{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))*sin(e + f*x), x)","F",0
375,0,0,0,0.000000," ","integrate(csc(f*x+e)*(b*sec(f*x+e))**(1/2),x)","\int \sqrt{b \sec{\left(e + f x \right)}} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))*csc(e + f*x), x)","F",0
376,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(b*sec(f*x+e))**(1/2),x)","\int \sqrt{b \sec{\left(e + f x \right)}} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))*csc(e + f*x)**3, x)","F",0
377,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,-1,0,0,0.000000," ","integrate(sin(f*x+e)**6*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
379,0,0,0,0.000000," ","integrate(sin(f*x+e)**4*(b*sec(f*x+e))**(1/2),x)","\int \sqrt{b \sec{\left(e + f x \right)}} \sin^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))*sin(e + f*x)**4, x)","F",0
380,0,0,0,0.000000," ","integrate(sin(f*x+e)**2*(b*sec(f*x+e))**(1/2),x)","\int \sqrt{b \sec{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))*sin(e + f*x)**2, x)","F",0
381,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**(1/2),x)","\int \sqrt{b \sec{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x)), x)","F",0
382,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(b*sec(f*x+e))**(1/2),x)","\int \sqrt{b \sec{\left(e + f x \right)}} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))*csc(e + f*x)**2, x)","F",0
383,0,0,0,0.000000," ","integrate(csc(f*x+e)**4*(b*sec(f*x+e))**(1/2),x)","\int \sqrt{b \sec{\left(e + f x \right)}} \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))*csc(e + f*x)**4, x)","F",0
384,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(3/2)*sin(f*x+e)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(3/2)*sin(f*x+e)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(3/2)*sin(f*x+e)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(3/2)*sin(f*x+e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate(csc(f*x+e)*(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3*(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(3/2)*sin(f*x+e)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(3/2)*sin(f*x+e)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
393,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(3/2)*sin(f*x+e)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**(3/2),x)","\int \left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((b*sec(e + f*x))**(3/2), x)","F",0
395,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2*(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
396,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(5/2)*sin(f*x+e)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(5/2)*sin(f*x+e)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(5/2)*sin(f*x+e)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(5/2)*sin(f*x+e),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate(csc(f*x+e)*(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3*(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5*(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(5/2)*sin(f*x+e)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(5/2)*sin(f*x+e)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(5/2)*sin(f*x+e)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**(5/2),x)","\int \left(b \sec{\left(e + f x \right)}\right)^{\frac{5}{2}}\, dx"," ",0,"Integral((b*sec(e + f*x))**(5/2), x)","F",0
408,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2*(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4*(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
410,-1,0,0,0.000000," ","integrate(sin(f*x+e)**7/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
411,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
412,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,0,0,0,0.000000," ","integrate(sin(f*x+e)/(b*sec(f*x+e))**(1/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)/sqrt(b*sec(e + f*x)), x)","F",0
414,0,0,0,0.000000," ","integrate(csc(f*x+e)/(b*sec(f*x+e))**(1/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)/sqrt(b*sec(e + f*x)), x)","F",0
415,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(b*sec(f*x+e))**(1/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/sqrt(b*sec(e + f*x)), x)","F",0
416,0,0,0,0.000000," ","integrate(csc(f*x+e)**5/(b*sec(f*x+e))**(1/2),x)","\int \frac{\csc^{5}{\left(e + f x \right)}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**5/sqrt(b*sec(e + f*x)), x)","F",0
417,-1,0,0,0.000000," ","integrate(sin(f*x+e)**6/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,0,0,0,0.000000," ","integrate(sin(f*x+e)**4/(b*sec(f*x+e))**(1/2),x)","\int \frac{\sin^{4}{\left(e + f x \right)}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)**4/sqrt(b*sec(e + f*x)), x)","F",0
419,0,0,0,0.000000," ","integrate(sin(f*x+e)**2/(b*sec(f*x+e))**(1/2),x)","\int \frac{\sin^{2}{\left(e + f x \right)}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)**2/sqrt(b*sec(e + f*x)), x)","F",0
420,0,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(b*sec(e + f*x)), x)","F",0
421,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(b*sec(f*x+e))**(1/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/sqrt(b*sec(e + f*x)), x)","F",0
422,0,0,0,0.000000," ","integrate(csc(f*x+e)**4/(b*sec(f*x+e))**(1/2),x)","\int \frac{\csc^{4}{\left(e + f x \right)}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**4/sqrt(b*sec(e + f*x)), x)","F",0
423,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
424,-1,0,0,0.000000," ","integrate(sin(f*x+e)**7/(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
425,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
426,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
427,0,0,0,0.000000," ","integrate(sin(f*x+e)/(b*sec(f*x+e))**(3/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)/(b*sec(e + f*x))**(3/2), x)","F",0
428,0,0,0,0.000000," ","integrate(csc(f*x+e)/(b*sec(f*x+e))**(3/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)/(b*sec(e + f*x))**(3/2), x)","F",0
429,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(b*sec(f*x+e))**(3/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/(b*sec(e + f*x))**(3/2), x)","F",0
430,0,0,0,0.000000," ","integrate(csc(f*x+e)**5/(b*sec(f*x+e))**(3/2),x)","\int \frac{\csc^{5}{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**5/(b*sec(e + f*x))**(3/2), x)","F",0
431,0,0,0,0.000000," ","integrate(sin(f*x+e)**4/(b*sec(f*x+e))**(3/2),x)","\int \frac{\sin^{4}{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**4/(b*sec(e + f*x))**(3/2), x)","F",0
432,0,0,0,0.000000," ","integrate(sin(f*x+e)**2/(b*sec(f*x+e))**(3/2),x)","\int \frac{\sin^{2}{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**2/(b*sec(e + f*x))**(3/2), x)","F",0
433,0,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(3/2),x)","\int \frac{1}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*sec(e + f*x))**(-3/2), x)","F",0
434,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(b*sec(f*x+e))**(3/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/(b*sec(e + f*x))**(3/2), x)","F",0
435,0,0,0,0.000000," ","integrate(csc(f*x+e)**4/(b*sec(f*x+e))**(3/2),x)","\int \frac{\csc^{4}{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**4/(b*sec(e + f*x))**(3/2), x)","F",0
436,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6/(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
437,-1,0,0,0.000000," ","integrate(sin(f*x+e)**7/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate(sin(f*x+e)**5/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,0,0,0,0.000000," ","integrate(sin(f*x+e)/(b*sec(f*x+e))**(5/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)/(b*sec(e + f*x))**(5/2), x)","F",0
441,-1,0,0,0.000000," ","integrate(csc(f*x+e)/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,-1,0,0,0.000000," ","integrate(csc(f*x+e)**3/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,-1,0,0,0.000000," ","integrate(csc(f*x+e)**5/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
444,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
446,0,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(5/2),x)","\int \frac{1}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((b*sec(e + f*x))**(-5/2), x)","F",0
447,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate(csc(f*x+e)**4/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate(csc(f*x+e)**6/(b*sec(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))**(9/2)*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))**(5/2)*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,0,0,0,0.000000," ","integrate((a*sin(f*x+e))**(1/2)*(b*sec(f*x+e))**(1/2),x)","\int \sqrt{a \sin{\left(e + f x \right)}} \sqrt{b \sec{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(a*sin(e + f*x))*sqrt(b*sec(e + f*x)), x)","F",0
453,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**(1/2)/(a*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{b \sec{\left(e + f x \right)}}}{\left(a \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))/(a*sin(e + f*x))**(3/2), x)","F",0
454,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(1/2)/(a*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
455,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(1/2)/(a*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))**(7/2)*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))**(3/2)*(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**(1/2)/(a*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{b \sec{\left(e + f x \right)}}}{\sqrt{a \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(b*sec(e + f*x))/sqrt(a*sin(e + f*x)), x)","F",0
459,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(1/2)/(a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**(1/2)/(a*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate(sin(f*x+e)**(9/2)/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate(sin(f*x+e)**(5/2)/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,0,0,0,0.000000," ","integrate(sin(f*x+e)**(1/2)/(b*sec(f*x+e))**(1/2),x)","\int \frac{\sqrt{\sin{\left(e + f x \right)}}}{\sqrt{b \sec{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(sin(e + f*x))/sqrt(b*sec(e + f*x)), x)","F",0
464,0,0,0,0.000000," ","integrate(1/sin(f*x+e)**(3/2)/(b*sec(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{b \sec{\left(e + f x \right)}} \sin^{\frac{3}{2}}{\left(e + f x \right)}}\, dx"," ",0,"Integral(1/(sqrt(b*sec(e + f*x))*sin(e + f*x)**(3/2)), x)","F",0
465,-1,0,0,0.000000," ","integrate(1/sin(f*x+e)**(7/2)/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,-1,0,0,0.000000," ","integrate(sin(f*x+e)**(3/2)/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
467,0,0,0,0.000000," ","integrate(1/sin(f*x+e)**(1/2)/(b*sec(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{b \sec{\left(e + f x \right)}} \sqrt{\sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/(sqrt(b*sec(e + f*x))*sqrt(sin(e + f*x))), x)","F",0
468,-1,0,0,0.000000," ","integrate(1/sin(f*x+e)**(5/2)/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate(1/sin(f*x+e)**(9/2)/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(1/sin(f*x+e)**(13/2)/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate(1/sin(f*x+e)**(17/2)/(b*sec(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))**(9/2)/(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))**(5/2)/(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,0,0,0,0.000000," ","integrate((a*sin(f*x+e))**(1/2)/(b*sec(f*x+e))**(3/2),x)","\int \frac{\sqrt{a \sin{\left(e + f x \right)}}}{\left(b \sec{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a*sin(e + f*x))/(b*sec(e + f*x))**(3/2), x)","F",0
475,-1,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(3/2)/(a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
476,-1,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(3/2)/(a*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))**(7/2)/(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,-1,0,0,0.000000," ","integrate((a*sin(f*x+e))**(3/2)/(b*sec(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(3/2)/(a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(3/2)/(a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(3/2)/(a*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate(1/(b*sec(f*x+e))**(3/2)/(a*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate((d*sec(b*x+a))**(5/2)*(c*sin(b*x+a))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate((d*sec(b*x+a))**(3/2)*(c*sin(b*x+a))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,0,0,0,0.000000," ","integrate((d*sec(b*x+a))**(1/2)*(c*sin(b*x+a))**m,x)","\int \left(c \sin{\left(a + b x \right)}\right)^{m} \sqrt{d \sec{\left(a + b x \right)}}\, dx"," ",0,"Integral((c*sin(a + b*x))**m*sqrt(d*sec(a + b*x)), x)","F",0
486,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**m/(d*sec(b*x+a))**(1/2),x)","\int \frac{\left(c \sin{\left(a + b x \right)}\right)^{m}}{\sqrt{d \sec{\left(a + b x \right)}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**m/sqrt(d*sec(a + b*x)), x)","F",0
487,0,0,0,0.000000," ","integrate((c*sin(b*x+a))**m/(d*sec(b*x+a))**(3/2),x)","\int \frac{\left(c \sin{\left(a + b x \right)}\right)^{m}}{\left(d \sec{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c*sin(a + b*x))**m/(d*sec(a + b*x))**(3/2), x)","F",0
488,0,0,0,0.000000," ","integrate(sec(f*x+e)**n*sin(f*x+e)**m,x)","\int \sin^{m}{\left(e + f x \right)} \sec^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral(sin(e + f*x)**m*sec(e + f*x)**n, x)","F",0
489,0,0,0,0.000000," ","integrate(sec(f*x+e)**n*(a*sin(f*x+e))**m,x)","\int \left(a \sin{\left(e + f x \right)}\right)^{m} \sec^{n}{\left(e + f x \right)}\, dx"," ",0,"Integral((a*sin(e + f*x))**m*sec(e + f*x)**n, x)","F",0
490,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**n*sin(f*x+e)**m,x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n} \sin^{m}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sec(e + f*x))**n*sin(e + f*x)**m, x)","F",0
491,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**n*(a*sin(f*x+e))**m,x)","\int \left(a \sin{\left(e + f x \right)}\right)^{m} \left(b \sec{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*sin(e + f*x))**m*(b*sec(e + f*x))**n, x)","F",0
492,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**n*sin(f*x+e)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**n*sin(f*x+e)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**n*sin(f*x+e),x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sec(e + f*x))**n*sin(e + f*x), x)","F",0
495,0,0,0,0.000000," ","integrate(csc(f*x+e)*(b*sec(f*x+e))**n,x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sec(e + f*x))**n*csc(e + f*x), x)","F",0
496,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(b*sec(f*x+e))**n,x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sec(e + f*x))**n*csc(e + f*x)**3, x)","F",0
497,-1,0,0,0.000000," ","integrate((b*sec(f*x+e))**n*sin(f*x+e)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
498,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**n*sin(f*x+e)**4,x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sec(e + f*x))**n*sin(e + f*x)**4, x)","F",0
499,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**n*sin(f*x+e)**2,x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sec(e + f*x))**n*sin(e + f*x)**2, x)","F",0
500,0,0,0,0.000000," ","integrate((b*sec(f*x+e))**n,x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((b*sec(e + f*x))**n, x)","F",0
501,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(b*sec(f*x+e))**n,x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sec(e + f*x))**n*csc(e + f*x)**2, x)","F",0
502,0,0,0,0.000000," ","integrate(csc(f*x+e)**4*(b*sec(f*x+e))**n,x)","\int \left(b \sec{\left(e + f x \right)}\right)^{n} \csc^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral((b*sec(e + f*x))**n*csc(e + f*x)**4, x)","F",0
503,-1,0,0,0.000000," ","integrate((b*sec(b*x+a))**n*(c*sin(b*x+a))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,0,0,0,0.000000," ","integrate((b*sec(b*x+a))**n*(c*sin(b*x+a))**(1/2),x)","\int \left(b \sec{\left(a + b x \right)}\right)^{n} \sqrt{c \sin{\left(a + b x \right)}}\, dx"," ",0,"Integral((b*sec(a + b*x))**n*sqrt(c*sin(a + b*x)), x)","F",0
505,0,0,0,0.000000," ","integrate((b*sec(b*x+a))**n/(c*sin(b*x+a))**(1/2),x)","\int \frac{\left(b \sec{\left(a + b x \right)}\right)^{n}}{\sqrt{c \sin{\left(a + b x \right)}}}\, dx"," ",0,"Integral((b*sec(a + b*x))**n/sqrt(c*sin(a + b*x)), x)","F",0
506,0,0,0,0.000000," ","integrate((b*sec(b*x+a))**n/(c*sin(b*x+a))**(3/2),x)","\int \frac{\left(b \sec{\left(a + b x \right)}\right)^{n}}{\left(c \sin{\left(a + b x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((b*sec(a + b*x))**n/(c*sin(a + b*x))**(3/2), x)","F",0
507,0,0,0,0.000000," ","integrate(sin(f*x+e)**4*(d*csc(f*x+e))**(1/2),x)","\int \sqrt{d \csc{\left(e + f x \right)}} \sin^{4}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(d*csc(e + f*x))*sin(e + f*x)**4, x)","F",0
508,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(d*csc(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,0,0,0,0.000000," ","integrate(sin(f*x+e)**2*(d*csc(f*x+e))**(1/2),x)","\int \sqrt{d \csc{\left(e + f x \right)}} \sin^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(d*csc(e + f*x))*sin(e + f*x)**2, x)","F",0
510,0,0,0,0.000000," ","integrate(sin(f*x+e)*(d*csc(f*x+e))**(1/2),x)","\int \sqrt{d \csc{\left(e + f x \right)}} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(d*csc(e + f*x))*sin(e + f*x), x)","F",0
511,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**(1/2),x)","\int \sqrt{d \csc{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(d*csc(e + f*x)), x)","F",0
512,0,0,0,0.000000," ","integrate(csc(f*x+e)*(d*csc(f*x+e))**(1/2),x)","\int \sqrt{d \csc{\left(e + f x \right)}} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(d*csc(e + f*x))*csc(e + f*x), x)","F",0
513,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(d*csc(f*x+e))**(1/2),x)","\int \sqrt{d \csc{\left(e + f x \right)}} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(d*csc(e + f*x))*csc(e + f*x)**2, x)","F",0
514,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(d*csc(f*x+e))**(1/2),x)","\int \sqrt{d \csc{\left(e + f x \right)}} \csc^{3}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(d*csc(e + f*x))*csc(e + f*x)**3, x)","F",0
515,-1,0,0,0.000000," ","integrate((d*csc(f*x+e))**(3/2)*sin(f*x+e)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate((d*csc(f*x+e))**(3/2)*sin(f*x+e)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate((d*csc(f*x+e))**(3/2)*sin(f*x+e)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate((d*csc(f*x+e))**(3/2)*sin(f*x+e)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**(3/2)*sin(f*x+e),x)","\int \left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}} \sin{\left(e + f x \right)}\, dx"," ",0,"Integral((d*csc(e + f*x))**(3/2)*sin(e + f*x), x)","F",0
520,0,0,0,0.000000," ","integrate((d*csc(f*x+e))**(3/2),x)","\int \left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((d*csc(e + f*x))**(3/2), x)","F",0
521,0,0,0,0.000000," ","integrate(csc(f*x+e)*(d*csc(f*x+e))**(3/2),x)","\int \left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}} \csc{\left(e + f x \right)}\, dx"," ",0,"Integral((d*csc(e + f*x))**(3/2)*csc(e + f*x), x)","F",0
522,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(d*csc(f*x+e))**(3/2),x)","\int \left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}} \csc^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((d*csc(e + f*x))**(3/2)*csc(e + f*x)**2, x)","F",0
523,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(d*csc(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,0,0,0,0.000000," ","integrate(sin(f*x+e)**2/(d*csc(f*x+e))**(1/2),x)","\int \frac{\sin^{2}{\left(e + f x \right)}}{\sqrt{d \csc{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)**2/sqrt(d*csc(e + f*x)), x)","F",0
525,0,0,0,0.000000," ","integrate(sin(f*x+e)/(d*csc(f*x+e))**(1/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\sqrt{d \csc{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sin(e + f*x)/sqrt(d*csc(e + f*x)), x)","F",0
526,0,0,0,0.000000," ","integrate(1/(d*csc(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{d \csc{\left(e + f x \right)}}}\, dx"," ",0,"Integral(1/sqrt(d*csc(e + f*x)), x)","F",0
527,0,0,0,0.000000," ","integrate(csc(f*x+e)/(d*csc(f*x+e))**(1/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\sqrt{d \csc{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)/sqrt(d*csc(e + f*x)), x)","F",0
528,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(d*csc(f*x+e))**(1/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\sqrt{d \csc{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/sqrt(d*csc(e + f*x)), x)","F",0
529,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(d*csc(f*x+e))**(1/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\sqrt{d \csc{\left(e + f x \right)}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/sqrt(d*csc(e + f*x)), x)","F",0
530,0,0,0,0.000000," ","integrate(sin(f*x+e)**2/(d*csc(f*x+e))**(3/2),x)","\int \frac{\sin^{2}{\left(e + f x \right)}}{\left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)**2/(d*csc(e + f*x))**(3/2), x)","F",0
531,0,0,0,0.000000," ","integrate(sin(f*x+e)/(d*csc(f*x+e))**(3/2),x)","\int \frac{\sin{\left(e + f x \right)}}{\left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(e + f*x)/(d*csc(e + f*x))**(3/2), x)","F",0
532,0,0,0,0.000000," ","integrate(1/(d*csc(f*x+e))**(3/2),x)","\int \frac{1}{\left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((d*csc(e + f*x))**(-3/2), x)","F",0
533,0,0,0,0.000000," ","integrate(csc(f*x+e)/(d*csc(f*x+e))**(3/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)/(d*csc(e + f*x))**(3/2), x)","F",0
534,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(d*csc(f*x+e))**(3/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**2/(d*csc(e + f*x))**(3/2), x)","F",0
535,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(d*csc(f*x+e))**(3/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**3/(d*csc(e + f*x))**(3/2), x)","F",0
536,0,0,0,0.000000," ","integrate(csc(f*x+e)**4/(d*csc(f*x+e))**(3/2),x)","\int \frac{\csc^{4}{\left(e + f x \right)}}{\left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**4/(d*csc(e + f*x))**(3/2), x)","F",0
537,0,0,0,0.000000," ","integrate(csc(f*x+e)**5/(d*csc(f*x+e))**(3/2),x)","\int \frac{\csc^{5}{\left(e + f x \right)}}{\left(d \csc{\left(e + f x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(csc(e + f*x)**5/(d*csc(e + f*x))**(3/2), x)","F",0
538,0,0,0,0.000000," ","integrate((b*csc(f*x+e))**n*(a*sin(f*x+e))**m,x)","\int \left(a \sin{\left(e + f x \right)}\right)^{m} \left(b \csc{\left(e + f x \right)}\right)^{n}\, dx"," ",0,"Integral((a*sin(e + f*x))**m*(b*csc(e + f*x))**n, x)","F",0
