1,1,75,0,0.530724," ","integrate(sin(x)**3*(a*cos(x)+b*sin(x)),x)","\frac{a \sin^{4}{\left(x \right)}}{4} + \frac{3 b x \sin^{4}{\left(x \right)}}{8} + \frac{3 b x \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{4} + \frac{3 b x \cos^{4}{\left(x \right)}}{8} - \frac{5 b \sin^{3}{\left(x \right)} \cos{\left(x \right)}}{8} - \frac{3 b \sin{\left(x \right)} \cos^{3}{\left(x \right)}}{8}"," ",0,"a*sin(x)**4/4 + 3*b*x*sin(x)**4/8 + 3*b*x*sin(x)**2*cos(x)**2/4 + 3*b*x*cos(x)**4/8 - 5*b*sin(x)**3*cos(x)/8 - 3*b*sin(x)*cos(x)**3/8","B",0
2,1,27,0,0.282428," ","integrate(sin(x)**2*(a*cos(x)+b*sin(x)),x)","\frac{a \sin^{3}{\left(x \right)}}{3} - b \sin^{2}{\left(x \right)} \cos{\left(x \right)} - \frac{2 b \cos^{3}{\left(x \right)}}{3}"," ",0,"a*sin(x)**3/3 - b*sin(x)**2*cos(x) - 2*b*cos(x)**3/3","A",0
3,1,37,0,0.163318," ","integrate(sin(x)*(a*cos(x)+b*sin(x)),x)","- \frac{a \cos^{2}{\left(x \right)}}{2} + \frac{b x \sin^{2}{\left(x \right)}}{2} + \frac{b x \cos^{2}{\left(x \right)}}{2} - \frac{b \sin{\left(x \right)} \cos{\left(x \right)}}{2}"," ",0,"-a*cos(x)**2/2 + b*x*sin(x)**2/2 + b*x*cos(x)**2/2 - b*sin(x)*cos(x)/2","A",0
4,1,8,0,0.046050," ","integrate(a*cos(x)+b*sin(x),x)","a \sin{\left(x \right)} - b \cos{\left(x \right)}"," ",0,"a*sin(x) - b*cos(x)","A",0
5,1,8,0,1.140218," ","integrate(csc(x)*(a*cos(x)+b*sin(x)),x)","a \log{\left(\sin{\left(x \right)} \right)} + b x"," ",0,"a*log(sin(x)) + b*x","A",0
6,1,24,0,1.830275," ","integrate(csc(x)**2*(a*cos(x)+b*sin(x)),x)","- \frac{a}{\sin{\left(x \right)}} + \frac{b \log{\left(\cos{\left(x \right)} - 1 \right)}}{2} - \frac{b \log{\left(\cos{\left(x \right)} + 1 \right)}}{2}"," ",0,"-a/sin(x) + b*log(cos(x) - 1)/2 - b*log(cos(x) + 1)/2","A",0
7,1,17,0,3.877569," ","integrate(csc(x)**3*(a*cos(x)+b*sin(x)),x)","- \frac{a}{2 \sin^{2}{\left(x \right)}} - \frac{b \cos{\left(x \right)}}{\sin{\left(x \right)}}"," ",0,"-a/(2*sin(x)**2) - b*cos(x)/sin(x)","A",0
8,-1,0,0,0.000000," ","integrate(sin(x)**3/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate(sin(x)**2/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,1,173,0,0.771911," ","integrate(sin(x)/(a*cos(x)+b*sin(x)),x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\- \frac{i x \sin{\left(x \right)}}{- 2 i b \sin{\left(x \right)} - 2 b \cos{\left(x \right)}} - \frac{x \cos{\left(x \right)}}{- 2 i b \sin{\left(x \right)} - 2 b \cos{\left(x \right)}} + \frac{i \cos{\left(x \right)}}{- 2 i b \sin{\left(x \right)} - 2 b \cos{\left(x \right)}} & \text{for}\: a = - i b \\\frac{i x \sin{\left(x \right)}}{2 i b \sin{\left(x \right)} - 2 b \cos{\left(x \right)}} - \frac{x \cos{\left(x \right)}}{2 i b \sin{\left(x \right)} - 2 b \cos{\left(x \right)}} - \frac{i \cos{\left(x \right)}}{2 i b \sin{\left(x \right)} - 2 b \cos{\left(x \right)}} & \text{for}\: a = i b \\- \frac{\log{\left(\cos{\left(x \right)} \right)}}{a} & \text{for}\: b = 0 \\- \frac{a \log{\left(\frac{a \cos{\left(x \right)}}{b} + \sin{\left(x \right)} \right)}}{a^{2} + b^{2}} + \frac{b x}{a^{2} + b^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (-I*x*sin(x)/(-2*I*b*sin(x) - 2*b*cos(x)) - x*cos(x)/(-2*I*b*sin(x) - 2*b*cos(x)) + I*cos(x)/(-2*I*b*sin(x) - 2*b*cos(x)), Eq(a, -I*b)), (I*x*sin(x)/(2*I*b*sin(x) - 2*b*cos(x)) - x*cos(x)/(2*I*b*sin(x) - 2*b*cos(x)) - I*cos(x)/(2*I*b*sin(x) - 2*b*cos(x)), Eq(a, I*b)), (-log(cos(x))/a, Eq(b, 0)), (-a*log(a*cos(x)/b + sin(x))/(a**2 + b**2) + b*x/(a**2 + b**2), True))","A",0
11,-2,0,0,0.000000," ","integrate(1/(a*cos(x)+b*sin(x)),x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
12,0,0,0,0.000000," ","integrate(csc(x)/(a*cos(x)+b*sin(x)),x)","\int \frac{\csc{\left(x \right)}}{a \cos{\left(x \right)} + b \sin{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)/(a*cos(x) + b*sin(x)), x)","F",0
13,0,0,0,0.000000," ","integrate(csc(x)**2/(a*cos(x)+b*sin(x)),x)","\int \frac{\csc^{2}{\left(x \right)}}{a \cos{\left(x \right)} + b \sin{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**2/(a*cos(x) + b*sin(x)), x)","F",0
14,0,0,0,0.000000," ","integrate(csc(x)**3/(a*cos(x)+b*sin(x)),x)","\int \frac{\csc^{3}{\left(x \right)}}{a \cos{\left(x \right)} + b \sin{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)**3/(a*cos(x) + b*sin(x)), x)","F",0
15,-1,0,0,0.000000," ","integrate(sin(x)**3/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,1,1017,0,2.196011," ","integrate(sin(x)**2/(a*cos(x)+b*sin(x))**2,x)","\begin{cases} \tilde{\infty} x & \text{for}\: a = 0 \wedge b = 0 \\\frac{2 x \sin^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} - \frac{4 i x \sin{\left(x \right)} \cos{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} + \frac{3 i \sin^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} + \frac{i \cos^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} & \text{for}\: a = - i b \\- \frac{2 i x \sin^{2}{\left(x \right)}}{- 8 i b^{2} \sin^{2}{\left(x \right)} + 16 b^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 8 i b^{2} \cos^{2}{\left(x \right)}} + \frac{4 x \sin{\left(x \right)} \cos{\left(x \right)}}{- 8 i b^{2} \sin^{2}{\left(x \right)} + 16 b^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 8 i b^{2} \cos^{2}{\left(x \right)}} + \frac{2 i x \cos^{2}{\left(x \right)}}{- 8 i b^{2} \sin^{2}{\left(x \right)} + 16 b^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 8 i b^{2} \cos^{2}{\left(x \right)}} - \frac{3 \sin^{2}{\left(x \right)}}{- 8 i b^{2} \sin^{2}{\left(x \right)} + 16 b^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 8 i b^{2} \cos^{2}{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{- 8 i b^{2} \sin^{2}{\left(x \right)} + 16 b^{2} \sin{\left(x \right)} \cos{\left(x \right)} + 8 i b^{2} \cos^{2}{\left(x \right)}} & \text{for}\: a = i b \\\frac{- x + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}}}{a^{2}} & \text{for}\: b = 0 \\- \frac{a^{4} \cos{\left(x \right)}}{a^{5} b \cos{\left(x \right)} + a^{4} b^{2} \sin{\left(x \right)} + 2 a^{3} b^{3} \cos{\left(x \right)} + 2 a^{2} b^{4} \sin{\left(x \right)} + a b^{5} \cos{\left(x \right)} + b^{6} \sin{\left(x \right)}} - \frac{a^{3} b x \cos{\left(x \right)}}{a^{5} b \cos{\left(x \right)} + a^{4} b^{2} \sin{\left(x \right)} + 2 a^{3} b^{3} \cos{\left(x \right)} + 2 a^{2} b^{4} \sin{\left(x \right)} + a b^{5} \cos{\left(x \right)} + b^{6} \sin{\left(x \right)}} - \frac{a^{2} b^{2} x \sin{\left(x \right)}}{a^{5} b \cos{\left(x \right)} + a^{4} b^{2} \sin{\left(x \right)} + 2 a^{3} b^{3} \cos{\left(x \right)} + 2 a^{2} b^{4} \sin{\left(x \right)} + a b^{5} \cos{\left(x \right)} + b^{6} \sin{\left(x \right)}} - \frac{2 a^{2} b^{2} \log{\left(\frac{a \cos{\left(x \right)}}{b} + \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{a^{5} b \cos{\left(x \right)} + a^{4} b^{2} \sin{\left(x \right)} + 2 a^{3} b^{3} \cos{\left(x \right)} + 2 a^{2} b^{4} \sin{\left(x \right)} + a b^{5} \cos{\left(x \right)} + b^{6} \sin{\left(x \right)}} - \frac{a^{2} b^{2} \cos{\left(x \right)}}{a^{5} b \cos{\left(x \right)} + a^{4} b^{2} \sin{\left(x \right)} + 2 a^{3} b^{3} \cos{\left(x \right)} + 2 a^{2} b^{4} \sin{\left(x \right)} + a b^{5} \cos{\left(x \right)} + b^{6} \sin{\left(x \right)}} + \frac{a b^{3} x \cos{\left(x \right)}}{a^{5} b \cos{\left(x \right)} + a^{4} b^{2} \sin{\left(x \right)} + 2 a^{3} b^{3} \cos{\left(x \right)} + 2 a^{2} b^{4} \sin{\left(x \right)} + a b^{5} \cos{\left(x \right)} + b^{6} \sin{\left(x \right)}} - \frac{2 a b^{3} \log{\left(\frac{a \cos{\left(x \right)}}{b} + \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{a^{5} b \cos{\left(x \right)} + a^{4} b^{2} \sin{\left(x \right)} + 2 a^{3} b^{3} \cos{\left(x \right)} + 2 a^{2} b^{4} \sin{\left(x \right)} + a b^{5} \cos{\left(x \right)} + b^{6} \sin{\left(x \right)}} + \frac{b^{4} x \sin{\left(x \right)}}{a^{5} b \cos{\left(x \right)} + a^{4} b^{2} \sin{\left(x \right)} + 2 a^{3} b^{3} \cos{\left(x \right)} + 2 a^{2} b^{4} \sin{\left(x \right)} + a b^{5} \cos{\left(x \right)} + b^{6} \sin{\left(x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x, Eq(a, 0) & Eq(b, 0)), (2*x*sin(x)**2/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) - 4*I*x*sin(x)*cos(x)/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) - 2*x*cos(x)**2/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) + 3*I*sin(x)**2/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) + I*cos(x)**2/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2), Eq(a, -I*b)), (-2*I*x*sin(x)**2/(-8*I*b**2*sin(x)**2 + 16*b**2*sin(x)*cos(x) + 8*I*b**2*cos(x)**2) + 4*x*sin(x)*cos(x)/(-8*I*b**2*sin(x)**2 + 16*b**2*sin(x)*cos(x) + 8*I*b**2*cos(x)**2) + 2*I*x*cos(x)**2/(-8*I*b**2*sin(x)**2 + 16*b**2*sin(x)*cos(x) + 8*I*b**2*cos(x)**2) - 3*sin(x)**2/(-8*I*b**2*sin(x)**2 + 16*b**2*sin(x)*cos(x) + 8*I*b**2*cos(x)**2) - cos(x)**2/(-8*I*b**2*sin(x)**2 + 16*b**2*sin(x)*cos(x) + 8*I*b**2*cos(x)**2), Eq(a, I*b)), ((-x + sin(x)/cos(x))/a**2, Eq(b, 0)), (-a**4*cos(x)/(a**5*b*cos(x) + a**4*b**2*sin(x) + 2*a**3*b**3*cos(x) + 2*a**2*b**4*sin(x) + a*b**5*cos(x) + b**6*sin(x)) - a**3*b*x*cos(x)/(a**5*b*cos(x) + a**4*b**2*sin(x) + 2*a**3*b**3*cos(x) + 2*a**2*b**4*sin(x) + a*b**5*cos(x) + b**6*sin(x)) - a**2*b**2*x*sin(x)/(a**5*b*cos(x) + a**4*b**2*sin(x) + 2*a**3*b**3*cos(x) + 2*a**2*b**4*sin(x) + a*b**5*cos(x) + b**6*sin(x)) - 2*a**2*b**2*log(a*cos(x)/b + sin(x))*cos(x)/(a**5*b*cos(x) + a**4*b**2*sin(x) + 2*a**3*b**3*cos(x) + 2*a**2*b**4*sin(x) + a*b**5*cos(x) + b**6*sin(x)) - a**2*b**2*cos(x)/(a**5*b*cos(x) + a**4*b**2*sin(x) + 2*a**3*b**3*cos(x) + 2*a**2*b**4*sin(x) + a*b**5*cos(x) + b**6*sin(x)) + a*b**3*x*cos(x)/(a**5*b*cos(x) + a**4*b**2*sin(x) + 2*a**3*b**3*cos(x) + 2*a**2*b**4*sin(x) + a*b**5*cos(x) + b**6*sin(x)) - 2*a*b**3*log(a*cos(x)/b + sin(x))*sin(x)/(a**5*b*cos(x) + a**4*b**2*sin(x) + 2*a**3*b**3*cos(x) + 2*a**2*b**4*sin(x) + a*b**5*cos(x) + b**6*sin(x)) + b**4*x*sin(x)/(a**5*b*cos(x) + a**4*b**2*sin(x) + 2*a**3*b**3*cos(x) + 2*a**2*b**4*sin(x) + a*b**5*cos(x) + b**6*sin(x)), True))","A",0
17,-1,0,0,0.000000," ","integrate(sin(x)/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,-1,0,0,0.000000," ","integrate(1/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,0,0,0,0.000000," ","integrate(csc(x)/(a*cos(x)+b*sin(x))**2,x)","\int \frac{\csc{\left(x \right)}}{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(csc(x)/(a*cos(x) + b*sin(x))**2, x)","F",0
20,0,0,0,0.000000," ","integrate(csc(x)**2/(a*cos(x)+b*sin(x))**2,x)","\int \frac{\csc^{2}{\left(x \right)}}{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(csc(x)**2/(a*cos(x) + b*sin(x))**2, x)","F",0
21,0,0,0,0.000000," ","integrate(csc(x)**3/(a*cos(x)+b*sin(x))**2,x)","\int \frac{\csc^{3}{\left(x \right)}}{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)}\right)^{2}}\, dx"," ",0,"Integral(csc(x)**3/(a*cos(x) + b*sin(x))**2, x)","F",0
22,-2,0,0,0.000000," ","integrate(sin(x)**3/(a*cos(x)+b*sin(x))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
23,-1,0,0,0.000000," ","integrate(sin(x)**2/(a*cos(x)+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate(sin(x)/(a*cos(x)+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate(1/(a*cos(x)+b*sin(x))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,0,0,0,0.000000," ","integrate(csc(x)/(a*cos(x)+b*sin(x))**3,x)","\int \frac{\csc{\left(x \right)}}{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral(csc(x)/(a*cos(x) + b*sin(x))**3, x)","F",0
27,0,0,0,0.000000," ","integrate(csc(x)**2/(a*cos(x)+b*sin(x))**3,x)","\int \frac{\csc^{2}{\left(x \right)}}{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral(csc(x)**2/(a*cos(x) + b*sin(x))**3, x)","F",0
28,0,0,0,0.000000," ","integrate(csc(x)**3/(a*cos(x)+b*sin(x))**3,x)","\int \frac{\csc^{3}{\left(x \right)}}{\left(a \cos{\left(x \right)} + b \sin{\left(x \right)}\right)^{3}}\, dx"," ",0,"Integral(csc(x)**3/(a*cos(x) + b*sin(x))**3, x)","F",0
29,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**n/(sin(d*x+c)**n),x)","\int \left(a \left(i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}\right)\right)^{n} \sin^{- n}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(I*sin(c + d*x) + cos(c + d*x)))**n*sin(c + d*x)**(-n), x)","F",0
30,1,175,0,3.104898," ","integrate(cos(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\begin{cases} \frac{5 a x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{b \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right) \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a*x*sin(c + d*x)**6/16 + 15*a*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a*x*cos(c + d*x)**6/16 + 5*a*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*a*sin(c + d*x)*cos(c + d*x)**5/(16*d) - b*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))*cos(c)**5, True))","A",0
31,1,87,0,1.605765," ","integrate(cos(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{b \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right) \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**5/(15*d) + 4*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a*sin(c + d*x)*cos(c + d*x)**4/d - b*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))*cos(c)**4, True))","A",0
32,1,128,0,0.876342," ","integrate(cos(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\begin{cases} \frac{3 a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{b \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right) \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*sin(c + d*x)**4/8 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a*x*cos(c + d*x)**4/8 + 3*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) - b*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))*cos(c)**3, True))","A",0
33,1,63,0,0.434457," ","integrate(cos(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\begin{cases} \frac{2 a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{b \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sin(c + d*x)**3/(3*d) + a*sin(c + d*x)*cos(c + d*x)**2/d - b*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))*cos(c)**2, True))","A",0
34,1,73,0,0.209707," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\begin{cases} \frac{a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{b \cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**2/2 + a*x*cos(c + d*x)**2/2 + a*sin(c + d*x)*cos(c + d*x)/(2*d) - b*cos(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))*cos(c), True))","A",0
35,1,31,0,0.140085," ","integrate(a*cos(d*x+c)+b*sin(d*x+c),x)","a \left(\begin{cases} \frac{\sin{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \cos{\left(c \right)} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} - \frac{\cos{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \sin{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*Piecewise((sin(c + d*x)/d, Ne(d, 0)), (x*cos(c), True)) + b*Piecewise((-cos(c + d*x)/d, Ne(d, 0)), (x*sin(c), True))","A",0
36,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))*sec(c + d*x), x)","F",0
37,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))*sec(c + d*x)**2, x)","F",0
38,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))*sec(c + d*x)**3, x)","F",0
39,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right) \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))*sec(c + d*x)**4, x)","F",0
40,0,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right) \sec^{5}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))*sec(c + d*x)**5, x)","F",0
41,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a*cos(d*x+c)+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,1,187,0,5.322949," ","integrate(cos(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\begin{cases} \frac{16 a^{2} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{2 a b \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{8 b^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{2} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**2*sin(c + d*x)**7/(35*d) + 8*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*a**2*sin(c + d*x)**3*cos(c + d*x)**4/d + a**2*sin(c + d*x)*cos(c + d*x)**6/d - 2*a*b*cos(c + d*x)**7/(7*d) + 8*b**2*sin(c + d*x)**7/(105*d) + 4*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + b**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**2*cos(c)**5, True))","A",0
44,1,340,0,3.480056," ","integrate(cos(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\begin{cases} \frac{5 a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{a b \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{b^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{b^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{b^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{2} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**2*x*sin(c + d*x)**6/16 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a**2*x*cos(c + d*x)**6/16 + 5*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) - a*b*cos(c + d*x)**6/(3*d) + b**2*x*sin(c + d*x)**6/16 + 3*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + b**2*x*cos(c + d*x)**6/16 + b**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + b**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - b**2*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**2*cos(c)**4, True))","A",0
45,1,138,0,1.751719," ","integrate(cos(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\begin{cases} \frac{8 a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{2 a b \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{2 b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{2} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**2*sin(c + d*x)**5/(15*d) + 4*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**2*sin(c + d*x)*cos(c + d*x)**4/d - 2*a*b*cos(c + d*x)**5/(5*d) + 2*b**2*sin(c + d*x)**5/(15*d) + b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**2*cos(c)**3, True))","A",0
46,1,238,0,1.045878," ","integrate(cos(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{a b \cos^{4}{\left(c + d x \right)}}{2 d} + \frac{b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{2} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**4/8 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**2*x*cos(c + d*x)**4/8 + 3*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) - a*b*cos(c + d*x)**4/(2*d) + b**2*x*sin(c + d*x)**4/8 + b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + b**2*x*cos(c + d*x)**4/8 + b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**2*cos(c)**2, True))","A",0
47,1,85,0,0.478306," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\begin{cases} \frac{2 a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{2 a b \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**2*sin(c + d*x)**3/(3*d) + a**2*sin(c + d*x)*cos(c + d*x)**2/d - 2*a*b*cos(c + d*x)**3/(3*d) + b**2*sin(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**2*cos(c), True))","A",0
48,1,128,0,0.273807," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{a b \cos^{2}{\left(c + d x \right)}}{d} + \frac{b^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{b^{2} x \cos^{2}{\left(c + d x \right)}}{2} - \frac{b^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{2} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**2/2 + a**2*x*cos(c + d*x)**2/2 + a**2*sin(c + d*x)*cos(c + d*x)/(2*d) - a*b*cos(c + d*x)**2/d + b**2*x*sin(c + d*x)**2/2 + b**2*x*cos(c + d*x)**2/2 - b**2*sin(c + d*x)*cos(c + d*x)/(2*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**2, True))","A",0
49,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**2*sec(c + d*x), x)","F",0
50,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**2*sec(c + d*x)**2, x)","F",0
51,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**2*sec(c + d*x)**3, x)","F",0
52,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2} \sec^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**2*sec(c + d*x)**4, x)","F",0
53,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
56,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,1,532,0,10.332785," ","integrate(cos(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\begin{cases} \frac{35 a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{35 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{105 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{35 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{35 a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{35 a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{385 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{511 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} + \frac{93 a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{3 a^{2} b \cos^{8}{\left(c + d x \right)}}{8 d} + \frac{15 a b^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 a b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{45 a b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{15 a b^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{15 a b^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 a b^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{73 a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{15 a b^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{b^{3} \sin^{8}{\left(c + d x \right)}}{24 d} + \frac{b^{3} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{6 d} + \frac{b^{3} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{3} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((35*a**3*x*sin(c + d*x)**8/128 + 35*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 105*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 35*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 35*a**3*x*cos(c + d*x)**8/128 + 35*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 385*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 511*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) + 93*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 3*a**2*b*cos(c + d*x)**8/(8*d) + 15*a*b**2*x*sin(c + d*x)**8/128 + 15*a*b**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 45*a*b**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 15*a*b**2*x*cos(c + d*x)**8/128 + 15*a*b**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*a*b**2*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) + 73*a*b**2*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 15*a*b**2*sin(c + d*x)*cos(c + d*x)**7/(128*d) + b**3*sin(c + d*x)**8/(24*d) + b**3*sin(c + d*x)**6*cos(c + d*x)**2/(6*d) + b**3*sin(c + d*x)**4*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**3*cos(c)**5, True))","A",0
58,1,233,0,5.527874," ","integrate(cos(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\begin{cases} \frac{16 a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{3 a^{2} b \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{8 a b^{2} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{4 a b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{b^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{2 b^{3} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{3} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**3*sin(c + d*x)**7/(35*d) + 8*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*a**3*sin(c + d*x)**3*cos(c + d*x)**4/d + a**3*sin(c + d*x)*cos(c + d*x)**6/d - 3*a**2*b*cos(c + d*x)**7/(7*d) + 8*a*b**2*sin(c + d*x)**7/(35*d) + 4*a*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + a*b**2*sin(c + d*x)**3*cos(c + d*x)**4/d - b**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 2*b**3*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**3*cos(c)**4, True))","A",0
59,1,400,0,3.694324," ","integrate(cos(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\begin{cases} \frac{5 a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{a^{2} b \cos^{6}{\left(c + d x \right)}}{2 d} + \frac{3 a b^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 a b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a b^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} - \frac{3 a b^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{b^{3} \sin^{6}{\left(c + d x \right)}}{12 d} + \frac{b^{3} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{3} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**3*x*sin(c + d*x)**6/16 + 15*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a**3*x*cos(c + d*x)**6/16 + 5*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - a**2*b*cos(c + d*x)**6/(2*d) + 3*a*b**2*x*sin(c + d*x)**6/16 + 9*a*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a*b**2*x*cos(c + d*x)**6/16 + 3*a*b**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a*b**2*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) - 3*a*b**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) + b**3*sin(c + d*x)**6/(12*d) + b**3*sin(c + d*x)**4*cos(c + d*x)**2/(4*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**3*cos(c)**3, True))","A",0
60,1,182,0,1.927522," ","integrate(cos(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\begin{cases} \frac{8 a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{3 a^{2} b \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{2 a b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{b^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{2 b^{3} \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{3} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**3*sin(c + d*x)**5/(15*d) + 4*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**3*sin(c + d*x)*cos(c + d*x)**4/d - 3*a**2*b*cos(c + d*x)**5/(5*d) + 2*a*b**2*sin(c + d*x)**5/(5*d) + a*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d - b**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 2*b**3*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**3*cos(c)**2, True))","A",0
61,1,272,0,1.119805," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{3 a^{2} b \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{3 a b^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a b^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 a b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{b^{3} \sin^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{3} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**4/8 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**3*x*cos(c + d*x)**4/8 + 3*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 3*a**2*b*cos(c + d*x)**4/(4*d) + 3*a*b**2*x*sin(c + d*x)**4/8 + 3*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a*b**2*x*cos(c + d*x)**4/8 + 3*a*b**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*a*b**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + b**3*sin(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**3*cos(c), True))","A",0
62,1,117,0,0.520411," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\begin{cases} \frac{2 a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{a^{2} b \cos^{3}{\left(c + d x \right)}}{d} + \frac{a b^{2} \sin^{3}{\left(c + d x \right)}}{d} - \frac{b^{3} \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{2 b^{3} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{3} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a**3*sin(c + d*x)**3/(3*d) + a**3*sin(c + d*x)*cos(c + d*x)**2/d - a**2*b*cos(c + d*x)**3/d + a*b**2*sin(c + d*x)**3/d - b**3*sin(c + d*x)**2*cos(c + d*x)/d - 2*b**3*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**3, True))","A",0
63,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{3} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**3*sec(c + d*x), x)","F",0
64,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{3} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**3*sec(c + d*x)**2, x)","F",0
65,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{3} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**3*sec(c + d*x)**3, x)","F",0
66,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(sec(d*x+c)**11*(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,1,367,0,15.615411," ","integrate(cos(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\begin{cases} \frac{128 a^{4} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{64 a^{4} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{16 a^{4} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{8 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{a^{4} \sin{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{d} - \frac{4 a^{3} b \cos^{9}{\left(c + d x \right)}}{9 d} + \frac{32 a^{2} b^{2} \sin^{9}{\left(c + d x \right)}}{105 d} + \frac{48 a^{2} b^{2} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{12 a^{2} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{2 a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{4 a b^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{8 a b^{3} \cos^{9}{\left(c + d x \right)}}{63 d} + \frac{8 b^{4} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{4 b^{4} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{b^{4} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{4} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((128*a**4*sin(c + d*x)**9/(315*d) + 64*a**4*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 16*a**4*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 8*a**4*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) + a**4*sin(c + d*x)*cos(c + d*x)**8/d - 4*a**3*b*cos(c + d*x)**9/(9*d) + 32*a**2*b**2*sin(c + d*x)**9/(105*d) + 48*a**2*b**2*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 12*a**2*b**2*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 2*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**6/d - 4*a*b**3*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 8*a*b**3*cos(c + d*x)**9/(63*d) + 8*b**4*sin(c + d*x)**9/(315*d) + 4*b**4*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + b**4*sin(c + d*x)**5*cos(c + d*x)**4/(5*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**4*cos(c)**5, True))","A",0
75,1,760,0,11.256675," ","integrate(cos(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\begin{cases} \frac{35 a^{4} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{35 a^{4} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{105 a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{35 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{35 a^{4} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{35 a^{4} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{385 a^{4} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{511 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} + \frac{93 a^{4} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{a^{3} b \cos^{8}{\left(c + d x \right)}}{2 d} + \frac{15 a^{2} b^{2} x \sin^{8}{\left(c + d x \right)}}{64} + \frac{15 a^{2} b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{45 a^{2} b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{15 a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{2} b^{2} x \cos^{8}{\left(c + d x \right)}}{64} + \frac{15 a^{2} b^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} + \frac{55 a^{2} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{64 d} + \frac{73 a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{64 d} - \frac{15 a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} + \frac{a b^{3} \sin^{8}{\left(c + d x \right)}}{6 d} + \frac{2 a b^{3} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a b^{3} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{3 b^{4} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 b^{4} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{9 b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 b^{4} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 b^{4} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 b^{4} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{11 b^{4} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{3 b^{4} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{4} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((35*a**4*x*sin(c + d*x)**8/128 + 35*a**4*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 105*a**4*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 35*a**4*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 35*a**4*x*cos(c + d*x)**8/128 + 35*a**4*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 385*a**4*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 511*a**4*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) + 93*a**4*sin(c + d*x)*cos(c + d*x)**7/(128*d) - a**3*b*cos(c + d*x)**8/(2*d) + 15*a**2*b**2*x*sin(c + d*x)**8/64 + 15*a**2*b**2*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + 45*a**2*b**2*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 15*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 15*a**2*b**2*x*cos(c + d*x)**8/64 + 15*a**2*b**2*sin(c + d*x)**7*cos(c + d*x)/(64*d) + 55*a**2*b**2*sin(c + d*x)**5*cos(c + d*x)**3/(64*d) + 73*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**5/(64*d) - 15*a**2*b**2*sin(c + d*x)*cos(c + d*x)**7/(64*d) + a*b**3*sin(c + d*x)**8/(6*d) + 2*a*b**3*sin(c + d*x)**6*cos(c + d*x)**2/(3*d) + a*b**3*sin(c + d*x)**4*cos(c + d*x)**4/d + 3*b**4*x*sin(c + d*x)**8/128 + 3*b**4*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 9*b**4*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*b**4*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*b**4*x*cos(c + d*x)**8/128 + 3*b**4*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*b**4*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 11*b**4*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 3*b**4*sin(c + d*x)*cos(c + d*x)**7/(128*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**4*cos(c)**4, True))","A",0
76,1,286,0,5.708021," ","integrate(cos(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\begin{cases} \frac{16 a^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 a^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{a^{4} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{4 a^{3} b \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{16 a^{2} b^{2} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 a^{2} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{4 a b^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{8 a b^{3} \cos^{7}{\left(c + d x \right)}}{35 d} + \frac{2 b^{4} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{b^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{4} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**4*sin(c + d*x)**7/(35*d) + 8*a**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*a**4*sin(c + d*x)**3*cos(c + d*x)**4/d + a**4*sin(c + d*x)*cos(c + d*x)**6/d - 4*a**3*b*cos(c + d*x)**7/(7*d) + 16*a**2*b**2*sin(c + d*x)**7/(35*d) + 8*a**2*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**4/d - 4*a*b**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 8*a*b**3*cos(c + d*x)**7/(35*d) + 2*b**4*sin(c + d*x)**7/(35*d) + b**4*sin(c + d*x)**5*cos(c + d*x)**2/(5*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**4*cos(c)**3, True))","A",0
77,1,563,0,3.988452," ","integrate(cos(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\begin{cases} \frac{5 a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 a^{3} b \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{3 a^{2} b^{2} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{9 a^{2} b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{9 a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} b^{2} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{3 a^{2} b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{3 a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} + \frac{a b^{3} \sin^{6}{\left(c + d x \right)}}{3 d} + \frac{a b^{3} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{b^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{b^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{4} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**4*x*sin(c + d*x)**6/16 + 15*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a**4*x*cos(c + d*x)**6/16 + 5*a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*a**3*b*cos(c + d*x)**6/(3*d) + 3*a**2*b**2*x*sin(c + d*x)**6/8 + 9*a**2*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 9*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 3*a**2*b**2*x*cos(c + d*x)**6/8 + 3*a**2*b**2*sin(c + d*x)**5*cos(c + d*x)/(8*d) + a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**3/d - 3*a**2*b**2*sin(c + d*x)*cos(c + d*x)**5/(8*d) + a*b**3*sin(c + d*x)**6/(3*d) + a*b**3*sin(c + d*x)**4*cos(c + d*x)**2/d + b**4*x*sin(c + d*x)**6/16 + 3*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + b**4*x*cos(c + d*x)**6/16 + b**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) - b**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - b**4*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**4*cos(c)**2, True))","A",0
78,1,206,0,1.993869," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\begin{cases} \frac{8 a^{4} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{4} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{4 a^{3} b \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{4 a^{2} b^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{2 a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{4 a b^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{8 a b^{3} \cos^{5}{\left(c + d x \right)}}{15 d} + \frac{b^{4} \sin^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{4} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**4*sin(c + d*x)**5/(15*d) + 4*a**4*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**4*sin(c + d*x)*cos(c + d*x)**4/d - 4*a**3*b*cos(c + d*x)**5/(5*d) + 4*a**2*b**2*sin(c + d*x)**5/(5*d) + 2*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)**2/d - 4*a*b**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 8*a*b**3*cos(c + d*x)**5/(15*d) + b**4*sin(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**4*cos(c), True))","A",0
79,1,381,0,1.216931," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\begin{cases} \frac{3 a^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{4} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{a^{3} b \cos^{4}{\left(c + d x \right)}}{d} + \frac{3 a^{2} b^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 a^{2} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 a^{2} b^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{3 a^{2} b^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{3 a^{2} b^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{a b^{3} \sin^{4}{\left(c + d x \right)}}{d} + \frac{3 b^{4} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 b^{4} x \cos^{4}{\left(c + d x \right)}}{8} - \frac{5 b^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 b^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{4} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*x*sin(c + d*x)**4/8 + 3*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**4*x*cos(c + d*x)**4/8 + 3*a**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*a**4*sin(c + d*x)*cos(c + d*x)**3/(8*d) - a**3*b*cos(c + d*x)**4/d + 3*a**2*b**2*x*sin(c + d*x)**4/4 + 3*a**2*b**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + 3*a**2*b**2*x*cos(c + d*x)**4/4 + 3*a**2*b**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) - 3*a**2*b**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) + a*b**3*sin(c + d*x)**4/d + 3*b**4*x*sin(c + d*x)**4/8 + 3*b**4*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*b**4*x*cos(c + d*x)**4/8 - 5*b**4*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*b**4*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**4, True))","A",0
80,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\int \left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{4} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*cos(c + d*x) + b*sin(c + d*x))**4*sec(c + d*x), x)","F",0
81,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate(sec(d*x+c)**11*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate(sec(d*x+c)**12*(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,1,1037,0,27.115666," ","integrate(cos(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\begin{cases} \frac{63 a^{5} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{315 a^{5} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{315 a^{5} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{315 a^{5} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{315 a^{5} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{63 a^{5} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{63 a^{5} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{147 a^{5} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{21 a^{5} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{237 a^{5} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{193 a^{5} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{a^{4} b \cos^{10}{\left(c + d x \right)}}{2 d} + \frac{35 a^{3} b^{2} x \sin^{10}{\left(c + d x \right)}}{128} + \frac{175 a^{3} b^{2} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{128} + \frac{175 a^{3} b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{175 a^{3} b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{64} + \frac{175 a^{3} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{128} + \frac{35 a^{3} b^{2} x \cos^{10}{\left(c + d x \right)}}{128} + \frac{35 a^{3} b^{2} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{245 a^{3} b^{2} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{192 d} + \frac{7 a^{3} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{3 d} + \frac{395 a^{3} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{192 d} - \frac{35 a^{3} b^{2} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{128 d} + \frac{a^{2} b^{3} \sin^{10}{\left(c + d x \right)}}{4 d} + \frac{5 a^{2} b^{3} \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{5 a^{2} b^{3} \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{2 d} + \frac{5 a^{2} b^{3} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{2 d} + \frac{15 a b^{4} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{75 a b^{4} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{75 a b^{4} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{75 a b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{75 a b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{15 a b^{4} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{15 a b^{4} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{35 a b^{4} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{a b^{4} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{2 d} - \frac{35 a b^{4} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{15 a b^{4} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} + \frac{b^{5} \sin^{10}{\left(c + d x \right)}}{60 d} + \frac{b^{5} \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{12 d} + \frac{b^{5} \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{5} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((63*a**5*x*sin(c + d*x)**10/256 + 315*a**5*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 315*a**5*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 315*a**5*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 315*a**5*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 63*a**5*x*cos(c + d*x)**10/256 + 63*a**5*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 147*a**5*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 21*a**5*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 237*a**5*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) + 193*a**5*sin(c + d*x)*cos(c + d*x)**9/(256*d) - a**4*b*cos(c + d*x)**10/(2*d) + 35*a**3*b**2*x*sin(c + d*x)**10/128 + 175*a**3*b**2*x*sin(c + d*x)**8*cos(c + d*x)**2/128 + 175*a**3*b**2*x*sin(c + d*x)**6*cos(c + d*x)**4/64 + 175*a**3*b**2*x*sin(c + d*x)**4*cos(c + d*x)**6/64 + 175*a**3*b**2*x*sin(c + d*x)**2*cos(c + d*x)**8/128 + 35*a**3*b**2*x*cos(c + d*x)**10/128 + 35*a**3*b**2*sin(c + d*x)**9*cos(c + d*x)/(128*d) + 245*a**3*b**2*sin(c + d*x)**7*cos(c + d*x)**3/(192*d) + 7*a**3*b**2*sin(c + d*x)**5*cos(c + d*x)**5/(3*d) + 395*a**3*b**2*sin(c + d*x)**3*cos(c + d*x)**7/(192*d) - 35*a**3*b**2*sin(c + d*x)*cos(c + d*x)**9/(128*d) + a**2*b**3*sin(c + d*x)**10/(4*d) + 5*a**2*b**3*sin(c + d*x)**8*cos(c + d*x)**2/(4*d) + 5*a**2*b**3*sin(c + d*x)**6*cos(c + d*x)**4/(2*d) + 5*a**2*b**3*sin(c + d*x)**4*cos(c + d*x)**6/(2*d) + 15*a*b**4*x*sin(c + d*x)**10/256 + 75*a*b**4*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 75*a*b**4*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 75*a*b**4*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 75*a*b**4*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 15*a*b**4*x*cos(c + d*x)**10/256 + 15*a*b**4*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 35*a*b**4*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + a*b**4*sin(c + d*x)**5*cos(c + d*x)**5/(2*d) - 35*a*b**4*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 15*a*b**4*sin(c + d*x)*cos(c + d*x)**9/(256*d) + b**5*sin(c + d*x)**10/(60*d) + b**5*sin(c + d*x)**8*cos(c + d*x)**2/(12*d) + b**5*sin(c + d*x)**6*cos(c + d*x)**4/(6*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**5*cos(c)**5, True))","A",0
93,1,440,0,16.228624," ","integrate(cos(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\begin{cases} \frac{128 a^{5} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{64 a^{5} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{16 a^{5} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{8 a^{5} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{a^{5} \sin{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{d} - \frac{5 a^{4} b \cos^{9}{\left(c + d x \right)}}{9 d} + \frac{32 a^{3} b^{2} \sin^{9}{\left(c + d x \right)}}{63 d} + \frac{16 a^{3} b^{2} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{7 d} + \frac{4 a^{3} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{10 a^{3} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{10 a^{2} b^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{20 a^{2} b^{3} \cos^{9}{\left(c + d x \right)}}{63 d} + \frac{8 a b^{4} \sin^{9}{\left(c + d x \right)}}{63 d} + \frac{4 a b^{4} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{7 d} + \frac{a b^{4} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{b^{5} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{4 b^{5} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{8 b^{5} \cos^{9}{\left(c + d x \right)}}{315 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{5} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((128*a**5*sin(c + d*x)**9/(315*d) + 64*a**5*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 16*a**5*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 8*a**5*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) + a**5*sin(c + d*x)*cos(c + d*x)**8/d - 5*a**4*b*cos(c + d*x)**9/(9*d) + 32*a**3*b**2*sin(c + d*x)**9/(63*d) + 16*a**3*b**2*sin(c + d*x)**7*cos(c + d*x)**2/(7*d) + 4*a**3*b**2*sin(c + d*x)**5*cos(c + d*x)**4/d + 10*a**3*b**2*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) - 10*a**2*b**3*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 20*a**2*b**3*cos(c + d*x)**9/(63*d) + 8*a*b**4*sin(c + d*x)**9/(63*d) + 4*a*b**4*sin(c + d*x)**7*cos(c + d*x)**2/(7*d) + a*b**4*sin(c + d*x)**5*cos(c + d*x)**4/d - b**5*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 4*b**5*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 8*b**5*cos(c + d*x)**9/(315*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**5*cos(c)**4, True))","A",0
94,1,826,0,11.543101," ","integrate(cos(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\begin{cases} \frac{35 a^{5} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{35 a^{5} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{105 a^{5} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{35 a^{5} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{35 a^{5} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{35 a^{5} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{385 a^{5} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{511 a^{5} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} + \frac{93 a^{5} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{5 a^{4} b \cos^{8}{\left(c + d x \right)}}{8 d} + \frac{25 a^{3} b^{2} x \sin^{8}{\left(c + d x \right)}}{64} + \frac{25 a^{3} b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{75 a^{3} b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{25 a^{3} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{25 a^{3} b^{2} x \cos^{8}{\left(c + d x \right)}}{64} + \frac{25 a^{3} b^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} + \frac{275 a^{3} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{192 d} + \frac{365 a^{3} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{192 d} - \frac{25 a^{3} b^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} + \frac{5 a^{2} b^{3} \sin^{8}{\left(c + d x \right)}}{12 d} + \frac{5 a^{2} b^{3} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{5 a^{2} b^{3} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{2 d} + \frac{15 a b^{4} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 a b^{4} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{45 a b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{15 a b^{4} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{15 a b^{4} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 a b^{4} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{55 a b^{4} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{15 a b^{4} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{b^{5} \sin^{8}{\left(c + d x \right)}}{24 d} + \frac{b^{5} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{5} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((35*a**5*x*sin(c + d*x)**8/128 + 35*a**5*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 105*a**5*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 35*a**5*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 35*a**5*x*cos(c + d*x)**8/128 + 35*a**5*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 385*a**5*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 511*a**5*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) + 93*a**5*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 5*a**4*b*cos(c + d*x)**8/(8*d) + 25*a**3*b**2*x*sin(c + d*x)**8/64 + 25*a**3*b**2*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + 75*a**3*b**2*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 25*a**3*b**2*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 25*a**3*b**2*x*cos(c + d*x)**8/64 + 25*a**3*b**2*sin(c + d*x)**7*cos(c + d*x)/(64*d) + 275*a**3*b**2*sin(c + d*x)**5*cos(c + d*x)**3/(192*d) + 365*a**3*b**2*sin(c + d*x)**3*cos(c + d*x)**5/(192*d) - 25*a**3*b**2*sin(c + d*x)*cos(c + d*x)**7/(64*d) + 5*a**2*b**3*sin(c + d*x)**8/(12*d) + 5*a**2*b**3*sin(c + d*x)**6*cos(c + d*x)**2/(3*d) + 5*a**2*b**3*sin(c + d*x)**4*cos(c + d*x)**4/(2*d) + 15*a*b**4*x*sin(c + d*x)**8/128 + 15*a*b**4*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 45*a*b**4*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*a*b**4*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 15*a*b**4*x*cos(c + d*x)**8/128 + 15*a*b**4*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*a*b**4*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 55*a*b**4*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 15*a*b**4*sin(c + d*x)*cos(c + d*x)**7/(128*d) + b**5*sin(c + d*x)**8/(24*d) + b**5*sin(c + d*x)**6*cos(c + d*x)**2/(6*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**5*cos(c)**3, True))","A",0
95,1,357,0,6.048629," ","integrate(cos(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\begin{cases} \frac{16 a^{5} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 a^{5} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 a^{5} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{a^{5} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{5 a^{4} b \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{16 a^{3} b^{2} \sin^{7}{\left(c + d x \right)}}{21 d} + \frac{8 a^{3} b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{10 a^{3} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{2 a^{2} b^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{d} - \frac{4 a^{2} b^{3} \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{2 a b^{4} \sin^{7}{\left(c + d x \right)}}{7 d} + \frac{a b^{4} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{b^{5} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{4 b^{5} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{8 b^{5} \cos^{7}{\left(c + d x \right)}}{105 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{5} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**5*sin(c + d*x)**7/(35*d) + 8*a**5*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*a**5*sin(c + d*x)**3*cos(c + d*x)**4/d + a**5*sin(c + d*x)*cos(c + d*x)**6/d - 5*a**4*b*cos(c + d*x)**7/(7*d) + 16*a**3*b**2*sin(c + d*x)**7/(21*d) + 8*a**3*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(3*d) + 10*a**3*b**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - 2*a**2*b**3*sin(c + d*x)**2*cos(c + d*x)**5/d - 4*a**2*b**3*cos(c + d*x)**7/(7*d) + 2*a*b**4*sin(c + d*x)**7/(7*d) + a*b**4*sin(c + d*x)**5*cos(c + d*x)**2/d - b**5*sin(c + d*x)**4*cos(c + d*x)**3/(3*d) - 4*b**5*sin(c + d*x)**2*cos(c + d*x)**5/(15*d) - 8*b**5*cos(c + d*x)**7/(105*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**5*cos(c)**2, True))","A",0
96,1,609,0,4.172740," ","integrate(cos(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\begin{cases} \frac{5 a^{5} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{5} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a^{5} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a^{5} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a^{5} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 a^{5} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 a^{5} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{5 a^{4} b \cos^{6}{\left(c + d x \right)}}{6 d} + \frac{5 a^{3} b^{2} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{15 a^{3} b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{15 a^{3} b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{5 a^{3} b^{2} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{5 a^{3} b^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 a^{3} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{5 a^{3} b^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} + \frac{5 a^{2} b^{3} \sin^{6}{\left(c + d x \right)}}{6 d} + \frac{5 a^{2} b^{3} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{5 a b^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a b^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a b^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 a b^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a b^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{5 a b^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{5 a b^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{b^{5} \sin^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{5} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**5*x*sin(c + d*x)**6/16 + 15*a**5*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a**5*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a**5*x*cos(c + d*x)**6/16 + 5*a**5*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*a**5*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*a**5*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 5*a**4*b*cos(c + d*x)**6/(6*d) + 5*a**3*b**2*x*sin(c + d*x)**6/8 + 15*a**3*b**2*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 15*a**3*b**2*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + 5*a**3*b**2*x*cos(c + d*x)**6/8 + 5*a**3*b**2*sin(c + d*x)**5*cos(c + d*x)/(8*d) + 5*a**3*b**2*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - 5*a**3*b**2*sin(c + d*x)*cos(c + d*x)**5/(8*d) + 5*a**2*b**3*sin(c + d*x)**6/(6*d) + 5*a**2*b**3*sin(c + d*x)**4*cos(c + d*x)**2/(2*d) + 5*a*b**4*x*sin(c + d*x)**6/16 + 15*a*b**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*a*b**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*a*b**4*x*cos(c + d*x)**6/16 + 5*a*b**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) - 5*a*b**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - 5*a*b**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) + b**5*sin(c + d*x)**6/(6*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**5*cos(c), True))","A",0
97,1,267,0,2.140647," ","integrate((a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\begin{cases} \frac{8 a^{5} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 a^{5} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a^{5} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a^{4} b \cos^{5}{\left(c + d x \right)}}{d} + \frac{4 a^{3} b^{2} \sin^{5}{\left(c + d x \right)}}{3 d} + \frac{10 a^{3} b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{10 a^{2} b^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{4 a^{2} b^{3} \cos^{5}{\left(c + d x \right)}}{3 d} + \frac{a b^{4} \sin^{5}{\left(c + d x \right)}}{d} - \frac{b^{5} \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{d} - \frac{4 b^{5} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{8 b^{5} \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{5} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**5*sin(c + d*x)**5/(15*d) + 4*a**5*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + a**5*sin(c + d*x)*cos(c + d*x)**4/d - a**4*b*cos(c + d*x)**5/d + 4*a**3*b**2*sin(c + d*x)**5/(3*d) + 10*a**3*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - 10*a**2*b**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 4*a**2*b**3*cos(c + d*x)**5/(3*d) + a*b**4*sin(c + d*x)**5/d - b**5*sin(c + d*x)**4*cos(c + d*x)/d - 4*b**5*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 8*b**5*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a*cos(c) + b*sin(c))**5, True))","A",0
98,-1,0,0,0.000000," ","integrate(sec(d*x+c)*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(sec(d*x+c)**11*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(sec(d*x+c)**12*(a*cos(d*x+c)+b*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,1,296,0,1.748558," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\begin{cases} \frac{\tilde{\infty} x \cos{\left(c \right)}}{\sin{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\- \frac{d x \sin{\left(c + d x \right)}}{2 i b d \sin{\left(c + d x \right)} + 2 b d \cos{\left(c + d x \right)}} + \frac{i d x \cos{\left(c + d x \right)}}{2 i b d \sin{\left(c + d x \right)} + 2 b d \cos{\left(c + d x \right)}} - \frac{\cos{\left(c + d x \right)}}{2 i b d \sin{\left(c + d x \right)} + 2 b d \cos{\left(c + d x \right)}} & \text{for}\: a = - i b \\- \frac{d x \sin{\left(c + d x \right)}}{- 2 i b d \sin{\left(c + d x \right)} + 2 b d \cos{\left(c + d x \right)}} - \frac{i d x \cos{\left(c + d x \right)}}{- 2 i b d \sin{\left(c + d x \right)} + 2 b d \cos{\left(c + d x \right)}} - \frac{\cos{\left(c + d x \right)}}{- 2 i b d \sin{\left(c + d x \right)} + 2 b d \cos{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{x \cos{\left(c \right)}}{a \cos{\left(c \right)} + b \sin{\left(c \right)}} & \text{for}\: d = 0 \\\frac{\log{\left(\sin{\left(c + d x \right)} \right)}}{b d} & \text{for}\: a = 0 \\\frac{a d x}{a^{2} d + b^{2} d} + \frac{b \log{\left(\cos{\left(c + d x \right)} + \frac{b \sin{\left(c + d x \right)}}{a} \right)}}{a^{2} d + b^{2} d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*cos(c)/sin(c), Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), (-d*x*sin(c + d*x)/(2*I*b*d*sin(c + d*x) + 2*b*d*cos(c + d*x)) + I*d*x*cos(c + d*x)/(2*I*b*d*sin(c + d*x) + 2*b*d*cos(c + d*x)) - cos(c + d*x)/(2*I*b*d*sin(c + d*x) + 2*b*d*cos(c + d*x)), Eq(a, -I*b)), (-d*x*sin(c + d*x)/(-2*I*b*d*sin(c + d*x) + 2*b*d*cos(c + d*x)) - I*d*x*cos(c + d*x)/(-2*I*b*d*sin(c + d*x) + 2*b*d*cos(c + d*x)) - cos(c + d*x)/(-2*I*b*d*sin(c + d*x) + 2*b*d*cos(c + d*x)), Eq(a, I*b)), (x*cos(c)/(a*cos(c) + b*sin(c)), Eq(d, 0)), (log(sin(c + d*x))/(b*d), Eq(a, 0)), (a*d*x/(a**2*d + b**2*d) + b*log(cos(c + d*x) + b*sin(c + d*x)/a)/(a**2*d + b**2*d), True))","A",0
115,-2,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
116,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \frac{\sec{\left(c + d x \right)}}{a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*cos(c + d*x) + b*sin(c + d*x)), x)","F",0
117,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*cos(c + d*x) + b*sin(c + d*x)), x)","F",0
118,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*cos(c + d*x) + b*sin(c + d*x)), x)","F",0
119,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a*cos(c + d*x) + b*sin(c + d*x)), x)","F",0
120,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a*cos(c + d*x) + b*sin(c + d*x)), x)","F",0
121,0,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a*cos(d*x+c)+b*sin(d*x+c)),x)","\int \frac{\sec^{6}{\left(c + d x \right)}}{a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**6/(a*cos(c + d*x) + b*sin(c + d*x)), x)","F",0
122,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,1,1552,0,6.382092," ","integrate(cos(d*x+c)**2/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\begin{cases} \frac{\tilde{\infty} x \cos^{2}{\left(c \right)}}{\sin^{2}{\left(c \right)}} & \text{for}\: a = 0 \wedge b = 0 \wedge d = 0 \\\frac{- x - \frac{\cos{\left(c + d x \right)}}{d \sin{\left(c + d x \right)}}}{b^{2}} & \text{for}\: a = 0 \\\frac{2 d x \sin^{2}{\left(c + d x \right)}}{- 8 b^{2} d \sin^{2}{\left(c + d x \right)} + 16 i b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 b^{2} d \cos^{2}{\left(c + d x \right)}} - \frac{4 i d x \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{- 8 b^{2} d \sin^{2}{\left(c + d x \right)} + 16 i b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 b^{2} d \cos^{2}{\left(c + d x \right)}} - \frac{2 d x \cos^{2}{\left(c + d x \right)}}{- 8 b^{2} d \sin^{2}{\left(c + d x \right)} + 16 i b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 b^{2} d \cos^{2}{\left(c + d x \right)}} - \frac{i \sin^{2}{\left(c + d x \right)}}{- 8 b^{2} d \sin^{2}{\left(c + d x \right)} + 16 i b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 b^{2} d \cos^{2}{\left(c + d x \right)}} - \frac{3 i \cos^{2}{\left(c + d x \right)}}{- 8 b^{2} d \sin^{2}{\left(c + d x \right)} + 16 i b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 b^{2} d \cos^{2}{\left(c + d x \right)}} & \text{for}\: a = - i b \\\frac{2 i d x \sin^{2}{\left(c + d x \right)}}{- 8 i b^{2} d \sin^{2}{\left(c + d x \right)} + 16 b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 i b^{2} d \cos^{2}{\left(c + d x \right)}} - \frac{4 d x \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{- 8 i b^{2} d \sin^{2}{\left(c + d x \right)} + 16 b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 i b^{2} d \cos^{2}{\left(c + d x \right)}} - \frac{2 i d x \cos^{2}{\left(c + d x \right)}}{- 8 i b^{2} d \sin^{2}{\left(c + d x \right)} + 16 b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 i b^{2} d \cos^{2}{\left(c + d x \right)}} - \frac{\sin^{2}{\left(c + d x \right)}}{- 8 i b^{2} d \sin^{2}{\left(c + d x \right)} + 16 b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 i b^{2} d \cos^{2}{\left(c + d x \right)}} - \frac{3 \cos^{2}{\left(c + d x \right)}}{- 8 i b^{2} d \sin^{2}{\left(c + d x \right)} + 16 b^{2} d \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + 8 i b^{2} d \cos^{2}{\left(c + d x \right)}} & \text{for}\: a = i b \\\frac{x \cos^{2}{\left(c \right)}}{\left(a \cos{\left(c \right)} + b \sin{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\\frac{a^{3} d x \cos{\left(c + d x \right)}}{a^{5} d \cos{\left(c + d x \right)} + a^{4} b d \sin{\left(c + d x \right)} + 2 a^{3} b^{2} d \cos{\left(c + d x \right)} + 2 a^{2} b^{3} d \sin{\left(c + d x \right)} + a b^{4} d \cos{\left(c + d x \right)} + b^{5} d \sin{\left(c + d x \right)}} + \frac{a^{2} b d x \sin{\left(c + d x \right)}}{a^{5} d \cos{\left(c + d x \right)} + a^{4} b d \sin{\left(c + d x \right)} + 2 a^{3} b^{2} d \cos{\left(c + d x \right)} + 2 a^{2} b^{3} d \sin{\left(c + d x \right)} + a b^{4} d \cos{\left(c + d x \right)} + b^{5} d \sin{\left(c + d x \right)}} + \frac{2 a^{2} b \log{\left(\cos{\left(c + d x \right)} + \frac{b \sin{\left(c + d x \right)}}{a} \right)} \cos{\left(c + d x \right)}}{a^{5} d \cos{\left(c + d x \right)} + a^{4} b d \sin{\left(c + d x \right)} + 2 a^{3} b^{2} d \cos{\left(c + d x \right)} + 2 a^{2} b^{3} d \sin{\left(c + d x \right)} + a b^{4} d \cos{\left(c + d x \right)} + b^{5} d \sin{\left(c + d x \right)}} - \frac{a^{2} b \cos{\left(c + d x \right)}}{a^{5} d \cos{\left(c + d x \right)} + a^{4} b d \sin{\left(c + d x \right)} + 2 a^{3} b^{2} d \cos{\left(c + d x \right)} + 2 a^{2} b^{3} d \sin{\left(c + d x \right)} + a b^{4} d \cos{\left(c + d x \right)} + b^{5} d \sin{\left(c + d x \right)}} - \frac{a b^{2} d x \cos{\left(c + d x \right)}}{a^{5} d \cos{\left(c + d x \right)} + a^{4} b d \sin{\left(c + d x \right)} + 2 a^{3} b^{2} d \cos{\left(c + d x \right)} + 2 a^{2} b^{3} d \sin{\left(c + d x \right)} + a b^{4} d \cos{\left(c + d x \right)} + b^{5} d \sin{\left(c + d x \right)}} + \frac{2 a b^{2} \log{\left(\cos{\left(c + d x \right)} + \frac{b \sin{\left(c + d x \right)}}{a} \right)} \sin{\left(c + d x \right)}}{a^{5} d \cos{\left(c + d x \right)} + a^{4} b d \sin{\left(c + d x \right)} + 2 a^{3} b^{2} d \cos{\left(c + d x \right)} + 2 a^{2} b^{3} d \sin{\left(c + d x \right)} + a b^{4} d \cos{\left(c + d x \right)} + b^{5} d \sin{\left(c + d x \right)}} - \frac{b^{3} d x \sin{\left(c + d x \right)}}{a^{5} d \cos{\left(c + d x \right)} + a^{4} b d \sin{\left(c + d x \right)} + 2 a^{3} b^{2} d \cos{\left(c + d x \right)} + 2 a^{2} b^{3} d \sin{\left(c + d x \right)} + a b^{4} d \cos{\left(c + d x \right)} + b^{5} d \sin{\left(c + d x \right)}} - \frac{b^{3} \cos{\left(c + d x \right)}}{a^{5} d \cos{\left(c + d x \right)} + a^{4} b d \sin{\left(c + d x \right)} + 2 a^{3} b^{2} d \cos{\left(c + d x \right)} + 2 a^{2} b^{3} d \sin{\left(c + d x \right)} + a b^{4} d \cos{\left(c + d x \right)} + b^{5} d \sin{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*x*cos(c)**2/sin(c)**2, Eq(a, 0) & Eq(b, 0) & Eq(d, 0)), ((-x - cos(c + d*x)/(d*sin(c + d*x)))/b**2, Eq(a, 0)), (2*d*x*sin(c + d*x)**2/(-8*b**2*d*sin(c + d*x)**2 + 16*I*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*b**2*d*cos(c + d*x)**2) - 4*I*d*x*sin(c + d*x)*cos(c + d*x)/(-8*b**2*d*sin(c + d*x)**2 + 16*I*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*b**2*d*cos(c + d*x)**2) - 2*d*x*cos(c + d*x)**2/(-8*b**2*d*sin(c + d*x)**2 + 16*I*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*b**2*d*cos(c + d*x)**2) - I*sin(c + d*x)**2/(-8*b**2*d*sin(c + d*x)**2 + 16*I*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*b**2*d*cos(c + d*x)**2) - 3*I*cos(c + d*x)**2/(-8*b**2*d*sin(c + d*x)**2 + 16*I*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*b**2*d*cos(c + d*x)**2), Eq(a, -I*b)), (2*I*d*x*sin(c + d*x)**2/(-8*I*b**2*d*sin(c + d*x)**2 + 16*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*I*b**2*d*cos(c + d*x)**2) - 4*d*x*sin(c + d*x)*cos(c + d*x)/(-8*I*b**2*d*sin(c + d*x)**2 + 16*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*I*b**2*d*cos(c + d*x)**2) - 2*I*d*x*cos(c + d*x)**2/(-8*I*b**2*d*sin(c + d*x)**2 + 16*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*I*b**2*d*cos(c + d*x)**2) - sin(c + d*x)**2/(-8*I*b**2*d*sin(c + d*x)**2 + 16*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*I*b**2*d*cos(c + d*x)**2) - 3*cos(c + d*x)**2/(-8*I*b**2*d*sin(c + d*x)**2 + 16*b**2*d*sin(c + d*x)*cos(c + d*x) + 8*I*b**2*d*cos(c + d*x)**2), Eq(a, I*b)), (x*cos(c)**2/(a*cos(c) + b*sin(c))**2, Eq(d, 0)), (a**3*d*x*cos(c + d*x)/(a**5*d*cos(c + d*x) + a**4*b*d*sin(c + d*x) + 2*a**3*b**2*d*cos(c + d*x) + 2*a**2*b**3*d*sin(c + d*x) + a*b**4*d*cos(c + d*x) + b**5*d*sin(c + d*x)) + a**2*b*d*x*sin(c + d*x)/(a**5*d*cos(c + d*x) + a**4*b*d*sin(c + d*x) + 2*a**3*b**2*d*cos(c + d*x) + 2*a**2*b**3*d*sin(c + d*x) + a*b**4*d*cos(c + d*x) + b**5*d*sin(c + d*x)) + 2*a**2*b*log(cos(c + d*x) + b*sin(c + d*x)/a)*cos(c + d*x)/(a**5*d*cos(c + d*x) + a**4*b*d*sin(c + d*x) + 2*a**3*b**2*d*cos(c + d*x) + 2*a**2*b**3*d*sin(c + d*x) + a*b**4*d*cos(c + d*x) + b**5*d*sin(c + d*x)) - a**2*b*cos(c + d*x)/(a**5*d*cos(c + d*x) + a**4*b*d*sin(c + d*x) + 2*a**3*b**2*d*cos(c + d*x) + 2*a**2*b**3*d*sin(c + d*x) + a*b**4*d*cos(c + d*x) + b**5*d*sin(c + d*x)) - a*b**2*d*x*cos(c + d*x)/(a**5*d*cos(c + d*x) + a**4*b*d*sin(c + d*x) + 2*a**3*b**2*d*cos(c + d*x) + 2*a**2*b**3*d*sin(c + d*x) + a*b**4*d*cos(c + d*x) + b**5*d*sin(c + d*x)) + 2*a*b**2*log(cos(c + d*x) + b*sin(c + d*x)/a)*sin(c + d*x)/(a**5*d*cos(c + d*x) + a**4*b*d*sin(c + d*x) + 2*a**3*b**2*d*cos(c + d*x) + 2*a**2*b**3*d*sin(c + d*x) + a*b**4*d*cos(c + d*x) + b**5*d*sin(c + d*x)) - b**3*d*x*sin(c + d*x)/(a**5*d*cos(c + d*x) + a**4*b*d*sin(c + d*x) + 2*a**3*b**2*d*cos(c + d*x) + 2*a**2*b**3*d*sin(c + d*x) + a*b**4*d*cos(c + d*x) + b**5*d*sin(c + d*x)) - b**3*cos(c + d*x)/(a**5*d*cos(c + d*x) + a**4*b*d*sin(c + d*x) + 2*a**3*b**2*d*cos(c + d*x) + 2*a**2*b**3*d*sin(c + d*x) + a*b**4*d*cos(c + d*x) + b**5*d*sin(c + d*x)), True))","A",0
125,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*cos(c + d*x) + b*sin(c + d*x))**2, x)","F",0
128,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*cos(c + d*x) + b*sin(c + d*x))**2, x)","F",0
129,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*cos(c + d*x) + b*sin(c + d*x))**2, x)","F",0
130,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a*cos(d*x+c)+b*sin(d*x+c))**2,x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a*cos(c + d*x) + b*sin(c + d*x))**2, x)","F",0
131,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-2,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
133,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*cos(c + d*x) + b*sin(c + d*x))**3, x)","F",0
137,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*cos(c + d*x) + b*sin(c + d*x))**3, x)","F",0
138,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*cos(c + d*x) + b*sin(c + d*x))**3, x)","F",0
139,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a*cos(c + d*x) + b*sin(c + d*x))**3, x)","F",0
140,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a*cos(d*x+c)+b*sin(d*x+c))**3,x)","\int \frac{\sec^{5}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**5/(a*cos(c + d*x) + b*sin(c + d*x))**3, x)","F",0
141,-2,0,0,0.000000," ","integrate(cos(d*x+c)**4/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Exception raised: AttributeError}"," ",0,"Exception raised: AttributeError","F(-2)",0
142,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate(1/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*cos(c + d*x) + b*sin(c + d*x))**4, x)","F",0
147,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*cos(c + d*x) + b*sin(c + d*x))**4, x)","F",0
148,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*cos(c + d*x) + b*sin(c + d*x))**4, x)","F",0
149,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a*cos(d*x+c)+b*sin(d*x+c))**4,x)","\int \frac{\sec^{4}{\left(c + d x \right)}}{\left(a \cos{\left(c + d x \right)} + b \sin{\left(c + d x \right)}\right)^{4}}\, dx"," ",0,"Integral(sec(c + d*x)**4/(a*cos(c + d*x) + b*sin(c + d*x))**4, x)","F",0
150,1,223,0,0.411543," ","integrate(cos(d*x+c)**5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\begin{cases} - \frac{\left(50331648 i a^{4} d^{4} e^{16 i c} e^{4 i d x} + 503316480 i a^{4} d^{4} e^{14 i c} e^{2 i d x} - 1006632960 i a^{4} d^{4} e^{10 i c} e^{- 2 i d x} - 251658240 i a^{4} d^{4} e^{8 i c} e^{- 4 i d x} - 33554432 i a^{4} d^{4} e^{6 i c} e^{- 6 i d x}\right) e^{- 12 i c}}{6442450944 a^{5} d^{5}} & \text{for}\: 6442450944 a^{5} d^{5} e^{12 i c} \neq 0 \\x \left(\frac{\left(e^{10 i c} + 5 e^{8 i c} + 10 e^{6 i c} + 10 e^{4 i c} + 5 e^{2 i c} + 1\right) e^{- 6 i c}}{32 a} - \frac{5}{16 a}\right) & \text{otherwise} \end{cases} + \frac{5 x}{16 a}"," ",0,"Piecewise((-(50331648*I*a**4*d**4*exp(16*I*c)*exp(4*I*d*x) + 503316480*I*a**4*d**4*exp(14*I*c)*exp(2*I*d*x) - 1006632960*I*a**4*d**4*exp(10*I*c)*exp(-2*I*d*x) - 251658240*I*a**4*d**4*exp(8*I*c)*exp(-4*I*d*x) - 33554432*I*a**4*d**4*exp(6*I*c)*exp(-6*I*d*x))*exp(-12*I*c)/(6442450944*a**5*d**5), Ne(6442450944*a**5*d**5*exp(12*I*c), 0)), (x*((exp(10*I*c) + 5*exp(8*I*c) + 10*exp(6*I*c) + 10*exp(4*I*c) + 5*exp(2*I*c) + 1)*exp(-6*I*c)/(32*a) - 5/(16*a)), True)) + 5*x/(16*a)","A",0
151,1,199,0,0.468398," ","integrate(cos(d*x+c)**4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\begin{cases} - \frac{\left(30720 i a^{4} d^{4} e^{12 i c} e^{3 i d x} + 368640 i a^{4} d^{4} e^{10 i c} e^{i d x} - 552960 i a^{4} d^{4} e^{8 i c} e^{- i d x} - 122880 i a^{4} d^{4} e^{6 i c} e^{- 3 i d x} - 18432 i a^{4} d^{4} e^{4 i c} e^{- 5 i d x}\right) e^{- 9 i c}}{1474560 a^{5} d^{5}} & \text{for}\: 1474560 a^{5} d^{5} e^{9 i c} \neq 0 \\\frac{x \left(e^{8 i c} + 4 e^{6 i c} + 6 e^{4 i c} + 4 e^{2 i c} + 1\right) e^{- 5 i c}}{16 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(30720*I*a**4*d**4*exp(12*I*c)*exp(3*I*d*x) + 368640*I*a**4*d**4*exp(10*I*c)*exp(I*d*x) - 552960*I*a**4*d**4*exp(8*I*c)*exp(-I*d*x) - 122880*I*a**4*d**4*exp(6*I*c)*exp(-3*I*d*x) - 18432*I*a**4*d**4*exp(4*I*c)*exp(-5*I*d*x))*exp(-9*I*c)/(1474560*a**5*d**5), Ne(1474560*a**5*d**5*exp(9*I*c), 0)), (x*(exp(8*I*c) + 4*exp(6*I*c) + 6*exp(4*I*c) + 4*exp(2*I*c) + 1)*exp(-5*I*c)/(16*a), True))","A",0
152,1,155,0,0.299883," ","integrate(cos(d*x+c)**3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\begin{cases} - \frac{\left(512 i a^{2} d^{2} e^{8 i c} e^{2 i d x} - 1536 i a^{2} d^{2} e^{4 i c} e^{- 2 i d x} - 256 i a^{2} d^{2} e^{2 i c} e^{- 4 i d x}\right) e^{- 6 i c}}{8192 a^{3} d^{3}} & \text{for}\: 8192 a^{3} d^{3} e^{6 i c} \neq 0 \\x \left(\frac{\left(e^{6 i c} + 3 e^{4 i c} + 3 e^{2 i c} + 1\right) e^{- 4 i c}}{8 a} - \frac{3}{8 a}\right) & \text{otherwise} \end{cases} + \frac{3 x}{8 a}"," ",0,"Piecewise((-(512*I*a**2*d**2*exp(8*I*c)*exp(2*I*d*x) - 1536*I*a**2*d**2*exp(4*I*c)*exp(-2*I*d*x) - 256*I*a**2*d**2*exp(2*I*c)*exp(-4*I*d*x))*exp(-6*I*c)/(8192*a**3*d**3), Ne(8192*a**3*d**3*exp(6*I*c), 0)), (x*((exp(6*I*c) + 3*exp(4*I*c) + 3*exp(2*I*c) + 1)*exp(-4*I*c)/(8*a) - 3/(8*a)), True)) + 3*x/(8*a)","A",0
153,1,129,0,0.482985," ","integrate(cos(d*x+c)**2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\begin{cases} - \frac{\left(24 i a^{2} d^{2} e^{5 i c} e^{i d x} - 48 i a^{2} d^{2} e^{3 i c} e^{- i d x} - 8 i a^{2} d^{2} e^{i c} e^{- 3 i d x}\right) e^{- 4 i c}}{96 a^{3} d^{3}} & \text{for}\: 96 a^{3} d^{3} e^{4 i c} \neq 0 \\\frac{x \left(e^{4 i c} + 2 e^{2 i c} + 1\right) e^{- 3 i c}}{4 a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(24*I*a**2*d**2*exp(5*I*c)*exp(I*d*x) - 48*I*a**2*d**2*exp(3*I*c)*exp(-I*d*x) - 8*I*a**2*d**2*exp(I*c)*exp(-3*I*d*x))*exp(-4*I*c)/(96*a**3*d**3), Ne(96*a**3*d**3*exp(4*I*c), 0)), (x*(exp(4*I*c) + 2*exp(2*I*c) + 1)*exp(-3*I*c)/(4*a), True))","A",0
154,1,61,0,0.205995," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\begin{cases} \frac{i e^{- 2 i c} e^{- 2 i d x}}{4 a d} & \text{for}\: 4 a d e^{2 i c} \neq 0 \\x \left(\frac{\left(e^{2 i c} + 1\right) e^{- 2 i c}}{2 a} - \frac{1}{2 a}\right) & \text{otherwise} \end{cases} + \frac{x}{2 a}"," ",0,"Piecewise((I*exp(-2*I*c)*exp(-2*I*d*x)/(4*a*d), Ne(4*a*d*exp(2*I*c), 0)), (x*((exp(2*I*c) + 1)*exp(-2*I*c)/(2*a) - 1/(2*a)), True)) + x/(2*a)","A",0
155,1,31,0,0.140829," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\begin{cases} \frac{i e^{- i c} e^{- i d x}}{a d} & \text{for}\: a d e^{i c} \neq 0 \\\frac{x e^{- i c}}{a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*exp(-I*c)*exp(-I*d*x)/(a*d), Ne(a*d*exp(I*c), 0)), (x*exp(-I*c)/a, True))","A",0
156,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)/(I*sin(c + d*x) + cos(c + d*x)), x)/a","F",0
157,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**2/(I*sin(c + d*x) + cos(c + d*x)), x)/a","F",0
158,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**3/(I*sin(c + d*x) + cos(c + d*x)), x)/a","F",0
159,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{4}{\left(c + d x \right)}}{i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**4/(I*sin(c + d*x) + cos(c + d*x)), x)/a","F",0
160,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{5}{\left(c + d x \right)}}{i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**5/(I*sin(c + d*x) + cos(c + d*x)), x)/a","F",0
161,0,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{6}{\left(c + d x \right)}}{i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**6/(I*sin(c + d*x) + cos(c + d*x)), x)/a","F",0
162,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7/(a*cos(d*x+c)+I*a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,1,233,0,0.590263," ","integrate(cos(d*x+c)**5/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\begin{cases} \frac{\left(- 176160768 i a^{10} d^{5} e^{19 i c} e^{3 i d x} - 2642411520 i a^{10} d^{5} e^{17 i c} e^{i d x} + 5284823040 i a^{10} d^{5} e^{15 i c} e^{- i d x} + 1761607680 i a^{10} d^{5} e^{13 i c} e^{- 3 i d x} + 528482304 i a^{10} d^{5} e^{11 i c} e^{- 5 i d x} + 75497472 i a^{10} d^{5} e^{9 i c} e^{- 7 i d x}\right) e^{- 16 i c}}{16911433728 a^{12} d^{6}} & \text{for}\: 16911433728 a^{12} d^{6} e^{16 i c} \neq 0 \\\frac{x \left(e^{10 i c} + 5 e^{8 i c} + 10 e^{6 i c} + 10 e^{4 i c} + 5 e^{2 i c} + 1\right) e^{- 7 i c}}{32 a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-176160768*I*a**10*d**5*exp(19*I*c)*exp(3*I*d*x) - 2642411520*I*a**10*d**5*exp(17*I*c)*exp(I*d*x) + 5284823040*I*a**10*d**5*exp(15*I*c)*exp(-I*d*x) + 1761607680*I*a**10*d**5*exp(13*I*c)*exp(-3*I*d*x) + 528482304*I*a**10*d**5*exp(11*I*c)*exp(-5*I*d*x) + 75497472*I*a**10*d**5*exp(9*I*c)*exp(-7*I*d*x))*exp(-16*I*c)/(16911433728*a**12*d**6), Ne(16911433728*a**12*d**6*exp(16*I*c), 0)), (x*(exp(10*I*c) + 5*exp(8*I*c) + 10*exp(6*I*c) + 10*exp(4*I*c) + 5*exp(2*I*c) + 1)*exp(-7*I*c)/(32*a**2), True))","A",0
164,1,190,0,0.370030," ","integrate(cos(d*x+c)**4/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\begin{cases} \frac{\left(- 24576 i a^{6} d^{3} e^{14 i c} e^{2 i d x} + 147456 i a^{6} d^{3} e^{10 i c} e^{- 2 i d x} + 49152 i a^{6} d^{3} e^{8 i c} e^{- 4 i d x} + 8192 i a^{6} d^{3} e^{6 i c} e^{- 6 i d x}\right) e^{- 12 i c}}{786432 a^{8} d^{4}} & \text{for}\: 786432 a^{8} d^{4} e^{12 i c} \neq 0 \\x \left(\frac{\left(e^{8 i c} + 4 e^{6 i c} + 6 e^{4 i c} + 4 e^{2 i c} + 1\right) e^{- 6 i c}}{16 a^{2}} - \frac{1}{4 a^{2}}\right) & \text{otherwise} \end{cases} + \frac{x}{4 a^{2}}"," ",0,"Piecewise(((-24576*I*a**6*d**3*exp(14*I*c)*exp(2*I*d*x) + 147456*I*a**6*d**3*exp(10*I*c)*exp(-2*I*d*x) + 49152*I*a**6*d**3*exp(8*I*c)*exp(-4*I*d*x) + 8192*I*a**6*d**3*exp(6*I*c)*exp(-6*I*d*x))*exp(-12*I*c)/(786432*a**8*d**4), Ne(786432*a**8*d**4*exp(12*I*c), 0)), (x*((exp(8*I*c) + 4*exp(6*I*c) + 6*exp(4*I*c) + 4*exp(2*I*c) + 1)*exp(-6*I*c)/(16*a**2) - 1/(4*a**2)), True)) + x/(4*a**2)","A",0
165,1,165,0,0.411256," ","integrate(cos(d*x+c)**3/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\begin{cases} \frac{\left(- 2560 i a^{6} d^{3} e^{10 i c} e^{i d x} + 7680 i a^{6} d^{3} e^{8 i c} e^{- i d x} + 2560 i a^{6} d^{3} e^{6 i c} e^{- 3 i d x} + 512 i a^{6} d^{3} e^{4 i c} e^{- 5 i d x}\right) e^{- 9 i c}}{20480 a^{8} d^{4}} & \text{for}\: 20480 a^{8} d^{4} e^{9 i c} \neq 0 \\\frac{x \left(e^{6 i c} + 3 e^{4 i c} + 3 e^{2 i c} + 1\right) e^{- 5 i c}}{8 a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-2560*I*a**6*d**3*exp(10*I*c)*exp(I*d*x) + 7680*I*a**6*d**3*exp(8*I*c)*exp(-I*d*x) + 2560*I*a**6*d**3*exp(6*I*c)*exp(-3*I*d*x) + 512*I*a**6*d**3*exp(4*I*c)*exp(-5*I*d*x))*exp(-9*I*c)/(20480*a**8*d**4), Ne(20480*a**8*d**4*exp(9*I*c), 0)), (x*(exp(6*I*c) + 3*exp(4*I*c) + 3*exp(2*I*c) + 1)*exp(-5*I*c)/(8*a**2), True))","A",0
166,1,119,0,0.227778," ","integrate(cos(d*x+c)**2/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\begin{cases} \frac{\left(16 i a^{2} d e^{4 i c} e^{- 2 i d x} + 4 i a^{2} d e^{2 i c} e^{- 4 i d x}\right) e^{- 6 i c}}{64 a^{4} d^{2}} & \text{for}\: 64 a^{4} d^{2} e^{6 i c} \neq 0 \\x \left(\frac{\left(e^{4 i c} + 2 e^{2 i c} + 1\right) e^{- 4 i c}}{4 a^{2}} - \frac{1}{4 a^{2}}\right) & \text{otherwise} \end{cases} + \frac{x}{4 a^{2}}"," ",0,"Piecewise(((16*I*a**2*d*exp(4*I*c)*exp(-2*I*d*x) + 4*I*a**2*d*exp(2*I*c)*exp(-4*I*d*x))*exp(-6*I*c)/(64*a**4*d**2), Ne(64*a**4*d**2*exp(6*I*c), 0)), (x*((exp(4*I*c) + 2*exp(2*I*c) + 1)*exp(-4*I*c)/(4*a**2) - 1/(4*a**2)), True)) + x/(4*a**2)","A",0
167,1,94,0,0.234021," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\begin{cases} \frac{\left(6 i a^{2} d e^{3 i c} e^{- i d x} + 2 i a^{2} d e^{i c} e^{- 3 i d x}\right) e^{- 4 i c}}{12 a^{4} d^{2}} & \text{for}\: 12 a^{4} d^{2} e^{4 i c} \neq 0 \\\frac{x \left(e^{2 i c} + 1\right) e^{- 3 i c}}{2 a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((6*I*a**2*d*exp(3*I*c)*exp(-I*d*x) + 2*I*a**2*d*exp(I*c)*exp(-3*I*d*x))*exp(-4*I*c)/(12*a**4*d**2), Ne(12*a**4*d**2*exp(4*I*c), 0)), (x*(exp(2*I*c) + 1)*exp(-3*I*c)/(2*a**2), True))","A",0
168,1,46,0,0.143009," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\begin{cases} \frac{i e^{- 2 i c} e^{- 2 i d x}}{2 a^{2} d} & \text{for}\: 2 a^{2} d e^{2 i c} \neq 0 \\\frac{x e^{- 2 i c}}{a^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*exp(-2*I*c)*exp(-2*I*d*x)/(2*a**2*d), Ne(2*a**2*d*exp(2*I*c), 0)), (x*exp(-2*I*c)/a**2, True))","A",0
169,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{- \sin^{2}{\left(c + d x \right)} + 2 i \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + \cos^{2}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)/(-sin(c + d*x)**2 + 2*I*sin(c + d*x)*cos(c + d*x) + cos(c + d*x)**2), x)/a**2","F",0
170,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{- \sin^{2}{\left(c + d x \right)} + 2 i \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + \cos^{2}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**2/(-sin(c + d*x)**2 + 2*I*sin(c + d*x)*cos(c + d*x) + cos(c + d*x)**2), x)/a**2","F",0
171,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{- \sin^{2}{\left(c + d x \right)} + 2 i \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + \cos^{2}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**3/(-sin(c + d*x)**2 + 2*I*sin(c + d*x)*cos(c + d*x) + cos(c + d*x)**2), x)/a**2","F",0
172,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec^{4}{\left(c + d x \right)}}{- \sin^{2}{\left(c + d x \right)} + 2 i \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + \cos^{2}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**4/(-sin(c + d*x)**2 + 2*I*sin(c + d*x)*cos(c + d*x) + cos(c + d*x)**2), x)/a**2","F",0
173,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\frac{\int \frac{\sec^{5}{\left(c + d x \right)}}{- \sin^{2}{\left(c + d x \right)} + 2 i \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} + \cos^{2}{\left(c + d x \right)}}\, dx}{a^{2}}"," ",0,"Integral(sec(c + d*x)**5/(-sin(c + d*x)**2 + 2*I*sin(c + d*x)*cos(c + d*x) + cos(c + d*x)**2), x)/a**2","F",0
174,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a*cos(d*x+c)+I*a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,1,228,0,0.444277," ","integrate(cos(d*x+c)**5/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\begin{cases} - \frac{\left(100663296 i a^{12} d^{4} e^{22 i c} e^{2 i d x} - 1006632960 i a^{12} d^{4} e^{18 i c} e^{- 2 i d x} - 503316480 i a^{12} d^{4} e^{16 i c} e^{- 4 i d x} - 167772160 i a^{12} d^{4} e^{14 i c} e^{- 6 i d x} - 25165824 i a^{12} d^{4} e^{12 i c} e^{- 8 i d x}\right) e^{- 20 i c}}{6442450944 a^{15} d^{5}} & \text{for}\: 6442450944 a^{15} d^{5} e^{20 i c} \neq 0 \\x \left(\frac{\left(e^{10 i c} + 5 e^{8 i c} + 10 e^{6 i c} + 10 e^{4 i c} + 5 e^{2 i c} + 1\right) e^{- 8 i c}}{32 a^{3}} - \frac{5}{32 a^{3}}\right) & \text{otherwise} \end{cases} + \frac{5 x}{32 a^{3}}"," ",0,"Piecewise((-(100663296*I*a**12*d**4*exp(22*I*c)*exp(2*I*d*x) - 1006632960*I*a**12*d**4*exp(18*I*c)*exp(-2*I*d*x) - 503316480*I*a**12*d**4*exp(16*I*c)*exp(-4*I*d*x) - 167772160*I*a**12*d**4*exp(14*I*c)*exp(-6*I*d*x) - 25165824*I*a**12*d**4*exp(12*I*c)*exp(-8*I*d*x))*exp(-20*I*c)/(6442450944*a**15*d**5), Ne(6442450944*a**15*d**5*exp(20*I*c), 0)), (x*((exp(10*I*c) + 5*exp(8*I*c) + 10*exp(6*I*c) + 10*exp(4*I*c) + 5*exp(2*I*c) + 1)*exp(-8*I*c)/(32*a**3) - 5/(32*a**3)), True)) + 5*x/(32*a**3)","A",0
176,1,201,0,0.477241," ","integrate(cos(d*x+c)**4/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\begin{cases} - \frac{\left(71680 i a^{12} d^{4} e^{17 i c} e^{i d x} - 286720 i a^{12} d^{4} e^{15 i c} e^{- i d x} - 143360 i a^{12} d^{4} e^{13 i c} e^{- 3 i d x} - 57344 i a^{12} d^{4} e^{11 i c} e^{- 5 i d x} - 10240 i a^{12} d^{4} e^{9 i c} e^{- 7 i d x}\right) e^{- 16 i c}}{1146880 a^{15} d^{5}} & \text{for}\: 1146880 a^{15} d^{5} e^{16 i c} \neq 0 \\\frac{x \left(e^{8 i c} + 4 e^{6 i c} + 6 e^{4 i c} + 4 e^{2 i c} + 1\right) e^{- 7 i c}}{16 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(71680*I*a**12*d**4*exp(17*I*c)*exp(I*d*x) - 286720*I*a**12*d**4*exp(15*I*c)*exp(-I*d*x) - 143360*I*a**12*d**4*exp(13*I*c)*exp(-3*I*d*x) - 57344*I*a**12*d**4*exp(11*I*c)*exp(-5*I*d*x) - 10240*I*a**12*d**4*exp(9*I*c)*exp(-7*I*d*x))*exp(-16*I*c)/(1146880*a**15*d**5), Ne(1146880*a**15*d**5*exp(16*I*c), 0)), (x*(exp(8*I*c) + 4*exp(6*I*c) + 6*exp(4*I*c) + 4*exp(2*I*c) + 1)*exp(-7*I*c)/(16*a**3), True))","A",0
177,1,160,0,0.313169," ","integrate(cos(d*x+c)**3/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\begin{cases} - \frac{\left(- 4608 i a^{6} d^{2} e^{10 i c} e^{- 2 i d x} - 2304 i a^{6} d^{2} e^{8 i c} e^{- 4 i d x} - 512 i a^{6} d^{2} e^{6 i c} e^{- 6 i d x}\right) e^{- 12 i c}}{24576 a^{9} d^{3}} & \text{for}\: 24576 a^{9} d^{3} e^{12 i c} \neq 0 \\x \left(\frac{\left(e^{6 i c} + 3 e^{4 i c} + 3 e^{2 i c} + 1\right) e^{- 6 i c}}{8 a^{3}} - \frac{1}{8 a^{3}}\right) & \text{otherwise} \end{cases} + \frac{x}{8 a^{3}}"," ",0,"Piecewise((-(-4608*I*a**6*d**2*exp(10*I*c)*exp(-2*I*d*x) - 2304*I*a**6*d**2*exp(8*I*c)*exp(-4*I*d*x) - 512*I*a**6*d**2*exp(6*I*c)*exp(-6*I*d*x))*exp(-12*I*c)/(24576*a**9*d**3), Ne(24576*a**9*d**3*exp(12*I*c), 0)), (x*((exp(6*I*c) + 3*exp(4*I*c) + 3*exp(2*I*c) + 1)*exp(-6*I*c)/(8*a**3) - 1/(8*a**3)), True)) + x/(8*a**3)","A",0
178,1,136,0,0.345183," ","integrate(cos(d*x+c)**2/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\begin{cases} - \frac{\left(- 120 i a^{6} d^{2} e^{8 i c} e^{- i d x} - 80 i a^{6} d^{2} e^{6 i c} e^{- 3 i d x} - 24 i a^{6} d^{2} e^{4 i c} e^{- 5 i d x}\right) e^{- 9 i c}}{480 a^{9} d^{3}} & \text{for}\: 480 a^{9} d^{3} e^{9 i c} \neq 0 \\\frac{x \left(e^{4 i c} + 2 e^{2 i c} + 1\right) e^{- 5 i c}}{4 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-(-120*I*a**6*d**2*exp(8*I*c)*exp(-I*d*x) - 80*I*a**6*d**2*exp(6*I*c)*exp(-3*I*d*x) - 24*I*a**6*d**2*exp(4*I*c)*exp(-5*I*d*x))*exp(-9*I*c)/(480*a**9*d**3), Ne(480*a**9*d**3*exp(9*I*c), 0)), (x*(exp(4*I*c) + 2*exp(2*I*c) + 1)*exp(-5*I*c)/(4*a**3), True))","A",0
179,1,97,0,0.221089," ","integrate(cos(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\begin{cases} \frac{\left(8 i a^{3} d e^{4 i c} e^{- 2 i d x} + 4 i a^{3} d e^{2 i c} e^{- 4 i d x}\right) e^{- 6 i c}}{32 a^{6} d^{2}} & \text{for}\: 32 a^{6} d^{2} e^{6 i c} \neq 0 \\\frac{x \left(e^{2 i c} + 1\right) e^{- 4 i c}}{2 a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((8*I*a**3*d*exp(4*I*c)*exp(-2*I*d*x) + 4*I*a**3*d*exp(2*I*c)*exp(-4*I*d*x))*exp(-6*I*c)/(32*a**6*d**2), Ne(32*a**6*d**2*exp(6*I*c), 0)), (x*(exp(2*I*c) + 1)*exp(-4*I*c)/(2*a**3), True))","A",0
180,1,46,0,0.146590," ","integrate(1/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\begin{cases} \frac{i e^{- 3 i c} e^{- 3 i d x}}{3 a^{3} d} & \text{for}\: 3 a^{3} d e^{3 i c} \neq 0 \\\frac{x e^{- 3 i c}}{a^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((I*exp(-3*I*c)*exp(-3*I*d*x)/(3*a**3*d), Ne(3*a**3*d*exp(3*I*c), 0)), (x*exp(-3*I*c)/a**3, True))","A",0
181,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec{\left(c + d x \right)}}{- i \sin^{3}{\left(c + d x \right)} - 3 \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} + 3 i \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \cos^{3}{\left(c + d x \right)}}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)/(-I*sin(c + d*x)**3 - 3*sin(c + d*x)**2*cos(c + d*x) + 3*I*sin(c + d*x)*cos(c + d*x)**2 + cos(c + d*x)**3), x)/a**3","F",0
182,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec^{2}{\left(c + d x \right)}}{- i \sin^{3}{\left(c + d x \right)} - 3 \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} + 3 i \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \cos^{3}{\left(c + d x \right)}}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**2/(-I*sin(c + d*x)**3 - 3*sin(c + d*x)**2*cos(c + d*x) + 3*I*sin(c + d*x)*cos(c + d*x)**2 + cos(c + d*x)**3), x)/a**3","F",0
183,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec^{3}{\left(c + d x \right)}}{- i \sin^{3}{\left(c + d x \right)} - 3 \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} + 3 i \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \cos^{3}{\left(c + d x \right)}}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**3/(-I*sin(c + d*x)**3 - 3*sin(c + d*x)**2*cos(c + d*x) + 3*I*sin(c + d*x)*cos(c + d*x)**2 + cos(c + d*x)**3), x)/a**3","F",0
184,0,0,0,0.000000," ","integrate(sec(d*x+c)**4/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec^{4}{\left(c + d x \right)}}{- i \sin^{3}{\left(c + d x \right)} - 3 \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} + 3 i \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \cos^{3}{\left(c + d x \right)}}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**4/(-I*sin(c + d*x)**3 - 3*sin(c + d*x)**2*cos(c + d*x) + 3*I*sin(c + d*x)*cos(c + d*x)**2 + cos(c + d*x)**3), x)/a**3","F",0
185,0,0,0,0.000000," ","integrate(sec(d*x+c)**5/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\frac{\int \frac{\sec^{5}{\left(c + d x \right)}}{- i \sin^{3}{\left(c + d x \right)} - 3 \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} + 3 i \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} + \cos^{3}{\left(c + d x \right)}}\, dx}{a^{3}}"," ",0,"Integral(sec(c + d*x)**5/(-I*sin(c + d*x)**3 - 3*sin(c + d*x)**2*cos(c + d*x) + 3*I*sin(c + d*x)*cos(c + d*x)**2 + cos(c + d*x)**3), x)/a**3","F",0
186,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6/(a*cos(d*x+c)+I*a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,0,0,0,0.000000," ","integrate((a*cos(d*x+c)+I*a*sin(d*x+c))**n/(cos(d*x+c)**n),x)","\int \left(a \left(i \sin{\left(c + d x \right)} + \cos{\left(c + d x \right)}\right)\right)^{n} \cos^{- n}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(I*sin(c + d*x) + cos(c + d*x)))**n*cos(c + d*x)**(-n), x)","F",0
188,1,17,0,0.134478," ","integrate(1/(sec(x)+tan(x)),x)","\log{\left(\tan{\left(x \right)} + \sec{\left(x \right)} \right)} - \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2}"," ",0,"log(tan(x) + sec(x)) - log(tan(x)**2 + 1)/2","B",0
189,0,0,0,0.000000," ","integrate(sin(x)/(sec(x)+tan(x)),x)","\int \frac{\sin{\left(x \right)}}{\tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(sin(x)/(tan(x) + sec(x)), x)","F",0
190,0,0,0,0.000000," ","integrate(cos(x)/(sec(x)+tan(x)),x)","\int \frac{\cos{\left(x \right)}}{\tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(cos(x)/(tan(x) + sec(x)), x)","F",0
191,0,0,0,0.000000," ","integrate(tan(x)/(sec(x)+tan(x)),x)","\int \frac{\tan{\left(x \right)}}{\tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(tan(x)/(tan(x) + sec(x)), x)","F",0
192,0,0,0,0.000000," ","integrate(cot(x)/(sec(x)+tan(x)),x)","\int \frac{\cot{\left(x \right)}}{\tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(cot(x)/(tan(x) + sec(x)), x)","F",0
193,0,0,0,0.000000," ","integrate(sec(x)/(sec(x)+tan(x)),x)","\int \frac{\sec{\left(x \right)}}{\tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)/(tan(x) + sec(x)), x)","F",0
194,0,0,0,0.000000," ","integrate(csc(x)/(sec(x)+tan(x)),x)","\int \frac{\csc{\left(x \right)}}{\tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)/(tan(x) + sec(x)), x)","F",0
195,1,17,0,0.141560," ","integrate(1/(sec(x)-tan(x)),x)","- \log{\left(- \tan{\left(x \right)} + \sec{\left(x \right)} \right)} + \frac{\log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{2}"," ",0,"-log(-tan(x) + sec(x)) + log(tan(x)**2 + 1)/2","B",0
196,0,0,0,0.000000," ","integrate(sin(x)/(sec(x)-tan(x)),x)","\int \frac{\sin{\left(x \right)}}{- \tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(sin(x)/(-tan(x) + sec(x)), x)","F",0
197,0,0,0,0.000000," ","integrate(cos(x)/(sec(x)-tan(x)),x)","\int \frac{\cos{\left(x \right)}}{- \tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(cos(x)/(-tan(x) + sec(x)), x)","F",0
198,0,0,0,0.000000," ","integrate(tan(x)/(sec(x)-tan(x)),x)","\int \frac{\tan{\left(x \right)}}{- \tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(tan(x)/(-tan(x) + sec(x)), x)","F",0
199,0,0,0,0.000000," ","integrate(cot(x)/(sec(x)-tan(x)),x)","\int \frac{\cot{\left(x \right)}}{- \tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(cot(x)/(-tan(x) + sec(x)), x)","F",0
200,0,0,0,0.000000," ","integrate(sec(x)/(sec(x)-tan(x)),x)","\int \frac{\sec{\left(x \right)}}{- \tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)/(-tan(x) + sec(x)), x)","F",0
201,0,0,0,0.000000," ","integrate(csc(x)/(sec(x)-tan(x)),x)","\int \frac{\csc{\left(x \right)}}{- \tan{\left(x \right)} + \sec{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)/(-tan(x) + sec(x)), x)","F",0
202,1,27,0,2.105761," ","integrate(csc(d*x+c)*(cot(d*x+c)+csc(d*x+c)),x)","\begin{cases} \frac{- \cot{\left(c + d x \right)} - \csc{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \left(\cot{\left(c \right)} + \csc{\left(c \right)}\right) \csc{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise(((-cot(c + d*x) - csc(c + d*x))/d, Ne(d, 0)), (x*(cot(c) + csc(c))*csc(c), True))","A",0
203,0,0,0,0.000000," ","integrate(sin(x)/(cot(x)+csc(x)),x)","\int \frac{\sin{\left(x \right)}}{\cot{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(sin(x)/(cot(x) + csc(x)), x)","F",0
204,0,0,0,0.000000," ","integrate(cos(x)/(cot(x)+csc(x)),x)","\int \frac{\cos{\left(x \right)}}{\cot{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(cos(x)/(cot(x) + csc(x)), x)","F",0
205,0,0,0,0.000000," ","integrate(tan(x)/(cot(x)+csc(x)),x)","\int \frac{\tan{\left(x \right)}}{\cot{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(tan(x)/(cot(x) + csc(x)), x)","F",0
206,0,0,0,0.000000," ","integrate(cot(x)/(cot(x)+csc(x)),x)","\int \frac{\cot{\left(x \right)}}{\cot{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(cot(x)/(cot(x) + csc(x)), x)","F",0
207,0,0,0,0.000000," ","integrate(sec(x)/(cot(x)+csc(x)),x)","\int \frac{\sec{\left(x \right)}}{\cot{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(sec(x)/(cot(x) + csc(x)), x)","F",0
208,0,0,0,0.000000," ","integrate(csc(x)/(cot(x)+csc(x)),x)","\int \frac{\csc{\left(x \right)}}{\cot{\left(x \right)} + \csc{\left(x \right)}}\, dx"," ",0,"Integral(csc(x)/(cot(x) + csc(x)), x)","F",0
209,0,0,0,0.000000," ","integrate(sin(x)/(-cot(x)+csc(x)),x)","- \int \frac{\sin{\left(x \right)}}{\cot{\left(x \right)} - \csc{\left(x \right)}}\, dx"," ",0,"-Integral(sin(x)/(cot(x) - csc(x)), x)","F",0
210,0,0,0,0.000000," ","integrate(cos(x)/(-cot(x)+csc(x)),x)","- \int \frac{\cos{\left(x \right)}}{\cot{\left(x \right)} - \csc{\left(x \right)}}\, dx"," ",0,"-Integral(cos(x)/(cot(x) - csc(x)), x)","F",0
211,0,0,0,0.000000," ","integrate(tan(x)/(-cot(x)+csc(x)),x)","- \int \frac{\tan{\left(x \right)}}{\cot{\left(x \right)} - \csc{\left(x \right)}}\, dx"," ",0,"-Integral(tan(x)/(cot(x) - csc(x)), x)","F",0
212,0,0,0,0.000000," ","integrate(cot(x)/(-cot(x)+csc(x)),x)","- \int \frac{\cot{\left(x \right)}}{\cot{\left(x \right)} - \csc{\left(x \right)}}\, dx"," ",0,"-Integral(cot(x)/(cot(x) - csc(x)), x)","F",0
213,0,0,0,0.000000," ","integrate(sec(x)/(-cot(x)+csc(x)),x)","- \int \frac{\sec{\left(x \right)}}{\cot{\left(x \right)} - \csc{\left(x \right)}}\, dx"," ",0,"-Integral(sec(x)/(cot(x) - csc(x)), x)","F",0
214,0,0,0,0.000000," ","integrate(csc(x)/(-cot(x)+csc(x)),x)","- \int \frac{\csc{\left(x \right)}}{\cot{\left(x \right)} - \csc{\left(x \right)}}\, dx"," ",0,"-Integral(csc(x)/(cot(x) - csc(x)), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(csc(d*x+c)+sin(d*x+c)),x)","\int \frac{1}{\sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(sin(c + d*x) + csc(c + d*x)), x)","F",0
216,0,0,0,0.000000," ","integrate(sin(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\int \frac{\sin{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)/(sin(c + d*x) + csc(c + d*x)), x)","F",0
217,0,0,0,0.000000," ","integrate(cos(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\int \frac{\cos{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)/(sin(c + d*x) + csc(c + d*x)), x)","F",0
218,0,0,0,0.000000," ","integrate(tan(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\int \frac{\tan{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)/(sin(c + d*x) + csc(c + d*x)), x)","F",0
219,0,0,0,0.000000," ","integrate(cot(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\int \frac{\cot{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)/(sin(c + d*x) + csc(c + d*x)), x)","F",0
220,0,0,0,0.000000," ","integrate(sec(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\int \frac{\sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(sin(c + d*x) + csc(c + d*x)), x)","F",0
221,0,0,0,0.000000," ","integrate(csc(d*x+c)/(csc(d*x+c)+sin(d*x+c)),x)","\int \frac{\csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)/(sin(c + d*x) + csc(c + d*x)), x)","F",0
222,0,0,0,0.000000," ","integrate(1/(csc(d*x+c)-sin(d*x+c)),x)","\int \frac{1}{- \sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(-sin(c + d*x) + csc(c + d*x)), x)","F",0
223,0,0,0,0.000000," ","integrate(sin(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\int \frac{\sin{\left(c + d x \right)}}{- \sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)/(-sin(c + d*x) + csc(c + d*x)), x)","F",0
224,0,0,0,0.000000," ","integrate(cos(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\int \frac{\cos{\left(c + d x \right)}}{- \sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)/(-sin(c + d*x) + csc(c + d*x)), x)","F",0
225,0,0,0,0.000000," ","integrate(tan(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\int \frac{\tan{\left(c + d x \right)}}{- \sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(tan(c + d*x)/(-sin(c + d*x) + csc(c + d*x)), x)","F",0
226,0,0,0,0.000000," ","integrate(cot(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\int \frac{\cot{\left(c + d x \right)}}{- \sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(cot(c + d*x)/(-sin(c + d*x) + csc(c + d*x)), x)","F",0
227,0,0,0,0.000000," ","integrate(sec(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\int \frac{\sec{\left(c + d x \right)}}{- \sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(-sin(c + d*x) + csc(c + d*x)), x)","F",0
228,0,0,0,0.000000," ","integrate(csc(d*x+c)/(csc(d*x+c)-sin(d*x+c)),x)","\int \frac{\csc{\left(c + d x \right)}}{- \sin{\left(c + d x \right)} + \csc{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)/(-sin(c + d*x) + csc(c + d*x)), x)","F",0
229,0,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right) \cos^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))*cos(c + d*x)**3, x)","F",0
230,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right) \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))*cos(c + d*x)**2, x)","F",0
231,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right) \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))*cos(c + d*x), x)","F",0
232,1,37,0,0.162835," ","integrate(a*sin(d*x+c)+b*tan(d*x+c),x)","a \left(\begin{cases} - \frac{\cos{\left(c + d x \right)}}{d} & \text{for}\: d \neq 0 \\x \sin{\left(c \right)} & \text{otherwise} \end{cases}\right) + b \left(\begin{cases} \frac{\log{\left(\tan^{2}{\left(c + d x \right)} + 1 \right)}}{2 d} & \text{for}\: d \neq 0 \\x \tan{\left(c \right)} & \text{otherwise} \end{cases}\right)"," ",0,"a*Piecewise((-cos(c + d*x)/d, Ne(d, 0)), (x*sin(c), True)) + b*Piecewise((log(tan(c + d*x)**2 + 1)/(2*d), Ne(d, 0)), (x*tan(c), True))","A",0
233,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))*sec(c + d*x), x)","F",0
234,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right) \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))*sec(c + d*x)**2, x)","F",0
235,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))*sec(c + d*x)**3, x)","F",0
236,0,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2} \cos^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**2*cos(c + d*x)**3, x)","F",0
237,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**2*cos(c + d*x)**2, x)","F",0
238,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**2*cos(c + d*x), x)","F",0
239,0,0,0,0.000000," ","integrate((a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**2, x)","F",0
240,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**2*sec(c + d*x), x)","F",0
241,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**2*sec(c + d*x)**2, x)","F",0
242,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**2*sec(c + d*x)**3, x)","F",0
243,0,0,0,0.000000," ","integrate(cos(d*x+c)**3*(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3} \cos^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**3*cos(c + d*x)**3, x)","F",0
244,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**3*cos(c + d*x)**2, x)","F",0
245,0,0,0,0.000000," ","integrate(cos(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**3*cos(c + d*x), x)","F",0
246,0,0,0,0.000000," ","integrate((a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**3, x)","F",0
247,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**3*sec(c + d*x), x)","F",0
248,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**3*sec(c + d*x)**2, x)","F",0
249,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
250,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
251,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a*sin(c + d*x) + b*tan(c + d*x)), x)","F",0
252,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \frac{\cos{\left(c + d x \right)}}{a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x)), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \frac{1}{a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(1/(a*sin(c + d*x) + b*tan(c + d*x)), x)","F",0
254,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \frac{\sec{\left(c + d x \right)}}{a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x)), x)","F",0
255,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*sin(c + d*x) + b*tan(c + d*x)), x)","F",0
256,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*sin(c + d*x) + b*tan(c + d*x)), x)","F",0
257,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a*sin(c + d*x) + b*tan(c + d*x))**2, x)","F",0
259,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \frac{\cos{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x))**2, x)","F",0
260,0,0,0,0.000000," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**(-2), x)","F",0
261,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x))**2, x)","F",0
262,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*sin(c + d*x) + b*tan(c + d*x))**2, x)","F",0
263,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*sin(c + d*x) + b*tan(c + d*x))**2, x)","F",0
264,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3/(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,0,0,0,0.000000," ","integrate(cos(d*x+c)**2/(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \frac{\cos^{2}{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(cos(c + d*x)**2/(a*sin(c + d*x) + b*tan(c + d*x))**3, x)","F",0
266,0,0,0,0.000000," ","integrate(cos(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \frac{\cos{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(cos(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x))**3, x)","F",0
267,0,0,0,0.000000," ","integrate(1/(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \frac{1}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**(-3), x)","F",0
268,0,0,0,0.000000," ","integrate(sec(d*x+c)/(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \frac{\sec{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)/(a*sin(c + d*x) + b*tan(c + d*x))**3, x)","F",0
269,0,0,0,0.000000," ","integrate(sec(d*x+c)**2/(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \frac{\sec^{2}{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**2/(a*sin(c + d*x) + b*tan(c + d*x))**3, x)","F",0
270,0,0,0,0.000000," ","integrate(sec(d*x+c)**3/(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \frac{\sec^{3}{\left(c + d x \right)}}{\left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sec(c + d*x)**3/(a*sin(c + d*x) + b*tan(c + d*x))**3, x)","F",0
271,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a*sin(d*x+c)+b*tan(d*x+c))**3,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{3} \cos^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**3*cos(c + d*x)**m, x)","F",0
272,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a*sin(d*x+c)+b*tan(d*x+c))**2,x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right)^{2} \cos^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))**2*cos(c + d*x)**m, x)","F",0
273,0,0,0,0.000000," ","integrate(cos(d*x+c)**m*(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \left(a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}\right) \cos^{m}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*sin(c + d*x) + b*tan(c + d*x))*cos(c + d*x)**m, x)","F",0
274,0,0,0,0.000000," ","integrate(cos(d*x+c)**m/(a*sin(d*x+c)+b*tan(d*x+c)),x)","\int \frac{\cos^{m}{\left(c + d x \right)}}{a \sin{\left(c + d x \right)} + b \tan{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**m/(a*sin(c + d*x) + b*tan(c + d*x)), x)","F",0
275,-1,0,0,0.000000," ","integrate(cos(x)*sin(x)/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,-1,0,0,0.000000," ","integrate(cos(x)*sin(x)**2/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
277,-1,0,0,0.000000," ","integrate(cos(x)*sin(x)**3/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
278,-1,0,0,0.000000," ","integrate(cos(x)**2*sin(x)/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
279,-1,0,0,0.000000," ","integrate(cos(x)**2*sin(x)**2/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
280,-1,0,0,0.000000," ","integrate(cos(x)**2*sin(x)**3/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate(cos(x)**3*sin(x)/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate(cos(x)**3*sin(x)**2/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate(cos(x)**3*sin(x)**3/(a*cos(x)+b*sin(x)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,1,991,0,2.101897," ","integrate(cos(x)*sin(x)/(a*cos(x)+b*sin(x))**2,x)","\begin{cases} \tilde{\infty} \log{\left(\sin{\left(x \right)} \right)} & \text{for}\: a = 0 \wedge b = 0 \\- \frac{\log{\left(\cos{\left(x \right)} \right)}}{a^{2}} & \text{for}\: b = 0 \\\frac{2 i x \sin^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} + \frac{4 x \sin{\left(x \right)} \cos{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} - \frac{2 i x \cos^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} - 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} & \text{for}\: a = - i b \\- \frac{2 i x \sin^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} + 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} + \frac{4 x \sin{\left(x \right)} \cos{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} + 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} + \frac{2 i x \cos^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} + 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} + 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} - \frac{\cos^{2}{\left(x \right)}}{8 b^{2} \sin^{2}{\left(x \right)} + 16 i b^{2} \sin{\left(x \right)} \cos{\left(x \right)} - 8 b^{2} \cos^{2}{\left(x \right)}} & \text{for}\: a = i b \\- \frac{a^{3} \log{\left(\frac{a \cos{\left(x \right)}}{b} + \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{a^{5} \cos{\left(x \right)} + a^{4} b \sin{\left(x \right)} + 2 a^{3} b^{2} \cos{\left(x \right)} + 2 a^{2} b^{3} \sin{\left(x \right)} + a b^{4} \cos{\left(x \right)} + b^{5} \sin{\left(x \right)}} + \frac{a^{3} \cos{\left(x \right)}}{a^{5} \cos{\left(x \right)} + a^{4} b \sin{\left(x \right)} + 2 a^{3} b^{2} \cos{\left(x \right)} + 2 a^{2} b^{3} \sin{\left(x \right)} + a b^{4} \cos{\left(x \right)} + b^{5} \sin{\left(x \right)}} + \frac{2 a^{2} b x \cos{\left(x \right)}}{a^{5} \cos{\left(x \right)} + a^{4} b \sin{\left(x \right)} + 2 a^{3} b^{2} \cos{\left(x \right)} + 2 a^{2} b^{3} \sin{\left(x \right)} + a b^{4} \cos{\left(x \right)} + b^{5} \sin{\left(x \right)}} - \frac{a^{2} b \log{\left(\frac{a \cos{\left(x \right)}}{b} + \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{a^{5} \cos{\left(x \right)} + a^{4} b \sin{\left(x \right)} + 2 a^{3} b^{2} \cos{\left(x \right)} + 2 a^{2} b^{3} \sin{\left(x \right)} + a b^{4} \cos{\left(x \right)} + b^{5} \sin{\left(x \right)}} + \frac{2 a b^{2} x \sin{\left(x \right)}}{a^{5} \cos{\left(x \right)} + a^{4} b \sin{\left(x \right)} + 2 a^{3} b^{2} \cos{\left(x \right)} + 2 a^{2} b^{3} \sin{\left(x \right)} + a b^{4} \cos{\left(x \right)} + b^{5} \sin{\left(x \right)}} + \frac{a b^{2} \log{\left(\frac{a \cos{\left(x \right)}}{b} + \sin{\left(x \right)} \right)} \cos{\left(x \right)}}{a^{5} \cos{\left(x \right)} + a^{4} b \sin{\left(x \right)} + 2 a^{3} b^{2} \cos{\left(x \right)} + 2 a^{2} b^{3} \sin{\left(x \right)} + a b^{4} \cos{\left(x \right)} + b^{5} \sin{\left(x \right)}} + \frac{a b^{2} \cos{\left(x \right)}}{a^{5} \cos{\left(x \right)} + a^{4} b \sin{\left(x \right)} + 2 a^{3} b^{2} \cos{\left(x \right)} + 2 a^{2} b^{3} \sin{\left(x \right)} + a b^{4} \cos{\left(x \right)} + b^{5} \sin{\left(x \right)}} + \frac{b^{3} \log{\left(\frac{a \cos{\left(x \right)}}{b} + \sin{\left(x \right)} \right)} \sin{\left(x \right)}}{a^{5} \cos{\left(x \right)} + a^{4} b \sin{\left(x \right)} + 2 a^{3} b^{2} \cos{\left(x \right)} + 2 a^{2} b^{3} \sin{\left(x \right)} + a b^{4} \cos{\left(x \right)} + b^{5} \sin{\left(x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((zoo*log(sin(x)), Eq(a, 0) & Eq(b, 0)), (-log(cos(x))/a**2, Eq(b, 0)), (2*I*x*sin(x)**2/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) + 4*x*sin(x)*cos(x)/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) - 2*I*x*cos(x)**2/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) + sin(x)**2/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) - cos(x)**2/(8*b**2*sin(x)**2 - 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2), Eq(a, -I*b)), (-2*I*x*sin(x)**2/(8*b**2*sin(x)**2 + 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) + 4*x*sin(x)*cos(x)/(8*b**2*sin(x)**2 + 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) + 2*I*x*cos(x)**2/(8*b**2*sin(x)**2 + 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) + sin(x)**2/(8*b**2*sin(x)**2 + 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2) - cos(x)**2/(8*b**2*sin(x)**2 + 16*I*b**2*sin(x)*cos(x) - 8*b**2*cos(x)**2), Eq(a, I*b)), (-a**3*log(a*cos(x)/b + sin(x))*cos(x)/(a**5*cos(x) + a**4*b*sin(x) + 2*a**3*b**2*cos(x) + 2*a**2*b**3*sin(x) + a*b**4*cos(x) + b**5*sin(x)) + a**3*cos(x)/(a**5*cos(x) + a**4*b*sin(x) + 2*a**3*b**2*cos(x) + 2*a**2*b**3*sin(x) + a*b**4*cos(x) + b**5*sin(x)) + 2*a**2*b*x*cos(x)/(a**5*cos(x) + a**4*b*sin(x) + 2*a**3*b**2*cos(x) + 2*a**2*b**3*sin(x) + a*b**4*cos(x) + b**5*sin(x)) - a**2*b*log(a*cos(x)/b + sin(x))*sin(x)/(a**5*cos(x) + a**4*b*sin(x) + 2*a**3*b**2*cos(x) + 2*a**2*b**3*sin(x) + a*b**4*cos(x) + b**5*sin(x)) + 2*a*b**2*x*sin(x)/(a**5*cos(x) + a**4*b*sin(x) + 2*a**3*b**2*cos(x) + 2*a**2*b**3*sin(x) + a*b**4*cos(x) + b**5*sin(x)) + a*b**2*log(a*cos(x)/b + sin(x))*cos(x)/(a**5*cos(x) + a**4*b*sin(x) + 2*a**3*b**2*cos(x) + 2*a**2*b**3*sin(x) + a*b**4*cos(x) + b**5*sin(x)) + a*b**2*cos(x)/(a**5*cos(x) + a**4*b*sin(x) + 2*a**3*b**2*cos(x) + 2*a**2*b**3*sin(x) + a*b**4*cos(x) + b**5*sin(x)) + b**3*log(a*cos(x)/b + sin(x))*sin(x)/(a**5*cos(x) + a**4*b*sin(x) + 2*a**3*b**2*cos(x) + 2*a**2*b**3*sin(x) + a*b**4*cos(x) + b**5*sin(x)), True))","A",0
285,-1,0,0,0.000000," ","integrate(cos(x)*sin(x)**2/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
286,-1,0,0,0.000000," ","integrate(cos(x)*sin(x)**3/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
287,-1,0,0,0.000000," ","integrate(cos(x)**2*sin(x)/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
288,-1,0,0,0.000000," ","integrate(cos(x)**2*sin(x)**2/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate(cos(x)**2*sin(x)**3/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate(cos(x)**3*sin(x)/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate(cos(x)**3*sin(x)**2/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate(cos(x)**3*sin(x)**3/(a*cos(x)+b*sin(x))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,0,0,0,0.000000," ","integrate(tan(x)/(b*cos(x)+a*sin(x)),x)","\int \frac{\tan{\left(x \right)}}{a \sin{\left(x \right)} + b \cos{\left(x \right)}}\, dx"," ",0,"Integral(tan(x)/(a*sin(x) + b*cos(x)), x)","F",0
294,0,0,0,0.000000," ","integrate(cot(x)/(b*cos(x)+a*sin(x)),x)","\int \frac{\cot{\left(x \right)}}{a \sin{\left(x \right)} + b \cos{\left(x \right)}}\, dx"," ",0,"Integral(cot(x)/(a*sin(x) + b*cos(x)), x)","F",0
