1,-1,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,-1,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3,1,197,0,124.075589," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**5,x)","\begin{cases} - \frac{422 \sin{\left(a + b x \right)} \sin^{4}{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{693 b} - \frac{608 \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{693 b} - \frac{256 \sin{\left(a + b x \right)} \cos^{5}{\left(2 a + 2 b x \right)}}{693 b} + \frac{151 \sin^{5}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{693 b} + \frac{272 \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{693 b} + \frac{128 \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{693 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \sin^{5}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-422*sin(a + b*x)*sin(2*a + 2*b*x)**4*cos(2*a + 2*b*x)/(693*b) - 608*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(2*a + 2*b*x)**3/(693*b) - 256*sin(a + b*x)*cos(2*a + 2*b*x)**5/(693*b) + 151*sin(2*a + 2*b*x)**5*cos(a + b*x)/(693*b) + 272*sin(2*a + 2*b*x)**3*cos(a + b*x)*cos(2*a + 2*b*x)**2/(693*b) + 128*sin(2*a + 2*b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**4/(693*b), Ne(b, 0)), (x*sin(a)*sin(2*a)**5, True))","A",0
4,1,163,0,40.276975," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**4,x)","\begin{cases} - \frac{104 \sin{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{315 b} - \frac{64 \sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{315 b} - \frac{107 \sin^{4}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{315 b} - \frac{16 \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{21 b} - \frac{128 \cos{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{315 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \sin^{4}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-104*sin(a + b*x)*sin(2*a + 2*b*x)**3*cos(2*a + 2*b*x)/(315*b) - 64*sin(a + b*x)*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)**3/(315*b) - 107*sin(2*a + 2*b*x)**4*cos(a + b*x)/(315*b) - 16*sin(2*a + 2*b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)**2/(21*b) - 128*cos(a + b*x)*cos(2*a + 2*b*x)**4/(315*b), Ne(b, 0)), (x*sin(a)*sin(2*a)**4, True))","A",0
5,1,126,0,11.905728," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**3,x)","\begin{cases} - \frac{22 \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{35 b} - \frac{16 \sin{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{35 b} + \frac{9 \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{35 b} + \frac{8 \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{35 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \sin^{3}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-22*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(2*a + 2*b*x)/(35*b) - 16*sin(a + b*x)*cos(2*a + 2*b*x)**3/(35*b) + 9*sin(2*a + 2*b*x)**3*cos(a + b*x)/(35*b) + 8*sin(2*a + 2*b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**2/(35*b), Ne(b, 0)), (x*sin(a)*sin(2*a)**3, True))","A",0
6,1,92,0,3.397140," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**2,x)","\begin{cases} - \frac{4 \sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{15 b} - \frac{7 \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{15 b} - \frac{8 \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{15 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-4*sin(a + b*x)*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)/(15*b) - 7*sin(2*a + 2*b*x)**2*cos(a + b*x)/(15*b) - 8*cos(a + b*x)*cos(2*a + 2*b*x)**2/(15*b), Ne(b, 0)), (x*sin(a)*sin(2*a)**2, True))","A",0
7,1,51,0,0.812661," ","integrate(sin(b*x+a)*sin(2*b*x+2*a),x)","\begin{cases} - \frac{2 \sin{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{3 b} + \frac{\sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin{\left(a \right)} \sin{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sin(a + b*x)*cos(2*a + 2*b*x)/(3*b) + sin(2*a + 2*b*x)*cos(a + b*x)/(3*b), Ne(b, 0)), (x*sin(a)*sin(2*a), True))","A",0
8,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**2*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**3*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
11,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**4*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**5*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
13,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
14,1,434,0,117.944919," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**4,x)","\begin{cases} \frac{3 x \sin^{2}{\left(a + b x \right)} \sin^{4}{\left(2 a + 2 b x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{8} + \frac{3 x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{16} + \frac{3 x \sin^{4}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{16} + \frac{3 x \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{8} + \frac{3 x \cos^{2}{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{16} - \frac{57 \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{160 b} - \frac{109 \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{480 b} - \frac{\sin{\left(a + b x \right)} \sin^{4}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{10 b} - \frac{2 \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{5 b} - \frac{4 \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{15 b} + \frac{7 \sin^{3}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{160 b} + \frac{19 \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{480 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \sin^{4}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x*sin(a + b*x)**2*sin(2*a + 2*b*x)**4/16 + 3*x*sin(a + b*x)**2*sin(2*a + 2*b*x)**2*cos(2*a + 2*b*x)**2/8 + 3*x*sin(a + b*x)**2*cos(2*a + 2*b*x)**4/16 + 3*x*sin(2*a + 2*b*x)**4*cos(a + b*x)**2/16 + 3*x*sin(2*a + 2*b*x)**2*cos(a + b*x)**2*cos(2*a + 2*b*x)**2/8 + 3*x*cos(a + b*x)**2*cos(2*a + 2*b*x)**4/16 - 57*sin(a + b*x)**2*sin(2*a + 2*b*x)**3*cos(2*a + 2*b*x)/(160*b) - 109*sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)**3/(480*b) - sin(a + b*x)*sin(2*a + 2*b*x)**4*cos(a + b*x)/(10*b) - 2*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)**2/(5*b) - 4*sin(a + b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**4/(15*b) + 7*sin(2*a + 2*b*x)**3*cos(a + b*x)**2*cos(2*a + 2*b*x)/(160*b) + 19*sin(2*a + 2*b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)**3/(480*b), Ne(b, 0)), (x*sin(a)**2*sin(2*a)**4, True))","A",0
15,1,362,0,40.095959," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**3,x)","\begin{cases} \frac{3 x \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{16} + \frac{3 x \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{8} + \frac{3 x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{8} - \frac{3 x \sin^{3}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{16} - \frac{3 x \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{16} + \frac{17 \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{96 b} - \frac{13 \sin{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{16 b} - \frac{7 \sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{8 b} - \frac{\sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{2 b} - \frac{49 \cos^{2}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{96 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \sin^{3}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x*sin(a + b*x)**2*sin(2*a + 2*b*x)**3/16 + 3*x*sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)**2/16 + 3*x*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)/8 + 3*x*sin(a + b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**3/8 - 3*x*sin(2*a + 2*b*x)**3*cos(a + b*x)**2/16 - 3*x*sin(2*a + 2*b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)**2/16 + 17*sin(a + b*x)**2*cos(2*a + 2*b*x)**3/(96*b) - 13*sin(a + b*x)*sin(2*a + 2*b*x)**3*cos(a + b*x)/(16*b) - 7*sin(a + b*x)*sin(2*a + 2*b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**2/(8*b) - sin(2*a + 2*b*x)**2*cos(a + b*x)**2*cos(2*a + 2*b*x)/(2*b) - 49*cos(a + b*x)**2*cos(2*a + 2*b*x)**3/(96*b), Ne(b, 0)), (x*sin(a)**2*sin(2*a)**3, True))","A",0
16,1,231,0,11.959658," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)}}{4} + \frac{x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{4} + \frac{x \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{x \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{4} - \frac{7 \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{24 b} - \frac{\sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{6 b} - \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{3 b} + \frac{\sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{24 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**2*sin(2*a + 2*b*x)**2/4 + x*sin(a + b*x)**2*cos(2*a + 2*b*x)**2/4 + x*sin(2*a + 2*b*x)**2*cos(a + b*x)**2/4 + x*cos(a + b*x)**2*cos(2*a + 2*b*x)**2/4 - 7*sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)/(24*b) - sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(a + b*x)/(6*b) - sin(a + b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**2/(3*b) + sin(2*a + 2*b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)/(24*b), Ne(b, 0)), (x*sin(a)**2*sin(2*a)**2, True))","A",0
17,1,133,0,3.298116," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a),x)","\begin{cases} \frac{x \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)}}{4} + \frac{x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{2} - \frac{x \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{4} - \frac{3 \sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{4 b} - \frac{\cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(a \right)} \sin{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**2*sin(2*a + 2*b*x)/4 + x*sin(a + b*x)*cos(a + b*x)*cos(2*a + 2*b*x)/2 - x*sin(2*a + 2*b*x)*cos(a + b*x)**2/4 - 3*sin(a + b*x)*sin(2*a + 2*b*x)*cos(a + b*x)/(4*b) - cos(a + b*x)**2*cos(2*a + 2*b*x)/(2*b), Ne(b, 0)), (x*sin(a)**2*sin(2*a), True))","A",0
18,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**2*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**3*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**4*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**5*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3*sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3*sin(2*b*x+2*a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,1,284,0,115.461517," ","integrate(sin(b*x+a)**3*sin(2*b*x+2*a)**3,x)","\begin{cases} - \frac{46 \sin^{3}{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{105 b} - \frac{16 \sin^{3}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{63 b} - \frac{13 \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{105 b} - \frac{8 \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{35 b} - \frac{4 \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{7 b} - \frac{64 \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{105 b} + \frac{94 \sin^{3}{\left(2 a + 2 b x \right)} \cos^{3}{\left(a + b x \right)}}{315 b} + \frac{32 \sin{\left(2 a + 2 b x \right)} \cos^{3}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{105 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} \sin^{3}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-46*sin(a + b*x)**3*sin(2*a + 2*b*x)**2*cos(2*a + 2*b*x)/(105*b) - 16*sin(a + b*x)**3*cos(2*a + 2*b*x)**3/(63*b) - 13*sin(a + b*x)**2*sin(2*a + 2*b*x)**3*cos(a + b*x)/(105*b) - 8*sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**2/(35*b) - 4*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(a + b*x)**2*cos(2*a + 2*b*x)/(7*b) - 64*sin(a + b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)**3/(105*b) + 94*sin(2*a + 2*b*x)**3*cos(a + b*x)**3/(315*b) + 32*sin(2*a + 2*b*x)*cos(a + b*x)**3*cos(2*a + 2*b*x)**2/(105*b), Ne(b, 0)), (x*sin(a)**3*sin(2*a)**3, True))","A",0
26,1,202,0,38.633685," ","integrate(sin(b*x+a)**3*sin(2*b*x+2*a)**2,x)","\begin{cases} - \frac{12 \sin^{3}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{35 b} - \frac{11 \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{35 b} - \frac{24 \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{35 b} + \frac{8 \sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{35 b} - \frac{38 \sin^{2}{\left(2 a + 2 b x \right)} \cos^{3}{\left(a + b x \right)}}{105 b} - \frac{32 \cos^{3}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{105 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} \sin^{2}{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*sin(a + b*x)**3*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)/(35*b) - 11*sin(a + b*x)**2*sin(2*a + 2*b*x)**2*cos(a + b*x)/(35*b) - 24*sin(a + b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)**2/(35*b) + 8*sin(a + b*x)*sin(2*a + 2*b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)/(35*b) - 38*sin(2*a + 2*b*x)**2*cos(a + b*x)**3/(105*b) - 32*cos(a + b*x)**3*cos(2*a + 2*b*x)**2/(105*b), Ne(b, 0)), (x*sin(a)**3*sin(2*a)**2, True))","A",0
27,1,117,0,11.215991," ","integrate(sin(b*x+a)**3*sin(2*b*x+2*a),x)","\begin{cases} - \frac{2 \sin^{3}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{5 b} - \frac{\sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{5 b} - \frac{4 \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{5 b} + \frac{2 \sin{\left(2 a + 2 b x \right)} \cos^{3}{\left(a + b x \right)}}{5 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(a \right)} \sin{\left(2 a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sin(a + b*x)**3*cos(2*a + 2*b*x)/(5*b) - sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(a + b*x)/(5*b) - 4*sin(a + b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)/(5*b) + 2*sin(2*a + 2*b*x)*cos(a + b*x)**3/(5*b), Ne(b, 0)), (x*sin(a)**3*sin(2*a), True))","A",0
28,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**2*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**4*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate(csc(2*b*x+2*a)**5*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
37,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,1,3636,0,21.207654," ","integrate(csc(b*x+a)*sin(2*b*x+2*a),x)","4 \left(\begin{cases} x & \text{for}\: a = 0 \wedge b = 0 \\0 & \text{for}\: b = 0 \\\frac{\sin{\left(b x \right)}}{b} & \text{for}\: a = 0 \\\frac{2 \log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{1}{\tan{\left(\frac{a}{2} \right)}} \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{1}{\tan{\left(\frac{a}{2} \right)}} \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{1}{\tan{\left(\frac{a}{2} \right)}} \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{1}{\tan{\left(\frac{a}{2} \right)}} \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)} \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)} - 2 \left(\begin{cases} x & \text{for}\: a = 0 \wedge b = 0 \\0 & \text{for}\: b = 0 \\\frac{\sin{\left(b x \right)}}{b} & \text{for}\: a = 0 \\\frac{2 \log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{1}{\tan{\left(\frac{a}{2} \right)}} \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{1}{\tan{\left(\frac{a}{2} \right)}} \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{1}{\tan{\left(\frac{a}{2} \right)}} \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{1}{\tan{\left(\frac{a}{2} \right)}} \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)} \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) - 2 \left(\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\\frac{x}{\sin{\left(a \right)}} & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: a = 0 \\\frac{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)}}{b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)}}{b} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)} \cos{\left(a \right)} + 4 \left(\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\\frac{x}{\sin{\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 = 0 \\\frac{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{4}{\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{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \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{2 \log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{2 \log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{\log{\left(\tan{\left(\frac{a}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \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{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)} \tan^{4}{\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{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \right)} \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{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \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{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \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{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \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{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{a}{2} \right)}} \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)}"," ",0,"4*Piecewise((x, Eq(a, 0) & Eq(b, 0)), (0, Eq(b, 0)), (sin(b*x)/b, Eq(a, 0)), (2*log(tan(a/2) + tan(b*x/2))*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(a/2) + tan(b*x/2))*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(a/2) + tan(b*x/2))*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(a/2) + tan(b*x/2))*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) - 1/tan(a/2))*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) - 1/tan(a/2))*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) - 1/tan(a/2))*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) - 1/tan(a/2))*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*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 - 2*Piecewise((x, Eq(a, 0) & Eq(b, 0)), (0, Eq(b, 0)), (sin(b*x)/b, Eq(a, 0)), (2*log(tan(a/2) + tan(b*x/2))*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(a/2) + tan(b*x/2))*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(a/2) + tan(b*x/2))*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(a/2) + tan(b*x/2))*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) - 1/tan(a/2))*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) - 1/tan(a/2))*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) - 1/tan(a/2))*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) - 1/tan(a/2))*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*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)) - 2*Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (x/sin(a), Eq(b, 0)), (log(tan(b*x/2))/b, Eq(a, 0)), (log(tan(a/2) + tan(b*x/2))/b - log(tan(b*x/2) - 1/tan(a/2))/b, True))*sin(a)*cos(a) + 4*Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (x/sin(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, 0)), (log(tan(a/2) + tan(b*x/2))*tan(a/2)**4*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) + log(tan(a/2) + tan(b*x/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) - 2*log(tan(a/2) + tan(b*x/2))*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) - 2*log(tan(a/2) + tan(b*x/2))*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) + log(tan(a/2) + tan(b*x/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) + log(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) - log(tan(b*x/2) - 1/tan(a/2))*tan(a/2)**4*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) - log(tan(b*x/2) - 1/tan(a/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) + 2*log(tan(b*x/2) - 1/tan(a/2))*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) + 2*log(tan(b*x/2) - 1/tan(a/2))*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) - log(tan(b*x/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) - log(tan(b*x/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)","B",0
41,0,0,0,0.000000," ","integrate(csc(b*x+a)*csc(2*b*x+2*a),x)","\int \csc{\left(a + b x \right)} \csc{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)*csc(2*a + 2*b*x), x)","F",0
42,0,0,0,0.000000," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)**2,x)","\int \csc{\left(a + b x \right)} \csc^{2}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)*csc(2*a + 2*b*x)**2, x)","F",0
43,0,0,0,0.000000," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)**3,x)","\int \csc{\left(a + b x \right)} \csc^{3}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)*csc(2*a + 2*b*x)**3, x)","F",0
44,0,0,0,0.000000," ","integrate(csc(b*x+a)*csc(2*b*x+2*a)**4,x)","\int \csc{\left(a + b x \right)} \csc^{4}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)*csc(2*a + 2*b*x)**4, x)","F",0
45,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
46,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*csc(2*b*x+2*a),x)","\int \csc^{2}{\left(a + b x \right)} \csc{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**2*csc(2*a + 2*b*x), x)","F",0
54,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*csc(2*b*x+2*a)**2,x)","\int \csc^{2}{\left(a + b x \right)} \csc^{2}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**2*csc(2*a + 2*b*x)**2, x)","F",0
55,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*csc(2*b*x+2*a)**3,x)","\int \csc^{2}{\left(a + b x \right)} \csc^{3}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**2*csc(2*a + 2*b*x)**3, x)","F",0
56,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*csc(2*b*x+2*a)**4,x)","\int \csc^{2}{\left(a + b x \right)} \csc^{4}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**2*csc(2*a + 2*b*x)**4, x)","F",0
57,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*csc(2*b*x+2*a)**5,x)","\int \csc^{2}{\left(a + b x \right)} \csc^{5}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**2*csc(2*a + 2*b*x)**5, x)","F",0
58,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2*csc(2*b*x+2*a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**10,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**9,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*csc(2*b*x+2*a),x)","\int \csc^{3}{\left(a + b x \right)} \csc{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**3*csc(2*a + 2*b*x), x)","F",0
70,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*csc(2*b*x+2*a)**2,x)","\int \csc^{3}{\left(a + b x \right)} \csc^{2}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**3*csc(2*a + 2*b*x)**2, x)","F",0
71,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*csc(2*b*x+2*a)**3,x)","\int \csc^{3}{\left(a + b x \right)} \csc^{3}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**3*csc(2*a + 2*b*x)**3, x)","F",0
72,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*csc(2*b*x+2*a)**4,x)","\int \csc^{3}{\left(a + b x \right)} \csc^{4}{\left(2 a + 2 b x \right)}\, dx"," ",0,"Integral(csc(a + b*x)**3*csc(2*a + 2*b*x)**4, x)","F",0
73,-1,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(sin(b*x+a)/sin(2*b*x+2*a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2/sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3*sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3*sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/sin(2*b*x+2*a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3/sin(2*b*x+2*a)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(csc(b*x+a)/sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
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112,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2/sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2/sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(csc(b*x+a)**2/sin(2*b*x+2*a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3/sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3/sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate(csc(b*x+a)**3/sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3*sin(2*b*x+2*a)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2*sin(2*b*x+2*a)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate(sin(b*x+a)*sin(2*b*x+2*a)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,0,0,0,0.000000," ","integrate(csc(b*x+a)*sin(2*b*x+2*a)**m,x)","\int \sin^{m}{\left(2 a + 2 b x \right)} \csc{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(2*a + 2*b*x)**m*csc(a + b*x), x)","F",0
127,0,0,0,0.000000," ","integrate(csc(b*x+a)**2*sin(2*b*x+2*a)**m,x)","\int \sin^{m}{\left(2 a + 2 b x \right)} \csc^{2}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(2*a + 2*b*x)**m*csc(a + b*x)**2, x)","F",0
128,0,0,0,0.000000," ","integrate(csc(b*x+a)**3*sin(2*b*x+2*a)**m,x)","\int \sin^{m}{\left(2 a + 2 b x \right)} \csc^{3}{\left(a + b x \right)}\, dx"," ",0,"Integral(sin(2*a + 2*b*x)**m*csc(a + b*x)**3, x)","F",0
129,-1,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,-1,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
131,1,199,0,113.174327," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**5,x)","\begin{cases} - \frac{151 \sin{\left(a + b x \right)} \sin^{5}{\left(2 a + 2 b x \right)}}{693 b} - \frac{272 \sin{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{693 b} - \frac{128 \sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{693 b} - \frac{422 \sin^{4}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{693 b} - \frac{608 \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{693 b} - \frac{256 \cos{\left(a + b x \right)} \cos^{5}{\left(2 a + 2 b x \right)}}{693 b} & \text{for}\: b \neq 0 \\x \sin^{5}{\left(2 a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-151*sin(a + b*x)*sin(2*a + 2*b*x)**5/(693*b) - 272*sin(a + b*x)*sin(2*a + 2*b*x)**3*cos(2*a + 2*b*x)**2/(693*b) - 128*sin(a + b*x)*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)**4/(693*b) - 422*sin(2*a + 2*b*x)**4*cos(a + b*x)*cos(2*a + 2*b*x)/(693*b) - 608*sin(2*a + 2*b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)**3/(693*b) - 256*cos(a + b*x)*cos(2*a + 2*b*x)**5/(693*b), Ne(b, 0)), (x*sin(2*a)**5*cos(a), True))","A",0
132,1,162,0,38.307662," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**4,x)","\begin{cases} \frac{107 \sin{\left(a + b x \right)} \sin^{4}{\left(2 a + 2 b x \right)}}{315 b} + \frac{16 \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{21 b} + \frac{128 \sin{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{315 b} - \frac{104 \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{315 b} - \frac{64 \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{315 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(2 a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((107*sin(a + b*x)*sin(2*a + 2*b*x)**4/(315*b) + 16*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(2*a + 2*b*x)**2/(21*b) + 128*sin(a + b*x)*cos(2*a + 2*b*x)**4/(315*b) - 104*sin(2*a + 2*b*x)**3*cos(a + b*x)*cos(2*a + 2*b*x)/(315*b) - 64*sin(2*a + 2*b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**3/(315*b), Ne(b, 0)), (x*sin(2*a)**4*cos(a), True))","A",0
133,1,128,0,11.274884," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**3,x)","\begin{cases} - \frac{9 \sin{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)}}{35 b} - \frac{8 \sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{35 b} - \frac{22 \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{35 b} - \frac{16 \cos{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{35 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(2 a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*sin(a + b*x)*sin(2*a + 2*b*x)**3/(35*b) - 8*sin(a + b*x)*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)**2/(35*b) - 22*sin(2*a + 2*b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)/(35*b) - 16*cos(a + b*x)*cos(2*a + 2*b*x)**3/(35*b), Ne(b, 0)), (x*sin(2*a)**3*cos(a), True))","A",0
134,1,90,0,3.116778," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**2,x)","\begin{cases} \frac{7 \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)}}{15 b} + \frac{8 \sin{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{15 b} - \frac{4 \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{15 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(2 a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((7*sin(a + b*x)*sin(2*a + 2*b*x)**2/(15*b) + 8*sin(a + b*x)*cos(2*a + 2*b*x)**2/(15*b) - 4*sin(2*a + 2*b*x)*cos(a + b*x)*cos(2*a + 2*b*x)/(15*b), Ne(b, 0)), (x*sin(2*a)**2*cos(a), True))","A",0
135,1,53,0,0.760140," ","integrate(cos(b*x+a)*sin(2*b*x+2*a),x)","\begin{cases} - \frac{\sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)}}{3 b} - \frac{2 \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{3 b} & \text{for}\: b \neq 0 \\x \sin{\left(2 a \right)} \cos{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-sin(a + b*x)*sin(2*a + 2*b*x)/(3*b) - 2*cos(a + b*x)*cos(2*a + 2*b*x)/(3*b), Ne(b, 0)), (x*sin(2*a)*cos(a), True))","A",0
136,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,1,434,0,116.231295," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**4,x)","\begin{cases} \frac{3 x \sin^{2}{\left(a + b x \right)} \sin^{4}{\left(2 a + 2 b x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{8} + \frac{3 x \sin^{2}{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{16} + \frac{3 x \sin^{4}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{16} + \frac{3 x \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{8} + \frac{3 x \cos^{2}{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{16} + \frac{7 \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{160 b} + \frac{19 \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{480 b} + \frac{\sin{\left(a + b x \right)} \sin^{4}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{10 b} + \frac{2 \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{5 b} + \frac{4 \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{4}{\left(2 a + 2 b x \right)}}{15 b} - \frac{57 \sin^{3}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{160 b} - \frac{109 \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{480 b} & \text{for}\: b \neq 0 \\x \sin^{4}{\left(2 a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*x*sin(a + b*x)**2*sin(2*a + 2*b*x)**4/16 + 3*x*sin(a + b*x)**2*sin(2*a + 2*b*x)**2*cos(2*a + 2*b*x)**2/8 + 3*x*sin(a + b*x)**2*cos(2*a + 2*b*x)**4/16 + 3*x*sin(2*a + 2*b*x)**4*cos(a + b*x)**2/16 + 3*x*sin(2*a + 2*b*x)**2*cos(a + b*x)**2*cos(2*a + 2*b*x)**2/8 + 3*x*cos(a + b*x)**2*cos(2*a + 2*b*x)**4/16 + 7*sin(a + b*x)**2*sin(2*a + 2*b*x)**3*cos(2*a + 2*b*x)/(160*b) + 19*sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)**3/(480*b) + sin(a + b*x)*sin(2*a + 2*b*x)**4*cos(a + b*x)/(10*b) + 2*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)**2/(5*b) + 4*sin(a + b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**4/(15*b) - 57*sin(2*a + 2*b*x)**3*cos(a + b*x)**2*cos(2*a + 2*b*x)/(160*b) - 109*sin(2*a + 2*b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)**3/(480*b), Ne(b, 0)), (x*sin(2*a)**4*cos(a)**2, True))","A",0
143,1,359,0,39.275561," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**3,x)","\begin{cases} - \frac{3 x \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)}}{16} - \frac{3 x \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{16} - \frac{3 x \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{8} - \frac{3 x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{8} + \frac{3 x \sin^{3}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{16} + \frac{3 x \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{16} - \frac{\sin^{2}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{96 b} - \frac{3 \sin{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{16 b} - \frac{\sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{8 b} - \frac{\sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{2 b} - \frac{31 \cos^{2}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{96 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(2 a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*x*sin(a + b*x)**2*sin(2*a + 2*b*x)**3/16 - 3*x*sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)**2/16 - 3*x*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)/8 - 3*x*sin(a + b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**3/8 + 3*x*sin(2*a + 2*b*x)**3*cos(a + b*x)**2/16 + 3*x*sin(2*a + 2*b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)**2/16 - sin(a + b*x)**2*cos(2*a + 2*b*x)**3/(96*b) - 3*sin(a + b*x)*sin(2*a + 2*b*x)**3*cos(a + b*x)/(16*b) - sin(a + b*x)*sin(2*a + 2*b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**2/(8*b) - sin(2*a + 2*b*x)**2*cos(a + b*x)**2*cos(2*a + 2*b*x)/(2*b) - 31*cos(a + b*x)**2*cos(2*a + 2*b*x)**3/(96*b), Ne(b, 0)), (x*sin(2*a)**3*cos(a)**2, True))","A",0
144,1,231,0,11.677316," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**2,x)","\begin{cases} \frac{x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)}}{4} + \frac{x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{4} + \frac{x \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{4} + \frac{x \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{4} + \frac{\sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(2 a + 2 b x \right)}}{24 b} + \frac{\sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{6 b} + \frac{\sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{3 b} - \frac{7 \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{24 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(2 a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a + b*x)**2*sin(2*a + 2*b*x)**2/4 + x*sin(a + b*x)**2*cos(2*a + 2*b*x)**2/4 + x*sin(2*a + 2*b*x)**2*cos(a + b*x)**2/4 + x*cos(a + b*x)**2*cos(2*a + 2*b*x)**2/4 + sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)/(24*b) + sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(a + b*x)/(6*b) + sin(a + b*x)*cos(a + b*x)*cos(2*a + 2*b*x)**2/(3*b) - 7*sin(2*a + 2*b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)/(24*b), Ne(b, 0)), (x*sin(2*a)**2*cos(a)**2, True))","A",0
145,1,131,0,3.240793," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a),x)","\begin{cases} - \frac{x \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)}}{4} - \frac{x \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{2} + \frac{x \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{4} - \frac{\sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)}}{4 b} - \frac{\cos^{2}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{2 b} & \text{for}\: b \neq 0 \\x \sin{\left(2 a \right)} \cos^{2}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-x*sin(a + b*x)**2*sin(2*a + 2*b*x)/4 - x*sin(a + b*x)*cos(a + b*x)*cos(2*a + 2*b*x)/2 + x*sin(2*a + 2*b*x)*cos(a + b*x)**2/4 - sin(a + b*x)*sin(2*a + 2*b*x)*cos(a + b*x)/(4*b) - cos(a + b*x)**2*cos(2*a + 2*b*x)/(2*b), Ne(b, 0)), (x*sin(2*a)*cos(a)**2, True))","A",0
146,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(2*b*x+2*a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,1,284,0,113.547437," ","integrate(cos(b*x+a)**3*sin(2*b*x+2*a)**3,x)","\begin{cases} - \frac{94 \sin^{3}{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)}}{315 b} - \frac{32 \sin^{3}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{105 b} - \frac{4 \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{7 b} - \frac{64 \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{105 b} + \frac{13 \sin{\left(a + b x \right)} \sin^{3}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{105 b} + \frac{8 \sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{35 b} - \frac{46 \sin^{2}{\left(2 a + 2 b x \right)} \cos^{3}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{105 b} - \frac{16 \cos^{3}{\left(a + b x \right)} \cos^{3}{\left(2 a + 2 b x \right)}}{63 b} & \text{for}\: b \neq 0 \\x \sin^{3}{\left(2 a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-94*sin(a + b*x)**3*sin(2*a + 2*b*x)**3/(315*b) - 32*sin(a + b*x)**3*sin(2*a + 2*b*x)*cos(2*a + 2*b*x)**2/(105*b) - 4*sin(a + b*x)**2*sin(2*a + 2*b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)/(7*b) - 64*sin(a + b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)**3/(105*b) + 13*sin(a + b*x)*sin(2*a + 2*b*x)**3*cos(a + b*x)**2/(105*b) + 8*sin(a + b*x)*sin(2*a + 2*b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)**2/(35*b) - 46*sin(2*a + 2*b*x)**2*cos(a + b*x)**3*cos(2*a + 2*b*x)/(105*b) - 16*cos(a + b*x)**3*cos(2*a + 2*b*x)**3/(63*b), Ne(b, 0)), (x*sin(2*a)**3*cos(a)**3, True))","A",0
154,1,202,0,38.317861," ","integrate(cos(b*x+a)**3*sin(2*b*x+2*a)**2,x)","\begin{cases} \frac{38 \sin^{3}{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)}}{105 b} + \frac{32 \sin^{3}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{105 b} + \frac{8 \sin^{2}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{35 b} + \frac{11 \sin{\left(a + b x \right)} \sin^{2}{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{35 b} + \frac{24 \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(2 a + 2 b x \right)}}{35 b} - \frac{12 \sin{\left(2 a + 2 b x \right)} \cos^{3}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{35 b} & \text{for}\: b \neq 0 \\x \sin^{2}{\left(2 a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((38*sin(a + b*x)**3*sin(2*a + 2*b*x)**2/(105*b) + 32*sin(a + b*x)**3*cos(2*a + 2*b*x)**2/(105*b) + 8*sin(a + b*x)**2*sin(2*a + 2*b*x)*cos(a + b*x)*cos(2*a + 2*b*x)/(35*b) + 11*sin(a + b*x)*sin(2*a + 2*b*x)**2*cos(a + b*x)**2/(35*b) + 24*sin(a + b*x)*cos(a + b*x)**2*cos(2*a + 2*b*x)**2/(35*b) - 12*sin(2*a + 2*b*x)*cos(a + b*x)**3*cos(2*a + 2*b*x)/(35*b), Ne(b, 0)), (x*sin(2*a)**2*cos(a)**3, True))","A",0
155,1,117,0,11.227463," ","integrate(cos(b*x+a)**3*sin(2*b*x+2*a),x)","\begin{cases} - \frac{2 \sin^{3}{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)}}{5 b} - \frac{4 \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{5 b} + \frac{\sin{\left(a + b x \right)} \sin{\left(2 a + 2 b x \right)} \cos^{2}{\left(a + b x \right)}}{5 b} - \frac{2 \cos^{3}{\left(a + b x \right)} \cos{\left(2 a + 2 b x \right)}}{5 b} & \text{for}\: b \neq 0 \\x \sin{\left(2 a \right)} \cos^{3}{\left(a \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sin(a + b*x)**3*sin(2*a + 2*b*x)/(5*b) - 4*sin(a + b*x)**2*cos(a + b*x)*cos(2*a + 2*b*x)/(5*b) + sin(a + b*x)*sin(2*a + 2*b*x)*cos(a + b*x)**2/(5*b) - 2*cos(a + b*x)**3*cos(2*a + 2*b*x)/(5*b), Ne(b, 0)), (x*sin(2*a)*cos(a)**3, True))","A",0
156,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(2*b*x+2*a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2/sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3/sin(2*b*x+2*a)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate(cos(x)/sin(2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate(csc(x)*sin(2*x)**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3*sin(2*b*x+2*a)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(2*b*x+2*a)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate(cos(b*x+a)*sin(2*b*x+2*a)**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,-1,0,0,0.000000," ","integrate(cos(b*x+a)**2*sin(b*x+a)**3*sin(2*b*x+2*a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
191,-1,0,0,0.000000," ","integrate(sin(b*x+a)*sin(d*x+c)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
192,1,921,0,32.887628," ","integrate(sin(b*x+a)*sin(d*x+c)**3,x)","\begin{cases} x \sin{\left(a \right)} \sin^{3}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x \sin{\left(a - 3 d x \right)} \sin^{3}{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a - 3 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(c + d x \right)} \cos{\left(a - 3 d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{x \cos{\left(a - 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8} + \frac{\sin{\left(a - 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{7 \sin^{3}{\left(c + d x \right)} \cos{\left(a - 3 d x \right)}}{24 d} + \frac{\sin{\left(c + d x \right)} \cos{\left(a - 3 d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: b = - 3 d \\\frac{3 x \sin{\left(a - d x \right)} \sin^{3}{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(c + d x \right)} \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \cos{\left(a - d x \right)} \cos^{3}{\left(c + d x \right)}}{8} + \frac{3 \sin{\left(a - d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{5 \sin^{3}{\left(c + d x \right)} \cos{\left(a - d x \right)}}{8 d} + \frac{3 \sin{\left(c + d x \right)} \cos{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: b = - d \\\frac{3 x \sin{\left(a + d x \right)} \sin^{3}{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \cos{\left(a + d x \right)} \cos^{3}{\left(c + d x \right)}}{8} + \frac{3 \sin{\left(a + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{5 \sin^{3}{\left(c + d x \right)} \cos{\left(a + d x \right)}}{8 d} - \frac{3 \sin{\left(c + d x \right)} \cos{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: b = d \\\frac{x \sin{\left(a + 3 d x \right)} \sin^{3}{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a + 3 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos{\left(a + 3 d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{x \cos{\left(a + 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8} + \frac{\sin{\left(a + 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{7 \sin^{3}{\left(c + d x \right)} \cos{\left(a + 3 d x \right)}}{24 d} - \frac{\sin{\left(c + d x \right)} \cos{\left(a + 3 d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: b = 3 d \\- \frac{b^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{3 b^{2} d \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{7 b d^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{6 b d^{2} \sin{\left(c + d x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} - \frac{9 d^{3} \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} - \frac{6 d^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)*sin(c)**3, Eq(b, 0) & Eq(d, 0)), (x*sin(a - 3*d*x)*sin(c + d*x)**3/8 - 3*x*sin(a - 3*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 - 3*x*sin(c + d*x)**2*cos(a - 3*d*x)*cos(c + d*x)/8 + x*cos(a - 3*d*x)*cos(c + d*x)**3/8 + sin(a - 3*d*x)*cos(c + d*x)**3/(8*d) + 7*sin(c + d*x)**3*cos(a - 3*d*x)/(24*d) + sin(c + d*x)*cos(a - 3*d*x)*cos(c + d*x)**2/(4*d), Eq(b, -3*d)), (3*x*sin(a - d*x)*sin(c + d*x)**3/8 + 3*x*sin(a - d*x)*sin(c + d*x)*cos(c + d*x)**2/8 - 3*x*sin(c + d*x)**2*cos(a - d*x)*cos(c + d*x)/8 - 3*x*cos(a - d*x)*cos(c + d*x)**3/8 + 3*sin(a - d*x)*cos(c + d*x)**3/(8*d) + 5*sin(c + d*x)**3*cos(a - d*x)/(8*d) + 3*sin(c + d*x)*cos(a - d*x)*cos(c + d*x)**2/(4*d), Eq(b, -d)), (3*x*sin(a + d*x)*sin(c + d*x)**3/8 + 3*x*sin(a + d*x)*sin(c + d*x)*cos(c + d*x)**2/8 + 3*x*sin(c + d*x)**2*cos(a + d*x)*cos(c + d*x)/8 + 3*x*cos(a + d*x)*cos(c + d*x)**3/8 + 3*sin(a + d*x)*cos(c + d*x)**3/(8*d) - 5*sin(c + d*x)**3*cos(a + d*x)/(8*d) - 3*sin(c + d*x)*cos(a + d*x)*cos(c + d*x)**2/(4*d), Eq(b, d)), (x*sin(a + 3*d*x)*sin(c + d*x)**3/8 - 3*x*sin(a + 3*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 + 3*x*sin(c + d*x)**2*cos(a + 3*d*x)*cos(c + d*x)/8 - x*cos(a + 3*d*x)*cos(c + d*x)**3/8 + sin(a + 3*d*x)*cos(c + d*x)**3/(8*d) - 7*sin(c + d*x)**3*cos(a + 3*d*x)/(24*d) - sin(c + d*x)*cos(a + 3*d*x)*cos(c + d*x)**2/(4*d), Eq(b, 3*d)), (-b**3*sin(c + d*x)**3*cos(a + b*x)/(b**4 - 10*b**2*d**2 + 9*d**4) + 3*b**2*d*sin(a + b*x)*sin(c + d*x)**2*cos(c + d*x)/(b**4 - 10*b**2*d**2 + 9*d**4) + 7*b*d**2*sin(c + d*x)**3*cos(a + b*x)/(b**4 - 10*b**2*d**2 + 9*d**4) + 6*b*d**2*sin(c + d*x)*cos(a + b*x)*cos(c + d*x)**2/(b**4 - 10*b**2*d**2 + 9*d**4) - 9*d**3*sin(a + b*x)*sin(c + d*x)**2*cos(c + d*x)/(b**4 - 10*b**2*d**2 + 9*d**4) - 6*d**3*sin(a + b*x)*cos(c + d*x)**3/(b**4 - 10*b**2*d**2 + 9*d**4), True))","A",0
193,1,408,0,6.695952," ","integrate(sin(b*x+a)*sin(d*x+c)**2,x)","\begin{cases} x \sin{\left(a \right)} \sin^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} - \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}\right) \sin{\left(a \right)} & \text{for}\: b = 0 \\\frac{x \sin{\left(a - 2 d x \right)} \sin^{2}{\left(c + d x \right)}}{4} - \frac{x \sin{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{4} - \frac{x \sin{\left(c + d x \right)} \cos{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{3 \sin{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{\cos{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: b = - 2 d \\\frac{x \sin{\left(a + 2 d x \right)} \sin^{2}{\left(c + d x \right)}}{4} - \frac{x \sin{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{x \sin{\left(c + d x \right)} \cos{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{3 \sin{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{\cos{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: b = 2 d \\- \frac{b^{2} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{b^{3} - 4 b d^{2}} + \frac{2 b d \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} + \frac{2 d^{2} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{b^{3} - 4 b d^{2}} + \frac{2 d^{2} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)*sin(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 - sin(c + d*x)*cos(c + d*x)/(2*d))*sin(a), Eq(b, 0)), (x*sin(a - 2*d*x)*sin(c + d*x)**2/4 - x*sin(a - 2*d*x)*cos(c + d*x)**2/4 - x*sin(c + d*x)*cos(a - 2*d*x)*cos(c + d*x)/2 - 3*sin(a - 2*d*x)*sin(c + d*x)*cos(c + d*x)/(4*d) + cos(a - 2*d*x)*cos(c + d*x)**2/(2*d), Eq(b, -2*d)), (x*sin(a + 2*d*x)*sin(c + d*x)**2/4 - x*sin(a + 2*d*x)*cos(c + d*x)**2/4 + x*sin(c + d*x)*cos(a + 2*d*x)*cos(c + d*x)/2 - 3*sin(a + 2*d*x)*sin(c + d*x)*cos(c + d*x)/(4*d) - cos(a + 2*d*x)*cos(c + d*x)**2/(2*d), Eq(b, 2*d)), (-b**2*sin(c + d*x)**2*cos(a + b*x)/(b**3 - 4*b*d**2) + 2*b*d*sin(a + b*x)*sin(c + d*x)*cos(c + d*x)/(b**3 - 4*b*d**2) + 2*d**2*sin(c + d*x)**2*cos(a + b*x)/(b**3 - 4*b*d**2) + 2*d**2*cos(a + b*x)*cos(c + d*x)**2/(b**3 - 4*b*d**2), True))","A",0
194,1,153,0,1.485606," ","integrate(sin(b*x+a)*sin(d*x+c),x)","\begin{cases} x \sin{\left(a \right)} \sin{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x \sin{\left(a - d x \right)} \sin{\left(c + d x \right)}}{2} - \frac{x \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{\sin{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = - d \\\frac{x \sin{\left(a + d x \right)} \sin{\left(c + d x \right)}}{2} + \frac{x \cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{\sin{\left(c + d x \right)} \cos{\left(a + d x \right)}}{2 d} & \text{for}\: b = d \\- \frac{b \sin{\left(c + d x \right)} \cos{\left(a + b x \right)}}{b^{2} - d^{2}} + \frac{d \sin{\left(a + b x \right)} \cos{\left(c + d x \right)}}{b^{2} - d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)*sin(c), Eq(b, 0) & Eq(d, 0)), (x*sin(a - d*x)*sin(c + d*x)/2 - x*cos(a - d*x)*cos(c + d*x)/2 - sin(a - d*x)*cos(c + d*x)/(2*d), Eq(b, -d)), (x*sin(a + d*x)*sin(c + d*x)/2 + x*cos(a + d*x)*cos(c + d*x)/2 - sin(c + d*x)*cos(a + d*x)/(2*d), Eq(b, d)), (-b*sin(c + d*x)*cos(a + b*x)/(b**2 - d**2) + d*sin(a + b*x)*cos(c + d*x)/(b**2 - d**2), True))","A",0
195,1,333,0,8.198644," ","integrate(csc(b*x+c)*sin(b*x+a),x)","\left(\begin{cases} 0 & \text{for}\: b = 0 \wedge c = 0 \\x & \text{for}\: c = 0 \\0 & \text{for}\: b = 0 \\- \frac{b x \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{b x}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{2 \log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)} + \left(\begin{cases} \tilde{\infty} x & \text{for}\: b = 0 \wedge c = 0 \\\frac{\log{\left(\sin{\left(b x \right)} \right)}}{b} & \text{for}\: c = 0 \\\frac{x}{\sin{\left(c \right)}} & \text{for}\: b = 0 \\\frac{2 b x \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)}"," ",0,"Piecewise((0, Eq(b, 0) & Eq(c, 0)), (x, Eq(c, 0)), (0, Eq(b, 0)), (-b*x*tan(c/2)**2/(b*tan(c/2)**2 + b) + b*x/(b*tan(c/2)**2 + b) - 2*log(tan(c/2) + tan(b*x/2))*tan(c/2)/(b*tan(c/2)**2 + b) - 2*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)/(b*tan(c/2)**2 + b) + 2*log(tan(b*x/2)**2 + 1)*tan(c/2)/(b*tan(c/2)**2 + b), True))*cos(a) + Piecewise((zoo*x, Eq(b, 0) & Eq(c, 0)), (log(sin(b*x))/b, Eq(c, 0)), (x/sin(c), Eq(b, 0)), (2*b*x*tan(c/2)/(b*tan(c/2)**2 + b) - log(tan(c/2) + tan(b*x/2))*tan(c/2)**2/(b*tan(c/2)**2 + b) + log(tan(c/2) + tan(b*x/2))/(b*tan(c/2)**2 + b) - log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**2/(b*tan(c/2)**2 + b) + log(tan(b*x/2) - 1/tan(c/2))/(b*tan(c/2)**2 + b) + log(tan(b*x/2)**2 + 1)*tan(c/2)**2/(b*tan(c/2)**2 + b) - log(tan(b*x/2)**2 + 1)/(b*tan(c/2)**2 + b), True))*sin(a)","B",0
196,1,3266,0,101.783241," ","integrate(csc(b*x+c)**2*sin(b*x+a),x)","\left(\begin{cases} 0 & \text{for}\: b = 0 \wedge \left(b = 0 \vee c = 0\right) \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: c = 0 \\- \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)} + \left(\begin{cases} \tilde{\infty} x & \text{for}\: b = 0 \wedge c = 0 \\- \frac{1}{b \sin{\left(b x \right)}} & \text{for}\: c = 0 \\\frac{x}{\sin^{2}{\left(c \right)}} & \text{for}\: b = 0 \\\frac{4 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{4 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{4 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{4 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{\tan^{6}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \tan^{5}{\left(\frac{c}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{\tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{\tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{2 \tan{\left(\frac{c}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{\tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)}"," ",0,"Piecewise((0, Eq(b, 0) & (Eq(b, 0) | Eq(c, 0))), (log(tan(b*x/2))/b, Eq(c, 0)), (-log(tan(c/2) + tan(b*x/2))*tan(c/2)**4*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(c/2) + tan(b*x/2))*tan(c/2)**3*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(c/2) + tan(b*x/2))*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + 2*log(tan(c/2) + tan(b*x/2))*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(c/2) + tan(b*x/2))*tan(c/2)*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(c/2) + tan(b*x/2))*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(c/2) + tan(b*x/2))*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**4*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**3*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - 2*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(b*x/2) - 1/tan(c/2))*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + tan(c/2)**4*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - 2*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - 2*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)), True))*cos(a) + Piecewise((zoo*x, Eq(b, 0) & Eq(c, 0)), (-1/(b*sin(b*x)), Eq(c, 0)), (x/sin(c)**2, Eq(b, 0)), (4*log(tan(c/2) + tan(b*x/2))*tan(c/2)**4*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + 4*log(tan(c/2) + tan(b*x/2))*tan(c/2)**3*tan(b*x/2)**2/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 4*log(tan(c/2) + tan(b*x/2))*tan(c/2)**3/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 4*log(tan(c/2) + tan(b*x/2))*tan(c/2)**2*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 4*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**4*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 4*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**3*tan(b*x/2)**2/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + 4*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**3/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + 4*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**2*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + tan(c/2)**6*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 2*tan(c/2)**5/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - tan(c/2)**4*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - tan(c/2)**2*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + 2*tan(c/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)), True))*sin(a)","B",0
197,-1,0,0,0.000000," ","integrate(csc(b*x+c)**3*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
198,-1,0,0,0.000000," ","integrate(csc(b*x+c)**4*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
199,-1,0,0,0.000000," ","integrate(csc(b*x+c)**5*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
200,-1,0,0,0.000000," ","integrate(csc(b*x+c)**6*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate(sin(b*x+a)**2*sin(d*x+c)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,1,408,0,6.513565," ","integrate(sin(b*x+a)**2*sin(d*x+c),x)","\begin{cases} x \sin^{2}{\left(a \right)} \sin{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x \sin^{2}{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)}}{4} - \frac{x \sin{\left(a - \frac{d x}{2} \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{2} - \frac{x \sin{\left(c + d x \right)} \cos^{2}{\left(a - \frac{d x}{2} \right)}}{4} - \frac{\sin^{2}{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{d} - \frac{\sin{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)}}{2 d} & \text{for}\: b = - \frac{d}{2} \\\frac{x \sin^{2}{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)}}{4} + \frac{x \sin{\left(a + \frac{d x}{2} \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{2} - \frac{x \sin{\left(c + d x \right)} \cos^{2}{\left(a + \frac{d x}{2} \right)}}{4} - \frac{\sin^{2}{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{d} + \frac{\sin{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)}}{2 d} & \text{for}\: b = \frac{d}{2} \\\left(\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}\right) \sin{\left(c \right)} & \text{for}\: d = 0 \\- \frac{2 b^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{4 b^{2} d - d^{3}} - \frac{2 b^{2} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{4 b^{2} d - d^{3}} - \frac{2 b d \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(a + b x \right)}}{4 b^{2} d - d^{3}} + \frac{d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{4 b^{2} d - d^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**2*sin(c), Eq(b, 0) & Eq(d, 0)), (x*sin(a - d*x/2)**2*sin(c + d*x)/4 - x*sin(a - d*x/2)*cos(a - d*x/2)*cos(c + d*x)/2 - x*sin(c + d*x)*cos(a - d*x/2)**2/4 - sin(a - d*x/2)**2*cos(c + d*x)/d - sin(a - d*x/2)*sin(c + d*x)*cos(a - d*x/2)/(2*d), Eq(b, -d/2)), (x*sin(a + d*x/2)**2*sin(c + d*x)/4 + x*sin(a + d*x/2)*cos(a + d*x/2)*cos(c + d*x)/2 - x*sin(c + d*x)*cos(a + d*x/2)**2/4 - sin(a + d*x/2)**2*cos(c + d*x)/d + sin(a + d*x/2)*sin(c + d*x)*cos(a + d*x/2)/(2*d), Eq(b, d/2)), ((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b))*sin(c), Eq(d, 0)), (-2*b**2*sin(a + b*x)**2*cos(c + d*x)/(4*b**2*d - d**3) - 2*b**2*cos(a + b*x)**2*cos(c + d*x)/(4*b**2*d - d**3) - 2*b*d*sin(a + b*x)*sin(c + d*x)*cos(a + b*x)/(4*b**2*d - d**3) + d**2*sin(a + b*x)**2*cos(c + d*x)/(4*b**2*d - d**3), True))","A",0
203,1,1027,0,22.695338," ","integrate(sin(b*x+a)**2*sin(d*x+c)**2,x)","\begin{cases} x \sin^{2}{\left(a \right)} \sin^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} - \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}\right) \sin^{2}{\left(a \right)} & \text{for}\: b = 0 \\\frac{3 x \sin^{2}{\left(a - d x \right)} \sin^{2}{\left(c + d x \right)}}{8} + \frac{x \sin^{2}{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{x \sin{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - d x \right)}}{8} + \frac{3 x \cos^{2}{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{5 \sin^{2}{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{\sin{\left(a - d x \right)} \cos{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8 d} & \text{for}\: b = - d \\\frac{3 x \sin^{2}{\left(a + d x \right)} \sin^{2}{\left(c + d x \right)}}{8} + \frac{x \sin^{2}{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{x \sin{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + d x \right)}}{8} + \frac{3 x \cos^{2}{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{5 \sin{\left(a + d x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + d x \right)}}{8 d} + \frac{\sin{\left(a + d x \right)} \cos{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8 d} - \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = d \\\left(\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}\right) \sin^{2}{\left(c \right)} & \text{for}\: d = 0 \\\frac{b^{3} d x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b^{3} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{2 b^{2} d \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{2 b d^{2} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{d^{3} \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{d^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**2*sin(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 - sin(c + d*x)*cos(c + d*x)/(2*d))*sin(a)**2, Eq(b, 0)), (3*x*sin(a - d*x)**2*sin(c + d*x)**2/8 + x*sin(a - d*x)**2*cos(c + d*x)**2/8 - x*sin(a - d*x)*sin(c + d*x)*cos(a - d*x)*cos(c + d*x)/2 + x*sin(c + d*x)**2*cos(a - d*x)**2/8 + 3*x*cos(a - d*x)**2*cos(c + d*x)**2/8 - 5*sin(a - d*x)**2*sin(c + d*x)*cos(c + d*x)/(8*d) + sin(a - d*x)*cos(a - d*x)*cos(c + d*x)**2/(2*d) + sin(c + d*x)*cos(a - d*x)**2*cos(c + d*x)/(8*d), Eq(b, -d)), (3*x*sin(a + d*x)**2*sin(c + d*x)**2/8 + x*sin(a + d*x)**2*cos(c + d*x)**2/8 + x*sin(a + d*x)*sin(c + d*x)*cos(a + d*x)*cos(c + d*x)/2 + x*sin(c + d*x)**2*cos(a + d*x)**2/8 + 3*x*cos(a + d*x)**2*cos(c + d*x)**2/8 - 5*sin(a + d*x)*sin(c + d*x)**2*cos(a + d*x)/(8*d) + sin(a + d*x)*cos(a + d*x)*cos(c + d*x)**2/(8*d) - sin(c + d*x)*cos(a + d*x)**2*cos(c + d*x)/(2*d), Eq(b, d)), ((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b))*sin(c)**2, Eq(d, 0)), (b**3*d*x*sin(a + b*x)**2*sin(c + d*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*sin(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*sin(c + d*x)**2*cos(a + b*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*cos(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b**3*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)/(4*b**3*d - 4*b*d**3) - b**3*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)/(4*b**3*d - 4*b*d**3) - 2*b**2*d*sin(a + b*x)*sin(c + d*x)**2*cos(a + b*x)/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(a + b*x)**2*sin(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(c + d*x)**2*cos(a + b*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*cos(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) + 2*b*d**2*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)/(4*b**3*d - 4*b*d**3) + d**3*sin(a + b*x)*sin(c + d*x)**2*cos(a + b*x)/(4*b**3*d - 4*b*d**3) + d**3*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3), True))","A",0
204,1,1999,0,113.789628," ","integrate(sin(b*x+a)**2*sin(d*x+c)**3,x)","\begin{cases} x \sin^{2}{\left(a \right)} \sin^{3}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{16} - \frac{3 x \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin{\left(a - \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{8} + \frac{x \sin{\left(a - \frac{3 d x}{2} \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8} - \frac{x \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{3 d x}{2} \right)}}{16} + \frac{3 x \sin{\left(c + d x \right)} \cos^{2}{\left(a - \frac{3 d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{\sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{5 \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{48 d} - \frac{\sin{\left(a - \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)}}{24 d} + \frac{5 \sin{\left(a - \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{9 \cos^{2}{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16 d} & \text{for}\: b = - \frac{3 d}{2} \\\frac{3 x \sin^{2}{\left(a - \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{16} + \frac{3 x \sin^{2}{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin{\left(a - \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a - \frac{d x}{2} \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{d x}{2} \right)}}{16} - \frac{3 x \sin{\left(c + d x \right)} \cos^{2}{\left(a - \frac{d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{\sin^{2}{\left(a - \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{31 \sin^{2}{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{48 d} - \frac{3 \sin{\left(a - \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)}}{8 d} - \frac{\sin{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{\cos^{2}{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{48 d} & \text{for}\: b = - \frac{d}{2} \\\frac{3 x \sin^{2}{\left(a + \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin{\left(a + \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a + \frac{d x}{2} \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{d x}{2} \right)}}{16} - \frac{3 x \sin{\left(c + d x \right)} \cos^{2}{\left(a + \frac{d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{\sin^{2}{\left(a + \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{31 \sin^{2}{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{48 d} + \frac{3 \sin{\left(a + \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)}}{8 d} + \frac{\sin{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{\cos^{2}{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{48 d} & \text{for}\: b = \frac{d}{2} \\\frac{x \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{16} - \frac{3 x \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin{\left(a + \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{8} - \frac{x \sin{\left(a + \frac{3 d x}{2} \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8} - \frac{x \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{3 d x}{2} \right)}}{16} + \frac{3 x \sin{\left(c + d x \right)} \cos^{2}{\left(a + \frac{3 d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{\sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{5 \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin{\left(a + \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)}}{24 d} - \frac{5 \sin{\left(a + \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{9 \cos^{2}{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16 d} & \text{for}\: b = \frac{3 d}{2} \\\left(\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}\right) \sin^{3}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{24 b^{4} \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{16 b^{4} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{24 b^{4} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{16 b^{4} \cos^{2}{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{24 b^{3} d \sin{\left(a + b x \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{78 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{40 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{42 b^{2} d^{2} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{40 b^{2} d^{2} \cos^{2}{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{42 b d^{3} \sin{\left(a + b x \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{36 b d^{3} \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{27 d^{4} \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{18 d^{4} \sin^{2}{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**2*sin(c)**3, Eq(b, 0) & Eq(d, 0)), (x*sin(a - 3*d*x/2)**2*sin(c + d*x)**3/16 - 3*x*sin(a - 3*d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/16 - 3*x*sin(a - 3*d*x/2)*sin(c + d*x)**2*cos(a - 3*d*x/2)*cos(c + d*x)/8 + x*sin(a - 3*d*x/2)*cos(a - 3*d*x/2)*cos(c + d*x)**3/8 - x*sin(c + d*x)**3*cos(a - 3*d*x/2)**2/16 + 3*x*sin(c + d*x)*cos(a - 3*d*x/2)**2*cos(c + d*x)**2/16 - sin(a - 3*d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/d - 5*sin(a - 3*d*x/2)**2*cos(c + d*x)**3/(48*d) - sin(a - 3*d*x/2)*sin(c + d*x)**3*cos(a - 3*d*x/2)/(24*d) + 5*sin(a - 3*d*x/2)*sin(c + d*x)*cos(a - 3*d*x/2)*cos(c + d*x)**2/(4*d) - 9*cos(a - 3*d*x/2)**2*cos(c + d*x)**3/(16*d), Eq(b, -3*d/2)), (3*x*sin(a - d*x/2)**2*sin(c + d*x)**3/16 + 3*x*sin(a - d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/16 - 3*x*sin(a - d*x/2)*sin(c + d*x)**2*cos(a - d*x/2)*cos(c + d*x)/8 - 3*x*sin(a - d*x/2)*cos(a - d*x/2)*cos(c + d*x)**3/8 - 3*x*sin(c + d*x)**3*cos(a - d*x/2)**2/16 - 3*x*sin(c + d*x)*cos(a - d*x/2)**2*cos(c + d*x)**2/16 - sin(a - d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/d - 31*sin(a - d*x/2)**2*cos(c + d*x)**3/(48*d) - 3*sin(a - d*x/2)*sin(c + d*x)**3*cos(a - d*x/2)/(8*d) - sin(a - d*x/2)*sin(c + d*x)*cos(a - d*x/2)*cos(c + d*x)**2/(4*d) - cos(a - d*x/2)**2*cos(c + d*x)**3/(48*d), Eq(b, -d/2)), (3*x*sin(a + d*x/2)**2*sin(c + d*x)**3/16 + 3*x*sin(a + d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/16 + 3*x*sin(a + d*x/2)*sin(c + d*x)**2*cos(a + d*x/2)*cos(c + d*x)/8 + 3*x*sin(a + d*x/2)*cos(a + d*x/2)*cos(c + d*x)**3/8 - 3*x*sin(c + d*x)**3*cos(a + d*x/2)**2/16 - 3*x*sin(c + d*x)*cos(a + d*x/2)**2*cos(c + d*x)**2/16 - sin(a + d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/d - 31*sin(a + d*x/2)**2*cos(c + d*x)**3/(48*d) + 3*sin(a + d*x/2)*sin(c + d*x)**3*cos(a + d*x/2)/(8*d) + sin(a + d*x/2)*sin(c + d*x)*cos(a + d*x/2)*cos(c + d*x)**2/(4*d) - cos(a + d*x/2)**2*cos(c + d*x)**3/(48*d), Eq(b, d/2)), (x*sin(a + 3*d*x/2)**2*sin(c + d*x)**3/16 - 3*x*sin(a + 3*d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/16 + 3*x*sin(a + 3*d*x/2)*sin(c + d*x)**2*cos(a + 3*d*x/2)*cos(c + d*x)/8 - x*sin(a + 3*d*x/2)*cos(a + 3*d*x/2)*cos(c + d*x)**3/8 - x*sin(c + d*x)**3*cos(a + 3*d*x/2)**2/16 + 3*x*sin(c + d*x)*cos(a + 3*d*x/2)**2*cos(c + d*x)**2/16 - sin(a + 3*d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/d - 5*sin(a + 3*d*x/2)**2*cos(c + d*x)**3/(48*d) + sin(a + 3*d*x/2)*sin(c + d*x)**3*cos(a + 3*d*x/2)/(24*d) - 5*sin(a + 3*d*x/2)*sin(c + d*x)*cos(a + 3*d*x/2)*cos(c + d*x)**2/(4*d) - 9*cos(a + 3*d*x/2)**2*cos(c + d*x)**3/(16*d), Eq(b, 3*d/2)), ((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b))*sin(c)**3, Eq(d, 0)), (-24*b**4*sin(a + b*x)**2*sin(c + d*x)**2*cos(c + d*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 16*b**4*sin(a + b*x)**2*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 24*b**4*sin(c + d*x)**2*cos(a + b*x)**2*cos(c + d*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 16*b**4*cos(a + b*x)**2*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 24*b**3*d*sin(a + b*x)*sin(c + d*x)**3*cos(a + b*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 78*b**2*d**2*sin(a + b*x)**2*sin(c + d*x)**2*cos(c + d*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 40*b**2*d**2*sin(a + b*x)**2*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 42*b**2*d**2*sin(c + d*x)**2*cos(a + b*x)**2*cos(c + d*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 40*b**2*d**2*cos(a + b*x)**2*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 42*b*d**3*sin(a + b*x)*sin(c + d*x)**3*cos(a + b*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 36*b*d**3*sin(a + b*x)*sin(c + d*x)*cos(a + b*x)*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 27*d**4*sin(a + b*x)**2*sin(c + d*x)**2*cos(c + d*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 18*d**4*sin(a + b*x)**2*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5), True))","A",0
205,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3*sin(d*x+c)**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,1,933,0,31.735018," ","integrate(sin(b*x+a)**3*sin(d*x+c),x)","\begin{cases} x \sin^{3}{\left(a \right)} \sin{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{3 x \sin^{3}{\left(a - d x \right)} \sin{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(a - d x \right)} \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a - d x \right)}}{8} - \frac{3 x \cos^{3}{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{\sin^{3}{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{3 \sin^{2}{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos{\left(a - d x \right)}}{4 d} + \frac{3 \sin{\left(c + d x \right)} \cos^{3}{\left(a - d x \right)}}{8 d} & \text{for}\: b = - d \\\frac{x \sin^{3}{\left(a - \frac{d x}{3} \right)} \sin{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(a - \frac{d x}{3} \right)} \cos{\left(a - \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a - \frac{d x}{3} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a - \frac{d x}{3} \right)}}{8} + \frac{x \cos^{3}{\left(a - \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{9 \sin^{3}{\left(a - \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 \sin^{2}{\left(a - \frac{d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{d x}{3} \right)}}{4 d} - \frac{\sin{\left(c + d x \right)} \cos^{3}{\left(a - \frac{d x}{3} \right)}}{8 d} & \text{for}\: b = - \frac{d}{3} \\\frac{x \sin^{3}{\left(a + \frac{d x}{3} \right)} \sin{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(a + \frac{d x}{3} \right)} \cos{\left(a + \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a + \frac{d x}{3} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + \frac{d x}{3} \right)}}{8} - \frac{x \cos^{3}{\left(a + \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{9 \sin^{3}{\left(a + \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{3 \sin^{2}{\left(a + \frac{d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{d x}{3} \right)}}{4 d} + \frac{\sin{\left(c + d x \right)} \cos^{3}{\left(a + \frac{d x}{3} \right)}}{8 d} & \text{for}\: b = \frac{d}{3} \\\frac{3 x \sin^{3}{\left(a + d x \right)} \sin{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(a + d x \right)} \cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + d x \right)}}{8} + \frac{3 x \cos^{3}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{5 \sin^{3}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 \sin{\left(a + d x \right)} \cos^{2}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{3 \sin{\left(c + d x \right)} \cos^{3}{\left(a + d x \right)}}{8 d} & \text{for}\: b = d \\- \frac{9 b^{3} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(a + b x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} - \frac{6 b^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(a + b x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} + \frac{7 b^{2} d \sin^{3}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} + \frac{6 b^{2} d \sin{\left(a + b x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} + \frac{3 b d^{2} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(a + b x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} - \frac{d^{3} \sin^{3}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**3*sin(c), Eq(b, 0) & Eq(d, 0)), (3*x*sin(a - d*x)**3*sin(c + d*x)/8 - 3*x*sin(a - d*x)**2*cos(a - d*x)*cos(c + d*x)/8 + 3*x*sin(a - d*x)*sin(c + d*x)*cos(a - d*x)**2/8 - 3*x*cos(a - d*x)**3*cos(c + d*x)/8 + sin(a - d*x)**3*cos(c + d*x)/(8*d) + 3*sin(a - d*x)**2*sin(c + d*x)*cos(a - d*x)/(4*d) + 3*sin(c + d*x)*cos(a - d*x)**3/(8*d), Eq(b, -d)), (x*sin(a - d*x/3)**3*sin(c + d*x)/8 - 3*x*sin(a - d*x/3)**2*cos(a - d*x/3)*cos(c + d*x)/8 - 3*x*sin(a - d*x/3)*sin(c + d*x)*cos(a - d*x/3)**2/8 + x*cos(a - d*x/3)**3*cos(c + d*x)/8 - 9*sin(a - d*x/3)**3*cos(c + d*x)/(8*d) - 3*sin(a - d*x/3)**2*sin(c + d*x)*cos(a - d*x/3)/(4*d) - sin(c + d*x)*cos(a - d*x/3)**3/(8*d), Eq(b, -d/3)), (x*sin(a + d*x/3)**3*sin(c + d*x)/8 + 3*x*sin(a + d*x/3)**2*cos(a + d*x/3)*cos(c + d*x)/8 - 3*x*sin(a + d*x/3)*sin(c + d*x)*cos(a + d*x/3)**2/8 - x*cos(a + d*x/3)**3*cos(c + d*x)/8 - 9*sin(a + d*x/3)**3*cos(c + d*x)/(8*d) + 3*sin(a + d*x/3)**2*sin(c + d*x)*cos(a + d*x/3)/(4*d) + sin(c + d*x)*cos(a + d*x/3)**3/(8*d), Eq(b, d/3)), (3*x*sin(a + d*x)**3*sin(c + d*x)/8 + 3*x*sin(a + d*x)**2*cos(a + d*x)*cos(c + d*x)/8 + 3*x*sin(a + d*x)*sin(c + d*x)*cos(a + d*x)**2/8 + 3*x*cos(a + d*x)**3*cos(c + d*x)/8 - 5*sin(a + d*x)**3*cos(c + d*x)/(8*d) - 3*sin(a + d*x)*cos(a + d*x)**2*cos(c + d*x)/(4*d) + 3*sin(c + d*x)*cos(a + d*x)**3/(8*d), Eq(b, d)), (-9*b**3*sin(a + b*x)**2*sin(c + d*x)*cos(a + b*x)/(9*b**4 - 10*b**2*d**2 + d**4) - 6*b**3*sin(c + d*x)*cos(a + b*x)**3/(9*b**4 - 10*b**2*d**2 + d**4) + 7*b**2*d*sin(a + b*x)**3*cos(c + d*x)/(9*b**4 - 10*b**2*d**2 + d**4) + 6*b**2*d*sin(a + b*x)*cos(a + b*x)**2*cos(c + d*x)/(9*b**4 - 10*b**2*d**2 + d**4) + 3*b*d**2*sin(a + b*x)**2*sin(c + d*x)*cos(a + b*x)/(9*b**4 - 10*b**2*d**2 + d**4) - d**3*sin(a + b*x)**3*cos(c + d*x)/(9*b**4 - 10*b**2*d**2 + d**4), True))","A",0
207,1,2030,0,113.351272," ","integrate(sin(b*x+a)**3*sin(d*x+c)**2,x)","\begin{cases} x \sin^{3}{\left(a \right)} \sin^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} - \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}\right) \sin^{3}{\left(a \right)} & \text{for}\: b = 0 \\\frac{3 x \sin^{3}{\left(a - 2 d x \right)} \sin^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin^{3}{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin^{2}{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a - 2 d x \right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - 2 d x \right)}}{16} - \frac{3 x \sin{\left(a - 2 d x \right)} \cos^{2}{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin{\left(c + d x \right)} \cos^{3}{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{13 \sin^{3}{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{\sin^{2}{\left(a - 2 d x \right)} \cos{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} - \frac{7 \sin{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{17 \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a - 2 d x \right)}}{96 d} + \frac{49 \cos^{3}{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{96 d} & \text{for}\: b = - 2 d \\\frac{x \sin^{3}{\left(a - \frac{2 d x}{3} \right)} \sin^{2}{\left(c + d x \right)}}{16} - \frac{x \sin^{3}{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin^{2}{\left(a - \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a - \frac{2 d x}{3} \right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{2 d x}{3} \right)}}{16} + \frac{3 x \sin{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{x \sin{\left(c + d x \right)} \cos^{3}{\left(a - \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{15 \sin^{3}{\left(a - \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{3 \sin^{2}{\left(a - \frac{2 d x}{3} \right)} \cos{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{9 \sin{\left(a - \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a - \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{21 \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a - \frac{2 d x}{3} \right)}}{32 d} + \frac{11 \cos^{3}{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{32 d} & \text{for}\: b = - \frac{2 d}{3} \\\frac{x \sin^{3}{\left(a + \frac{2 d x}{3} \right)} \sin^{2}{\left(c + d x \right)}}{16} - \frac{x \sin^{3}{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a + \frac{2 d x}{3} \right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{2 d x}{3} \right)}}{16} + \frac{3 x \sin{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{x \sin{\left(c + d x \right)} \cos^{3}{\left(a + \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{15 \sin^{3}{\left(a + \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{3 \sin^{2}{\left(a + \frac{2 d x}{3} \right)} \cos{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{9 \sin{\left(a + \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{21 \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + \frac{2 d x}{3} \right)}}{32 d} - \frac{11 \cos^{3}{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{32 d} & \text{for}\: b = \frac{2 d}{3} \\\frac{3 x \sin^{3}{\left(a + 2 d x \right)} \sin^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin^{3}{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a + 2 d x \right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + 2 d x \right)}}{16} - \frac{3 x \sin{\left(a + 2 d x \right)} \cos^{2}{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin{\left(c + d x \right)} \cos^{3}{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{13 \sin^{3}{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{\sin^{2}{\left(a + 2 d x \right)} \cos{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} - \frac{7 \sin{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{17 \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + 2 d x \right)}}{96 d} - \frac{49 \cos^{3}{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{96 d} & \text{for}\: b = 2 d \\- \frac{27 b^{4} \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{18 b^{4} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{42 b^{3} d \sin^{3}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{36 b^{3} d \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{78 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{42 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{40 b^{2} d^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{40 b^{2} d^{2} \cos^{3}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{24 b d^{3} \sin^{3}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{24 d^{4} \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{24 d^{4} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{16 d^{4} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{16 d^{4} \cos^{3}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**3*sin(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 - sin(c + d*x)*cos(c + d*x)/(2*d))*sin(a)**3, Eq(b, 0)), (3*x*sin(a - 2*d*x)**3*sin(c + d*x)**2/16 - 3*x*sin(a - 2*d*x)**3*cos(c + d*x)**2/16 - 3*x*sin(a - 2*d*x)**2*sin(c + d*x)*cos(a - 2*d*x)*cos(c + d*x)/8 + 3*x*sin(a - 2*d*x)*sin(c + d*x)**2*cos(a - 2*d*x)**2/16 - 3*x*sin(a - 2*d*x)*cos(a - 2*d*x)**2*cos(c + d*x)**2/16 - 3*x*sin(c + d*x)*cos(a - 2*d*x)**3*cos(c + d*x)/8 - 13*sin(a - 2*d*x)**3*sin(c + d*x)*cos(c + d*x)/(16*d) + sin(a - 2*d*x)**2*cos(a - 2*d*x)*cos(c + d*x)**2/(2*d) - 7*sin(a - 2*d*x)*sin(c + d*x)*cos(a - 2*d*x)**2*cos(c + d*x)/(8*d) - 17*sin(c + d*x)**2*cos(a - 2*d*x)**3/(96*d) + 49*cos(a - 2*d*x)**3*cos(c + d*x)**2/(96*d), Eq(b, -2*d)), (x*sin(a - 2*d*x/3)**3*sin(c + d*x)**2/16 - x*sin(a - 2*d*x/3)**3*cos(c + d*x)**2/16 - 3*x*sin(a - 2*d*x/3)**2*sin(c + d*x)*cos(a - 2*d*x/3)*cos(c + d*x)/8 - 3*x*sin(a - 2*d*x/3)*sin(c + d*x)**2*cos(a - 2*d*x/3)**2/16 + 3*x*sin(a - 2*d*x/3)*cos(a - 2*d*x/3)**2*cos(c + d*x)**2/16 + x*sin(c + d*x)*cos(a - 2*d*x/3)**3*cos(c + d*x)/8 - 15*sin(a - 2*d*x/3)**3*sin(c + d*x)*cos(c + d*x)/(16*d) + 3*sin(a - 2*d*x/3)**2*cos(a - 2*d*x/3)*cos(c + d*x)**2/(2*d) + 9*sin(a - 2*d*x/3)*sin(c + d*x)*cos(a - 2*d*x/3)**2*cos(c + d*x)/(8*d) + 21*sin(c + d*x)**2*cos(a - 2*d*x/3)**3/(32*d) + 11*cos(a - 2*d*x/3)**3*cos(c + d*x)**2/(32*d), Eq(b, -2*d/3)), (x*sin(a + 2*d*x/3)**3*sin(c + d*x)**2/16 - x*sin(a + 2*d*x/3)**3*cos(c + d*x)**2/16 + 3*x*sin(a + 2*d*x/3)**2*sin(c + d*x)*cos(a + 2*d*x/3)*cos(c + d*x)/8 - 3*x*sin(a + 2*d*x/3)*sin(c + d*x)**2*cos(a + 2*d*x/3)**2/16 + 3*x*sin(a + 2*d*x/3)*cos(a + 2*d*x/3)**2*cos(c + d*x)**2/16 - x*sin(c + d*x)*cos(a + 2*d*x/3)**3*cos(c + d*x)/8 - 15*sin(a + 2*d*x/3)**3*sin(c + d*x)*cos(c + d*x)/(16*d) - 3*sin(a + 2*d*x/3)**2*cos(a + 2*d*x/3)*cos(c + d*x)**2/(2*d) + 9*sin(a + 2*d*x/3)*sin(c + d*x)*cos(a + 2*d*x/3)**2*cos(c + d*x)/(8*d) - 21*sin(c + d*x)**2*cos(a + 2*d*x/3)**3/(32*d) - 11*cos(a + 2*d*x/3)**3*cos(c + d*x)**2/(32*d), Eq(b, 2*d/3)), (3*x*sin(a + 2*d*x)**3*sin(c + d*x)**2/16 - 3*x*sin(a + 2*d*x)**3*cos(c + d*x)**2/16 + 3*x*sin(a + 2*d*x)**2*sin(c + d*x)*cos(a + 2*d*x)*cos(c + d*x)/8 + 3*x*sin(a + 2*d*x)*sin(c + d*x)**2*cos(a + 2*d*x)**2/16 - 3*x*sin(a + 2*d*x)*cos(a + 2*d*x)**2*cos(c + d*x)**2/16 + 3*x*sin(c + d*x)*cos(a + 2*d*x)**3*cos(c + d*x)/8 - 13*sin(a + 2*d*x)**3*sin(c + d*x)*cos(c + d*x)/(16*d) - sin(a + 2*d*x)**2*cos(a + 2*d*x)*cos(c + d*x)**2/(2*d) - 7*sin(a + 2*d*x)*sin(c + d*x)*cos(a + 2*d*x)**2*cos(c + d*x)/(8*d) + 17*sin(c + d*x)**2*cos(a + 2*d*x)**3/(96*d) - 49*cos(a + 2*d*x)**3*cos(c + d*x)**2/(96*d), Eq(b, 2*d)), (-27*b**4*sin(a + b*x)**2*sin(c + d*x)**2*cos(a + b*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 18*b**4*sin(c + d*x)**2*cos(a + b*x)**3/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 42*b**3*d*sin(a + b*x)**3*sin(c + d*x)*cos(c + d*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 36*b**3*d*sin(a + b*x)*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 78*b**2*d**2*sin(a + b*x)**2*sin(c + d*x)**2*cos(a + b*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 42*b**2*d**2*sin(a + b*x)**2*cos(a + b*x)*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 40*b**2*d**2*sin(c + d*x)**2*cos(a + b*x)**3/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 40*b**2*d**2*cos(a + b*x)**3*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 24*b*d**3*sin(a + b*x)**3*sin(c + d*x)*cos(c + d*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 24*d**4*sin(a + b*x)**2*sin(c + d*x)**2*cos(a + b*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 24*d**4*sin(a + b*x)**2*cos(a + b*x)*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 16*d**4*sin(c + d*x)**2*cos(a + b*x)**3/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 16*d**4*cos(a + b*x)**3*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4), True))","A",0
208,-1,0,0,0.000000," ","integrate(sin(b*x+a)**3*sin(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
209,-1,0,0,0.000000," ","integrate(cos(d*x+c)**n*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
210,1,918,0,32.159763," ","integrate(cos(d*x+c)**3*sin(b*x+a),x)","\begin{cases} x \sin{\left(a \right)} \cos^{3}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\- \frac{3 x \sin{\left(a - 3 d x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{x \sin{\left(a - 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8} - \frac{x \sin^{3}{\left(c + d x \right)} \cos{\left(a - 3 d x \right)}}{8} + \frac{3 x \sin{\left(c + d x \right)} \cos{\left(a - 3 d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{\sin{\left(a - 3 d x \right)} \sin^{3}{\left(c + d x \right)}}{24 d} - \frac{\sin{\left(a - 3 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{3 \cos{\left(a - 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = - 3 d \\\frac{3 x \sin{\left(a - d x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a - d x \right)} \cos^{3}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{3}{\left(c + d x \right)} \cos{\left(a - d x \right)}}{8} + \frac{3 x \sin{\left(c + d x \right)} \cos{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 \sin{\left(a - d x \right)} \sin^{3}{\left(c + d x \right)}}{8 d} + \frac{3 \sin{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{\cos{\left(a - d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = - d \\\frac{3 x \sin{\left(a + d x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a + d x \right)} \cos^{3}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{3}{\left(c + d x \right)} \cos{\left(a + d x \right)}}{8} - \frac{3 x \sin{\left(c + d x \right)} \cos{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 \sin{\left(a + d x \right)} \sin^{3}{\left(c + d x \right)}}{8 d} + \frac{3 \sin{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{\cos{\left(a + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = d \\- \frac{3 x \sin{\left(a + 3 d x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{x \sin{\left(a + 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8} + \frac{x \sin^{3}{\left(c + d x \right)} \cos{\left(a + 3 d x \right)}}{8} - \frac{3 x \sin{\left(c + d x \right)} \cos{\left(a + 3 d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{\sin{\left(a + 3 d x \right)} \sin^{3}{\left(c + d x \right)}}{24 d} - \frac{\sin{\left(a + 3 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} - \frac{3 \cos{\left(a + 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: b = 3 d \\- \frac{b^{3} \cos{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} - \frac{3 b^{2} d \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{6 b d^{2} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)} \cos{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{7 b d^{2} \cos{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{6 d^{3} \sin{\left(a + b x \right)} \sin^{3}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{9 d^{3} \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)*cos(c)**3, Eq(b, 0) & Eq(d, 0)), (-3*x*sin(a - 3*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + x*sin(a - 3*d*x)*cos(c + d*x)**3/8 - x*sin(c + d*x)**3*cos(a - 3*d*x)/8 + 3*x*sin(c + d*x)*cos(a - 3*d*x)*cos(c + d*x)**2/8 - sin(a - 3*d*x)*sin(c + d*x)**3/(24*d) - sin(a - 3*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) + 3*cos(a - 3*d*x)*cos(c + d*x)**3/(8*d), Eq(b, -3*d)), (3*x*sin(a - d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + 3*x*sin(a - d*x)*cos(c + d*x)**3/8 + 3*x*sin(c + d*x)**3*cos(a - d*x)/8 + 3*x*sin(c + d*x)*cos(a - d*x)*cos(c + d*x)**2/8 + 3*sin(a - d*x)*sin(c + d*x)**3/(8*d) + 3*sin(a - d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) - cos(a - d*x)*cos(c + d*x)**3/(8*d), Eq(b, -d)), (3*x*sin(a + d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + 3*x*sin(a + d*x)*cos(c + d*x)**3/8 - 3*x*sin(c + d*x)**3*cos(a + d*x)/8 - 3*x*sin(c + d*x)*cos(a + d*x)*cos(c + d*x)**2/8 + 3*sin(a + d*x)*sin(c + d*x)**3/(8*d) + 3*sin(a + d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) + cos(a + d*x)*cos(c + d*x)**3/(8*d), Eq(b, d)), (-3*x*sin(a + 3*d*x)*sin(c + d*x)**2*cos(c + d*x)/8 + x*sin(a + 3*d*x)*cos(c + d*x)**3/8 + x*sin(c + d*x)**3*cos(a + 3*d*x)/8 - 3*x*sin(c + d*x)*cos(a + 3*d*x)*cos(c + d*x)**2/8 - sin(a + 3*d*x)*sin(c + d*x)**3/(24*d) - sin(a + 3*d*x)*sin(c + d*x)*cos(c + d*x)**2/(4*d) - 3*cos(a + 3*d*x)*cos(c + d*x)**3/(8*d), Eq(b, 3*d)), (-b**3*cos(a + b*x)*cos(c + d*x)**3/(b**4 - 10*b**2*d**2 + 9*d**4) - 3*b**2*d*sin(a + b*x)*sin(c + d*x)*cos(c + d*x)**2/(b**4 - 10*b**2*d**2 + 9*d**4) + 6*b*d**2*sin(c + d*x)**2*cos(a + b*x)*cos(c + d*x)/(b**4 - 10*b**2*d**2 + 9*d**4) + 7*b*d**2*cos(a + b*x)*cos(c + d*x)**3/(b**4 - 10*b**2*d**2 + 9*d**4) + 6*d**3*sin(a + b*x)*sin(c + d*x)**3/(b**4 - 10*b**2*d**2 + 9*d**4) + 9*d**3*sin(a + b*x)*sin(c + d*x)*cos(c + d*x)**2/(b**4 - 10*b**2*d**2 + 9*d**4), True))","A",0
211,1,405,0,6.539187," ","integrate(cos(d*x+c)**2*sin(b*x+a),x)","\begin{cases} x \sin{\left(a \right)} \cos^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}\right) \sin{\left(a \right)} & \text{for}\: b = 0 \\- \frac{x \sin{\left(a - 2 d x \right)} \sin^{2}{\left(c + d x \right)}}{4} + \frac{x \sin{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{x \sin{\left(c + d x \right)} \cos{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{\sin{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{\cos{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: b = - 2 d \\- \frac{x \sin{\left(a + 2 d x \right)} \sin^{2}{\left(c + d x \right)}}{4} + \frac{x \sin{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{4} - \frac{x \sin{\left(c + d x \right)} \cos{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{\sin{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{\cos{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: b = 2 d \\- \frac{b^{2} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} - \frac{2 b d \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} + \frac{2 d^{2} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{b^{3} - 4 b d^{2}} + \frac{2 d^{2} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)*cos(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 + sin(c + d*x)*cos(c + d*x)/(2*d))*sin(a), Eq(b, 0)), (-x*sin(a - 2*d*x)*sin(c + d*x)**2/4 + x*sin(a - 2*d*x)*cos(c + d*x)**2/4 + x*sin(c + d*x)*cos(a - 2*d*x)*cos(c + d*x)/2 - sin(a - 2*d*x)*sin(c + d*x)*cos(c + d*x)/(4*d) + cos(a - 2*d*x)*cos(c + d*x)**2/(2*d), Eq(b, -2*d)), (-x*sin(a + 2*d*x)*sin(c + d*x)**2/4 + x*sin(a + 2*d*x)*cos(c + d*x)**2/4 - x*sin(c + d*x)*cos(a + 2*d*x)*cos(c + d*x)/2 - sin(a + 2*d*x)*sin(c + d*x)*cos(c + d*x)/(4*d) - cos(a + 2*d*x)*cos(c + d*x)**2/(2*d), Eq(b, 2*d)), (-b**2*cos(a + b*x)*cos(c + d*x)**2/(b**3 - 4*b*d**2) - 2*b*d*sin(a + b*x)*sin(c + d*x)*cos(c + d*x)/(b**3 - 4*b*d**2) + 2*d**2*sin(c + d*x)**2*cos(a + b*x)/(b**3 - 4*b*d**2) + 2*d**2*cos(a + b*x)*cos(c + d*x)**2/(b**3 - 4*b*d**2), True))","A",0
212,1,155,0,1.454375," ","integrate(cos(d*x+c)*sin(b*x+a),x)","\begin{cases} x \sin{\left(a \right)} \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x \sin{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{x \sin{\left(c + d x \right)} \cos{\left(a - d x \right)}}{2} + \frac{\cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = - d \\\frac{x \sin{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{x \sin{\left(c + d x \right)} \cos{\left(a + d x \right)}}{2} - \frac{\cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = d \\- \frac{b \cos{\left(a + b x \right)} \cos{\left(c + d x \right)}}{b^{2} - d^{2}} - \frac{d \sin{\left(a + b x \right)} \sin{\left(c + d x \right)}}{b^{2} - d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)*cos(c), Eq(b, 0) & Eq(d, 0)), (x*sin(a - d*x)*cos(c + d*x)/2 + x*sin(c + d*x)*cos(a - d*x)/2 + cos(a - d*x)*cos(c + d*x)/(2*d), Eq(b, -d)), (x*sin(a + d*x)*cos(c + d*x)/2 - x*sin(c + d*x)*cos(a + d*x)/2 - cos(a + d*x)*cos(c + d*x)/(2*d), Eq(b, d)), (-b*cos(a + b*x)*cos(c + d*x)/(b**2 - d**2) - d*sin(a + b*x)*sin(c + d*x)/(b**2 - d**2), True))","A",0
213,1,435,0,10.124944," ","integrate(sec(b*x+c)*sin(b*x+a),x)","\left(\begin{cases} - x & \text{for}\: c = \frac{\pi}{2} \\x & \text{for}\: c = - \frac{\pi}{2} \\0 & \text{for}\: b = 0 \\- \frac{2 b x \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)} + \left(\begin{cases} - \frac{\log{\left(\sin{\left(b x \right)} \right)}}{b} & \text{for}\: c = \frac{\pi}{2} \\\frac{\log{\left(\sin{\left(b x \right)} \right)}}{b} & \text{for}\: c = - \frac{\pi}{2} \\\frac{x}{\cos{\left(c \right)}} & \text{for}\: b = 0 \\- \frac{b x \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{b x}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{2 \log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)}"," ",0,"Piecewise((-x, Eq(c, pi/2)), (x, Eq(c, -pi/2)), (0, Eq(b, 0)), (-2*b*x*tan(c/2)/(b*tan(c/2)**2 + b) - log(tan(b*x/2)**2 + 1)*tan(c/2)**2/(b*tan(c/2)**2 + b) + log(tan(b*x/2)**2 + 1)/(b*tan(c/2)**2 + b) + log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**2/(b*tan(c/2)**2 + b) - log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))/(b*tan(c/2)**2 + b) + log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**2/(b*tan(c/2)**2 + b) - log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))/(b*tan(c/2)**2 + b), True))*cos(a) + Piecewise((-log(sin(b*x))/b, Eq(c, pi/2)), (log(sin(b*x))/b, Eq(c, -pi/2)), (x/cos(c), Eq(b, 0)), (-b*x*tan(c/2)**2/(b*tan(c/2)**2 + b) + b*x/(b*tan(c/2)**2 + b) + 2*log(tan(b*x/2)**2 + 1)*tan(c/2)/(b*tan(c/2)**2 + b) - 2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)/(b*tan(c/2)**2 + b) - 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)/(b*tan(c/2)**2 + b), True))*sin(a)","B",0
214,1,5552,0,165.057663," ","integrate(sec(b*x+c)**2*sin(b*x+a),x)","\left(\begin{cases} \frac{x}{\cos^{2}{\left(c \right)}} & \text{for}\: b = 0 \\- \frac{1}{b \sin{\left(b x \right)}} & \text{for}\: c = - \frac{\pi}{2} \vee c = \frac{\pi}{2} \\- \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{6}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{4}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{8 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{6}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{4}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{8 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{4 \tan^{5}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{8 \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{8 \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{4 \tan{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)} + \left(\begin{cases} \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: c = \frac{\pi}{2} \\0 & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: c = - \frac{\pi}{2} \\- \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{8 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{8 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2 \tan^{4}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)}"," ",0,"Piecewise((x/cos(c)**2, Eq(b, 0)), (-1/(b*sin(b*x)), Eq(c, -pi/2) | Eq(c, pi/2)), (-log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**6*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**6/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 4*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**5*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 3*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**4*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 3*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**4/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 8*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**3*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 3*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**2*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 3*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 4*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**6*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**6/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 4*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**5*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 3*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**4*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 3*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**4/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 8*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**3*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 3*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**2*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 3*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 4*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 4*tan(c/2)**5/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 8*tan(c/2)**4*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 8*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 4*tan(c/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b), True))*sin(a) + Piecewise((log(tan(b*x/2))/b, Eq(c, pi/2)), (0, Eq(b, 0)), (log(tan(b*x/2))/b, Eq(c, -pi/2)), (-2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**3*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 8*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**3*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 8*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 2*tan(c/2)**4/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 4*tan(c/2)**3*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 4*tan(c/2)*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b), True))*cos(a)","B",0
215,-2,0,0,0.000000," ","integrate(sec(b*x+c)**3*sin(b*x+a),x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
216,-1,0,0,0.000000," ","integrate(sec(b*x+c)**4*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,-1,0,0,0.000000," ","integrate(sec(b*x+c)**5*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
218,-1,0,0,0.000000," ","integrate(sec(b*x+c)**6*sin(b*x+a),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
219,-1,0,0,0.000000," ","integrate(cos(d*x+c)**n*sin(b*x+a)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
220,1,408,0,6.696503," ","integrate(cos(d*x+c)*sin(b*x+a)**2,x)","\begin{cases} x \sin^{2}{\left(a \right)} \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x \sin^{2}{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{4} + \frac{x \sin{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)}}{2} - \frac{x \cos^{2}{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{4} + \frac{\sin^{2}{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)}}{d} - \frac{\sin{\left(a - \frac{d x}{2} \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = - \frac{d}{2} \\\frac{x \sin^{2}{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{4} - \frac{x \sin{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)}}{2} - \frac{x \cos^{2}{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{4} + \frac{\sin^{2}{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)}}{d} + \frac{\sin{\left(a + \frac{d x}{2} \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = \frac{d}{2} \\\left(\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}\right) \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{2 b^{2} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)}}{4 b^{2} d - d^{3}} + \frac{2 b^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{4 b^{2} d - d^{3}} - \frac{2 b d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos{\left(c + d x \right)}}{4 b^{2} d - d^{3}} - \frac{d^{2} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)}}{4 b^{2} d - d^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**2*cos(c), Eq(b, 0) & Eq(d, 0)), (x*sin(a - d*x/2)**2*cos(c + d*x)/4 + x*sin(a - d*x/2)*sin(c + d*x)*cos(a - d*x/2)/2 - x*cos(a - d*x/2)**2*cos(c + d*x)/4 + sin(a - d*x/2)**2*sin(c + d*x)/d - sin(a - d*x/2)*cos(a - d*x/2)*cos(c + d*x)/(2*d), Eq(b, -d/2)), (x*sin(a + d*x/2)**2*cos(c + d*x)/4 - x*sin(a + d*x/2)*sin(c + d*x)*cos(a + d*x/2)/2 - x*cos(a + d*x/2)**2*cos(c + d*x)/4 + sin(a + d*x/2)**2*sin(c + d*x)/d + sin(a + d*x/2)*cos(a + d*x/2)*cos(c + d*x)/(2*d), Eq(b, d/2)), ((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b))*cos(c), Eq(d, 0)), (2*b**2*sin(a + b*x)**2*sin(c + d*x)/(4*b**2*d - d**3) + 2*b**2*sin(c + d*x)*cos(a + b*x)**2/(4*b**2*d - d**3) - 2*b*d*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)/(4*b**2*d - d**3) - d**2*sin(a + b*x)**2*sin(c + d*x)/(4*b**2*d - d**3), True))","A",0
221,1,1027,0,22.977015," ","integrate(cos(d*x+c)**2*sin(b*x+a)**2,x)","\begin{cases} x \sin^{2}{\left(a \right)} \cos^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}\right) \sin^{2}{\left(a \right)} & \text{for}\: b = 0 \\\frac{x \sin^{2}{\left(a - d x \right)} \sin^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{x \sin{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - d x \right)}}{8} + \frac{x \cos^{2}{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{\sin^{2}{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{\sin{\left(a - d x \right)} \cos{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{3 \sin{\left(c + d x \right)} \cos^{2}{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8 d} & \text{for}\: b = - d \\\frac{x \sin^{2}{\left(a + d x \right)} \sin^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{x \sin{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + d x \right)}}{8} + \frac{x \cos^{2}{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{\sin{\left(a + d x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + d x \right)}}{8 d} - \frac{5 \sin{\left(a + d x \right)} \cos{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = d \\\left(\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}\right) \cos^{2}{\left(c \right)} & \text{for}\: d = 0 \\\frac{b^{3} d x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{2 b^{2} d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{2 b d^{2} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{d^{3} \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{d^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**2*cos(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 + sin(c + d*x)*cos(c + d*x)/(2*d))*sin(a)**2, Eq(b, 0)), (x*sin(a - d*x)**2*sin(c + d*x)**2/8 + 3*x*sin(a - d*x)**2*cos(c + d*x)**2/8 + x*sin(a - d*x)*sin(c + d*x)*cos(a - d*x)*cos(c + d*x)/2 + 3*x*sin(c + d*x)**2*cos(a - d*x)**2/8 + x*cos(a - d*x)**2*cos(c + d*x)**2/8 + sin(a - d*x)**2*sin(c + d*x)*cos(c + d*x)/(8*d) + sin(a - d*x)*cos(a - d*x)*cos(c + d*x)**2/(2*d) + 3*sin(c + d*x)*cos(a - d*x)**2*cos(c + d*x)/(8*d), Eq(b, -d)), (x*sin(a + d*x)**2*sin(c + d*x)**2/8 + 3*x*sin(a + d*x)**2*cos(c + d*x)**2/8 - x*sin(a + d*x)*sin(c + d*x)*cos(a + d*x)*cos(c + d*x)/2 + 3*x*sin(c + d*x)**2*cos(a + d*x)**2/8 + x*cos(a + d*x)**2*cos(c + d*x)**2/8 + sin(a + d*x)*sin(c + d*x)**2*cos(a + d*x)/(8*d) - 5*sin(a + d*x)*cos(a + d*x)*cos(c + d*x)**2/(8*d) + sin(c + d*x)*cos(a + d*x)**2*cos(c + d*x)/(2*d), Eq(b, d)), ((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b))*cos(c)**2, Eq(d, 0)), (b**3*d*x*sin(a + b*x)**2*sin(c + d*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*sin(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*sin(c + d*x)**2*cos(a + b*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*cos(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) + b**3*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)/(4*b**3*d - 4*b*d**3) + b**3*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)/(4*b**3*d - 4*b*d**3) - 2*b**2*d*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(a + b*x)**2*sin(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(c + d*x)**2*cos(a + b*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*cos(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) - 2*b*d**2*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)/(4*b**3*d - 4*b*d**3) + d**3*sin(a + b*x)*sin(c + d*x)**2*cos(a + b*x)/(4*b**3*d - 4*b*d**3) + d**3*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3), True))","A",0
222,1,1999,0,115.102817," ","integrate(cos(d*x+c)**3*sin(b*x+a)**2,x)","\begin{cases} x \sin^{2}{\left(a \right)} \cos^{3}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\- \frac{3 x \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16} + \frac{x \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} - \frac{x \sin{\left(a - \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)}}{8} + \frac{3 x \sin{\left(a - \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{16} - \frac{x \cos^{2}{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{5 \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{5 \sin{\left(a - \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{\sin{\left(a - \frac{3 d x}{2} \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{24 d} + \frac{9 \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{3 d x}{2} \right)}}{16 d} & \text{for}\: b = - \frac{3 d}{2} \\\frac{3 x \sin^{2}{\left(a - \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16} + \frac{3 x \sin^{2}{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{3 x \sin{\left(a - \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)}}{8} + \frac{3 x \sin{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{16} - \frac{3 x \cos^{2}{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{31 \sin^{2}{\left(a - \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin^{2}{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{\sin{\left(a - \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{3 \sin{\left(a - \frac{d x}{2} \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{\sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{d x}{2} \right)}}{48 d} & \text{for}\: b = - \frac{d}{2} \\\frac{3 x \sin^{2}{\left(a + \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16} + \frac{3 x \sin^{2}{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} - \frac{3 x \sin{\left(a + \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)}}{8} - \frac{3 x \sin{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{16} - \frac{3 x \cos^{2}{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{31 \sin^{2}{\left(a + \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin^{2}{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{\sin{\left(a + \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{3 \sin{\left(a + \frac{d x}{2} \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{\sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{d x}{2} \right)}}{48 d} & \text{for}\: b = \frac{d}{2} \\- \frac{3 x \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16} + \frac{x \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{x \sin{\left(a + \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)}}{8} - \frac{3 x \sin{\left(a + \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{16} - \frac{x \cos^{2}{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{5 \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{5 \sin{\left(a + \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{\sin{\left(a + \frac{3 d x}{2} \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{24 d} + \frac{9 \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{3 d x}{2} \right)}}{16 d} & \text{for}\: b = \frac{3 d}{2} \\\left(\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}\right) \cos^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{16 b^{4} \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{24 b^{4} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{16 b^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{24 b^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{24 b^{3} d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{40 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{78 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{40 b^{2} d^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{42 b^{2} d^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{36 b d^{3} \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)} \cos{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{42 b d^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{18 d^{4} \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{27 d^{4} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**2*cos(c)**3, Eq(b, 0) & Eq(d, 0)), (-3*x*sin(a - 3*d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/16 + x*sin(a - 3*d*x/2)**2*cos(c + d*x)**3/16 - x*sin(a - 3*d*x/2)*sin(c + d*x)**3*cos(a - 3*d*x/2)/8 + 3*x*sin(a - 3*d*x/2)*sin(c + d*x)*cos(a - 3*d*x/2)*cos(c + d*x)**2/8 + 3*x*sin(c + d*x)**2*cos(a - 3*d*x/2)**2*cos(c + d*x)/16 - x*cos(a - 3*d*x/2)**2*cos(c + d*x)**3/16 + 5*sin(a - 3*d*x/2)**2*sin(c + d*x)**3/(48*d) + sin(a - 3*d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/d + 5*sin(a - 3*d*x/2)*sin(c + d*x)**2*cos(a - 3*d*x/2)*cos(c + d*x)/(4*d) - sin(a - 3*d*x/2)*cos(a - 3*d*x/2)*cos(c + d*x)**3/(24*d) + 9*sin(c + d*x)**3*cos(a - 3*d*x/2)**2/(16*d), Eq(b, -3*d/2)), (3*x*sin(a - d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/16 + 3*x*sin(a - d*x/2)**2*cos(c + d*x)**3/16 + 3*x*sin(a - d*x/2)*sin(c + d*x)**3*cos(a - d*x/2)/8 + 3*x*sin(a - d*x/2)*sin(c + d*x)*cos(a - d*x/2)*cos(c + d*x)**2/8 - 3*x*sin(c + d*x)**2*cos(a - d*x/2)**2*cos(c + d*x)/16 - 3*x*cos(a - d*x/2)**2*cos(c + d*x)**3/16 + 31*sin(a - d*x/2)**2*sin(c + d*x)**3/(48*d) + sin(a - d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/d - sin(a - d*x/2)*sin(c + d*x)**2*cos(a - d*x/2)*cos(c + d*x)/(4*d) - 3*sin(a - d*x/2)*cos(a - d*x/2)*cos(c + d*x)**3/(8*d) + sin(c + d*x)**3*cos(a - d*x/2)**2/(48*d), Eq(b, -d/2)), (3*x*sin(a + d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/16 + 3*x*sin(a + d*x/2)**2*cos(c + d*x)**3/16 - 3*x*sin(a + d*x/2)*sin(c + d*x)**3*cos(a + d*x/2)/8 - 3*x*sin(a + d*x/2)*sin(c + d*x)*cos(a + d*x/2)*cos(c + d*x)**2/8 - 3*x*sin(c + d*x)**2*cos(a + d*x/2)**2*cos(c + d*x)/16 - 3*x*cos(a + d*x/2)**2*cos(c + d*x)**3/16 + 31*sin(a + d*x/2)**2*sin(c + d*x)**3/(48*d) + sin(a + d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/d + sin(a + d*x/2)*sin(c + d*x)**2*cos(a + d*x/2)*cos(c + d*x)/(4*d) + 3*sin(a + d*x/2)*cos(a + d*x/2)*cos(c + d*x)**3/(8*d) + sin(c + d*x)**3*cos(a + d*x/2)**2/(48*d), Eq(b, d/2)), (-3*x*sin(a + 3*d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/16 + x*sin(a + 3*d*x/2)**2*cos(c + d*x)**3/16 + x*sin(a + 3*d*x/2)*sin(c + d*x)**3*cos(a + 3*d*x/2)/8 - 3*x*sin(a + 3*d*x/2)*sin(c + d*x)*cos(a + 3*d*x/2)*cos(c + d*x)**2/8 + 3*x*sin(c + d*x)**2*cos(a + 3*d*x/2)**2*cos(c + d*x)/16 - x*cos(a + 3*d*x/2)**2*cos(c + d*x)**3/16 + 5*sin(a + 3*d*x/2)**2*sin(c + d*x)**3/(48*d) + sin(a + 3*d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/d - 5*sin(a + 3*d*x/2)*sin(c + d*x)**2*cos(a + 3*d*x/2)*cos(c + d*x)/(4*d) + sin(a + 3*d*x/2)*cos(a + 3*d*x/2)*cos(c + d*x)**3/(24*d) + 9*sin(c + d*x)**3*cos(a + 3*d*x/2)**2/(16*d), Eq(b, 3*d/2)), ((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 - sin(a + b*x)*cos(a + b*x)/(2*b))*cos(c)**3, Eq(d, 0)), (16*b**4*sin(a + b*x)**2*sin(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 24*b**4*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 16*b**4*sin(c + d*x)**3*cos(a + b*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 24*b**4*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 24*b**3*d*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 40*b**2*d**2*sin(a + b*x)**2*sin(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 78*b**2*d**2*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 40*b**2*d**2*sin(c + d*x)**3*cos(a + b*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 42*b**2*d**2*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 36*b*d**3*sin(a + b*x)*sin(c + d*x)**2*cos(a + b*x)*cos(c + d*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 42*b*d**3*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 18*d**4*sin(a + b*x)**2*sin(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 27*d**4*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5), True))","A",0
223,-1,0,0,0.000000," ","integrate(cos(d*x+c)**n*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,1,933,0,32.621603," ","integrate(cos(d*x+c)*sin(b*x+a)**3,x)","\begin{cases} x \sin^{3}{\left(a \right)} \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{3 x \sin^{3}{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos{\left(a - d x \right)}}{8} + \frac{3 x \sin{\left(a - d x \right)} \cos^{2}{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(c + d x \right)} \cos^{3}{\left(a - d x \right)}}{8} - \frac{\sin^{3}{\left(a - d x \right)} \sin{\left(c + d x \right)}}{8 d} + \frac{3 \sin^{2}{\left(a - d x \right)} \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{3 \cos^{3}{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8 d} & \text{for}\: b = - d \\\frac{x \sin^{3}{\left(a - \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(a - \frac{d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{d x}{3} \right)}}{8} - \frac{3 x \sin{\left(a - \frac{d x}{3} \right)} \cos^{2}{\left(a - \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{x \sin{\left(c + d x \right)} \cos^{3}{\left(a - \frac{d x}{3} \right)}}{8} + \frac{9 \sin^{3}{\left(a - \frac{d x}{3} \right)} \sin{\left(c + d x \right)}}{8 d} - \frac{3 \sin^{2}{\left(a - \frac{d x}{3} \right)} \cos{\left(a - \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{\cos^{3}{\left(a - \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8 d} & \text{for}\: b = - \frac{d}{3} \\\frac{x \sin^{3}{\left(a + \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(a + \frac{d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{d x}{3} \right)}}{8} - \frac{3 x \sin{\left(a + \frac{d x}{3} \right)} \cos^{2}{\left(a + \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8} + \frac{x \sin{\left(c + d x \right)} \cos^{3}{\left(a + \frac{d x}{3} \right)}}{8} + \frac{9 \sin^{3}{\left(a + \frac{d x}{3} \right)} \sin{\left(c + d x \right)}}{8 d} + \frac{3 \sin^{2}{\left(a + \frac{d x}{3} \right)} \cos{\left(a + \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{\cos^{3}{\left(a + \frac{d x}{3} \right)} \cos{\left(c + d x \right)}}{8 d} & \text{for}\: b = \frac{d}{3} \\\frac{3 x \sin^{3}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos{\left(a + d x \right)}}{8} + \frac{3 x \sin{\left(a + d x \right)} \cos^{2}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(c + d x \right)} \cos^{3}{\left(a + d x \right)}}{8} + \frac{5 \sin^{3}{\left(a + d x \right)} \sin{\left(c + d x \right)}}{8 d} + \frac{3 \sin{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + d x \right)}}{4 d} + \frac{3 \cos^{3}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{8 d} & \text{for}\: b = d \\- \frac{9 b^{3} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos{\left(c + d x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} - \frac{6 b^{3} \cos^{3}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} - \frac{7 b^{2} d \sin^{3}{\left(a + b x \right)} \sin{\left(c + d x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} - \frac{6 b^{2} d \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} + \frac{3 b d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos{\left(c + d x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} + \frac{d^{3} \sin^{3}{\left(a + b x \right)} \sin{\left(c + d x \right)}}{9 b^{4} - 10 b^{2} d^{2} + d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**3*cos(c), Eq(b, 0) & Eq(d, 0)), (3*x*sin(a - d*x)**3*cos(c + d*x)/8 + 3*x*sin(a - d*x)**2*sin(c + d*x)*cos(a - d*x)/8 + 3*x*sin(a - d*x)*cos(a - d*x)**2*cos(c + d*x)/8 + 3*x*sin(c + d*x)*cos(a - d*x)**3/8 - sin(a - d*x)**3*sin(c + d*x)/(8*d) + 3*sin(a - d*x)**2*cos(a - d*x)*cos(c + d*x)/(4*d) + 3*cos(a - d*x)**3*cos(c + d*x)/(8*d), Eq(b, -d)), (x*sin(a - d*x/3)**3*cos(c + d*x)/8 + 3*x*sin(a - d*x/3)**2*sin(c + d*x)*cos(a - d*x/3)/8 - 3*x*sin(a - d*x/3)*cos(a - d*x/3)**2*cos(c + d*x)/8 - x*sin(c + d*x)*cos(a - d*x/3)**3/8 + 9*sin(a - d*x/3)**3*sin(c + d*x)/(8*d) - 3*sin(a - d*x/3)**2*cos(a - d*x/3)*cos(c + d*x)/(4*d) - cos(a - d*x/3)**3*cos(c + d*x)/(8*d), Eq(b, -d/3)), (x*sin(a + d*x/3)**3*cos(c + d*x)/8 - 3*x*sin(a + d*x/3)**2*sin(c + d*x)*cos(a + d*x/3)/8 - 3*x*sin(a + d*x/3)*cos(a + d*x/3)**2*cos(c + d*x)/8 + x*sin(c + d*x)*cos(a + d*x/3)**3/8 + 9*sin(a + d*x/3)**3*sin(c + d*x)/(8*d) + 3*sin(a + d*x/3)**2*cos(a + d*x/3)*cos(c + d*x)/(4*d) + cos(a + d*x/3)**3*cos(c + d*x)/(8*d), Eq(b, d/3)), (3*x*sin(a + d*x)**3*cos(c + d*x)/8 - 3*x*sin(a + d*x)**2*sin(c + d*x)*cos(a + d*x)/8 + 3*x*sin(a + d*x)*cos(a + d*x)**2*cos(c + d*x)/8 - 3*x*sin(c + d*x)*cos(a + d*x)**3/8 + 5*sin(a + d*x)**3*sin(c + d*x)/(8*d) + 3*sin(a + d*x)*sin(c + d*x)*cos(a + d*x)**2/(4*d) + 3*cos(a + d*x)**3*cos(c + d*x)/(8*d), Eq(b, d)), (-9*b**3*sin(a + b*x)**2*cos(a + b*x)*cos(c + d*x)/(9*b**4 - 10*b**2*d**2 + d**4) - 6*b**3*cos(a + b*x)**3*cos(c + d*x)/(9*b**4 - 10*b**2*d**2 + d**4) - 7*b**2*d*sin(a + b*x)**3*sin(c + d*x)/(9*b**4 - 10*b**2*d**2 + d**4) - 6*b**2*d*sin(a + b*x)*sin(c + d*x)*cos(a + b*x)**2/(9*b**4 - 10*b**2*d**2 + d**4) + 3*b*d**2*sin(a + b*x)**2*cos(a + b*x)*cos(c + d*x)/(9*b**4 - 10*b**2*d**2 + d**4) + d**3*sin(a + b*x)**3*sin(c + d*x)/(9*b**4 - 10*b**2*d**2 + d**4), True))","A",0
225,1,2020,0,117.133404," ","integrate(cos(d*x+c)**2*sin(b*x+a)**3,x)","\begin{cases} x \sin^{3}{\left(a \right)} \cos^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}\right) \sin^{3}{\left(a \right)} & \text{for}\: b = 0 \\- \frac{3 x \sin^{3}{\left(a - 2 d x \right)} \sin^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin^{3}{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin^{2}{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a - 2 d x \right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - 2 d x \right)}}{16} + \frac{3 x \sin{\left(a - 2 d x \right)} \cos^{2}{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin{\left(c + d x \right)} \cos^{3}{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 \sin^{3}{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{\sin^{2}{\left(a - 2 d x \right)} \cos{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} - \frac{\sin{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{\sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a - 2 d x \right)}}{96 d} + \frac{31 \cos^{3}{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{96 d} & \text{for}\: b = - 2 d \\- \frac{x \sin^{3}{\left(a - \frac{2 d x}{3} \right)} \sin^{2}{\left(c + d x \right)}}{16} + \frac{x \sin^{3}{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin^{2}{\left(a - \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a - \frac{2 d x}{3} \right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{2 d x}{3} \right)}}{16} - \frac{3 x \sin{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{x \sin{\left(c + d x \right)} \cos^{3}{\left(a - \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{\sin^{3}{\left(a - \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{3 \sin^{2}{\left(a - \frac{2 d x}{3} \right)} \cos{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{15 \sin{\left(a - \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a - \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{27 \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a - \frac{2 d x}{3} \right)}}{32 d} + \frac{5 \cos^{3}{\left(a - \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{32 d} & \text{for}\: b = - \frac{2 d}{3} \\- \frac{x \sin^{3}{\left(a + \frac{2 d x}{3} \right)} \sin^{2}{\left(c + d x \right)}}{16} + \frac{x \sin^{3}{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin^{2}{\left(a + \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a + \frac{2 d x}{3} \right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{2 d x}{3} \right)}}{16} - \frac{3 x \sin{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{x \sin{\left(c + d x \right)} \cos^{3}{\left(a + \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8} - \frac{\sin^{3}{\left(a + \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{3 \sin^{2}{\left(a + \frac{2 d x}{3} \right)} \cos{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{15 \sin{\left(a + \frac{2 d x}{3} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + \frac{2 d x}{3} \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{27 \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + \frac{2 d x}{3} \right)}}{32 d} - \frac{5 \cos^{3}{\left(a + \frac{2 d x}{3} \right)} \cos^{2}{\left(c + d x \right)}}{32 d} & \text{for}\: b = \frac{2 d}{3} \\- \frac{3 x \sin^{3}{\left(a + 2 d x \right)} \sin^{2}{\left(c + d x \right)}}{16} + \frac{3 x \sin^{3}{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin^{2}{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a + 2 d x \right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + 2 d x \right)}}{16} + \frac{3 x \sin{\left(a + 2 d x \right)} \cos^{2}{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{16} - \frac{3 x \sin{\left(c + d x \right)} \cos^{3}{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{8} - \frac{3 \sin^{3}{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{\sin^{2}{\left(a + 2 d x \right)} \cos{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} - \frac{\sin{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{\sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + 2 d x \right)}}{96 d} - \frac{31 \cos^{3}{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{96 d} & \text{for}\: b = 2 d \\- \frac{27 b^{4} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{18 b^{4} \cos^{3}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{42 b^{3} d \sin^{3}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{36 b^{3} d \sin{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{42 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{78 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{40 b^{2} d^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{40 b^{2} d^{2} \cos^{3}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} + \frac{24 b d^{3} \sin^{3}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{24 d^{4} \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{24 d^{4} \sin^{2}{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{16 d^{4} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(a + b x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} - \frac{16 d^{4} \cos^{3}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{27 b^{5} - 120 b^{3} d^{2} + 48 b d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(a)**3*cos(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 + sin(c + d*x)*cos(c + d*x)/(2*d))*sin(a)**3, Eq(b, 0)), (-3*x*sin(a - 2*d*x)**3*sin(c + d*x)**2/16 + 3*x*sin(a - 2*d*x)**3*cos(c + d*x)**2/16 + 3*x*sin(a - 2*d*x)**2*sin(c + d*x)*cos(a - 2*d*x)*cos(c + d*x)/8 - 3*x*sin(a - 2*d*x)*sin(c + d*x)**2*cos(a - 2*d*x)**2/16 + 3*x*sin(a - 2*d*x)*cos(a - 2*d*x)**2*cos(c + d*x)**2/16 + 3*x*sin(c + d*x)*cos(a - 2*d*x)**3*cos(c + d*x)/8 - 3*sin(a - 2*d*x)**3*sin(c + d*x)*cos(c + d*x)/(16*d) + sin(a - 2*d*x)**2*cos(a - 2*d*x)*cos(c + d*x)**2/(2*d) - sin(a - 2*d*x)*sin(c + d*x)*cos(a - 2*d*x)**2*cos(c + d*x)/(8*d) + sin(c + d*x)**2*cos(a - 2*d*x)**3/(96*d) + 31*cos(a - 2*d*x)**3*cos(c + d*x)**2/(96*d), Eq(b, -2*d)), (-x*sin(a - 2*d*x/3)**3*sin(c + d*x)**2/16 + x*sin(a - 2*d*x/3)**3*cos(c + d*x)**2/16 + 3*x*sin(a - 2*d*x/3)**2*sin(c + d*x)*cos(a - 2*d*x/3)*cos(c + d*x)/8 + 3*x*sin(a - 2*d*x/3)*sin(c + d*x)**2*cos(a - 2*d*x/3)**2/16 - 3*x*sin(a - 2*d*x/3)*cos(a - 2*d*x/3)**2*cos(c + d*x)**2/16 - x*sin(c + d*x)*cos(a - 2*d*x/3)**3*cos(c + d*x)/8 - sin(a - 2*d*x/3)**3*sin(c + d*x)*cos(c + d*x)/(16*d) + 3*sin(a - 2*d*x/3)**2*cos(a - 2*d*x/3)*cos(c + d*x)**2/(2*d) + 15*sin(a - 2*d*x/3)*sin(c + d*x)*cos(a - 2*d*x/3)**2*cos(c + d*x)/(8*d) + 27*sin(c + d*x)**2*cos(a - 2*d*x/3)**3/(32*d) + 5*cos(a - 2*d*x/3)**3*cos(c + d*x)**2/(32*d), Eq(b, -2*d/3)), (-x*sin(a + 2*d*x/3)**3*sin(c + d*x)**2/16 + x*sin(a + 2*d*x/3)**3*cos(c + d*x)**2/16 - 3*x*sin(a + 2*d*x/3)**2*sin(c + d*x)*cos(a + 2*d*x/3)*cos(c + d*x)/8 + 3*x*sin(a + 2*d*x/3)*sin(c + d*x)**2*cos(a + 2*d*x/3)**2/16 - 3*x*sin(a + 2*d*x/3)*cos(a + 2*d*x/3)**2*cos(c + d*x)**2/16 + x*sin(c + d*x)*cos(a + 2*d*x/3)**3*cos(c + d*x)/8 - sin(a + 2*d*x/3)**3*sin(c + d*x)*cos(c + d*x)/(16*d) - 3*sin(a + 2*d*x/3)**2*cos(a + 2*d*x/3)*cos(c + d*x)**2/(2*d) + 15*sin(a + 2*d*x/3)*sin(c + d*x)*cos(a + 2*d*x/3)**2*cos(c + d*x)/(8*d) - 27*sin(c + d*x)**2*cos(a + 2*d*x/3)**3/(32*d) - 5*cos(a + 2*d*x/3)**3*cos(c + d*x)**2/(32*d), Eq(b, 2*d/3)), (-3*x*sin(a + 2*d*x)**3*sin(c + d*x)**2/16 + 3*x*sin(a + 2*d*x)**3*cos(c + d*x)**2/16 - 3*x*sin(a + 2*d*x)**2*sin(c + d*x)*cos(a + 2*d*x)*cos(c + d*x)/8 - 3*x*sin(a + 2*d*x)*sin(c + d*x)**2*cos(a + 2*d*x)**2/16 + 3*x*sin(a + 2*d*x)*cos(a + 2*d*x)**2*cos(c + d*x)**2/16 - 3*x*sin(c + d*x)*cos(a + 2*d*x)**3*cos(c + d*x)/8 - 3*sin(a + 2*d*x)**3*sin(c + d*x)*cos(c + d*x)/(16*d) - sin(a + 2*d*x)**2*cos(a + 2*d*x)*cos(c + d*x)**2/(2*d) - sin(a + 2*d*x)*sin(c + d*x)*cos(a + 2*d*x)**2*cos(c + d*x)/(8*d) - sin(c + d*x)**2*cos(a + 2*d*x)**3/(96*d) - 31*cos(a + 2*d*x)**3*cos(c + d*x)**2/(96*d), Eq(b, 2*d)), (-27*b**4*sin(a + b*x)**2*cos(a + b*x)*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 18*b**4*cos(a + b*x)**3*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 42*b**3*d*sin(a + b*x)**3*sin(c + d*x)*cos(c + d*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 36*b**3*d*sin(a + b*x)*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 42*b**2*d**2*sin(a + b*x)**2*sin(c + d*x)**2*cos(a + b*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 78*b**2*d**2*sin(a + b*x)**2*cos(a + b*x)*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 40*b**2*d**2*sin(c + d*x)**2*cos(a + b*x)**3/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 40*b**2*d**2*cos(a + b*x)**3*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) + 24*b*d**3*sin(a + b*x)**3*sin(c + d*x)*cos(c + d*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 24*d**4*sin(a + b*x)**2*sin(c + d*x)**2*cos(a + b*x)/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 24*d**4*sin(a + b*x)**2*cos(a + b*x)*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 16*d**4*sin(c + d*x)**2*cos(a + b*x)**3/(27*b**5 - 120*b**3*d**2 + 48*b*d**4) - 16*d**4*cos(a + b*x)**3*cos(c + d*x)**2/(27*b**5 - 120*b**3*d**2 + 48*b*d**4), True))","A",0
226,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*sin(b*x+a)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
227,1,333,0,8.033616," ","integrate(cos(b*x+a)/sin(b*x+c),x)","- \left(\begin{cases} 0 & \text{for}\: b = 0 \wedge c = 0 \\x & \text{for}\: c = 0 \\0 & \text{for}\: b = 0 \\- \frac{b x \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{b x}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{2 \log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)} + \left(\begin{cases} \tilde{\infty} x & \text{for}\: b = 0 \wedge c = 0 \\\frac{\log{\left(\sin{\left(b x \right)} \right)}}{b} & \text{for}\: c = 0 \\\frac{x}{\sin{\left(c \right)}} & \text{for}\: b = 0 \\\frac{2 b x \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)}"," ",0,"-Piecewise((0, Eq(b, 0) & Eq(c, 0)), (x, Eq(c, 0)), (0, Eq(b, 0)), (-b*x*tan(c/2)**2/(b*tan(c/2)**2 + b) + b*x/(b*tan(c/2)**2 + b) - 2*log(tan(c/2) + tan(b*x/2))*tan(c/2)/(b*tan(c/2)**2 + b) - 2*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)/(b*tan(c/2)**2 + b) + 2*log(tan(b*x/2)**2 + 1)*tan(c/2)/(b*tan(c/2)**2 + b), True))*sin(a) + Piecewise((zoo*x, Eq(b, 0) & Eq(c, 0)), (log(sin(b*x))/b, Eq(c, 0)), (x/sin(c), Eq(b, 0)), (2*b*x*tan(c/2)/(b*tan(c/2)**2 + b) - log(tan(c/2) + tan(b*x/2))*tan(c/2)**2/(b*tan(c/2)**2 + b) + log(tan(c/2) + tan(b*x/2))/(b*tan(c/2)**2 + b) - log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**2/(b*tan(c/2)**2 + b) + log(tan(b*x/2) - 1/tan(c/2))/(b*tan(c/2)**2 + b) + log(tan(b*x/2)**2 + 1)*tan(c/2)**2/(b*tan(c/2)**2 + b) - log(tan(b*x/2)**2 + 1)/(b*tan(c/2)**2 + b), True))*cos(a)","B",0
228,1,3266,0,102.512533," ","integrate(cos(b*x+a)/sin(b*x+c)**2,x)","- \left(\begin{cases} 0 & \text{for}\: b = 0 \wedge \left(b = 0 \vee c = 0\right) \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: c = 0 \\- \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} + \frac{\tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} - \frac{\tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{3}{\left(\frac{c}{2} \right)} + b \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan{\left(\frac{c}{2} \right)} - b \tan{\left(\frac{b x}{2} \right)}} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)} + \left(\begin{cases} \tilde{\infty} x & \text{for}\: b = 0 \wedge c = 0 \\- \frac{1}{b \sin{\left(b x \right)}} & \text{for}\: c = 0 \\\frac{x}{\sin^{2}{\left(c \right)}} & \text{for}\: b = 0 \\\frac{4 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{4 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{4 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{4 \log{\left(\tan{\left(\frac{c}{2} \right)} + \tan{\left(\frac{b x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{4 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{1}{\tan{\left(\frac{c}{2} \right)}} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{\tan^{6}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{2 \tan^{5}{\left(\frac{c}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{\tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} - \frac{\tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{2 \tan{\left(\frac{c}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} + \frac{\tan{\left(\frac{b x}{2} \right)}}{2 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + 2 b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{4}{\left(\frac{c}{2} \right)} + 2 b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - 2 b \tan^{2}{\left(\frac{c}{2} \right)} - 2 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)}"," ",0,"-Piecewise((0, Eq(b, 0) & (Eq(b, 0) | Eq(c, 0))), (log(tan(b*x/2))/b, Eq(c, 0)), (-log(tan(c/2) + tan(b*x/2))*tan(c/2)**4*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(c/2) + tan(b*x/2))*tan(c/2)**3*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(c/2) + tan(b*x/2))*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + 2*log(tan(c/2) + tan(b*x/2))*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(c/2) + tan(b*x/2))*tan(c/2)*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(c/2) + tan(b*x/2))*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(c/2) + tan(b*x/2))*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**4*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**3*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - 2*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + log(tan(b*x/2) - 1/tan(c/2))*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) + tan(c/2)**4*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - 2*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - 2*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)) - tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2) + b*tan(c/2)**3*tan(b*x/2)**2 - b*tan(c/2)**3 + b*tan(c/2)*tan(b*x/2)**2 - b*tan(c/2) - b*tan(b*x/2)), True))*sin(a) + Piecewise((zoo*x, Eq(b, 0) & Eq(c, 0)), (-1/(b*sin(b*x)), Eq(c, 0)), (x/sin(c)**2, Eq(b, 0)), (4*log(tan(c/2) + tan(b*x/2))*tan(c/2)**4*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + 4*log(tan(c/2) + tan(b*x/2))*tan(c/2)**3*tan(b*x/2)**2/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 4*log(tan(c/2) + tan(b*x/2))*tan(c/2)**3/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 4*log(tan(c/2) + tan(b*x/2))*tan(c/2)**2*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 4*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**4*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 4*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**3*tan(b*x/2)**2/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + 4*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**3/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + 4*log(tan(b*x/2) - 1/tan(c/2))*tan(c/2)**2*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + tan(c/2)**6*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - 2*tan(c/2)**5/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - tan(c/2)**4*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) - tan(c/2)**2*tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + 2*tan(c/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)) + tan(b*x/2)/(2*b*tan(c/2)**5*tan(b*x/2) + 2*b*tan(c/2)**4*tan(b*x/2)**2 - 2*b*tan(c/2)**4 + 2*b*tan(c/2)**2*tan(b*x/2)**2 - 2*b*tan(c/2)**2 - 2*b*tan(c/2)*tan(b*x/2)), True))*cos(a)","B",0
229,-1,0,0,0.000000," ","integrate(cos(b*x+a)/sin(b*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
230,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+c)**3,x)","\int \sin{\left(a + b x \right)} \tan^{3}{\left(b x + c \right)}\, dx"," ",0,"Integral(sin(a + b*x)*tan(b*x + c)**3, x)","F",0
231,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+c)**2,x)","\int \sin{\left(a + b x \right)} \tan^{2}{\left(b x + c \right)}\, dx"," ",0,"Integral(sin(a + b*x)*tan(b*x + c)**2, x)","F",0
232,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(b*x+c),x)","\int \sin{\left(a + b x \right)} \tan{\left(b x + c \right)}\, dx"," ",0,"Integral(sin(a + b*x)*tan(b*x + c), x)","F",0
233,0,0,0,0.000000," ","integrate(cot(b*x+c)*sin(b*x+a),x)","\int \sin{\left(a + b x \right)} \cot{\left(b x + c \right)}\, dx"," ",0,"Integral(sin(a + b*x)*cot(b*x + c), x)","F",0
234,0,0,0,0.000000," ","integrate(cot(b*x+c)**2*sin(b*x+a),x)","\int \sin{\left(a + b x \right)} \cot^{2}{\left(b x + c \right)}\, dx"," ",0,"Integral(sin(a + b*x)*cot(b*x + c)**2, x)","F",0
235,0,0,0,0.000000," ","integrate(cot(b*x+c)**3*sin(b*x+a),x)","\int \sin{\left(a + b x \right)} \cot^{3}{\left(b x + c \right)}\, dx"," ",0,"Integral(sin(a + b*x)*cot(b*x + c)**3, x)","F",0
236,0,0,0,0.000000," ","integrate(sin(b*x+a)*tan(d*x+c),x)","\int \sin{\left(a + b x \right)} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral(sin(a + b*x)*tan(c + d*x), x)","F",0
237,0,0,0,0.000000," ","integrate(cot(d*x+c)*sin(b*x+a),x)","\int \sin{\left(a + b x \right)} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral(sin(a + b*x)*cot(c + d*x), x)","F",0
238,1,918,0,32.436391," ","integrate(cos(b*x+a)*cos(d*x+c)**3,x)","\begin{cases} x \cos{\left(a \right)} \cos^{3}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{x \sin{\left(a - 3 d x \right)} \sin^{3}{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a - 3 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(c + d x \right)} \cos{\left(a - 3 d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{x \cos{\left(a - 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8} - \frac{3 \sin{\left(a - 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{\sin^{3}{\left(c + d x \right)} \cos{\left(a - 3 d x \right)}}{24 d} - \frac{\sin{\left(c + d x \right)} \cos{\left(a - 3 d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: b = - 3 d \\- \frac{3 x \sin{\left(a - d x \right)} \sin^{3}{\left(c + d x \right)}}{8} - \frac{3 x \sin{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \cos{\left(a - d x \right)} \cos^{3}{\left(c + d x \right)}}{8} + \frac{\sin{\left(a - d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 \sin^{3}{\left(c + d x \right)} \cos{\left(a - d x \right)}}{8 d} + \frac{3 \sin{\left(c + d x \right)} \cos{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: b = - d \\\frac{3 x \sin{\left(a + d x \right)} \sin^{3}{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{3 x \cos{\left(a + d x \right)} \cos^{3}{\left(c + d x \right)}}{8} - \frac{\sin{\left(a + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{3 \sin^{3}{\left(c + d x \right)} \cos{\left(a + d x \right)}}{8 d} + \frac{3 \sin{\left(c + d x \right)} \cos{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: b = d \\- \frac{x \sin{\left(a + 3 d x \right)} \sin^{3}{\left(c + d x \right)}}{8} + \frac{3 x \sin{\left(a + 3 d x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(c + d x \right)} \cos{\left(a + 3 d x \right)} \cos{\left(c + d x \right)}}{8} + \frac{x \cos{\left(a + 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8} + \frac{3 \sin{\left(a + 3 d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{\sin^{3}{\left(c + d x \right)} \cos{\left(a + 3 d x \right)}}{24 d} - \frac{\sin{\left(c + d x \right)} \cos{\left(a + 3 d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: b = 3 d \\\frac{b^{3} \sin{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} - \frac{3 b^{2} d \sin{\left(c + d x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} - \frac{6 b d^{2} \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} - \frac{7 b d^{2} \sin{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{6 d^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} + \frac{9 d^{3} \sin{\left(c + d x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{b^{4} - 10 b^{2} d^{2} + 9 d^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(a)*cos(c)**3, Eq(b, 0) & Eq(d, 0)), (x*sin(a - 3*d*x)*sin(c + d*x)**3/8 - 3*x*sin(a - 3*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 - 3*x*sin(c + d*x)**2*cos(a - 3*d*x)*cos(c + d*x)/8 + x*cos(a - 3*d*x)*cos(c + d*x)**3/8 - 3*sin(a - 3*d*x)*cos(c + d*x)**3/(8*d) - sin(c + d*x)**3*cos(a - 3*d*x)/(24*d) - sin(c + d*x)*cos(a - 3*d*x)*cos(c + d*x)**2/(4*d), Eq(b, -3*d)), (-3*x*sin(a - d*x)*sin(c + d*x)**3/8 - 3*x*sin(a - d*x)*sin(c + d*x)*cos(c + d*x)**2/8 + 3*x*sin(c + d*x)**2*cos(a - d*x)*cos(c + d*x)/8 + 3*x*cos(a - d*x)*cos(c + d*x)**3/8 + sin(a - d*x)*cos(c + d*x)**3/(8*d) + 3*sin(c + d*x)**3*cos(a - d*x)/(8*d) + 3*sin(c + d*x)*cos(a - d*x)*cos(c + d*x)**2/(4*d), Eq(b, -d)), (3*x*sin(a + d*x)*sin(c + d*x)**3/8 + 3*x*sin(a + d*x)*sin(c + d*x)*cos(c + d*x)**2/8 + 3*x*sin(c + d*x)**2*cos(a + d*x)*cos(c + d*x)/8 + 3*x*cos(a + d*x)*cos(c + d*x)**3/8 - sin(a + d*x)*cos(c + d*x)**3/(8*d) + 3*sin(c + d*x)**3*cos(a + d*x)/(8*d) + 3*sin(c + d*x)*cos(a + d*x)*cos(c + d*x)**2/(4*d), Eq(b, d)), (-x*sin(a + 3*d*x)*sin(c + d*x)**3/8 + 3*x*sin(a + 3*d*x)*sin(c + d*x)*cos(c + d*x)**2/8 - 3*x*sin(c + d*x)**2*cos(a + 3*d*x)*cos(c + d*x)/8 + x*cos(a + 3*d*x)*cos(c + d*x)**3/8 + 3*sin(a + 3*d*x)*cos(c + d*x)**3/(8*d) - sin(c + d*x)**3*cos(a + 3*d*x)/(24*d) - sin(c + d*x)*cos(a + 3*d*x)*cos(c + d*x)**2/(4*d), Eq(b, 3*d)), (b**3*sin(a + b*x)*cos(c + d*x)**3/(b**4 - 10*b**2*d**2 + 9*d**4) - 3*b**2*d*sin(c + d*x)*cos(a + b*x)*cos(c + d*x)**2/(b**4 - 10*b**2*d**2 + 9*d**4) - 6*b*d**2*sin(a + b*x)*sin(c + d*x)**2*cos(c + d*x)/(b**4 - 10*b**2*d**2 + 9*d**4) - 7*b*d**2*sin(a + b*x)*cos(c + d*x)**3/(b**4 - 10*b**2*d**2 + 9*d**4) + 6*d**3*sin(c + d*x)**3*cos(a + b*x)/(b**4 - 10*b**2*d**2 + 9*d**4) + 9*d**3*sin(c + d*x)*cos(a + b*x)*cos(c + d*x)**2/(b**4 - 10*b**2*d**2 + 9*d**4), True))","A",0
239,1,405,0,6.679868," ","integrate(cos(b*x+a)*cos(d*x+c)**2,x)","\begin{cases} x \cos{\left(a \right)} \cos^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}\right) \cos{\left(a \right)} & \text{for}\: b = 0 \\- \frac{x \sin{\left(a - 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{x \sin^{2}{\left(c + d x \right)} \cos{\left(a - 2 d x \right)}}{4} + \frac{x \cos{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{4} - \frac{\sin{\left(a - 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} - \frac{\sin{\left(c + d x \right)} \cos{\left(a - 2 d x \right)} \cos{\left(c + d x \right)}}{4 d} & \text{for}\: b = - 2 d \\\frac{x \sin{\left(a + 2 d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{x \sin^{2}{\left(c + d x \right)} \cos{\left(a + 2 d x \right)}}{4} + \frac{x \cos{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{\sin{\left(a + 2 d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} - \frac{\sin{\left(c + d x \right)} \cos{\left(a + 2 d x \right)} \cos{\left(c + d x \right)}}{4 d} & \text{for}\: b = 2 d \\\frac{b^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} - \frac{2 b d \sin{\left(c + d x \right)} \cos{\left(a + b x \right)} \cos{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} - \frac{2 d^{2} \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} - \frac{2 d^{2} \sin{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{b^{3} - 4 b d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(a)*cos(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 + sin(c + d*x)*cos(c + d*x)/(2*d))*cos(a), Eq(b, 0)), (-x*sin(a - 2*d*x)*sin(c + d*x)*cos(c + d*x)/2 - x*sin(c + d*x)**2*cos(a - 2*d*x)/4 + x*cos(a - 2*d*x)*cos(c + d*x)**2/4 - sin(a - 2*d*x)*cos(c + d*x)**2/(2*d) - sin(c + d*x)*cos(a - 2*d*x)*cos(c + d*x)/(4*d), Eq(b, -2*d)), (x*sin(a + 2*d*x)*sin(c + d*x)*cos(c + d*x)/2 - x*sin(c + d*x)**2*cos(a + 2*d*x)/4 + x*cos(a + 2*d*x)*cos(c + d*x)**2/4 + sin(a + 2*d*x)*cos(c + d*x)**2/(2*d) - sin(c + d*x)*cos(a + 2*d*x)*cos(c + d*x)/(4*d), Eq(b, 2*d)), (b**2*sin(a + b*x)*cos(c + d*x)**2/(b**3 - 4*b*d**2) - 2*b*d*sin(c + d*x)*cos(a + b*x)*cos(c + d*x)/(b**3 - 4*b*d**2) - 2*d**2*sin(a + b*x)*sin(c + d*x)**2/(b**3 - 4*b*d**2) - 2*d**2*sin(a + b*x)*cos(c + d*x)**2/(b**3 - 4*b*d**2), True))","A",0
240,1,153,0,1.476159," ","integrate(cos(b*x+a)*cos(d*x+c),x)","\begin{cases} x \cos{\left(a \right)} \cos{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\- \frac{x \sin{\left(a - d x \right)} \sin{\left(c + d x \right)}}{2} + \frac{x \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2} - \frac{\sin{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = - d \\\frac{x \sin{\left(a + d x \right)} \sin{\left(c + d x \right)}}{2} + \frac{x \cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(a + d x \right)}}{2 d} & \text{for}\: b = d \\\frac{b \sin{\left(a + b x \right)} \cos{\left(c + d x \right)}}{b^{2} - d^{2}} - \frac{d \sin{\left(c + d x \right)} \cos{\left(a + b x \right)}}{b^{2} - d^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(a)*cos(c), Eq(b, 0) & Eq(d, 0)), (-x*sin(a - d*x)*sin(c + d*x)/2 + x*cos(a - d*x)*cos(c + d*x)/2 - sin(a - d*x)*cos(c + d*x)/(2*d), Eq(b, -d)), (x*sin(a + d*x)*sin(c + d*x)/2 + x*cos(a + d*x)*cos(c + d*x)/2 + sin(c + d*x)*cos(a + d*x)/(2*d), Eq(b, d)), (b*sin(a + b*x)*cos(c + d*x)/(b**2 - d**2) - d*sin(c + d*x)*cos(a + b*x)/(b**2 - d**2), True))","A",0
241,1,435,0,10.434985," ","integrate(cos(b*x+a)*sec(b*x+c),x)","- \left(\begin{cases} - x & \text{for}\: c = \frac{\pi}{2} \\x & \text{for}\: c = - \frac{\pi}{2} \\0 & \text{for}\: b = 0 \\- \frac{2 b x \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)} + \left(\begin{cases} - \frac{\log{\left(\sin{\left(b x \right)} \right)}}{b} & \text{for}\: c = \frac{\pi}{2} \\\frac{\log{\left(\sin{\left(b x \right)} \right)}}{b} & \text{for}\: c = - \frac{\pi}{2} \\\frac{x}{\cos{\left(c \right)}} & \text{for}\: b = 0 \\- \frac{b x \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{b x}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} + \frac{2 \log{\left(\tan^{2}{\left(\frac{b x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} - \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{2}{\left(\frac{c}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)}"," ",0,"-Piecewise((-x, Eq(c, pi/2)), (x, Eq(c, -pi/2)), (0, Eq(b, 0)), (-2*b*x*tan(c/2)/(b*tan(c/2)**2 + b) - log(tan(b*x/2)**2 + 1)*tan(c/2)**2/(b*tan(c/2)**2 + b) + log(tan(b*x/2)**2 + 1)/(b*tan(c/2)**2 + b) + log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**2/(b*tan(c/2)**2 + b) - log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))/(b*tan(c/2)**2 + b) + log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**2/(b*tan(c/2)**2 + b) - log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))/(b*tan(c/2)**2 + b), True))*sin(a) + Piecewise((-log(sin(b*x))/b, Eq(c, pi/2)), (log(sin(b*x))/b, Eq(c, -pi/2)), (x/cos(c), Eq(b, 0)), (-b*x*tan(c/2)**2/(b*tan(c/2)**2 + b) + b*x/(b*tan(c/2)**2 + b) + 2*log(tan(b*x/2)**2 + 1)*tan(c/2)/(b*tan(c/2)**2 + b) - 2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)/(b*tan(c/2)**2 + b) - 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)/(b*tan(c/2)**2 + b), True))*cos(a)","B",0
242,1,5552,0,160.750152," ","integrate(cos(b*x+a)*sec(b*x+c)**2,x)","\left(\begin{cases} \frac{x}{\cos^{2}{\left(c \right)}} & \text{for}\: b = 0 \\- \frac{1}{b \sin{\left(b x \right)}} & \text{for}\: c = - \frac{\pi}{2} \vee c = \frac{\pi}{2} \\- \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{6}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{4}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{8 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{6}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{4}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{8 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{3 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\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)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{4 \tan^{5}{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{8 \tan^{4}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} + \frac{8 \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} - \frac{4 \tan{\left(\frac{c}{2} \right)}}{b \tan^{6}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{6}{\left(\frac{c}{2} \right)} - 4 b \tan^{5}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{4}{\left(\frac{c}{2} \right)} - b \tan^{2}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{c}{2} \right)} + 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} + b \tan^{2}{\left(\frac{b x}{2} \right)} - b} & \text{otherwise} \end{cases}\right) \cos{\left(a \right)} - \left(\begin{cases} \frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: c = \frac{\pi}{2} \\0 & \text{for}\: b = 0 \\\frac{\log{\left(\tan{\left(\frac{b x}{2} \right)} \right)}}{b} & \text{for}\: c = - \frac{\pi}{2} \\- \frac{2 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{8 \log{\left(\tan{\left(\frac{b x}{2} \right)} - \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} - 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} - 1} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{3}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{8 \log{\left(\tan{\left(\frac{b x}{2} \right)} + \frac{\tan{\left(\frac{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan^{2}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{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{c}{2} \right)}}{\tan{\left(\frac{c}{2} \right)} + 1} - \frac{1}{\tan{\left(\frac{c}{2} \right)} + 1} \right)} \tan{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{2 \tan^{4}{\left(\frac{c}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} - \frac{4 \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)}}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} + \frac{2}{b \tan^{4}{\left(\frac{c}{2} \right)} \tan^{2}{\left(\frac{b x}{2} \right)} - b \tan^{4}{\left(\frac{c}{2} \right)} - 4 b \tan^{3}{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - 4 b \tan{\left(\frac{c}{2} \right)} \tan{\left(\frac{b x}{2} \right)} - b \tan^{2}{\left(\frac{b x}{2} \right)} + b} & \text{otherwise} \end{cases}\right) \sin{\left(a \right)}"," ",0,"Piecewise((x/cos(c)**2, Eq(b, 0)), (-1/(b*sin(b*x)), Eq(c, -pi/2) | Eq(c, pi/2)), (-log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**6*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**6/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 4*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**5*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 3*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**4*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 3*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**4/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 8*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**3*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 3*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**2*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 3*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 4*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**6*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**6/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 4*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**5*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 3*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**4*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 3*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**4/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 8*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**3*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 3*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**2*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 3*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 4*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(b*x/2)**2/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 4*tan(c/2)**5/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 8*tan(c/2)**4*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) + 8*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b) - 4*tan(c/2)/(b*tan(c/2)**6*tan(b*x/2)**2 - b*tan(c/2)**6 - 4*b*tan(c/2)**5*tan(b*x/2) - b*tan(c/2)**4*tan(b*x/2)**2 + b*tan(c/2)**4 - b*tan(c/2)**2*tan(b*x/2)**2 + b*tan(c/2)**2 + 4*b*tan(c/2)*tan(b*x/2) + b*tan(b*x/2)**2 - b), True))*cos(a) - Piecewise((log(tan(b*x/2))/b, Eq(c, pi/2)), (0, Eq(b, 0)), (log(tan(b*x/2))/b, Eq(c, -pi/2)), (-2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**3*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 8*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) - tan(c/2)/(tan(c/2) - 1) - 1/(tan(c/2) - 1))*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**3*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**3/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 8*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)**2*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)*tan(b*x/2)**2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2*log(tan(b*x/2) + tan(c/2)/(tan(c/2) + 1) - 1/(tan(c/2) + 1))*tan(c/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 2*tan(c/2)**4/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 4*tan(c/2)**3*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) - 4*tan(c/2)*tan(b*x/2)/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b) + 2/(b*tan(c/2)**4*tan(b*x/2)**2 - b*tan(c/2)**4 - 4*b*tan(c/2)**3*tan(b*x/2) - 4*b*tan(c/2)*tan(b*x/2) - b*tan(b*x/2)**2 + b), True))*sin(a)","B",0
243,-2,0,0,0.000000," ","integrate(cos(b*x+a)*sec(b*x+c)**3,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
244,1,2009,0,114.287334," ","integrate(cos(b*x+a)**2*cos(d*x+c)**3,x)","\begin{cases} x \cos^{2}{\left(a \right)} \cos^{3}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\frac{3 x \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16} - \frac{x \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{x \sin{\left(a - \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)}}{8} - \frac{3 x \sin{\left(a - \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{16} + \frac{x \cos^{2}{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{11 \sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin^{2}{\left(a - \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{3 \sin{\left(a - \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{5 \sin{\left(a - \frac{3 d x}{2} \right)} \cos{\left(a - \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{7 \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{3 d x}{2} \right)}}{16 d} & \text{for}\: b = - \frac{3 d}{2} \\- \frac{3 x \sin^{2}{\left(a - \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16} - \frac{3 x \sin^{2}{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} - \frac{3 x \sin{\left(a - \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)}}{8} - \frac{3 x \sin{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{16} + \frac{3 x \cos^{2}{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{49 \sin^{2}{\left(a - \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin^{2}{\left(a - \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{7 \sin{\left(a - \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{13 \sin{\left(a - \frac{d x}{2} \right)} \cos{\left(a - \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{17 \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a - \frac{d x}{2} \right)}}{48 d} & \text{for}\: b = - \frac{d}{2} \\- \frac{3 x \sin^{2}{\left(a + \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16} - \frac{3 x \sin^{2}{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{3 x \sin{\left(a + \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)}}{8} + \frac{3 x \sin{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{16} + \frac{3 x \cos^{2}{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{49 \sin^{2}{\left(a + \frac{d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin^{2}{\left(a + \frac{d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{7 \sin{\left(a + \frac{d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{13 \sin{\left(a + \frac{d x}{2} \right)} \cos{\left(a + \frac{d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{17 \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{d x}{2} \right)}}{48 d} & \text{for}\: b = \frac{d}{2} \\\frac{3 x \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16} - \frac{x \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} - \frac{x \sin{\left(a + \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)}}{8} + \frac{3 x \sin{\left(a + \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{3 x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{16} + \frac{x \cos^{2}{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{16} + \frac{11 \sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin^{3}{\left(c + d x \right)}}{48 d} + \frac{\sin^{2}{\left(a + \frac{3 d x}{2} \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{3 \sin{\left(a + \frac{3 d x}{2} \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos{\left(c + d x \right)}}{4 d} + \frac{5 \sin{\left(a + \frac{3 d x}{2} \right)} \cos{\left(a + \frac{3 d x}{2} \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{7 \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + \frac{3 d x}{2} \right)}}{16 d} & \text{for}\: b = \frac{3 d}{2} \\\left(\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}\right) \cos^{3}{\left(c \right)} & \text{for}\: d = 0 \\\frac{16 b^{4} \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{24 b^{4} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{16 b^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{24 b^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{24 b^{3} d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{40 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \sin^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{42 b^{2} d^{2} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{40 b^{2} d^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{78 b^{2} d^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{36 b d^{3} \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)} \cos{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} - \frac{42 b d^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{3}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{18 d^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} + \frac{27 d^{4} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{48 b^{4} d - 120 b^{2} d^{3} + 27 d^{5}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(a)**2*cos(c)**3, Eq(b, 0) & Eq(d, 0)), (3*x*sin(a - 3*d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/16 - x*sin(a - 3*d*x/2)**2*cos(c + d*x)**3/16 + x*sin(a - 3*d*x/2)*sin(c + d*x)**3*cos(a - 3*d*x/2)/8 - 3*x*sin(a - 3*d*x/2)*sin(c + d*x)*cos(a - 3*d*x/2)*cos(c + d*x)**2/8 - 3*x*sin(c + d*x)**2*cos(a - 3*d*x/2)**2*cos(c + d*x)/16 + x*cos(a - 3*d*x/2)**2*cos(c + d*x)**3/16 + 11*sin(a - 3*d*x/2)**2*sin(c + d*x)**3/(48*d) + sin(a - 3*d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/d + 3*sin(a - 3*d*x/2)*sin(c + d*x)**2*cos(a - 3*d*x/2)*cos(c + d*x)/(4*d) - 5*sin(a - 3*d*x/2)*cos(a - 3*d*x/2)*cos(c + d*x)**3/(8*d) + 7*sin(c + d*x)**3*cos(a - 3*d*x/2)**2/(16*d), Eq(b, -3*d/2)), (-3*x*sin(a - d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/16 - 3*x*sin(a - d*x/2)**2*cos(c + d*x)**3/16 - 3*x*sin(a - d*x/2)*sin(c + d*x)**3*cos(a - d*x/2)/8 - 3*x*sin(a - d*x/2)*sin(c + d*x)*cos(a - d*x/2)*cos(c + d*x)**2/8 + 3*x*sin(c + d*x)**2*cos(a - d*x/2)**2*cos(c + d*x)/16 + 3*x*cos(a - d*x/2)**2*cos(c + d*x)**3/16 + 49*sin(a - d*x/2)**2*sin(c + d*x)**3/(48*d) + sin(a - d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/d - 7*sin(a - d*x/2)*sin(c + d*x)**2*cos(a - d*x/2)*cos(c + d*x)/(4*d) - 13*sin(a - d*x/2)*cos(a - d*x/2)*cos(c + d*x)**3/(8*d) - 17*sin(c + d*x)**3*cos(a - d*x/2)**2/(48*d), Eq(b, -d/2)), (-3*x*sin(a + d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/16 - 3*x*sin(a + d*x/2)**2*cos(c + d*x)**3/16 + 3*x*sin(a + d*x/2)*sin(c + d*x)**3*cos(a + d*x/2)/8 + 3*x*sin(a + d*x/2)*sin(c + d*x)*cos(a + d*x/2)*cos(c + d*x)**2/8 + 3*x*sin(c + d*x)**2*cos(a + d*x/2)**2*cos(c + d*x)/16 + 3*x*cos(a + d*x/2)**2*cos(c + d*x)**3/16 + 49*sin(a + d*x/2)**2*sin(c + d*x)**3/(48*d) + sin(a + d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/d + 7*sin(a + d*x/2)*sin(c + d*x)**2*cos(a + d*x/2)*cos(c + d*x)/(4*d) + 13*sin(a + d*x/2)*cos(a + d*x/2)*cos(c + d*x)**3/(8*d) - 17*sin(c + d*x)**3*cos(a + d*x/2)**2/(48*d), Eq(b, d/2)), (3*x*sin(a + 3*d*x/2)**2*sin(c + d*x)**2*cos(c + d*x)/16 - x*sin(a + 3*d*x/2)**2*cos(c + d*x)**3/16 - x*sin(a + 3*d*x/2)*sin(c + d*x)**3*cos(a + 3*d*x/2)/8 + 3*x*sin(a + 3*d*x/2)*sin(c + d*x)*cos(a + 3*d*x/2)*cos(c + d*x)**2/8 - 3*x*sin(c + d*x)**2*cos(a + 3*d*x/2)**2*cos(c + d*x)/16 + x*cos(a + 3*d*x/2)**2*cos(c + d*x)**3/16 + 11*sin(a + 3*d*x/2)**2*sin(c + d*x)**3/(48*d) + sin(a + 3*d*x/2)**2*sin(c + d*x)*cos(c + d*x)**2/d - 3*sin(a + 3*d*x/2)*sin(c + d*x)**2*cos(a + 3*d*x/2)*cos(c + d*x)/(4*d) + 5*sin(a + 3*d*x/2)*cos(a + 3*d*x/2)*cos(c + d*x)**3/(8*d) + 7*sin(c + d*x)**3*cos(a + 3*d*x/2)**2/(16*d), Eq(b, 3*d/2)), ((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 + sin(a + b*x)*cos(a + b*x)/(2*b))*cos(c)**3, Eq(d, 0)), (16*b**4*sin(a + b*x)**2*sin(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 24*b**4*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 16*b**4*sin(c + d*x)**3*cos(a + b*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 24*b**4*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 24*b**3*d*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 40*b**2*d**2*sin(a + b*x)**2*sin(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 42*b**2*d**2*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 40*b**2*d**2*sin(c + d*x)**3*cos(a + b*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 78*b**2*d**2*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 36*b*d**3*sin(a + b*x)*sin(c + d*x)**2*cos(a + b*x)*cos(c + d*x)/(48*b**4*d - 120*b**2*d**3 + 27*d**5) - 42*b*d**3*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**3/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 18*d**4*sin(c + d*x)**3*cos(a + b*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5) + 27*d**4*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)**2/(48*b**4*d - 120*b**2*d**3 + 27*d**5), True))","A",0
245,1,1027,0,23.829623," ","integrate(cos(b*x+a)**2*cos(d*x+c)**2,x)","\begin{cases} x \cos^{2}{\left(a \right)} \cos^{2}{\left(c \right)} & \text{for}\: b = 0 \wedge d = 0 \\\left(\frac{x \sin^{2}{\left(c + d x \right)}}{2} + \frac{x \cos^{2}{\left(c + d x \right)}}{2} + \frac{\sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d}\right) \cos^{2}{\left(a \right)} & \text{for}\: b = 0 \\\frac{3 x \sin^{2}{\left(a - d x \right)} \sin^{2}{\left(c + d x \right)}}{8} + \frac{x \sin^{2}{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{8} - \frac{x \sin{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos{\left(a - d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a - d x \right)}}{8} + \frac{3 x \cos^{2}{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 \sin^{2}{\left(a - d x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{\sin{\left(a - d x \right)} \cos{\left(a - d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(a - d x \right)} \cos{\left(c + d x \right)}}{8 d} & \text{for}\: b = - d \\\frac{3 x \sin^{2}{\left(a + d x \right)} \sin^{2}{\left(c + d x \right)}}{8} + \frac{x \sin^{2}{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{x \sin{\left(a + d x \right)} \sin{\left(c + d x \right)} \cos{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2} + \frac{x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + d x \right)}}{8} + \frac{3 x \cos^{2}{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 \sin{\left(a + d x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + d x \right)}}{8 d} + \frac{\sin{\left(a + d x \right)} \cos{\left(a + d x \right)} \cos^{2}{\left(c + d x \right)}}{8 d} + \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(a + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: b = d \\\left(\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}\right) \cos^{2}{\left(c \right)} & \text{for}\: d = 0 \\\frac{b^{3} d x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} d x \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} \sin^{2}{\left(a + b x \right)} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{b^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} + \frac{2 b^{2} d \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{b d^{3} x \cos^{2}{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{2 b d^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(a + b x \right)} \cos{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{d^{3} \sin{\left(a + b x \right)} \sin^{2}{\left(c + d x \right)} \cos{\left(a + b x \right)}}{4 b^{3} d - 4 b d^{3}} - \frac{d^{3} \sin{\left(a + b x \right)} \cos{\left(a + b x \right)} \cos^{2}{\left(c + d x \right)}}{4 b^{3} d - 4 b d^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*cos(a)**2*cos(c)**2, Eq(b, 0) & Eq(d, 0)), ((x*sin(c + d*x)**2/2 + x*cos(c + d*x)**2/2 + sin(c + d*x)*cos(c + d*x)/(2*d))*cos(a)**2, Eq(b, 0)), (3*x*sin(a - d*x)**2*sin(c + d*x)**2/8 + x*sin(a - d*x)**2*cos(c + d*x)**2/8 - x*sin(a - d*x)*sin(c + d*x)*cos(a - d*x)*cos(c + d*x)/2 + x*sin(c + d*x)**2*cos(a - d*x)**2/8 + 3*x*cos(a - d*x)**2*cos(c + d*x)**2/8 + 3*sin(a - d*x)**2*sin(c + d*x)*cos(c + d*x)/(8*d) - sin(a - d*x)*cos(a - d*x)*cos(c + d*x)**2/(2*d) + sin(c + d*x)*cos(a - d*x)**2*cos(c + d*x)/(8*d), Eq(b, -d)), (3*x*sin(a + d*x)**2*sin(c + d*x)**2/8 + x*sin(a + d*x)**2*cos(c + d*x)**2/8 + x*sin(a + d*x)*sin(c + d*x)*cos(a + d*x)*cos(c + d*x)/2 + x*sin(c + d*x)**2*cos(a + d*x)**2/8 + 3*x*cos(a + d*x)**2*cos(c + d*x)**2/8 + 3*sin(a + d*x)*sin(c + d*x)**2*cos(a + d*x)/(8*d) + sin(a + d*x)*cos(a + d*x)*cos(c + d*x)**2/(8*d) + sin(c + d*x)*cos(a + d*x)**2*cos(c + d*x)/(2*d), Eq(b, d)), ((x*sin(a + b*x)**2/2 + x*cos(a + b*x)**2/2 + sin(a + b*x)*cos(a + b*x)/(2*b))*cos(c)**2, Eq(d, 0)), (b**3*d*x*sin(a + b*x)**2*sin(c + d*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*sin(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*sin(c + d*x)**2*cos(a + b*x)**2/(4*b**3*d - 4*b*d**3) + b**3*d*x*cos(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) + b**3*sin(a + b*x)**2*sin(c + d*x)*cos(c + d*x)/(4*b**3*d - 4*b*d**3) + b**3*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)/(4*b**3*d - 4*b*d**3) + 2*b**2*d*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(a + b*x)**2*sin(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*sin(c + d*x)**2*cos(a + b*x)**2/(4*b**3*d - 4*b*d**3) - b*d**3*x*cos(a + b*x)**2*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3) - 2*b*d**2*sin(c + d*x)*cos(a + b*x)**2*cos(c + d*x)/(4*b**3*d - 4*b*d**3) - d**3*sin(a + b*x)*sin(c + d*x)**2*cos(a + b*x)/(4*b**3*d - 4*b*d**3) - d**3*sin(a + b*x)*cos(a + b*x)*cos(c + d*x)**2/(4*b**3*d - 4*b*d**3), True))","A",0
246,-1,0,0,0.000000," ","integrate(cos(b*x+a)**3*cos(d*x+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(b*x+c)**3,x)","\int \cos{\left(a + b x \right)} \tan^{3}{\left(b x + c \right)}\, dx"," ",0,"Integral(cos(a + b*x)*tan(b*x + c)**3, x)","F",0
248,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(b*x+c)**2,x)","\int \cos{\left(a + b x \right)} \tan^{2}{\left(b x + c \right)}\, dx"," ",0,"Integral(cos(a + b*x)*tan(b*x + c)**2, x)","F",0
249,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(b*x+c),x)","\int \cos{\left(a + b x \right)} \tan{\left(b x + c \right)}\, dx"," ",0,"Integral(cos(a + b*x)*tan(b*x + c), x)","F",0
250,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+c),x)","\int \cos{\left(a + b x \right)} \cot{\left(b x + c \right)}\, dx"," ",0,"Integral(cos(a + b*x)*cot(b*x + c), x)","F",0
251,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+c)**2,x)","\int \cos{\left(a + b x \right)} \cot^{2}{\left(b x + c \right)}\, dx"," ",0,"Integral(cos(a + b*x)*cot(b*x + c)**2, x)","F",0
252,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(b*x+c)**3,x)","\int \cos{\left(a + b x \right)} \cot^{3}{\left(b x + c \right)}\, dx"," ",0,"Integral(cos(a + b*x)*cot(b*x + c)**3, x)","F",0
253,0,0,0,0.000000," ","integrate(cos(b*x+a)*tan(d*x+c),x)","\int \cos{\left(a + b x \right)} \tan{\left(c + d x \right)}\, dx"," ",0,"Integral(cos(a + b*x)*tan(c + d*x), x)","F",0
254,0,0,0,0.000000," ","integrate(cos(b*x+a)*cot(d*x+c),x)","\int \cos{\left(a + b x \right)} \cot{\left(c + d x \right)}\, dx"," ",0,"Integral(cos(a + b*x)*cot(c + d*x), x)","F",0
