1,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(7/2)*(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
2,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(5/2)*(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
3,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
4,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(1/2)*(c-c*sin(f*x+e))**(1/2),x)","\int \sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \cos^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1))*cos(e + f*x)**2, x)","F",0
5,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \cos^{2}{\left(e + f x \right)}}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*cos(e + f*x)**2/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
6,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \cos^{2}{\left(e + f x \right)}}{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*cos(e + f*x)**2/(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
7,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \cos^{2}{\left(e + f x \right)}}{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(a*(sin(e + f*x) + 1))*cos(e + f*x)**2/(-c*(sin(e + f*x) - 1))**(5/2), x)","F",0
8,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
11,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
12,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
13,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
14,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
18,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
25,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
28,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
37,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
38,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
39,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(17/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
45,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}} \cos^{2}{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral((-c*(sin(e + f*x) - 1))**(3/2)*cos(e + f*x)**2/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
46,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \cos^{2}{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)}}\, dx"," ",0,"Integral(sqrt(-c*(sin(e + f*x) - 1))*cos(e + f*x)**2/sqrt(a*(sin(e + f*x) + 1)), x)","F",0
47,0,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\cos^{2}{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral(cos(e + f*x)**2/(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
48,0,0,0,0.000000," ","integrate(cos(f*x+e)**2/(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(1/2),x)","\int \frac{\cos^{2}{\left(e + f x \right)}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(e + f*x)**2/(sqrt(a*(sin(e + f*x) + 1))*(-c*(sin(e + f*x) - 1))**(3/2)), x)","F",0
49,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
51,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}} \cos^{2}{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((-c*(sin(e + f*x) - 1))**(3/2)*cos(e + f*x)**2/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
53,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(3/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \cos^{2}{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(sin(e + f*x) - 1))*cos(e + f*x)**2/(a*(sin(e + f*x) + 1))**(3/2), x)","F",0
54,0,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\cos^{2}{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral(cos(e + f*x)**2/((a*(sin(e + f*x) + 1))**(3/2)*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
55,0,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{\cos^{2}{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(e + f*x)**2/((a*(sin(e + f*x) + 1))**(3/2)*(-c*(sin(e + f*x) - 1))**(3/2)), x)","F",0
56,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(9/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(5/2),x)","\int \frac{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \cos^{2}{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(-c*(sin(e + f*x) - 1))*cos(e + f*x)**2/(a*(sin(e + f*x) + 1))**(5/2), x)","F",0
62,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**2,x)","c^{2} \left(\int \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}\, dx + \int \left(- 2 \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}\right)\, dx + \int \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"c**2*(Integral((a*sin(e + f*x) + a)**m*cos(e + f*x)**2, x) + Integral(-2*(a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2, x) + Integral((a*sin(e + f*x) + a)**m*sin(e + f*x)**2*cos(e + f*x)**2, x))","F",0
68,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e)),x)","- c \left(\int \left(- \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}\right)\, dx + \int \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}\, dx\right)"," ",0,"-c*(Integral(-(a*sin(e + f*x) + a)**m*cos(e + f*x)**2, x) + Integral((a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2, x))","F",0
69,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m,x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \cos^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*cos(e + f*x)**2, x)","F",0
70,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e)),x)","- \frac{\int \frac{\left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{\sin{\left(e + f x \right)} - 1}\, dx}{c}"," ",0,"-Integral((a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(sin(e + f*x) - 1), x)/c","F",0
71,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**2,x)","\frac{\int \frac{\left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{\sin^{2}{\left(e + f x \right)} - 2 \sin{\left(e + f x \right)} + 1}\, dx}{c^{2}}"," ",0,"Integral((a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(sin(e + f*x)**2 - 2*sin(e + f*x) + 1), x)/c**2","F",0
72,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(1/2),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)} \cos^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*sqrt(-c*(sin(e + f*x) - 1))*cos(e + f*x)**2, x)","F",0
76,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \cos^{2}{\left(e + f x \right)}}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*cos(e + f*x)**2/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
77,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(3/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \cos^{2}{\left(e + f x \right)}}{\left(- c \left(\sin{\left(e + f x \right)} - 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*cos(e + f*x)**2/(-c*(sin(e + f*x) - 1))**(3/2), x)","F",0
78,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \cos^{2}{\left(e + f x \right)}}{\sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*cos(e + f*x)**2/sqrt(-c*(sin(e + f*x) - 1)), x)","F",0
80,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+c*sin(f*x+e))**m/(a-a*sin(f*x+e))**(1/2),x)","\int \frac{\left(c \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \cos^{2}{\left(e + f x \right)}}{\sqrt{- a \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((c*(sin(e + f*x) + 1))**m*cos(e + f*x)**2/sqrt(-a*(sin(e + f*x) - 1)), x)","F",0
81,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-5-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
82,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-4-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
83,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-3-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-2-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m/((c-c*sin(f*x+e))**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(7/2)*(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(5/2)*(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
92,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
93,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
94,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
99,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
100,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
117,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
118,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(9/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(13/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**(7/2)/(c-c*sin(f*x+e))**(15/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
127,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
128,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
129,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
130,0,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(1/2)/(c-c*sin(f*x+e))**(1/2),x)","\int \frac{\left(g \cos{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\sqrt{a \left(\sin{\left(e + f x \right)} + 1\right)} \sqrt{- c \left(\sin{\left(e + f x \right)} - 1\right)}}\, dx"," ",0,"Integral((g*cos(e + f*x))**(3/2)/(sqrt(a*(sin(e + f*x) + 1))*sqrt(-c*(sin(e + f*x) - 1))), x)","F",0
131,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
132,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
133,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
134,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
135,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
136,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
137,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
138,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
139,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
140,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
141,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(3/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
142,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(9/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(7/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
144,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(5/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
145,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
146,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c-c*sin(f*x+e))**(1/2)/(a+a*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
147,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
148,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
149,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+a*sin(f*x+e))**(5/2)/(c-c*sin(f*x+e))**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
151,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
152,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
153,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
154,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
155,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
158,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
159,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
160,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
161,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
165,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/(c-c*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
166,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(c+c*sin(f*x+e))**m/(a-a*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
167,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-3-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
168,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-2-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
169,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
170,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m/((c-c*sin(f*x+e))**m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
171,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(1-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(2-m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(1-2*m)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-1+m),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5-2*m)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3-2*m)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(1-2*m)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-2*m)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-3-2*m)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-5-2*m)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-2*m)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-m-n)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(3+n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
183,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-m-n)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(2+n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
184,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-m-n)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(1+n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
185,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-m-n)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
186,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-m-n)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-1+n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
187,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-m-n)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-2+n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
188,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-m-n)*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**(-3+n),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
189,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))**p*(a+a*sin(f*x+e))**m*(c-c*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
190,1,42,0,1.311481," ","integrate(cos(d*x+c)*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{a \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{a \sin^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{2}{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sin(c + d*x)**4/(4*d) + a*sin(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**2*cos(c), True))","A",0
191,1,41,0,0.564718," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a \sin^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sin(c + d*x)**3/(3*d) + a*sin(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)*cos(c), True))","A",0
192,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c)),x)","a \left(\int \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)*csc(c + d*x), x) + Integral(sin(c + d*x)*cos(c + d*x)*csc(c + d*x), x))","F",0
193,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2*(a+a*sin(d*x+c)),x)","a \left(\int \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)*csc(c + d*x)**2, x) + Integral(sin(c + d*x)*cos(c + d*x)*csc(c + d*x)**2, x))","F",0
194,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3*(a+a*sin(d*x+c)),x)","a \left(\int \cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)*csc(c + d*x)**3, x) + Integral(sin(c + d*x)*cos(c + d*x)*csc(c + d*x)**3, x))","F",0
195,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**4*(a+a*sin(d*x+c)),x)","a \left(\int \cos{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)*csc(c + d*x)**4, x) + Integral(sin(c + d*x)*cos(c + d*x)*csc(c + d*x)**4, x))","F",0
196,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
197,1,63,0,2.602961," ","integrate(cos(d*x+c)*sin(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{a^{2} \sin^{4}{\left(c + d x \right)}}{2 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{2}{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sin(c + d*x)**5/(5*d) + a**2*sin(c + d*x)**4/(2*d) + a**2*sin(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**2*cos(c), True))","A",0
198,1,63,0,1.275416," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{2 a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{2} \sin^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*sin(c + d*x)**4/(4*d) + 2*a**2*sin(c + d*x)**3/(3*d) + a**2*sin(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)*cos(c), True))","A",0
199,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 2 \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(cos(c + d*x)*csc(c + d*x), x) + Integral(2*sin(c + d*x)*cos(c + d*x)*csc(c + d*x), x) + Integral(sin(c + d*x)**2*cos(c + d*x)*csc(c + d*x), x))","F",0
200,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int 2 \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(cos(c + d*x)*csc(c + d*x)**2, x) + Integral(2*sin(c + d*x)*cos(c + d*x)*csc(c + d*x)**2, x) + Integral(sin(c + d*x)**2*cos(c + d*x)*csc(c + d*x)**2, x))","F",0
201,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int \cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx + \int 2 \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(cos(c + d*x)*csc(c + d*x)**3, x) + Integral(2*sin(c + d*x)*cos(c + d*x)*csc(c + d*x)**3, x) + Integral(sin(c + d*x)**2*cos(c + d*x)*csc(c + d*x)**3, x))","F",0
202,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
203,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
204,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**6*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
205,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**7*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
206,1,80,0,8.627660," ","integrate(cos(d*x+c)*sin(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} \sin^{7}{\left(c + d x \right)}}{7 d} + \frac{a^{3} \sin^{6}{\left(c + d x \right)}}{2 d} + \frac{3 a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{a^{3} \sin^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{3}{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*sin(c + d*x)**7/(7*d) + a**3*sin(c + d*x)**6/(2*d) + 3*a**3*sin(c + d*x)**5/(5*d) + a**3*sin(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**3*cos(c), True))","A",0
207,1,82,0,5.138562," ","integrate(cos(d*x+c)*sin(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} \sin^{6}{\left(c + d x \right)}}{6 d} + \frac{3 a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{3 a^{3} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{2}{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*sin(c + d*x)**6/(6*d) + 3*a**3*sin(c + d*x)**5/(5*d) + 3*a**3*sin(c + d*x)**4/(4*d) + a**3*sin(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**2*cos(c), True))","A",0
208,1,76,0,2.553162," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{3 a^{3} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{a^{3} \sin^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*sin(c + d*x)**5/(5*d) + 3*a**3*sin(c + d*x)**4/(4*d) + a**3*sin(c + d*x)**3/d + a**3*sin(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)*cos(c), True))","A",0
209,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))**3,x)","a^{3} \left(\int \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 3 \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 3 \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(cos(c + d*x)*csc(c + d*x), x) + Integral(3*sin(c + d*x)*cos(c + d*x)*csc(c + d*x), x) + Integral(3*sin(c + d*x)**2*cos(c + d*x)*csc(c + d*x), x) + Integral(sin(c + d*x)**3*cos(c + d*x)*csc(c + d*x), x))","F",0
210,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","a^{3} \left(\int \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int 3 \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int 3 \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(cos(c + d*x)*csc(c + d*x)**2, x) + Integral(3*sin(c + d*x)*cos(c + d*x)*csc(c + d*x)**2, x) + Integral(3*sin(c + d*x)**2*cos(c + d*x)*csc(c + d*x)**2, x) + Integral(sin(c + d*x)**3*cos(c + d*x)*csc(c + d*x)**2, x))","F",0
211,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
212,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
213,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
214,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**6*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
215,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**7*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**8*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,1,97,0,19.922875," ","integrate(cos(d*x+c)*sin(d*x+c)**4*(a+a*sin(d*x+c))**4,x)","\begin{cases} \frac{a^{4} \sin^{9}{\left(c + d x \right)}}{9 d} + \frac{a^{4} \sin^{8}{\left(c + d x \right)}}{2 d} + \frac{6 a^{4} \sin^{7}{\left(c + d x \right)}}{7 d} + \frac{2 a^{4} \sin^{6}{\left(c + d x \right)}}{3 d} + \frac{a^{4} \sin^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{4} \sin^{4}{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*sin(c + d*x)**9/(9*d) + a**4*sin(c + d*x)**8/(2*d) + 6*a**4*sin(c + d*x)**7/(7*d) + 2*a**4*sin(c + d*x)**6/(3*d) + a**4*sin(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)**4*sin(c)**4*cos(c), True))","A",0
218,1,95,0,11.721926," ","integrate(cos(d*x+c)*sin(d*x+c)**3*(a+a*sin(d*x+c))**4,x)","\begin{cases} \frac{a^{4} \sin^{8}{\left(c + d x \right)}}{8 d} + \frac{4 a^{4} \sin^{7}{\left(c + d x \right)}}{7 d} + \frac{a^{4} \sin^{6}{\left(c + d x \right)}}{d} + \frac{4 a^{4} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{a^{4} \sin^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{4} \sin^{3}{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*sin(c + d*x)**8/(8*d) + 4*a**4*sin(c + d*x)**7/(7*d) + a**4*sin(c + d*x)**6/d + 4*a**4*sin(c + d*x)**5/(5*d) + a**4*sin(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*sin(c) + a)**4*sin(c)**3*cos(c), True))","A",0
219,1,95,0,7.239551," ","integrate(cos(d*x+c)*sin(d*x+c)**2*(a+a*sin(d*x+c))**4,x)","\begin{cases} \frac{a^{4} \sin^{7}{\left(c + d x \right)}}{7 d} + \frac{2 a^{4} \sin^{6}{\left(c + d x \right)}}{3 d} + \frac{6 a^{4} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{a^{4} \sin^{4}{\left(c + d x \right)}}{d} + \frac{a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{4} \sin^{2}{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*sin(c + d*x)**7/(7*d) + 2*a**4*sin(c + d*x)**6/(3*d) + 6*a**4*sin(c + d*x)**5/(5*d) + a**4*sin(c + d*x)**4/d + a**4*sin(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**4*sin(c)**2*cos(c), True))","A",0
220,1,97,0,3.872088," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))**4,x)","\begin{cases} \frac{a^{4} \sin^{6}{\left(c + d x \right)}}{6 d} + \frac{4 a^{4} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{3 a^{4} \sin^{4}{\left(c + d x \right)}}{2 d} + \frac{4 a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{a^{4} \sin^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{4} \sin{\left(c \right)} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*sin(c + d*x)**6/(6*d) + 4*a**4*sin(c + d*x)**5/(5*d) + 3*a**4*sin(c + d*x)**4/(2*d) + 4*a**4*sin(c + d*x)**3/(3*d) + a**4*sin(c + d*x)**2/(2*d), Ne(d, 0)), (x*(a*sin(c) + a)**4*sin(c)*cos(c), True))","A",0
221,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))**4,x)","a^{4} \left(\int \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 4 \sin{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 6 \sin^{2}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 4 \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin^{4}{\left(c + d x \right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a**4*(Integral(cos(c + d*x)*csc(c + d*x), x) + Integral(4*sin(c + d*x)*cos(c + d*x)*csc(c + d*x), x) + Integral(6*sin(c + d*x)**2*cos(c + d*x)*csc(c + d*x), x) + Integral(4*sin(c + d*x)**3*cos(c + d*x)*csc(c + d*x), x) + Integral(sin(c + d*x)**4*cos(c + d*x)*csc(c + d*x), x))","F",0
222,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
223,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
224,1,80,0,3.200507," ","integrate(cos(d*x+c)*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} + \frac{\sin^{4}{\left(c + d x \right)}}{4 a d} - \frac{\sin^{3}{\left(c + d x \right)}}{3 a d} + \frac{\sin^{2}{\left(c + d x \right)}}{2 a d} - \frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)} \cos{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(c + d*x) + 1)/(a*d) + sin(c + d*x)**4/(4*a*d) - sin(c + d*x)**3/(3*a*d) + sin(c + d*x)**2/(2*a*d) - sin(c + d*x)/(a*d), Ne(d, 0)), (x*sin(c)**4*cos(c)/(a*sin(c) + a), True))","A",0
225,1,66,0,1.960058," ","integrate(cos(d*x+c)*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} + \frac{\sin^{3}{\left(c + d x \right)}}{3 a d} - \frac{\sin^{2}{\left(c + d x \right)}}{2 a d} + \frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(sin(c + d*x) + 1)/(a*d) + sin(c + d*x)**3/(3*a*d) - sin(c + d*x)**2/(2*a*d) + sin(c + d*x)/(a*d), Ne(d, 0)), (x*sin(c)**3*cos(c)/(a*sin(c) + a), True))","A",0
226,1,53,0,1.110350," ","integrate(cos(d*x+c)*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} + \frac{\sin^{2}{\left(c + d x \right)}}{2 a d} - \frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(c + d*x) + 1)/(a*d) + sin(c + d*x)**2/(2*a*d) - sin(c + d*x)/(a*d), Ne(d, 0)), (x*sin(c)**2*cos(c)/(a*sin(c) + a), True))","A",0
227,1,37,0,0.683803," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} + \frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-log(sin(c + d*x) + 1)/(a*d) + sin(c + d*x)/(a*d), Ne(d, 0)), (x*sin(c)*cos(c)/(a*sin(c) + a), True))","A",0
228,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
229,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
230,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**3/(sin(c + d*x) + 1), x)/a","F",0
231,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**4/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**4/(sin(c + d*x) + 1), x)/a","F",0
232,1,201,0,4.339844," ","integrate(cos(d*x+c)*sin(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} + \frac{\sin^{4}{\left(c + d x \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} - \frac{2 \sin^{3}{\left(c + d x \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} + \frac{6 \sin^{2}{\left(c + d x \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} - \frac{12}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*log(sin(c + d*x) + 1)*sin(c + d*x)/(3*a**2*d*sin(c + d*x) + 3*a**2*d) - 12*log(sin(c + d*x) + 1)/(3*a**2*d*sin(c + d*x) + 3*a**2*d) + sin(c + d*x)**4/(3*a**2*d*sin(c + d*x) + 3*a**2*d) - 2*sin(c + d*x)**3/(3*a**2*d*sin(c + d*x) + 3*a**2*d) + 6*sin(c + d*x)**2/(3*a**2*d*sin(c + d*x) + 3*a**2*d) - 12/(3*a**2*d*sin(c + d*x) + 3*a**2*d), Ne(d, 0)), (x*sin(c)**4*cos(c)/(a*sin(c) + a)**2, True))","A",0
233,1,170,0,2.807682," ","integrate(cos(d*x+c)*sin(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} + \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} + \frac{\sin^{3}{\left(c + d x \right)}}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} - \frac{3 \sin^{2}{\left(c + d x \right)}}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} + \frac{6}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**2*d*sin(c + d*x) + 2*a**2*d) + 6*log(sin(c + d*x) + 1)/(2*a**2*d*sin(c + d*x) + 2*a**2*d) + sin(c + d*x)**3/(2*a**2*d*sin(c + d*x) + 2*a**2*d) - 3*sin(c + d*x)**2/(2*a**2*d*sin(c + d*x) + 2*a**2*d) + 6/(2*a**2*d*sin(c + d*x) + 2*a**2*d), Ne(d, 0)), (x*sin(c)**3*cos(c)/(a*sin(c) + a)**2, True))","A",0
234,1,126,0,1.451625," ","integrate(cos(d*x+c)*sin(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} - \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{\sin^{2}{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} - \frac{2}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*log(sin(c + d*x) + 1)*sin(c + d*x)/(a**2*d*sin(c + d*x) + a**2*d) - 2*log(sin(c + d*x) + 1)/(a**2*d*sin(c + d*x) + a**2*d) + sin(c + d*x)**2/(a**2*d*sin(c + d*x) + a**2*d) - 2/(a**2*d*sin(c + d*x) + a**2*d), Ne(d, 0)), (x*sin(c)**2*cos(c)/(a*sin(c) + a)**2, True))","A",0
235,1,95,0,1.044198," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{1}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((log(sin(c + d*x) + 1)*sin(c + d*x)/(a**2*d*sin(c + d*x) + a**2*d) + log(sin(c + d*x) + 1)/(a**2*d*sin(c + d*x) + a**2*d) + 1/(a**2*d*sin(c + d*x) + a**2*d), Ne(d, 0)), (x*sin(c)*cos(c)/(a*sin(c) + a)**2, True))","A",0
236,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
237,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
238,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**3/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
239,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**4/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
240,1,394,0,8.058299," ","integrate(cos(d*x+c)*sin(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{60 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{6 a^{3} d \sin^{2}{\left(c + d x \right)} + 12 a^{3} d \sin{\left(c + d x \right)} + 6 a^{3} d} - \frac{120 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{6 a^{3} d \sin^{2}{\left(c + d x \right)} + 12 a^{3} d \sin{\left(c + d x \right)} + 6 a^{3} d} - \frac{60 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{6 a^{3} d \sin^{2}{\left(c + d x \right)} + 12 a^{3} d \sin{\left(c + d x \right)} + 6 a^{3} d} + \frac{2 \sin^{5}{\left(c + d x \right)}}{6 a^{3} d \sin^{2}{\left(c + d x \right)} + 12 a^{3} d \sin{\left(c + d x \right)} + 6 a^{3} d} - \frac{5 \sin^{4}{\left(c + d x \right)}}{6 a^{3} d \sin^{2}{\left(c + d x \right)} + 12 a^{3} d \sin{\left(c + d x \right)} + 6 a^{3} d} + \frac{20 \sin^{3}{\left(c + d x \right)}}{6 a^{3} d \sin^{2}{\left(c + d x \right)} + 12 a^{3} d \sin{\left(c + d x \right)} + 6 a^{3} d} - \frac{120 \sin{\left(c + d x \right)}}{6 a^{3} d \sin^{2}{\left(c + d x \right)} + 12 a^{3} d \sin{\left(c + d x \right)} + 6 a^{3} d} - \frac{90}{6 a^{3} d \sin^{2}{\left(c + d x \right)} + 12 a^{3} d \sin{\left(c + d x \right)} + 6 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{5}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-60*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(6*a**3*d*sin(c + d*x)**2 + 12*a**3*d*sin(c + d*x) + 6*a**3*d) - 120*log(sin(c + d*x) + 1)*sin(c + d*x)/(6*a**3*d*sin(c + d*x)**2 + 12*a**3*d*sin(c + d*x) + 6*a**3*d) - 60*log(sin(c + d*x) + 1)/(6*a**3*d*sin(c + d*x)**2 + 12*a**3*d*sin(c + d*x) + 6*a**3*d) + 2*sin(c + d*x)**5/(6*a**3*d*sin(c + d*x)**2 + 12*a**3*d*sin(c + d*x) + 6*a**3*d) - 5*sin(c + d*x)**4/(6*a**3*d*sin(c + d*x)**2 + 12*a**3*d*sin(c + d*x) + 6*a**3*d) + 20*sin(c + d*x)**3/(6*a**3*d*sin(c + d*x)**2 + 12*a**3*d*sin(c + d*x) + 6*a**3*d) - 120*sin(c + d*x)/(6*a**3*d*sin(c + d*x)**2 + 12*a**3*d*sin(c + d*x) + 6*a**3*d) - 90/(6*a**3*d*sin(c + d*x)**2 + 12*a**3*d*sin(c + d*x) + 6*a**3*d), Ne(d, 0)), (x*sin(c)**5*cos(c)/(a*sin(c) + a)**3, True))","A",0
241,1,347,0,5.468270," ","integrate(cos(d*x+c)*sin(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{24 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{\sin^{4}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{4 \sin^{3}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{24 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{18}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((12*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 24*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 12*log(sin(c + d*x) + 1)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + sin(c + d*x)**4/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 4*sin(c + d*x)**3/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 24*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 18/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Ne(d, 0)), (x*sin(c)**4*cos(c)/(a*sin(c) + a)**3, True))","A",0
242,1,303,0,3.055952," ","integrate(cos(d*x+c)*sin(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{2 \sin^{3}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{12 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{9}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-6*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 12*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 6*log(sin(c + d*x) + 1)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 2*sin(c + d*x)**3/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 12*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 9/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Ne(d, 0)), (x*sin(c)**3*cos(c)/(a*sin(c) + a)**3, True))","A",0
243,1,257,0,1.932568," ","integrate(cos(d*x+c)*sin(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{4 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{4 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{3}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 4*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 2*log(sin(c + d*x) + 1)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 4*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 3/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Ne(d, 0)), (x*sin(c)**2*cos(c)/(a*sin(c) + a)**3, True))","A",0
244,1,99,0,1.700763," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{2 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{1}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-2*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 1/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Ne(d, 0)), (x*sin(c)*cos(c)/(a*sin(c) + a)**3, True))","A",0
245,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
246,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
247,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**3/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
248,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**4/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
249,1,588,0,10.053792," ","integrate(cos(d*x+c)*sin(d*x+c)**5/(a+a*sin(d*x+c))**4,x)","\begin{cases} \frac{60 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{3}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{180 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{180 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{60 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{3 \sin^{5}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} - \frac{15 \sin^{4}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{180 \sin^{2}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{270 \sin{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{110}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{5}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((60*log(sin(c + d*x) + 1)*sin(c + d*x)**3/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 180*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 180*log(sin(c + d*x) + 1)*sin(c + d*x)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 60*log(sin(c + d*x) + 1)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 3*sin(c + d*x)**5/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) - 15*sin(c + d*x)**4/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 180*sin(c + d*x)**2/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 270*sin(c + d*x)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 110/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d), Ne(d, 0)), (x*sin(c)**5*cos(c)/(a*sin(c) + a)**4, True))","A",0
250,1,527,0,5.565639," ","integrate(cos(d*x+c)*sin(d*x+c)**4/(a+a*sin(d*x+c))**4,x)","\begin{cases} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{3}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{36 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{36 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} + \frac{3 \sin^{4}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{36 \sin^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{54 \sin{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{22}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-12*log(sin(c + d*x) + 1)*sin(c + d*x)**3/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 36*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 36*log(sin(c + d*x) + 1)*sin(c + d*x)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 12*log(sin(c + d*x) + 1)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) + 3*sin(c + d*x)**4/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 36*sin(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 54*sin(c + d*x)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 22/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d), Ne(d, 0)), (x*sin(c)**4*cos(c)/(a*sin(c) + a)**4, True))","A",0
251,1,466,0,3.475744," ","integrate(cos(d*x+c)*sin(d*x+c)**3/(a+a*sin(d*x+c))**4,x)","\begin{cases} \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{3}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{18 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{18 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{18 \sin^{2}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{27 \sin{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{11}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*log(sin(c + d*x) + 1)*sin(c + d*x)**3/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 18*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 18*log(sin(c + d*x) + 1)*sin(c + d*x)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 6*log(sin(c + d*x) + 1)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 18*sin(c + d*x)**2/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 27*sin(c + d*x)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 11/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d), Ne(d, 0)), (x*sin(c)**3*cos(c)/(a*sin(c) + a)**4, True))","A",0
252,1,192,0,3.264234," ","integrate(cos(d*x+c)*sin(d*x+c)**2/(a+a*sin(d*x+c))**4,x)","\begin{cases} - \frac{3 \sin^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{3 \sin{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{1}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*sin(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 3*sin(c + d*x)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 1/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d), Ne(d, 0)), (x*sin(c)**2*cos(c)/(a*sin(c) + a)**4, True))","A",0
253,1,129,0,3.494581," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))**4,x)","\begin{cases} - \frac{3 \sin{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} - \frac{1}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{4}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*sin(c + d*x)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) - 1/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d), Ne(d, 0)), (x*sin(c)*cos(c)/(a*sin(c) + a)**4, True))","A",0
254,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))**4,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin^{4}{\left(c + d x \right)} + 4 \sin^{3}{\left(c + d x \right)} + 6 \sin^{2}{\left(c + d x \right)} + 4 \sin{\left(c + d x \right)} + 1}\, dx}{a^{4}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)/(sin(c + d*x)**4 + 4*sin(c + d*x)**3 + 6*sin(c + d*x)**2 + 4*sin(c + d*x) + 1), x)/a**4","F",0
255,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2/(a+a*sin(d*x+c))**4,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin^{4}{\left(c + d x \right)} + 4 \sin^{3}{\left(c + d x \right)} + 6 \sin^{2}{\left(c + d x \right)} + 4 \sin{\left(c + d x \right)} + 1}\, dx}{a^{4}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**2/(sin(c + d*x)**4 + 4*sin(c + d*x)**3 + 6*sin(c + d*x)**2 + 4*sin(c + d*x) + 1), x)/a**4","F",0
256,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3/(a+a*sin(d*x+c))**4,x)","\frac{\int \frac{\cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin^{4}{\left(c + d x \right)} + 4 \sin^{3}{\left(c + d x \right)} + 6 \sin^{2}{\left(c + d x \right)} + 4 \sin{\left(c + d x \right)} + 1}\, dx}{a^{4}}"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**3/(sin(c + d*x)**4 + 4*sin(c + d*x)**3 + 6*sin(c + d*x)**2 + 4*sin(c + d*x) + 1), x)/a**4","F",0
257,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*cos(c + d*x)*csc(c + d*x), x)","F",0
258,1,1833,0,61.694105," ","integrate(cos(d*x+c)*sin(d*x+c)**n*(a+a*sin(d*x+c))**4,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{4} \sin^{n}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{a^{4} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} - \frac{4 a^{4}}{d \sin{\left(c + d x \right)}} - \frac{3 a^{4}}{d \sin^{2}{\left(c + d x \right)}} - \frac{4 a^{4}}{3 d \sin^{3}{\left(c + d x \right)}} - \frac{a^{4}}{4 d \sin^{4}{\left(c + d x \right)}} & \text{for}\: n = -5 \\\frac{4 a^{4} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{4} \sin{\left(c + d x \right)}}{d} - \frac{6 a^{4}}{d \sin{\left(c + d x \right)}} - \frac{2 a^{4}}{d \sin^{2}{\left(c + d x \right)}} - \frac{a^{4}}{3 d \sin^{3}{\left(c + d x \right)}} & \text{for}\: n = -4 \\\frac{6 a^{4} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{4} \sin^{2}{\left(c + d x \right)}}{2 d} + \frac{4 a^{4} \sin{\left(c + d x \right)}}{d} - \frac{4 a^{4}}{d \sin{\left(c + d x \right)}} - \frac{a^{4}}{2 d \sin^{2}{\left(c + d x \right)}} & \text{for}\: n = -3 \\\frac{4 a^{4} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{2 a^{4} \sin^{2}{\left(c + d x \right)}}{d} + \frac{6 a^{4} \sin{\left(c + d x \right)}}{d} - \frac{a^{4}}{d \sin{\left(c + d x \right)}} & \text{for}\: n = -2 \\\frac{a^{4} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{4} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{4 a^{4} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{3 a^{4} \sin^{2}{\left(c + d x \right)}}{d} + \frac{4 a^{4} \sin{\left(c + d x \right)}}{d} & \text{for}\: n = -1 \\\frac{a^{4} n^{4} \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{4 a^{4} n^{4} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{6 a^{4} n^{4} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{4 a^{4} n^{4} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{a^{4} n^{4} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{10 a^{4} n^{3} \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{44 a^{4} n^{3} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{72 a^{4} n^{3} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{52 a^{4} n^{3} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{14 a^{4} n^{3} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{35 a^{4} n^{2} \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{164 a^{4} n^{2} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{294 a^{4} n^{2} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{236 a^{4} n^{2} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{71 a^{4} n^{2} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{50 a^{4} n \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{244 a^{4} n \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{468 a^{4} n \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{428 a^{4} n \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{154 a^{4} n \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{24 a^{4} \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{120 a^{4} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{240 a^{4} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{240 a^{4} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} + \frac{120 a^{4} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{5} + 15 d n^{4} + 85 d n^{3} + 225 d n^{2} + 274 d n + 120 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**4*sin(c)**n*cos(c), Eq(d, 0)), (a**4*log(sin(c + d*x))/d - 4*a**4/(d*sin(c + d*x)) - 3*a**4/(d*sin(c + d*x)**2) - 4*a**4/(3*d*sin(c + d*x)**3) - a**4/(4*d*sin(c + d*x)**4), Eq(n, -5)), (4*a**4*log(sin(c + d*x))/d + a**4*sin(c + d*x)/d - 6*a**4/(d*sin(c + d*x)) - 2*a**4/(d*sin(c + d*x)**2) - a**4/(3*d*sin(c + d*x)**3), Eq(n, -4)), (6*a**4*log(sin(c + d*x))/d + a**4*sin(c + d*x)**2/(2*d) + 4*a**4*sin(c + d*x)/d - 4*a**4/(d*sin(c + d*x)) - a**4/(2*d*sin(c + d*x)**2), Eq(n, -3)), (4*a**4*log(sin(c + d*x))/d + a**4*sin(c + d*x)**3/(3*d) + 2*a**4*sin(c + d*x)**2/d + 6*a**4*sin(c + d*x)/d - a**4/(d*sin(c + d*x)), Eq(n, -2)), (a**4*log(sin(c + d*x))/d + a**4*sin(c + d*x)**4/(4*d) + 4*a**4*sin(c + d*x)**3/(3*d) + 3*a**4*sin(c + d*x)**2/d + 4*a**4*sin(c + d*x)/d, Eq(n, -1)), (a**4*n**4*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 4*a**4*n**4*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 6*a**4*n**4*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 4*a**4*n**4*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + a**4*n**4*sin(c + d*x)*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 10*a**4*n**3*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 44*a**4*n**3*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 72*a**4*n**3*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 52*a**4*n**3*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 14*a**4*n**3*sin(c + d*x)*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 35*a**4*n**2*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 164*a**4*n**2*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 294*a**4*n**2*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 236*a**4*n**2*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 71*a**4*n**2*sin(c + d*x)*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 50*a**4*n*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 244*a**4*n*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 468*a**4*n*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 428*a**4*n*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 154*a**4*n*sin(c + d*x)*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 24*a**4*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 120*a**4*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 240*a**4*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 240*a**4*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d) + 120*a**4*sin(c + d*x)*sin(c + d*x)**n/(d*n**5 + 15*d*n**4 + 85*d*n**3 + 225*d*n**2 + 274*d*n + 120*d), True))","A",0
259,1,1061,0,27.521014," ","integrate(cos(d*x+c)*sin(d*x+c)**n*(a+a*sin(d*x+c))**3,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{n}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{a^{3} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} - \frac{3 a^{3}}{d \sin{\left(c + d x \right)}} - \frac{3 a^{3}}{2 d \sin^{2}{\left(c + d x \right)}} - \frac{a^{3}}{3 d \sin^{3}{\left(c + d x \right)}} & \text{for}\: n = -4 \\\frac{3 a^{3} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{3} \sin{\left(c + d x \right)}}{d} - \frac{3 a^{3}}{d \sin{\left(c + d x \right)}} - \frac{a^{3}}{2 d \sin^{2}{\left(c + d x \right)}} & \text{for}\: n = -3 \\\frac{3 a^{3} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{3} \sin^{2}{\left(c + d x \right)}}{2 d} + \frac{3 a^{3} \sin{\left(c + d x \right)}}{d} - \frac{a^{3}}{d \sin{\left(c + d x \right)}} & \text{for}\: n = -2 \\\frac{a^{3} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{3 a^{3} \sin^{2}{\left(c + d x \right)}}{2 d} + \frac{3 a^{3} \sin{\left(c + d x \right)}}{d} & \text{for}\: n = -1 \\\frac{a^{3} n^{3} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{3 a^{3} n^{3} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{3 a^{3} n^{3} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{a^{3} n^{3} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{6 a^{3} n^{2} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{21 a^{3} n^{2} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{24 a^{3} n^{2} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{9 a^{3} n^{2} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{11 a^{3} n \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{42 a^{3} n \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{57 a^{3} n \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{26 a^{3} n \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{6 a^{3} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{24 a^{3} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{36 a^{3} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} + \frac{24 a^{3} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{4} + 10 d n^{3} + 35 d n^{2} + 50 d n + 24 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**3*sin(c)**n*cos(c), Eq(d, 0)), (a**3*log(sin(c + d*x))/d - 3*a**3/(d*sin(c + d*x)) - 3*a**3/(2*d*sin(c + d*x)**2) - a**3/(3*d*sin(c + d*x)**3), Eq(n, -4)), (3*a**3*log(sin(c + d*x))/d + a**3*sin(c + d*x)/d - 3*a**3/(d*sin(c + d*x)) - a**3/(2*d*sin(c + d*x)**2), Eq(n, -3)), (3*a**3*log(sin(c + d*x))/d + a**3*sin(c + d*x)**2/(2*d) + 3*a**3*sin(c + d*x)/d - a**3/(d*sin(c + d*x)), Eq(n, -2)), (a**3*log(sin(c + d*x))/d + a**3*sin(c + d*x)**3/(3*d) + 3*a**3*sin(c + d*x)**2/(2*d) + 3*a**3*sin(c + d*x)/d, Eq(n, -1)), (a**3*n**3*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 3*a**3*n**3*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 3*a**3*n**3*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + a**3*n**3*sin(c + d*x)*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 6*a**3*n**2*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 21*a**3*n**2*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 24*a**3*n**2*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 9*a**3*n**2*sin(c + d*x)*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 11*a**3*n*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 42*a**3*n*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 57*a**3*n*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 26*a**3*n*sin(c + d*x)*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 6*a**3*sin(c + d*x)**4*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 24*a**3*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 36*a**3*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d) + 24*a**3*sin(c + d*x)*sin(c + d*x)**n/(d*n**4 + 10*d*n**3 + 35*d*n**2 + 50*d*n + 24*d), True))","A",0
260,1,530,0,12.063730," ","integrate(cos(d*x+c)*sin(d*x+c)**n*(a+a*sin(d*x+c))**2,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{n}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{a^{2} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} - \frac{2 a^{2}}{d \sin{\left(c + d x \right)}} - \frac{a^{2}}{2 d \sin^{2}{\left(c + d x \right)}} & \text{for}\: n = -3 \\\frac{2 a^{2} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{2} \sin{\left(c + d x \right)}}{d} - \frac{a^{2}}{d \sin{\left(c + d x \right)}} & \text{for}\: n = -2 \\\frac{a^{2} \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a^{2} \sin^{2}{\left(c + d x \right)}}{2 d} + \frac{2 a^{2} \sin{\left(c + d x \right)}}{d} & \text{for}\: n = -1 \\\frac{a^{2} n^{2} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} + \frac{2 a^{2} n^{2} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} + \frac{a^{2} n^{2} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} + \frac{3 a^{2} n \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} + \frac{8 a^{2} n \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} + \frac{5 a^{2} n \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} + \frac{2 a^{2} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} + \frac{6 a^{2} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} + \frac{6 a^{2} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{3} + 6 d n^{2} + 11 d n + 6 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**2*sin(c)**n*cos(c), Eq(d, 0)), (a**2*log(sin(c + d*x))/d - 2*a**2/(d*sin(c + d*x)) - a**2/(2*d*sin(c + d*x)**2), Eq(n, -3)), (2*a**2*log(sin(c + d*x))/d + a**2*sin(c + d*x)/d - a**2/(d*sin(c + d*x)), Eq(n, -2)), (a**2*log(sin(c + d*x))/d + a**2*sin(c + d*x)**2/(2*d) + 2*a**2*sin(c + d*x)/d, Eq(n, -1)), (a**2*n**2*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d) + 2*a**2*n**2*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d) + a**2*n**2*sin(c + d*x)*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d) + 3*a**2*n*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d) + 8*a**2*n*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d) + 5*a**2*n*sin(c + d*x)*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d) + 2*a**2*sin(c + d*x)**3*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d) + 6*a**2*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d) + 6*a**2*sin(c + d*x)*sin(c + d*x)**n/(d*n**3 + 6*d*n**2 + 11*d*n + 6*d), True))","A",0
261,1,190,0,5.083816," ","integrate(cos(d*x+c)*sin(d*x+c)**n*(a+a*sin(d*x+c)),x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right) \sin^{n}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{a \log{\left(\sin{\left(c + d x \right)} \right)}}{d} - \frac{a}{d \sin{\left(c + d x \right)}} & \text{for}\: n = -2 \\\frac{a \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a \sin{\left(c + d x \right)}}{d} & \text{for}\: n = -1 \\\frac{a n \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{2} + 3 d n + 2 d} + \frac{a n \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{2} + 3 d n + 2 d} + \frac{a \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{2} + 3 d n + 2 d} + \frac{2 a \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{2} + 3 d n + 2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)*sin(c)**n*cos(c), Eq(d, 0)), (a*log(sin(c + d*x))/d - a/(d*sin(c + d*x)), Eq(n, -2)), (a*log(sin(c + d*x))/d + a*sin(c + d*x)/d, Eq(n, -1)), (a*n*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**2 + 3*d*n + 2*d) + a*n*sin(c + d*x)*sin(c + d*x)**n/(d*n**2 + 3*d*n + 2*d) + a*sin(c + d*x)**2*sin(c + d*x)**n/(d*n**2 + 3*d*n + 2*d) + 2*a*sin(c + d*x)*sin(c + d*x)**n/(d*n**2 + 3*d*n + 2*d), True))","A",0
262,-1,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)**n/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,-1,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)**n/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)**n/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,-1,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)**n/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
266,1,192,0,4.337110," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{a x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{a x \cos^{6}{\left(c + d x \right)}}{16} + \frac{a \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 a \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{3}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**6/16 + 3*a*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + a*x*cos(c + d*x)**6/16 + a*sin(c + d*x)**5*cos(c + d*x)/(16*d) - a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - a*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - a*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*a*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**3*cos(c)**2, True))","A",0
267,1,144,0,2.519603," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 a \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**4/8 + a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a*x*cos(c + d*x)**4/8 + a*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - a*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*a*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**2*cos(c)**2, True))","A",0
268,1,119,0,1.228290," ","integrate(cos(d*x+c)**2*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{a \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**4/8 + a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a*x*cos(c + d*x)**4/8 + a*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a*sin(c + d*x)*cos(c + d*x)**3/(8*d) - a*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)*cos(c)**2, True))","A",0
269,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+a*sin(d*x+c)),x)","a \left(\int \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)**2*csc(c + d*x), x) + Integral(sin(c + d*x)*cos(c + d*x)**2*csc(c + d*x), x))","F",0
270,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+a*sin(d*x+c)),x)","a \left(\int \cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)**2*csc(c + d*x)**2, x) + Integral(sin(c + d*x)*cos(c + d*x)**2*csc(c + d*x)**2, x))","F",0
271,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3*(a+a*sin(d*x+c)),x)","a \left(\int \cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)**2*csc(c + d*x)**3, x) + Integral(sin(c + d*x)*cos(c + d*x)**2*csc(c + d*x)**3, x))","F",0
272,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
273,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
274,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**6*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,1,275,0,7.685546," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a^{2} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{4 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{8 a^{2} \cos^{7}{\left(c + d x \right)}}{105 d} - \frac{2 a^{2} \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{3}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**6/8 + 3*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + a**2*x*cos(c + d*x)**6/8 + a**2*sin(c + d*x)**5*cos(c + d*x)/(8*d) - a**2*sin(c + d*x)**4*cos(c + d*x)**3/(3*d) - a**2*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - 4*a**2*sin(c + d*x)**2*cos(c + d*x)**5/(15*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - a**2*sin(c + d*x)*cos(c + d*x)**5/(8*d) - 8*a**2*cos(c + d*x)**7/(105*d) - 2*a**2*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**3*cos(c)**2, True))","A",0
276,1,309,0,4.787885," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{2 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{4 a^{2} \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**6/16 + 3*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + a**2*x*sin(c + d*x)**4/8 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a**2*x*cos(c + d*x)**6/16 + a**2*x*cos(c + d*x)**4/8 + a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) - a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 2*a**2*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) - a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 4*a**2*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**2*cos(c)**2, True))","A",0
277,1,172,0,2.479728," ","integrate(cos(d*x+c)**2*sin(d*x+c)*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} - \frac{2 a^{2} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{a^{2} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**4/4 + a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + a**2*x*cos(c + d*x)**4/4 + a**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - a**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) - 2*a**2*cos(c + d*x)**5/(15*d) - a**2*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)*cos(c)**2, True))","A",0
278,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 2 \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(cos(c + d*x)**2*csc(c + d*x), x) + Integral(2*sin(c + d*x)*cos(c + d*x)**2*csc(c + d*x), x) + Integral(sin(c + d*x)**2*cos(c + d*x)**2*csc(c + d*x), x))","F",0
279,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int \cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int 2 \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(cos(c + d*x)**2*csc(c + d*x)**2, x) + Integral(2*sin(c + d*x)*cos(c + d*x)**2*csc(c + d*x)**2, x) + Integral(sin(c + d*x)**2*cos(c + d*x)**2*csc(c + d*x)**2, x))","F",0
280,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
281,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
282,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
283,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**6*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
284,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**7*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
285,1,379,0,7.838043," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{a^{3} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{4 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{8 a^{3} \cos^{7}{\left(c + d x \right)}}{105 d} - \frac{2 a^{3} \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**6/16 + 9*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + a**3*x*sin(c + d*x)**4/8 + 9*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**3*x*cos(c + d*x)**6/16 + a**3*x*cos(c + d*x)**4/8 + 3*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) - a**3*sin(c + d*x)**4*cos(c + d*x)**3/(3*d) - a**3*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) + a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 4*a**3*sin(c + d*x)**2*cos(c + d*x)**5/(15*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**3/d - 3*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 8*a**3*cos(c + d*x)**7/(105*d) - 2*a**3*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**2*cos(c)**2, True))","A",0
286,1,328,0,4.876035," ","integrate(cos(d*x+c)**2*sin(d*x+c)*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \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^{4}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{3 a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 a^{3} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{a^{3} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x*sin(c + d*x)**6/16 + 3*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a**3*x*sin(c + d*x)**4/8 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a**3*x*cos(c + d*x)**6/16 + 3*a**3*x*cos(c + d*x)**4/8 + a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) - a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 3*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**3/d - a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*a**3*cos(c + d*x)**5/(5*d) - a**3*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)*cos(c)**2, True))","A",0
287,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+a*sin(d*x+c))**3,x)","a^{3} \left(\int \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 3 \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int 3 \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(cos(c + d*x)**2*csc(c + d*x), x) + Integral(3*sin(c + d*x)*cos(c + d*x)**2*csc(c + d*x), x) + Integral(3*sin(c + d*x)**2*cos(c + d*x)**2*csc(c + d*x), x) + Integral(sin(c + d*x)**3*cos(c + d*x)**2*csc(c + d*x), x))","F",0
288,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
289,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
290,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
291,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
292,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**6*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
293,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**7*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
294,1,381,0,5.091106," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**4,x)","\begin{cases} \frac{a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a^{4} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{3 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{4} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{4} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{a^{4} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{3 a^{4} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{4 a^{4} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{3 a^{4} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} + \frac{a^{4} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{8 a^{4} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{4 a^{4} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{4} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**4*x*sin(c + d*x)**6/16 + 3*a**4*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a**4*x*sin(c + d*x)**4/4 + 3*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a**4*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + a**4*x*sin(c + d*x)**2/2 + a**4*x*cos(c + d*x)**6/16 + 3*a**4*x*cos(c + d*x)**4/4 + a**4*x*cos(c + d*x)**2/2 + a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) - a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 3*a**4*sin(c + d*x)**3*cos(c + d*x)/(4*d) - 4*a**4*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 3*a**4*sin(c + d*x)*cos(c + d*x)**3/(4*d) + a**4*sin(c + d*x)*cos(c + d*x)/(2*d) - 8*a**4*cos(c + d*x)**5/(15*d) - 4*a**4*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(a*sin(c) + a)**4*cos(c)**2, True))","A",0
295,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
296,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
297,1,1360,0,33.857829," ","integrate(cos(d*x+c)**2*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{45 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{225 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{450 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{450 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{225 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{45 d x}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{90 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{420 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{1280 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} - \frac{420 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{640 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} - \frac{90 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{128}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)} \cos^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((45*d*x*tan(c/2 + d*x/2)**10/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 225*d*x*tan(c/2 + d*x/2)**8/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 450*d*x*tan(c/2 + d*x/2)**6/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 450*d*x*tan(c/2 + d*x/2)**4/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 225*d*x*tan(c/2 + d*x/2)**2/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 45*d*x/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 90*tan(c/2 + d*x/2)**9/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 420*tan(c/2 + d*x/2)**7/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 1280*tan(c/2 + d*x/2)**4/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) - 420*tan(c/2 + d*x/2)**3/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 640*tan(c/2 + d*x/2)**2/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) - 90*tan(c/2 + d*x/2)/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 128/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d), Ne(d, 0)), (x*sin(c)**4*cos(c)**2/(a*sin(c) + a), True))","A",0
298,1,1049,0,19.757122," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{9 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{36 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{54 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{36 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{9 d x}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{18 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{66 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{96 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{66 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{128 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{18 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{32}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-9*d*x*tan(c/2 + d*x/2)**8/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 36*d*x*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 54*d*x*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 36*d*x*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 9*d*x/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 18*tan(c/2 + d*x/2)**7/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 66*tan(c/2 + d*x/2)**5/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 96*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 66*tan(c/2 + d*x/2)**3/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 128*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 18*tan(c/2 + d*x/2)/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 32/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**2/(a*sin(c) + a), True))","A",0
299,1,563,0,11.345559," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{3 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{9 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{9 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{3 d x}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{6 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{24 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} - \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} + \frac{8}{6 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*d*x*tan(c/2 + d*x/2)**6/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 9*d*x*tan(c/2 + d*x/2)**4/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 9*d*x*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 3*d*x/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 6*tan(c/2 + d*x/2)**5/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 24*tan(c/2 + d*x/2)**2/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) - 6*tan(c/2 + d*x/2)/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d) + 8/(6*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 18*a*d*tan(c/2 + d*x/2)**2 + 6*a*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**2/(a*sin(c) + a), True))","A",0
300,1,366,0,6.175160," ","integrate(cos(d*x+c)**2*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{d x}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{2 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} + \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} - \frac{4}{2 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{2}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-d*x*tan(c/2 + d*x/2)**4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*d*x*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - d*x/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 2*tan(c/2 + d*x/2)**3/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4*tan(c/2 + d*x/2)**2/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) + 2*tan(c/2 + d*x/2)/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d) - 4/(2*a*d*tan(c/2 + d*x/2)**4 + 4*a*d*tan(c/2 + d*x/2)**2 + 2*a*d), Ne(d, 0)), (x*sin(c)*cos(c)**2/(a*sin(c) + a), True))","A",0
301,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
302,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
303,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**3/(sin(c + d*x) + 1), x)/a","F",0
304,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**4/(sin(c + d*x) + 1), x)/a","F",0
305,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**5/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{5}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**5/(sin(c + d*x) + 1), x)/a","F",0
306,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
307,1,3580,0,61.076150," ","integrate(cos(d*x+c)**2*sin(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{81 d x \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{81 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{324 d x \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{324 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{486 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{486 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{324 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{324 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{81 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{81 d x}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{162 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{162 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{594 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{594 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{942 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{430 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{862 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{94 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{256}{24 a^{2} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)} \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-81*d*x*tan(c/2 + d*x/2)**9/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 81*d*x*tan(c/2 + d*x/2)**8/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 324*d*x*tan(c/2 + d*x/2)**7/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 324*d*x*tan(c/2 + d*x/2)**6/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 486*d*x*tan(c/2 + d*x/2)**5/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 486*d*x*tan(c/2 + d*x/2)**4/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 324*d*x*tan(c/2 + d*x/2)**3/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 324*d*x*tan(c/2 + d*x/2)**2/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 81*d*x*tan(c/2 + d*x/2)/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 81*d*x/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 162*tan(c/2 + d*x/2)**8/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 162*tan(c/2 + d*x/2)**7/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 594*tan(c/2 + d*x/2)**6/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 594*tan(c/2 + d*x/2)**5/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 942*tan(c/2 + d*x/2)**4/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 430*tan(c/2 + d*x/2)**3/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 862*tan(c/2 + d*x/2)**2/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 94*tan(c/2 + d*x/2)/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d) - 256/(24*a**2*d*tan(c/2 + d*x/2)**9 + 24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**7 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**5 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**3 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d*tan(c/2 + d*x/2) + 24*a**2*d), Ne(d, 0)), (x*sin(c)**4*cos(c)**2/(a*sin(c) + a)**2, True))","A",0
308,1,2263,0,37.331160," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{9 d x \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{9 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{27 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{27 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{27 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{27 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{9 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{9 d x}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{18 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{18 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{48 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{36 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{66 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{10 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{28}{3 a^{2} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*d*x*tan(c/2 + d*x/2)**7/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 9*d*x*tan(c/2 + d*x/2)**6/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 27*d*x*tan(c/2 + d*x/2)**5/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 27*d*x*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 27*d*x*tan(c/2 + d*x/2)**3/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 27*d*x*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 9*d*x*tan(c/2 + d*x/2)/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 9*d*x/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 18*tan(c/2 + d*x/2)**6/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 18*tan(c/2 + d*x/2)**5/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 48*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 36*tan(c/2 + d*x/2)**3/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 66*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 10*tan(c/2 + d*x/2)/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d) + 28/(3*a**2*d*tan(c/2 + d*x/2)**7 + 3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**5 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**3 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d*tan(c/2 + d*x/2) + 3*a**2*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**2/(a*sin(c) + a)**2, True))","A",0
309,1,1248,0,21.854613," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{5 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{5 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{10 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{10 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{5 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{5 d x}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{10 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{10 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{22 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} - \frac{16}{2 a^{2} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-5*d*x*tan(c/2 + d*x/2)**5/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 5*d*x*tan(c/2 + d*x/2)**4/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 10*d*x*tan(c/2 + d*x/2)**3/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 10*d*x*tan(c/2 + d*x/2)**2/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 5*d*x*tan(c/2 + d*x/2)/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 5*d*x/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 10*tan(c/2 + d*x/2)**4/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 10*tan(c/2 + d*x/2)**3/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 22*tan(c/2 + d*x/2)**2/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 6*tan(c/2 + d*x/2)/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d) - 16/(2*a**2*d*tan(c/2 + d*x/2)**5 + 2*a**2*d*tan(c/2 + d*x/2)**4 + 4*a**2*d*tan(c/2 + d*x/2)**3 + 4*a**2*d*tan(c/2 + d*x/2)**2 + 2*a**2*d*tan(c/2 + d*x/2) + 2*a**2*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**2/(a*sin(c) + a)**2, True))","A",0
310,1,479,0,11.904677," ","integrate(cos(d*x+c)**2*sin(d*x+c)/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{2 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{2 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{2 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{2 d x}{a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{4 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{6}{a^{2} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*d*x*tan(c/2 + d*x/2)**3/(a**2*d*tan(c/2 + d*x/2)**3 + a**2*d*tan(c/2 + d*x/2)**2 + a**2*d*tan(c/2 + d*x/2) + a**2*d) + 2*d*x*tan(c/2 + d*x/2)**2/(a**2*d*tan(c/2 + d*x/2)**3 + a**2*d*tan(c/2 + d*x/2)**2 + a**2*d*tan(c/2 + d*x/2) + a**2*d) + 2*d*x*tan(c/2 + d*x/2)/(a**2*d*tan(c/2 + d*x/2)**3 + a**2*d*tan(c/2 + d*x/2)**2 + a**2*d*tan(c/2 + d*x/2) + a**2*d) + 2*d*x/(a**2*d*tan(c/2 + d*x/2)**3 + a**2*d*tan(c/2 + d*x/2)**2 + a**2*d*tan(c/2 + d*x/2) + a**2*d) + 4*tan(c/2 + d*x/2)**2/(a**2*d*tan(c/2 + d*x/2)**3 + a**2*d*tan(c/2 + d*x/2)**2 + a**2*d*tan(c/2 + d*x/2) + a**2*d) + 2*tan(c/2 + d*x/2)/(a**2*d*tan(c/2 + d*x/2)**3 + a**2*d*tan(c/2 + d*x/2)**2 + a**2*d*tan(c/2 + d*x/2) + a**2*d) + 6/(a**2*d*tan(c/2 + d*x/2)**3 + a**2*d*tan(c/2 + d*x/2)**2 + a**2*d*tan(c/2 + d*x/2) + a**2*d), Ne(d, 0)), (x*sin(c)*cos(c)**2/(a*sin(c) + a)**2, True))","A",0
311,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
312,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
313,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**3/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
314,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**4/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
315,1,2264,0,63.547944," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{33 d x \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{99 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{165 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{231 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{231 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{165 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{99 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{33 d x}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{66 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{198 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{308 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{420 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{322 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{246 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{104}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 42 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 30 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-33*d*x*tan(c/2 + d*x/2)**7/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 99*d*x*tan(c/2 + d*x/2)**6/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 165*d*x*tan(c/2 + d*x/2)**5/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 231*d*x*tan(c/2 + d*x/2)**4/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 231*d*x*tan(c/2 + d*x/2)**3/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 165*d*x*tan(c/2 + d*x/2)**2/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 99*d*x*tan(c/2 + d*x/2)/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 33*d*x/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 66*tan(c/2 + d*x/2)**6/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 198*tan(c/2 + d*x/2)**5/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 308*tan(c/2 + d*x/2)**4/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 420*tan(c/2 + d*x/2)**3/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 322*tan(c/2 + d*x/2)**2/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 246*tan(c/2 + d*x/2)/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 104/(6*a**3*d*tan(c/2 + d*x/2)**7 + 18*a**3*d*tan(c/2 + d*x/2)**6 + 30*a**3*d*tan(c/2 + d*x/2)**5 + 42*a**3*d*tan(c/2 + d*x/2)**4 + 42*a**3*d*tan(c/2 + d*x/2)**3 + 30*a**3*d*tan(c/2 + d*x/2)**2 + 18*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**2/(a*sin(c) + a)**3, True))","A",0
316,1,1246,0,38.822164," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{9 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{27 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{36 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{36 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{27 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{9 d x}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{18 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{54 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{58 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{66 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{28}{3 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*d*x*tan(c/2 + d*x/2)**5/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 27*d*x*tan(c/2 + d*x/2)**4/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 36*d*x*tan(c/2 + d*x/2)**3/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 36*d*x*tan(c/2 + d*x/2)**2/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 27*d*x*tan(c/2 + d*x/2)/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 9*d*x/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 18*tan(c/2 + d*x/2)**4/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 54*tan(c/2 + d*x/2)**3/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 58*tan(c/2 + d*x/2)**2/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 66*tan(c/2 + d*x/2)/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) + 28/(3*a**3*d*tan(c/2 + d*x/2)**5 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 12*a**3*d*tan(c/2 + d*x/2)**3 + 12*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**2/(a*sin(c) + a)**3, True))","A",0
317,1,529,0,22.210640," ","integrate(cos(d*x+c)**2*sin(d*x+c)/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{3 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{9 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{9 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{3 d x}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{6 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{24 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{10}{3 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{2}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*d*x*tan(c/2 + d*x/2)**3/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) - 9*d*x*tan(c/2 + d*x/2)**2/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) - 9*d*x*tan(c/2 + d*x/2)/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) - 3*d*x/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) - 6*tan(c/2 + d*x/2)**2/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) - 24*tan(c/2 + d*x/2)/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d) - 10/(3*a**3*d*tan(c/2 + d*x/2)**3 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 9*a**3*d*tan(c/2 + d*x/2) + 3*a**3*d), Ne(d, 0)), (x*sin(c)*cos(c)**2/(a*sin(c) + a)**3, True))","A",0
318,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
319,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
320,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**3/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
321,1,1501,0,109.193367," ","integrate(cos(f*x+e)**2*sin(f*x+e)/(a+a*sin(f*x+e))**6,x)","\begin{cases} - \frac{630 \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{6} f} - \frac{630 \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{6} f} - \frac{1890 \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{6} f} - \frac{882 \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{6} f} - \frac{1218 \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{6} f} - \frac{162 \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{6} f} - \frac{198 \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{315 a^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{6} f} - \frac{22}{315 a^{6} f \tan^{9}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan^{8}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{7}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 39690 a^{6} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 26460 a^{6} f \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 11340 a^{6} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2835 a^{6} f \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 315 a^{6} f} & \text{for}\: f \neq 0 \\\frac{x \sin{\left(e \right)} \cos^{2}{\left(e \right)}}{\left(a \sin{\left(e \right)} + a\right)^{6}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-630*tan(e/2 + f*x/2)**7/(315*a**6*f*tan(e/2 + f*x/2)**9 + 2835*a**6*f*tan(e/2 + f*x/2)**8 + 11340*a**6*f*tan(e/2 + f*x/2)**7 + 26460*a**6*f*tan(e/2 + f*x/2)**6 + 39690*a**6*f*tan(e/2 + f*x/2)**5 + 39690*a**6*f*tan(e/2 + f*x/2)**4 + 26460*a**6*f*tan(e/2 + f*x/2)**3 + 11340*a**6*f*tan(e/2 + f*x/2)**2 + 2835*a**6*f*tan(e/2 + f*x/2) + 315*a**6*f) - 630*tan(e/2 + f*x/2)**6/(315*a**6*f*tan(e/2 + f*x/2)**9 + 2835*a**6*f*tan(e/2 + f*x/2)**8 + 11340*a**6*f*tan(e/2 + f*x/2)**7 + 26460*a**6*f*tan(e/2 + f*x/2)**6 + 39690*a**6*f*tan(e/2 + f*x/2)**5 + 39690*a**6*f*tan(e/2 + f*x/2)**4 + 26460*a**6*f*tan(e/2 + f*x/2)**3 + 11340*a**6*f*tan(e/2 + f*x/2)**2 + 2835*a**6*f*tan(e/2 + f*x/2) + 315*a**6*f) - 1890*tan(e/2 + f*x/2)**5/(315*a**6*f*tan(e/2 + f*x/2)**9 + 2835*a**6*f*tan(e/2 + f*x/2)**8 + 11340*a**6*f*tan(e/2 + f*x/2)**7 + 26460*a**6*f*tan(e/2 + f*x/2)**6 + 39690*a**6*f*tan(e/2 + f*x/2)**5 + 39690*a**6*f*tan(e/2 + f*x/2)**4 + 26460*a**6*f*tan(e/2 + f*x/2)**3 + 11340*a**6*f*tan(e/2 + f*x/2)**2 + 2835*a**6*f*tan(e/2 + f*x/2) + 315*a**6*f) - 882*tan(e/2 + f*x/2)**4/(315*a**6*f*tan(e/2 + f*x/2)**9 + 2835*a**6*f*tan(e/2 + f*x/2)**8 + 11340*a**6*f*tan(e/2 + f*x/2)**7 + 26460*a**6*f*tan(e/2 + f*x/2)**6 + 39690*a**6*f*tan(e/2 + f*x/2)**5 + 39690*a**6*f*tan(e/2 + f*x/2)**4 + 26460*a**6*f*tan(e/2 + f*x/2)**3 + 11340*a**6*f*tan(e/2 + f*x/2)**2 + 2835*a**6*f*tan(e/2 + f*x/2) + 315*a**6*f) - 1218*tan(e/2 + f*x/2)**3/(315*a**6*f*tan(e/2 + f*x/2)**9 + 2835*a**6*f*tan(e/2 + f*x/2)**8 + 11340*a**6*f*tan(e/2 + f*x/2)**7 + 26460*a**6*f*tan(e/2 + f*x/2)**6 + 39690*a**6*f*tan(e/2 + f*x/2)**5 + 39690*a**6*f*tan(e/2 + f*x/2)**4 + 26460*a**6*f*tan(e/2 + f*x/2)**3 + 11340*a**6*f*tan(e/2 + f*x/2)**2 + 2835*a**6*f*tan(e/2 + f*x/2) + 315*a**6*f) - 162*tan(e/2 + f*x/2)**2/(315*a**6*f*tan(e/2 + f*x/2)**9 + 2835*a**6*f*tan(e/2 + f*x/2)**8 + 11340*a**6*f*tan(e/2 + f*x/2)**7 + 26460*a**6*f*tan(e/2 + f*x/2)**6 + 39690*a**6*f*tan(e/2 + f*x/2)**5 + 39690*a**6*f*tan(e/2 + f*x/2)**4 + 26460*a**6*f*tan(e/2 + f*x/2)**3 + 11340*a**6*f*tan(e/2 + f*x/2)**2 + 2835*a**6*f*tan(e/2 + f*x/2) + 315*a**6*f) - 198*tan(e/2 + f*x/2)/(315*a**6*f*tan(e/2 + f*x/2)**9 + 2835*a**6*f*tan(e/2 + f*x/2)**8 + 11340*a**6*f*tan(e/2 + f*x/2)**7 + 26460*a**6*f*tan(e/2 + f*x/2)**6 + 39690*a**6*f*tan(e/2 + f*x/2)**5 + 39690*a**6*f*tan(e/2 + f*x/2)**4 + 26460*a**6*f*tan(e/2 + f*x/2)**3 + 11340*a**6*f*tan(e/2 + f*x/2)**2 + 2835*a**6*f*tan(e/2 + f*x/2) + 315*a**6*f) - 22/(315*a**6*f*tan(e/2 + f*x/2)**9 + 2835*a**6*f*tan(e/2 + f*x/2)**8 + 11340*a**6*f*tan(e/2 + f*x/2)**7 + 26460*a**6*f*tan(e/2 + f*x/2)**6 + 39690*a**6*f*tan(e/2 + f*x/2)**5 + 39690*a**6*f*tan(e/2 + f*x/2)**4 + 26460*a**6*f*tan(e/2 + f*x/2)**3 + 11340*a**6*f*tan(e/2 + f*x/2)**2 + 2835*a**6*f*tan(e/2 + f*x/2) + 315*a**6*f), Ne(f, 0)), (x*sin(e)*cos(e)**2/(a*sin(e) + a)**6, True))","A",0
322,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
323,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sin(c + d*x)**2*cos(c + d*x)**2, x)","F",0
324,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sin(c + d*x)*cos(c + d*x)**2, x)","F",0
325,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*cos(c + d*x)**2*csc(c + d*x), x)","F",0
326,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*cos(c + d*x)**2*csc(c + d*x)**2, x)","F",0
327,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*cos(c + d*x)**2*csc(c + d*x)**3, x)","F",0
328,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
329,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
330,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
331,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)*(a+a*sin(d*x+c))**(3/2),x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**(3/2)*sin(c + d*x)*cos(c + d*x)**2, x)","F",0
332,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
333,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
334,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
335,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
336,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
337,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2*cos(c + d*x)**2/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
338,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sin(c + d*x)*cos(c + d*x)**2/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
339,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
340,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**2/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
341,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**3/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
342,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
343,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
344,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(c + d*x)**2*cos(c + d*x)**2/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
345,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sin(c + d*x)*cos(c + d*x)**2/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
346,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
347,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**2/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
348,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**3/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
349,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,1,90,0,7.827502," ","integrate(cos(d*x+c)**3*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 a \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{a \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} - \frac{a \cos^{6}{\left(c + d x \right)}}{12 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{3}{\left(c \right)} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sin(c + d*x)**7/(35*d) + a*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) - a*sin(c + d*x)**2*cos(c + d*x)**4/(4*d) - a*cos(c + d*x)**6/(12*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**3*cos(c)**3, True))","A",0
351,1,90,0,4.305501," ","integrate(cos(d*x+c)**3*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} - \frac{a \cos^{6}{\left(c + d x \right)}}{12 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{2}{\left(c \right)} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sin(c + d*x)**5/(15*d) + a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - a*sin(c + d*x)**2*cos(c + d*x)**4/(4*d) - a*cos(c + d*x)**6/(12*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**2*cos(c)**3, True))","A",0
352,1,66,0,2.386853," ","integrate(cos(d*x+c)**3*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{a \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin{\left(c \right)} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*a*sin(c + d*x)**5/(15*d) + a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - a*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)*cos(c)**3, True))","A",0
353,1,60,0,1.215359," ","integrate(cos(d*x+c)**3*(a+a*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{a \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \cos^{3}{\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 - a*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a*sin(c) + a)*cos(c)**3, True))","A",0
354,0,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)*(a+a*sin(d*x+c)),x)","a \left(\int \cos^{3}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)**3*csc(c + d*x), x) + Integral(sin(c + d*x)*cos(c + d*x)**3*csc(c + d*x), x))","F",0
355,0,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)**2*(a+a*sin(d*x+c)),x)","a \left(\int \cos^{3}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)**3*csc(c + d*x)**2, x) + Integral(sin(c + d*x)*cos(c + d*x)**3*csc(c + d*x)**2, x))","F",0
356,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)**3*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
357,1,277,0,20.003469," ","integrate(cos(d*x+c)**3*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{12 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{8 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*tan(c/2 + d*x/2)**5/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 12*tan(c/2 + d*x/2)**4/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 8*tan(c/2 + d*x/2)**3/(3*a*d*tan(c/2 + d*x/2)**8 + 12*a*d*tan(c/2 + d*x/2)**6 + 18*a*d*tan(c/2 + d*x/2)**4 + 12*a*d*tan(c/2 + d*x/2)**2 + 3*a*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**3/(a*sin(c) + a), True))","A",0
358,1,224,0,10.744649," ","integrate(cos(d*x+c)**3*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{6 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{8 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{6 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*tan(c/2 + d*x/2)**4/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 8*tan(c/2 + d*x/2)**3/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 6*tan(c/2 + d*x/2)**2/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d), Ne(d, 0)), (x*sin(c)*cos(c)**3/(a*sin(c) + a), True))","A",0
359,1,158,0,5.868472," ","integrate(cos(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{2 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} - \frac{2 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} + \frac{2 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*tan(c/2 + d*x/2)**3/(a*d*tan(c/2 + d*x/2)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d) - 2*tan(c/2 + d*x/2)**2/(a*d*tan(c/2 + d*x/2)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d) + 2*tan(c/2 + d*x/2)/(a*d*tan(c/2 + d*x/2)**4 + 2*a*d*tan(c/2 + d*x/2)**2 + a*d), Ne(d, 0)), (x*cos(c)**3/(a*sin(c) + a), True))","A",0
360,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
361,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
362,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
363,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
364,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
365,1,272,0,19.382470," ","integrate(cos(d*x+c)**4*sin(d*x+c)**4*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{3 a x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 a x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{9 a x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 a \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{a \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{11 a \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{4 a \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{3 a \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{8 a \cos^{9}{\left(c + d x \right)}}{315 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{4}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*sin(c + d*x)**8/128 + 3*a*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 9*a*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a*x*cos(c + d*x)**8/128 + 3*a*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*a*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - a*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 11*a*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 4*a*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 3*a*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 8*a*cos(c + d*x)**9/(315*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**4*cos(c)**4, True))","A",0
366,1,248,0,11.406706," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{3 a x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 a x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{9 a x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 a \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{11 a \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 a \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{2 a \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{3}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*sin(c + d*x)**8/128 + 3*a*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 9*a*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a*x*cos(c + d*x)**8/128 + 3*a*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*a*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 11*a*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - a*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*a*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 2*a*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**3*cos(c)**4, True))","A",0
367,1,192,0,6.938380," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{a x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{a x \cos^{6}{\left(c + d x \right)}}{16} + \frac{a \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 a \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**6/16 + 3*a*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + a*x*cos(c + d*x)**6/16 + a*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - a*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - a*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*a*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**2*cos(c)**4, True))","A",0
368,1,167,0,4.240980," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{a x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{a x \cos^{6}{\left(c + d x \right)}}{16} + \frac{a \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{a \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**6/16 + 3*a*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + a*x*cos(c + d*x)**6/16 + a*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - a*sin(c + d*x)*cos(c + d*x)**5/(16*d) - a*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)*cos(c)**4, True))","A",0
369,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)*(a+a*sin(d*x+c)),x)","a \left(\int \cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)**4*csc(c + d*x), x) + Integral(sin(c + d*x)*cos(c + d*x)**4*csc(c + d*x), x))","F",0
370,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
371,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
372,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
373,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
374,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
375,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
376,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**8*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
377,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**9*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
378,1,554,0,34.602192," ","integrate(cos(d*x+c)**4*sin(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 a^{2} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{3 a^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{3 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{9 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a^{2} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{3 a^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a^{2} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 a^{2} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{3 a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} - \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{11 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{2 a^{2} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{7 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{11 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{8 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{3 a^{2} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{3 a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{16 a^{2} \cos^{9}{\left(c + d x \right)}}{315 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{4}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**10/256 + 15*a**2*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 3*a**2*x*sin(c + d*x)**8/128 + 15*a**2*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 3*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 9*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a**2*x*cos(c + d*x)**10/256 + 3*a**2*x*cos(c + d*x)**8/128 + 3*a**2*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*a**2*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 3*a**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) - a**2*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 11*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 2*a**2*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 7*a**2*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 11*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 8*a**2*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 3*a**2*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 3*a**2*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 16*a**2*cos(c + d*x)**9/(315*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**4*cos(c)**4, True))","A",0
379,1,335,0,22.160833," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{8}{\left(c + d x \right)}}{64} + \frac{3 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \cos^{8}{\left(c + d x \right)}}{64} + \frac{3 a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} + \frac{11 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{64 d} - \frac{a^{2} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{11 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{64 d} - \frac{4 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{8 a^{2} \cos^{9}{\left(c + d x \right)}}{315 d} - \frac{2 a^{2} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{3}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**8/64 + 3*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + 9*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 3*a**2*x*cos(c + d*x)**8/64 + 3*a**2*sin(c + d*x)**7*cos(c + d*x)/(64*d) + 11*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(64*d) - a**2*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 11*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(64*d) - 4*a**2*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*a**2*sin(c + d*x)*cos(c + d*x)**7/(64*d) - 8*a**2*cos(c + d*x)**9/(315*d) - 2*a**2*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**3*cos(c)**4, True))","A",0
380,1,420,0,14.016149," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{11 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{2 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{4 a^{2} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**8/128 + 3*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + a**2*x*sin(c + d*x)**6/16 + 9*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a**2*x*cos(c + d*x)**8/128 + a**2*x*cos(c + d*x)**6/16 + 3*a**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) + a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) - 11*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) + a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - 2*a**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*a**2*sin(c + d*x)*cos(c + d*x)**7/(128*d) - a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 4*a**2*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**2*cos(c)**4, True))","A",0
381,1,223,0,8.006624," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{2 a^{2} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{a^{2} \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**6/8 + 3*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + a**2*x*cos(c + d*x)**6/8 + a**2*sin(c + d*x)**5*cos(c + d*x)/(8*d) + a**2*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - a**2*sin(c + d*x)*cos(c + d*x)**5/(8*d) - 2*a**2*cos(c + d*x)**7/(35*d) - a**2*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)*cos(c)**4, True))","A",0
382,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
383,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
384,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
386,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
387,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
388,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**9*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**10*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
391,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**11*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
392,1,648,0,50.882681," ","integrate(cos(d*x+c)**4*sin(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{9 a^{3} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{45 a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{3 a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{45 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{3 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{45 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{9 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{45 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{9 a^{3} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{3 a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{9 a^{3} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{21 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{3 a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} - \frac{a^{3} \sin^{6}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{11 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{6 a^{3} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{3 a^{3} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{21 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{11 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{8 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{105 d} - \frac{12 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{9 a^{3} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{16 a^{3} \cos^{11}{\left(c + d x \right)}}{1155 d} - \frac{8 a^{3} \cos^{9}{\left(c + d x \right)}}{105 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{4}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**3*x*sin(c + d*x)**10/256 + 45*a**3*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 3*a**3*x*sin(c + d*x)**8/128 + 45*a**3*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 3*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 45*a**3*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 9*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 45*a**3*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 9*a**3*x*cos(c + d*x)**10/256 + 3*a**3*x*cos(c + d*x)**8/128 + 9*a**3*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 21*a**3*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 3*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) - a**3*sin(c + d*x)**6*cos(c + d*x)**5/(5*d) - 3*a**3*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 11*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 6*a**3*sin(c + d*x)**4*cos(c + d*x)**7/(35*d) - 3*a**3*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 21*a**3*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 11*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 8*a**3*sin(c + d*x)**2*cos(c + d*x)**9/(105*d) - 12*a**3*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 9*a**3*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 16*a**3*cos(c + d*x)**11/(1155*d) - 8*a**3*cos(c + d*x)**9/(105*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**4*cos(c)**4, True))","A",0
393,1,595,0,33.512636," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{9 a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{9 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{27 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{9 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a^{3} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{9 a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a^{3} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{9 a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} - \frac{a^{3} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{33 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{3 a^{3} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{7 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{33 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{12 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{9 a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{8 a^{3} \cos^{9}{\left(c + d x \right)}}{105 d} - \frac{2 a^{3} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{3}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**10/256 + 15*a**3*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 9*a**3*x*sin(c + d*x)**8/128 + 15*a**3*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 9*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*a**3*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 27*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 9*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a**3*x*cos(c + d*x)**10/256 + 9*a**3*x*cos(c + d*x)**8/128 + 3*a**3*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*a**3*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 9*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) - a**3*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 33*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 3*a**3*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 7*a**3*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 33*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 12*a**3*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 9*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 8*a**3*cos(c + d*x)**9/(105*d) - 2*a**3*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**3*cos(c)**4, True))","A",0
394,1,486,0,21.624838," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{9 a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{9 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{27 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{9 a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{9 a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{33 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{a^{3} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{33 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{4 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{3 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{9 a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{8 a^{3} \cos^{9}{\left(c + d x \right)}}{315 d} - \frac{6 a^{3} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**3*x*sin(c + d*x)**8/128 + 9*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + a**3*x*sin(c + d*x)**6/16 + 27*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 9*a**3*x*cos(c + d*x)**8/128 + a**3*x*cos(c + d*x)**6/16 + 9*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 33*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) + a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) - a**3*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 33*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) + a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - 4*a**3*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 3*a**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 9*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 8*a**3*cos(c + d*x)**9/(315*d) - 6*a**3*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**2*cos(c)**4, True))","A",0
395,1,440,0,13.193517," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{3 a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{9 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{9 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{3 a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{11 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} - \frac{3 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{6 a^{3} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{a^{3} \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**8/128 + 3*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 3*a**3*x*sin(c + d*x)**6/16 + 9*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 9*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 9*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a**3*x*cos(c + d*x)**8/128 + 3*a**3*x*cos(c + d*x)**6/16 + 3*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) + 3*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) - 11*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) + a**3*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) - 3*a**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 6*a**3*cos(c + d*x)**7/(35*d) - a**3*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)*cos(c)**4, True))","A",0
396,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
397,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
398,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
399,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
400,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
401,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
402,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
403,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**8*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
404,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**9*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
405,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**10*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
406,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**11*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,1,746,0,34.276248," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c))**4,x)","\begin{cases} \frac{3 a^{4} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 a^{4} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{9 a^{4} x \sin^{8}{\left(c + d x \right)}}{64} + \frac{15 a^{4} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{9 a^{4} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{a^{4} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{27 a^{4} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{3 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^{8}{\left(c + d x \right)}}{256} + \frac{9 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{4} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a^{4} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{9 a^{4} x \cos^{8}{\left(c + d x \right)}}{64} + \frac{a^{4} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{4} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 a^{4} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{9 a^{4} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} - \frac{a^{4} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{33 a^{4} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{64 d} + \frac{a^{4} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{4 a^{4} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{7 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{33 a^{4} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{64 d} + \frac{a^{4} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{16 a^{4} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{4 a^{4} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 a^{4} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{9 a^{4} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{a^{4} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{32 a^{4} \cos^{9}{\left(c + d x \right)}}{315 d} - \frac{8 a^{4} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{4} \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**4*x*sin(c + d*x)**10/256 + 15*a**4*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 9*a**4*x*sin(c + d*x)**8/64 + 15*a**4*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 9*a**4*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + a**4*x*sin(c + d*x)**6/16 + 15*a**4*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 27*a**4*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 3*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)**8/256 + 9*a**4*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 3*a**4*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a**4*x*cos(c + d*x)**10/256 + 9*a**4*x*cos(c + d*x)**8/64 + a**4*x*cos(c + d*x)**6/16 + 3*a**4*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*a**4*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 9*a**4*sin(c + d*x)**7*cos(c + d*x)/(64*d) - a**4*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 33*a**4*sin(c + d*x)**5*cos(c + d*x)**3/(64*d) + a**4*sin(c + d*x)**5*cos(c + d*x)/(16*d) - 4*a**4*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 7*a**4*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 33*a**4*sin(c + d*x)**3*cos(c + d*x)**5/(64*d) + a**4*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - 16*a**4*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 4*a**4*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*a**4*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 9*a**4*sin(c + d*x)*cos(c + d*x)**7/(64*d) - a**4*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 32*a**4*cos(c + d*x)**9/(315*d) - 8*a**4*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a*sin(c) + a)**4*sin(c)**2*cos(c)**4, True))","A",0
408,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
409,1,2635,0,88.918183," ","integrate(cos(d*x+c)**4*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{105 d x \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{735 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{2205 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{3675 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{3675 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{2205 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{735 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{105 d x}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{210 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{1400 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{6790 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{17920 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{8960 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{6790 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{5376 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{1400 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{1792 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{210 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{256}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)} \cos^{4}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((105*d*x*tan(c/2 + d*x/2)**14/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 735*d*x*tan(c/2 + d*x/2)**12/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 2205*d*x*tan(c/2 + d*x/2)**10/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 3675*d*x*tan(c/2 + d*x/2)**8/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 3675*d*x*tan(c/2 + d*x/2)**6/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 2205*d*x*tan(c/2 + d*x/2)**4/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 735*d*x*tan(c/2 + d*x/2)**2/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 105*d*x/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 210*tan(c/2 + d*x/2)**13/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 1400*tan(c/2 + d*x/2)**11/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 6790*tan(c/2 + d*x/2)**9/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 17920*tan(c/2 + d*x/2)**8/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 8960*tan(c/2 + d*x/2)**6/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 6790*tan(c/2 + d*x/2)**5/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 5376*tan(c/2 + d*x/2)**4/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 1400*tan(c/2 + d*x/2)**3/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 1792*tan(c/2 + d*x/2)**2/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 210*tan(c/2 + d*x/2)/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 256/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d), Ne(d, 0)), (x*sin(c)**4*cos(c)**4/(a*sin(c) + a), True))","A",0
410,1,2067,0,72.096786," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{15 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{90 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{225 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{300 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{225 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{90 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{15 d x}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{30 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{170 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{960 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} + \frac{1140 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{640 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{1140 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} + \frac{170 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{384 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} + \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{64}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{4}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*d*x*tan(c/2 + d*x/2)**12/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 90*d*x*tan(c/2 + d*x/2)**10/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 225*d*x*tan(c/2 + d*x/2)**8/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 300*d*x*tan(c/2 + d*x/2)**6/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 225*d*x*tan(c/2 + d*x/2)**4/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 90*d*x*tan(c/2 + d*x/2)**2/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 15*d*x/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 30*tan(c/2 + d*x/2)**11/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 170*tan(c/2 + d*x/2)**9/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 960*tan(c/2 + d*x/2)**8/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) + 1140*tan(c/2 + d*x/2)**7/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 640*tan(c/2 + d*x/2)**6/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 1140*tan(c/2 + d*x/2)**5/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) + 170*tan(c/2 + d*x/2)**3/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 384*tan(c/2 + d*x/2)**2/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) + 30*tan(c/2 + d*x/2)/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 64/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**4/(a*sin(c) + a), True))","A",0
411,1,1464,0,53.157550," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{15 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{75 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{150 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{150 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{75 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{15 d x}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{30 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} - \frac{180 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{480 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} - \frac{160 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{180 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{160 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} - \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} + \frac{32}{120 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1200 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 120 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*d*x*tan(c/2 + d*x/2)**10/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 75*d*x*tan(c/2 + d*x/2)**8/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 150*d*x*tan(c/2 + d*x/2)**6/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 150*d*x*tan(c/2 + d*x/2)**4/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 75*d*x*tan(c/2 + d*x/2)**2/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 15*d*x/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 30*tan(c/2 + d*x/2)**9/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) - 180*tan(c/2 + d*x/2)**7/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 480*tan(c/2 + d*x/2)**6/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) - 160*tan(c/2 + d*x/2)**4/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 180*tan(c/2 + d*x/2)**3/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 160*tan(c/2 + d*x/2)**2/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) - 30*tan(c/2 + d*x/2)/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d) + 32/(120*a*d*tan(c/2 + d*x/2)**10 + 600*a*d*tan(c/2 + d*x/2)**8 + 1200*a*d*tan(c/2 + d*x/2)**6 + 1200*a*d*tan(c/2 + d*x/2)**4 + 600*a*d*tan(c/2 + d*x/2)**2 + 120*a*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**4/(a*sin(c) + a), True))","A",0
412,1,1134,0,24.777454," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{3 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{12 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{18 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{12 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{3 d x}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{6 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{48 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{42 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{48 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{42 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{16 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} + \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} - \frac{16}{24 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{4}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*d*x*tan(c/2 + d*x/2)**8/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 12*d*x*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 18*d*x*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 12*d*x*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 3*d*x/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 6*tan(c/2 + d*x/2)**7/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 48*tan(c/2 + d*x/2)**6/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 42*tan(c/2 + d*x/2)**5/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 48*tan(c/2 + d*x/2)**4/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 42*tan(c/2 + d*x/2)**3/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 16*tan(c/2 + d*x/2)**2/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) + 6*tan(c/2 + d*x/2)/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d) - 16/(24*a*d*tan(c/2 + d*x/2)**8 + 96*a*d*tan(c/2 + d*x/2)**6 + 144*a*d*tan(c/2 + d*x/2)**4 + 96*a*d*tan(c/2 + d*x/2)**2 + 24*a*d), Ne(d, 0)), (x*sin(c)*cos(c)**4/(a*sin(c) + a), True))","A",0
413,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
414,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{4}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
415,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{4}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)**3/(sin(c + d*x) + 1), x)/a","F",0
416,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
417,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
418,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
420,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
421,1,2271,0,143.137668," ","integrate(cos(d*x+c)**4*sin(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{165 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{990 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{2475 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{3300 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{2475 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{990 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{165 d x}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{330 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{1870 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{2820 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{5120 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{2820 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{7680 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{1870 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{3072 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{330 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{512}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{4}{\left(c \right)} \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((165*d*x*tan(c/2 + d*x/2)**12/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 990*d*x*tan(c/2 + d*x/2)**10/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 2475*d*x*tan(c/2 + d*x/2)**8/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 3300*d*x*tan(c/2 + d*x/2)**6/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 2475*d*x*tan(c/2 + d*x/2)**4/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 990*d*x*tan(c/2 + d*x/2)**2/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 165*d*x/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 330*tan(c/2 + d*x/2)**11/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 1870*tan(c/2 + d*x/2)**9/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 2820*tan(c/2 + d*x/2)**7/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 5120*tan(c/2 + d*x/2)**6/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 2820*tan(c/2 + d*x/2)**5/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 7680*tan(c/2 + d*x/2)**4/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 1870*tan(c/2 + d*x/2)**3/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 3072*tan(c/2 + d*x/2)**2/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 330*tan(c/2 + d*x/2)/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 512/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d), Ne(d, 0)), (x*sin(c)**4*cos(c)**4/(a*sin(c) + a)**2, True))","A",0
422,1,1608,0,94.092998," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{15 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{75 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{150 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{150 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{75 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{15 d x}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{30 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{140 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{80 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{400 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} + \frac{140 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{240 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} + \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} - \frac{48}{20 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 200 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 100 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 20 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*d*x*tan(c/2 + d*x/2)**10/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 75*d*x*tan(c/2 + d*x/2)**8/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 150*d*x*tan(c/2 + d*x/2)**6/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 150*d*x*tan(c/2 + d*x/2)**4/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 75*d*x*tan(c/2 + d*x/2)**2/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 15*d*x/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 30*tan(c/2 + d*x/2)**9/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 140*tan(c/2 + d*x/2)**7/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 80*tan(c/2 + d*x/2)**6/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 400*tan(c/2 + d*x/2)**4/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) + 140*tan(c/2 + d*x/2)**3/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 240*tan(c/2 + d*x/2)**2/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) + 30*tan(c/2 + d*x/2)/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d) - 48/(20*a**2*d*tan(c/2 + d*x/2)**10 + 100*a**2*d*tan(c/2 + d*x/2)**8 + 200*a**2*d*tan(c/2 + d*x/2)**6 + 200*a**2*d*tan(c/2 + d*x/2)**4 + 100*a**2*d*tan(c/2 + d*x/2)**2 + 20*a**2*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**4/(a*sin(c) + a)**2, True))","A",0
423,1,1153,0,59.860388," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{21 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{84 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{126 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{84 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{21 d x}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{42 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{90 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{192 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{90 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{256 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} - \frac{42 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} + \frac{64}{24 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 144 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 96 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((21*d*x*tan(c/2 + d*x/2)**8/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 84*d*x*tan(c/2 + d*x/2)**6/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 126*d*x*tan(c/2 + d*x/2)**4/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 84*d*x*tan(c/2 + d*x/2)**2/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 21*d*x/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 42*tan(c/2 + d*x/2)**7/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 90*tan(c/2 + d*x/2)**5/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 192*tan(c/2 + d*x/2)**4/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 90*tan(c/2 + d*x/2)**3/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 256*tan(c/2 + d*x/2)**2/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) - 42*tan(c/2 + d*x/2)/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d) + 64/(24*a**2*d*tan(c/2 + d*x/2)**8 + 96*a**2*d*tan(c/2 + d*x/2)**6 + 144*a**2*d*tan(c/2 + d*x/2)**4 + 96*a**2*d*tan(c/2 + d*x/2)**2 + 24*a**2*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**4/(a*sin(c) + a)**2, True))","A",0
424,1,694,0,36.058851," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{3 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{9 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{9 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{3 d x}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{6 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{6 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{24 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{6 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{10}{3 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-3*d*x*tan(c/2 + d*x/2)**6/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 9*d*x*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 9*d*x*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 3*d*x/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 6*tan(c/2 + d*x/2)**5/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 6*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 24*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 6*tan(c/2 + d*x/2)/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 10/(3*a**2*d*tan(c/2 + d*x/2)**6 + 9*a**2*d*tan(c/2 + d*x/2)**4 + 9*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d), Ne(d, 0)), (x*sin(c)*cos(c)**4/(a*sin(c) + a)**2, True))","A",0
425,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
426,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\cos^{4}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
427,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
428,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
429,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
430,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
431,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
432,1,3578,0,147.461779," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{51 d x \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{51 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{204 d x \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{204 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{306 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{306 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{204 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{204 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{51 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{51 d x}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{102 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{102 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{374 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{342 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{618 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{266 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{538 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{58 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{160}{8 a^{3} d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((51*d*x*tan(c/2 + d*x/2)**9/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 51*d*x*tan(c/2 + d*x/2)**8/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 204*d*x*tan(c/2 + d*x/2)**7/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 204*d*x*tan(c/2 + d*x/2)**6/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 306*d*x*tan(c/2 + d*x/2)**5/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 306*d*x*tan(c/2 + d*x/2)**4/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 204*d*x*tan(c/2 + d*x/2)**3/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 204*d*x*tan(c/2 + d*x/2)**2/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 51*d*x*tan(c/2 + d*x/2)/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 51*d*x/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 102*tan(c/2 + d*x/2)**8/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 102*tan(c/2 + d*x/2)**7/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 374*tan(c/2 + d*x/2)**6/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 342*tan(c/2 + d*x/2)**5/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 618*tan(c/2 + d*x/2)**4/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 266*tan(c/2 + d*x/2)**3/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 538*tan(c/2 + d*x/2)**2/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 58*tan(c/2 + d*x/2)/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d) + 160/(8*a**3*d*tan(c/2 + d*x/2)**9 + 8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**7 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**5 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**3 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d*tan(c/2 + d*x/2) + 8*a**3*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**4/(a*sin(c) + a)**3, True))","A",0
433,1,2264,0,95.056905," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{33 d x \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{33 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{99 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{99 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{99 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{99 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{33 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{33 d x}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{66 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{66 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{192 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{120 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{246 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{38 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} - \frac{104}{6 a^{3} d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-33*d*x*tan(c/2 + d*x/2)**7/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 33*d*x*tan(c/2 + d*x/2)**6/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 99*d*x*tan(c/2 + d*x/2)**5/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 99*d*x*tan(c/2 + d*x/2)**4/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 99*d*x*tan(c/2 + d*x/2)**3/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 99*d*x*tan(c/2 + d*x/2)**2/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 33*d*x*tan(c/2 + d*x/2)/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 33*d*x/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 66*tan(c/2 + d*x/2)**6/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 66*tan(c/2 + d*x/2)**5/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 192*tan(c/2 + d*x/2)**4/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 120*tan(c/2 + d*x/2)**3/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 246*tan(c/2 + d*x/2)**2/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 38*tan(c/2 + d*x/2)/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d) - 104/(6*a**3*d*tan(c/2 + d*x/2)**7 + 6*a**3*d*tan(c/2 + d*x/2)**6 + 18*a**3*d*tan(c/2 + d*x/2)**5 + 18*a**3*d*tan(c/2 + d*x/2)**4 + 18*a**3*d*tan(c/2 + d*x/2)**3 + 18*a**3*d*tan(c/2 + d*x/2)**2 + 6*a**3*d*tan(c/2 + d*x/2) + 6*a**3*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**4/(a*sin(c) + a)**3, True))","A",0
434,1,1244,0,61.269319," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{9 d x \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{9 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{18 d x \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{18 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{9 d x \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{9 d x}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{18 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{14 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{42 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{10 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} + \frac{28}{2 a^{3} d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{4}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*d*x*tan(c/2 + d*x/2)**5/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 9*d*x*tan(c/2 + d*x/2)**4/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 18*d*x*tan(c/2 + d*x/2)**3/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 18*d*x*tan(c/2 + d*x/2)**2/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 9*d*x*tan(c/2 + d*x/2)/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 9*d*x/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 18*tan(c/2 + d*x/2)**4/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 14*tan(c/2 + d*x/2)**3/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 42*tan(c/2 + d*x/2)**2/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 10*tan(c/2 + d*x/2)/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d) + 28/(2*a**3*d*tan(c/2 + d*x/2)**5 + 2*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**3 + 4*a**3*d*tan(c/2 + d*x/2)**2 + 2*a**3*d*tan(c/2 + d*x/2) + 2*a**3*d), Ne(d, 0)), (x*sin(c)*cos(c)**4/(a*sin(c) + a)**3, True))","A",0
435,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
436,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\cos^{4}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
437,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
438,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
439,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
440,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*sin(f*x+e)/(a+a*sin(f*x+e))**6,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
441,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*sin(f*x+e)**2/(a+a*sin(f*x+e))**7,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
442,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*sin(f*x+e)**3/(a+a*sin(f*x+e))**8,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
443,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*sin(c + d*x)**2*cos(c + d*x)**4, x)","F",0
444,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
445,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)*(a+a*sin(d*x+c))**(1/2),x)","\int \sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)} \cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a*(sin(c + d*x) + 1))*cos(c + d*x)**4*csc(c + d*x), x)","F",0
446,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
447,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
448,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
449,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
450,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
451,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
452,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**8*(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
453,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
454,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
455,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
456,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
457,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
458,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
459,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
460,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
461,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
462,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**8*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
463,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**9*(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
464,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2*cos(c + d*x)**4/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
465,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
466,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+a*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sqrt{a \left(\sin{\left(c + d x \right)} + 1\right)}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)/sqrt(a*(sin(c + d*x) + 1)), x)","F",0
467,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
468,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
469,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
470,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
471,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6/(a+a*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
473,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
474,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
475,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+a*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)/(a*(sin(c + d*x) + 1))**(3/2), x)","F",0
476,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6/(a+a*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**4/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
482,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
483,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
484,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
485,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
486,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+a*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**n*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
491,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**n*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
492,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**n/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
493,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**n/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
494,1,136,0,42.244223," ","integrate(cos(d*x+c)**5*sin(d*x+c)**5*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{11}{\left(c + d x \right)}}{693 d} + \frac{4 a \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{63 d} + \frac{a \sin^{7}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{7 d} - \frac{a \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{12 d} - \frac{a \cos^{10}{\left(c + d x \right)}}{60 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{5}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**11/(693*d) + 4*a*sin(c + d*x)**9*cos(c + d*x)**2/(63*d) + a*sin(c + d*x)**7*cos(c + d*x)**4/(7*d) - a*sin(c + d*x)**4*cos(c + d*x)**6/(6*d) - a*sin(c + d*x)**2*cos(c + d*x)**8/(12*d) - a*cos(c + d*x)**10/(60*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**5*cos(c)**5, True))","A",0
495,1,136,0,27.035984," ","integrate(cos(d*x+c)**5*sin(d*x+c)**4*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{4 a \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{a \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} - \frac{a \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{12 d} - \frac{a \cos^{10}{\left(c + d x \right)}}{60 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{4}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**9/(315*d) + 4*a*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + a*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) - a*sin(c + d*x)**4*cos(c + d*x)**6/(6*d) - a*sin(c + d*x)**2*cos(c + d*x)**8/(12*d) - a*cos(c + d*x)**10/(60*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**4*cos(c)**5, True))","A",0
496,1,114,0,17.225230," ","integrate(cos(d*x+c)**5*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{4 a \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{a \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{a \cos^{8}{\left(c + d x \right)}}{24 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{3}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**9/(315*d) + 4*a*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + a*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) - a*sin(c + d*x)**2*cos(c + d*x)**6/(6*d) - a*cos(c + d*x)**8/(24*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**3*cos(c)**5, True))","A",0
497,1,114,0,10.441063," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 a \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{a \cos^{8}{\left(c + d x \right)}}{24 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{2}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**7/(105*d) + 4*a*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + a*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - a*sin(c + d*x)**2*cos(c + d*x)**6/(6*d) - a*cos(c + d*x)**8/(24*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**2*cos(c)**5, True))","A",0
498,1,90,0,6.258097," ","integrate(cos(d*x+c)**5*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 a \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{a \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**7/(105*d) + 4*a*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + a*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - a*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)*cos(c)**5, True))","A",0
499,0,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)*(a+a*sin(d*x+c)),x)","a \left(\int \cos^{5}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(cos(c + d*x)**5*csc(c + d*x), x) + Integral(sin(c + d*x)*cos(c + d*x)**5*csc(c + d*x), x))","F",0
500,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
501,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
503,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
504,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
505,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**7*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
506,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**8*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**9*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
508,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**10*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
509,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**11*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
510,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**12*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
511,1,189,0,26.150797," ","integrate(cos(d*x+c)**5*sin(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{16 a^{2} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{8 a^{2} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{2 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} - \frac{a^{2} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{12 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{a^{2} \cos^{10}{\left(c + d x \right)}}{60 d} - \frac{a^{2} \cos^{8}{\left(c + d x \right)}}{24 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{3}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**2*sin(c + d*x)**9/(315*d) + 8*a**2*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 2*a**2*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) - a**2*sin(c + d*x)**4*cos(c + d*x)**6/(6*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**8/(12*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**6/(6*d) - a**2*cos(c + d*x)**10/(60*d) - a**2*cos(c + d*x)**8/(24*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**3*cos(c)**5, True))","A",0
512,1,190,0,16.757555," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{8 a^{2} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{4 a^{2} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{8 a^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{4 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \cos^{8}{\left(c + d x \right)}}{12 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{2}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**2*sin(c + d*x)**9/(315*d) + 4*a**2*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 8*a**2*sin(c + d*x)**7/(105*d) + a**2*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 4*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + a**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**6/(3*d) - a**2*cos(c + d*x)**8/(12*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**2*cos(c)**5, True))","A",0
513,1,139,0,9.876886," ","integrate(cos(d*x+c)**5*sin(d*x+c)*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{16 a^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{8 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{2 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{a^{2} \cos^{8}{\left(c + d x \right)}}{24 d} - \frac{a^{2} \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a**2*sin(c + d*x)**7/(105*d) + 8*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + 2*a**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**6/(6*d) - a**2*cos(c + d*x)**8/(24*d) - a**2*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)*cos(c)**5, True))","A",0
514,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
515,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
516,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
517,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
518,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
519,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
520,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**7*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
521,1,255,0,30.001004," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{8 a^{3} \sin^{9}{\left(c + d x \right)}}{105 d} + \frac{12 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{8 a^{3} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{3 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{4 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} - \frac{a^{3} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{6 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{12 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{2 d} - \frac{a^{3} \cos^{10}{\left(c + d x \right)}}{60 d} - \frac{a^{3} \cos^{8}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{2}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**3*sin(c + d*x)**9/(105*d) + 12*a**3*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 8*a**3*sin(c + d*x)**7/(105*d) + 3*a**3*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 4*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) - a**3*sin(c + d*x)**4*cos(c + d*x)**6/(6*d) + a**3*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**8/(12*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**6/(2*d) - a**3*cos(c + d*x)**10/(60*d) - a**3*cos(c + d*x)**8/(8*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**2*cos(c)**5, True))","A",0
522,1,202,0,17.299611," ","integrate(cos(d*x+c)**5*sin(d*x+c)*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{8 a^{3} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{4 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{8 a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{a^{3} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{4 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{2 d} - \frac{a^{3} \cos^{8}{\left(c + d x \right)}}{8 d} - \frac{a^{3} \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**3*sin(c + d*x)**9/(315*d) + 4*a**3*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 8*a**3*sin(c + d*x)**7/(35*d) + a**3*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 4*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + a**3*sin(c + d*x)**3*cos(c + d*x)**4/d - a**3*sin(c + d*x)**2*cos(c + d*x)**6/(2*d) - a**3*cos(c + d*x)**8/(8*d) - a**3*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)*cos(c)**5, True))","A",0
523,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
524,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
525,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
526,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
527,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
528,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
529,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**7*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
530,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
531,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
532,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
533,1,981,0,81.792375," ","integrate(cos(d*x+c)**5*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{420 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{672 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{140 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{576 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{140 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{672 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{420 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{5}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((420*tan(c/2 + d*x/2)**10/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 672*tan(c/2 + d*x/2)**9/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 140*tan(c/2 + d*x/2)**8/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 576*tan(c/2 + d*x/2)**7/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 140*tan(c/2 + d*x/2)**6/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 672*tan(c/2 + d*x/2)**5/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 420*tan(c/2 + d*x/2)**4/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**5/(a*sin(c) + a), True))","A",0
534,1,862,0,51.017837," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{40 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{60 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{24 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{40 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{24 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{60 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{40 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{5}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((40*tan(c/2 + d*x/2)**9/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 60*tan(c/2 + d*x/2)**8/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 24*tan(c/2 + d*x/2)**7/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 40*tan(c/2 + d*x/2)**6/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 24*tan(c/2 + d*x/2)**5/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 60*tan(c/2 + d*x/2)**4/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 40*tan(c/2 + d*x/2)**3/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**5/(a*sin(c) + a), True))","A",0
535,1,741,0,30.743916," ","integrate(cos(d*x+c)**5*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{30 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{40 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{16 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{40 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{5}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*tan(c/2 + d*x/2)**8/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 40*tan(c/2 + d*x/2)**7/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*tan(c/2 + d*x/2)**6/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 16*tan(c/2 + d*x/2)**5/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*tan(c/2 + d*x/2)**4/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 40*tan(c/2 + d*x/2)**3/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*tan(c/2 + d*x/2)**2/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d), Ne(d, 0)), (x*sin(c)*cos(c)**5/(a*sin(c) + a), True))","A",0
536,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
537,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
538,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
539,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
540,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
541,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
542,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
543,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**8/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
544,1,682,0,128.340953," ","integrate(cos(d*x+c)**5*sin(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{60 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{192 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{280 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{192 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{60 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{5}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((60*tan(c/2 + d*x/2)**8/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 192*tan(c/2 + d*x/2)**7/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 280*tan(c/2 + d*x/2)**6/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 192*tan(c/2 + d*x/2)**5/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 60*tan(c/2 + d*x/2)**4/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**5/(a*sin(c) + a)**2, True))","A",0
545,1,588,0,82.056562," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{40 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{120 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{176 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{120 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{40 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{5}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((40*tan(c/2 + d*x/2)**7/(15*a**2*d*tan(c/2 + d*x/2)**10 + 75*a**2*d*tan(c/2 + d*x/2)**8 + 150*a**2*d*tan(c/2 + d*x/2)**6 + 150*a**2*d*tan(c/2 + d*x/2)**4 + 75*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 120*tan(c/2 + d*x/2)**6/(15*a**2*d*tan(c/2 + d*x/2)**10 + 75*a**2*d*tan(c/2 + d*x/2)**8 + 150*a**2*d*tan(c/2 + d*x/2)**6 + 150*a**2*d*tan(c/2 + d*x/2)**4 + 75*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 176*tan(c/2 + d*x/2)**5/(15*a**2*d*tan(c/2 + d*x/2)**10 + 75*a**2*d*tan(c/2 + d*x/2)**8 + 150*a**2*d*tan(c/2 + d*x/2)**6 + 150*a**2*d*tan(c/2 + d*x/2)**4 + 75*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 120*tan(c/2 + d*x/2)**4/(15*a**2*d*tan(c/2 + d*x/2)**10 + 75*a**2*d*tan(c/2 + d*x/2)**8 + 150*a**2*d*tan(c/2 + d*x/2)**6 + 150*a**2*d*tan(c/2 + d*x/2)**4 + 75*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 40*tan(c/2 + d*x/2)**3/(15*a**2*d*tan(c/2 + d*x/2)**10 + 75*a**2*d*tan(c/2 + d*x/2)**8 + 150*a**2*d*tan(c/2 + d*x/2)**6 + 150*a**2*d*tan(c/2 + d*x/2)**4 + 75*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**5/(a*sin(c) + a)**2, True))","A",0
546,1,493,0,53.001715," ","integrate(cos(d*x+c)**5*sin(d*x+c)/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{6 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{16 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{24 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{16 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{6 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{5}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*tan(c/2 + d*x/2)**6/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 16*tan(c/2 + d*x/2)**5/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 24*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 16*tan(c/2 + d*x/2)**3/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 6*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d), Ne(d, 0)), (x*sin(c)*cos(c)**5/(a*sin(c) + a)**2, True))","A",0
547,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
548,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
549,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
550,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
551,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
552,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
553,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**7/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
554,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
555,1,1698,0,135.281698," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{8 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{32 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{48 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{32 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{8 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{4 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{16 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{24 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{16 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{4 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{8 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{8 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{32 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{20 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{32 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} + \frac{8 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} - \frac{8 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{5}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**8/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 32*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**6/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 48*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**4/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 32*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 8*log(tan(c/2 + d*x/2) + 1)/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 4*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**8/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 16*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**6/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 24*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 16*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 4*log(tan(c/2 + d*x/2)**2 + 1)/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 8*tan(c/2 + d*x/2)**7/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 8*tan(c/2 + d*x/2)**6/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 32*tan(c/2 + d*x/2)**5/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 20*tan(c/2 + d*x/2)**4/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 32*tan(c/2 + d*x/2)**3/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) + 8*tan(c/2 + d*x/2)**2/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d) - 8*tan(c/2 + d*x/2)/(a**3*d*tan(c/2 + d*x/2)**8 + 4*a**3*d*tan(c/2 + d*x/2)**6 + 6*a**3*d*tan(c/2 + d*x/2)**4 + 4*a**3*d*tan(c/2 + d*x/2)**2 + a**3*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**5/(a*sin(c) + a)**3, True))","A",0
556,1,1102,0,86.477241," ","integrate(cos(d*x+c)**5*sin(d*x+c)/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{24 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{72 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{72 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{24 \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{12 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{36 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{36 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{12 \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{24 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{18 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{56 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} - \frac{18 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} + \frac{24 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{5}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-24*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**6/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) - 72*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**4/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) - 72*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**2/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) - 24*log(tan(c/2 + d*x/2) + 1)/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) + 12*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**6/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) + 36*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) + 36*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) + 12*log(tan(c/2 + d*x/2)**2 + 1)/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) + 24*tan(c/2 + d*x/2)**5/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) - 18*tan(c/2 + d*x/2)**4/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) + 56*tan(c/2 + d*x/2)**3/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) - 18*tan(c/2 + d*x/2)**2/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d) + 24*tan(c/2 + d*x/2)/(3*a**3*d*tan(c/2 + d*x/2)**6 + 9*a**3*d*tan(c/2 + d*x/2)**4 + 9*a**3*d*tan(c/2 + d*x/2)**2 + 3*a**3*d), Ne(d, 0)), (x*sin(c)*cos(c)**5/(a*sin(c) + a)**3, True))","A",0
557,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
558,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
559,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
560,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
561,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
562,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
563,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
564,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
565,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
566,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
567,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
568,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
569,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
570,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
571,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
572,1,318,0,44.943773," ","integrate(cos(d*x+c)**6*sin(d*x+c)**4*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{3 a x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 a x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{15 a x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{15 a x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{15 a x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{3 a x \cos^{10}{\left(c + d x \right)}}{256} + \frac{3 a \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 a \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{a \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} - \frac{a \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{7 a \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{4 a \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{3 a \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{8 a \cos^{11}{\left(c + d x \right)}}{693 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{4}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*sin(c + d*x)**10/256 + 15*a*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 15*a*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 15*a*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 15*a*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 3*a*x*cos(c + d*x)**10/256 + 3*a*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*a*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + a*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) - a*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 7*a*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 4*a*sin(c + d*x)**2*cos(c + d*x)**9/(63*d) - 3*a*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 8*a*cos(c + d*x)**11/(693*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**4*cos(c)**6, True))","A",0
573,1,294,0,29.349208," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{3 a x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 a x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{15 a x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{15 a x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{15 a x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{3 a x \cos^{10}{\left(c + d x \right)}}{256} + \frac{3 a \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 a \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{a \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} - \frac{7 a \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{3 a \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{2 a \cos^{9}{\left(c + d x \right)}}{63 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{3}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*sin(c + d*x)**10/256 + 15*a*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 15*a*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 15*a*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 15*a*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 3*a*x*cos(c + d*x)**10/256 + 3*a*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*a*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + a*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) - 7*a*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - a*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 3*a*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 2*a*cos(c + d*x)**9/(63*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**3*cos(c)**6, True))","A",0
574,1,248,0,18.971197," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{5 a x \sin^{8}{\left(c + d x \right)}}{128} + \frac{5 a x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 a x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{5 a x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{5 a x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 a \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 a \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{73 a \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{5 a \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{2 a \cos^{9}{\left(c + d x \right)}}{63 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{2}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a*x*sin(c + d*x)**8/128 + 5*a*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*a*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 5*a*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 5*a*x*cos(c + d*x)**8/128 + 5*a*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*a*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 73*a*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) - a*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 5*a*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 2*a*cos(c + d*x)**9/(63*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**2*cos(c)**6, True))","A",0
575,1,223,0,11.233400," ","integrate(cos(d*x+c)**6*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{5 a x \sin^{8}{\left(c + d x \right)}}{128} + \frac{5 a x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 a x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{5 a x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{5 a x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 a \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 a \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{73 a \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} - \frac{5 a \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{a \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a*x*sin(c + d*x)**8/128 + 5*a*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*a*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 5*a*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 5*a*x*cos(c + d*x)**8/128 + 5*a*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*a*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 73*a*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) - 5*a*sin(c + d*x)*cos(c + d*x)**7/(128*d) - a*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)*cos(c)**6, True))","A",0
576,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
577,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
578,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
579,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
580,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
581,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
582,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**7*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
583,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**8*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
584,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**9*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
585,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**10*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
586,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**11*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
587,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**12*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
588,1,656,0,63.182431," ","integrate(cos(d*x+c)**6*sin(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{5 a^{2} x \sin^{12}{\left(c + d x \right)}}{1024} + \frac{15 a^{2} x \sin^{10}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{512} + \frac{3 a^{2} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{75 a^{2} x \sin^{8}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{1024} + \frac{15 a^{2} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{25 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{256} + \frac{15 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{75 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{1024} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{512} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{5 a^{2} x \cos^{12}{\left(c + d x \right)}}{1024} + \frac{3 a^{2} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{5 a^{2} \sin^{11}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{1024 d} + \frac{85 a^{2} \sin^{9}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3072 d} + \frac{3 a^{2} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{33 a^{2} \sin^{7}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{512 d} + \frac{7 a^{2} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{33 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{512 d} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} - \frac{2 a^{2} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{85 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{3072 d} - \frac{7 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{8 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{11}{\left(c + d x \right)}}{1024 d} - \frac{3 a^{2} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{16 a^{2} \cos^{11}{\left(c + d x \right)}}{693 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{4}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**2*x*sin(c + d*x)**12/1024 + 15*a**2*x*sin(c + d*x)**10*cos(c + d*x)**2/512 + 3*a**2*x*sin(c + d*x)**10/256 + 75*a**2*x*sin(c + d*x)**8*cos(c + d*x)**4/1024 + 15*a**2*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 25*a**2*x*sin(c + d*x)**6*cos(c + d*x)**6/256 + 15*a**2*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 75*a**2*x*sin(c + d*x)**4*cos(c + d*x)**8/1024 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**10/512 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 5*a**2*x*cos(c + d*x)**12/1024 + 3*a**2*x*cos(c + d*x)**10/256 + 5*a**2*sin(c + d*x)**11*cos(c + d*x)/(1024*d) + 85*a**2*sin(c + d*x)**9*cos(c + d*x)**3/(3072*d) + 3*a**2*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 33*a**2*sin(c + d*x)**7*cos(c + d*x)**5/(512*d) + 7*a**2*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) - 33*a**2*sin(c + d*x)**5*cos(c + d*x)**7/(512*d) + a**2*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) - 2*a**2*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 85*a**2*sin(c + d*x)**3*cos(c + d*x)**9/(3072*d) - 7*a**2*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 8*a**2*sin(c + d*x)**2*cos(c + d*x)**9/(63*d) - 5*a**2*sin(c + d*x)*cos(c + d*x)**11/(1024*d) - 3*a**2*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 16*a**2*cos(c + d*x)**11/(693*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**4*cos(c)**6, True))","A",0
589,1,384,0,40.490775," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{10}{\left(c + d x \right)}}{128} + \frac{15 a^{2} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{128} + \frac{15 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{64} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a^{2} x \cos^{10}{\left(c + d x \right)}}{128} + \frac{3 a^{2} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{7 a^{2} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{64 d} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{a^{2} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{7 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{4 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{3 a^{2} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{128 d} - \frac{8 a^{2} \cos^{11}{\left(c + d x \right)}}{693 d} - \frac{2 a^{2} \cos^{9}{\left(c + d x \right)}}{63 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{3}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**10/128 + 15*a**2*x*sin(c + d*x)**8*cos(c + d*x)**2/128 + 15*a**2*x*sin(c + d*x)**6*cos(c + d*x)**4/64 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**6/64 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**8/128 + 3*a**2*x*cos(c + d*x)**10/128 + 3*a**2*sin(c + d*x)**9*cos(c + d*x)/(128*d) + 7*a**2*sin(c + d*x)**7*cos(c + d*x)**3/(64*d) + a**2*sin(c + d*x)**5*cos(c + d*x)**5/(5*d) - a**2*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 7*a**2*sin(c + d*x)**3*cos(c + d*x)**7/(64*d) - 4*a**2*sin(c + d*x)**2*cos(c + d*x)**9/(63*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 3*a**2*sin(c + d*x)*cos(c + d*x)**9/(128*d) - 8*a**2*cos(c + d*x)**11/(693*d) - 2*a**2*cos(c + d*x)**9/(63*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**3*cos(c)**6, True))","A",0
590,1,529,0,27.323107," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 a^{2} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{5 a^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{5 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{5 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a^{2} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{5 a^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a^{2} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 a^{2} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{5 a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{55 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} - \frac{7 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{73 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} - \frac{2 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{3 a^{2} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{4 a^{2} \cos^{9}{\left(c + d x \right)}}{63 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin^{2}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**10/256 + 15*a**2*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 5*a**2*x*sin(c + d*x)**8/128 + 15*a**2*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 5*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 5*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a**2*x*cos(c + d*x)**10/256 + 5*a**2*x*cos(c + d*x)**8/128 + 3*a**2*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*a**2*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 5*a**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + a**2*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 55*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) - 7*a**2*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) + 73*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) - 2*a**2*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 3*a**2*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 5*a**2*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 4*a**2*cos(c + d*x)**9/(63*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)**2*cos(c)**6, True))","A",0
591,1,282,0,16.873370," ","integrate(cos(d*x+c)**6*sin(d*x+c)*(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{5 a^{2} x \sin^{8}{\left(c + d x \right)}}{64} + \frac{5 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{5 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a^{2} x \cos^{8}{\left(c + d x \right)}}{64} + \frac{5 a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} + \frac{55 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{192 d} + \frac{73 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{192 d} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{2 a^{2} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{a^{2} \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{2} \sin{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**2*x*sin(c + d*x)**8/64 + 5*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 5*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 5*a**2*x*cos(c + d*x)**8/64 + 5*a**2*sin(c + d*x)**7*cos(c + d*x)/(64*d) + 55*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(192*d) + 73*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(192*d) - a**2*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 5*a**2*sin(c + d*x)*cos(c + d*x)**7/(64*d) - 2*a**2*cos(c + d*x)**9/(63*d) - a**2*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(a*sin(c) + a)**2*sin(c)*cos(c)**6, True))","A",0
592,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
593,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
594,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
595,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
596,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
597,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
598,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**7*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
599,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**8*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
600,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**9*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
601,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**10*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
602,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**11*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
603,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**12*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
604,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**13*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
605,1,748,0,92.942084," ","integrate(cos(d*x+c)**6*sin(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{15 a^{3} x \sin^{12}{\left(c + d x \right)}}{1024} + \frac{45 a^{3} x \sin^{10}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{512} + \frac{3 a^{3} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{225 a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{1024} + \frac{15 a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{75 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{256} + \frac{15 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{225 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{1024} + \frac{15 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{45 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{512} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{15 a^{3} x \cos^{12}{\left(c + d x \right)}}{1024} + \frac{3 a^{3} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{15 a^{3} \sin^{11}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{1024 d} + \frac{85 a^{3} \sin^{9}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{1024 d} + \frac{3 a^{3} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{99 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{512 d} + \frac{7 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{a^{3} \sin^{6}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{99 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{512 d} + \frac{a^{3} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} - \frac{2 a^{3} \sin^{4}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{21 d} - \frac{3 a^{3} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{85 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{1024 d} - \frac{7 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{8 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{11}{\left(c + d x \right)}}{231 d} - \frac{4 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{21 d} - \frac{15 a^{3} \sin{\left(c + d x \right)} \cos^{11}{\left(c + d x \right)}}{1024 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{16 a^{3} \cos^{13}{\left(c + d x \right)}}{3003 d} - \frac{8 a^{3} \cos^{11}{\left(c + d x \right)}}{231 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{4}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*a**3*x*sin(c + d*x)**12/1024 + 45*a**3*x*sin(c + d*x)**10*cos(c + d*x)**2/512 + 3*a**3*x*sin(c + d*x)**10/256 + 225*a**3*x*sin(c + d*x)**8*cos(c + d*x)**4/1024 + 15*a**3*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 75*a**3*x*sin(c + d*x)**6*cos(c + d*x)**6/256 + 15*a**3*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 225*a**3*x*sin(c + d*x)**4*cos(c + d*x)**8/1024 + 15*a**3*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 45*a**3*x*sin(c + d*x)**2*cos(c + d*x)**10/512 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 15*a**3*x*cos(c + d*x)**12/1024 + 3*a**3*x*cos(c + d*x)**10/256 + 15*a**3*sin(c + d*x)**11*cos(c + d*x)/(1024*d) + 85*a**3*sin(c + d*x)**9*cos(c + d*x)**3/(1024*d) + 3*a**3*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 99*a**3*sin(c + d*x)**7*cos(c + d*x)**5/(512*d) + 7*a**3*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) - a**3*sin(c + d*x)**6*cos(c + d*x)**7/(7*d) - 99*a**3*sin(c + d*x)**5*cos(c + d*x)**7/(512*d) + a**3*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) - 2*a**3*sin(c + d*x)**4*cos(c + d*x)**9/(21*d) - 3*a**3*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 85*a**3*sin(c + d*x)**3*cos(c + d*x)**9/(1024*d) - 7*a**3*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 8*a**3*sin(c + d*x)**2*cos(c + d*x)**11/(231*d) - 4*a**3*sin(c + d*x)**2*cos(c + d*x)**9/(21*d) - 15*a**3*sin(c + d*x)*cos(c + d*x)**11/(1024*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 16*a**3*cos(c + d*x)**13/(3003*d) - 8*a**3*cos(c + d*x)**11/(231*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**4*cos(c)**6, True))","A",0
606,1,699,0,63.752232," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{5 a^{3} x \sin^{12}{\left(c + d x \right)}}{1024} + \frac{15 a^{3} x \sin^{10}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{512} + \frac{9 a^{3} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{75 a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{1024} + \frac{45 a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{25 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{256} + \frac{45 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{75 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{1024} + \frac{45 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{512} + \frac{45 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{5 a^{3} x \cos^{12}{\left(c + d x \right)}}{1024} + \frac{9 a^{3} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{5 a^{3} \sin^{11}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{1024 d} + \frac{85 a^{3} \sin^{9}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3072 d} + \frac{9 a^{3} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{33 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{512 d} + \frac{21 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{33 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{512 d} + \frac{3 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} - \frac{3 a^{3} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{85 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{3072 d} - \frac{21 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{4 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{21 d} - \frac{a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{5 a^{3} \sin{\left(c + d x \right)} \cos^{11}{\left(c + d x \right)}}{1024 d} - \frac{9 a^{3} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{8 a^{3} \cos^{11}{\left(c + d x \right)}}{231 d} - \frac{2 a^{3} \cos^{9}{\left(c + d x \right)}}{63 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{3}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**3*x*sin(c + d*x)**12/1024 + 15*a**3*x*sin(c + d*x)**10*cos(c + d*x)**2/512 + 9*a**3*x*sin(c + d*x)**10/256 + 75*a**3*x*sin(c + d*x)**8*cos(c + d*x)**4/1024 + 45*a**3*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 25*a**3*x*sin(c + d*x)**6*cos(c + d*x)**6/256 + 45*a**3*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 75*a**3*x*sin(c + d*x)**4*cos(c + d*x)**8/1024 + 45*a**3*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**10/512 + 45*a**3*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 5*a**3*x*cos(c + d*x)**12/1024 + 9*a**3*x*cos(c + d*x)**10/256 + 5*a**3*sin(c + d*x)**11*cos(c + d*x)/(1024*d) + 85*a**3*sin(c + d*x)**9*cos(c + d*x)**3/(3072*d) + 9*a**3*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 33*a**3*sin(c + d*x)**7*cos(c + d*x)**5/(512*d) + 21*a**3*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) - 33*a**3*sin(c + d*x)**5*cos(c + d*x)**7/(512*d) + 3*a**3*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) - 3*a**3*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 85*a**3*sin(c + d*x)**3*cos(c + d*x)**9/(3072*d) - 21*a**3*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 4*a**3*sin(c + d*x)**2*cos(c + d*x)**9/(21*d) - a**3*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 5*a**3*sin(c + d*x)*cos(c + d*x)**11/(1024*d) - 9*a**3*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 8*a**3*cos(c + d*x)**11/(231*d) - 2*a**3*cos(c + d*x)**9/(63*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**3*cos(c)**6, True))","A",0
607,1,597,0,41.840121," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{9 a^{3} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{45 a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{5 a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{45 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{5 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{45 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{15 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{45 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{5 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{9 a^{3} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{5 a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{9 a^{3} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{21 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{5 a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{3 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{55 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} - \frac{a^{3} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{21 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{73 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} - \frac{4 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{3 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{9 a^{3} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{5 a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{8 a^{3} \cos^{11}{\left(c + d x \right)}}{693 d} - \frac{2 a^{3} \cos^{9}{\left(c + d x \right)}}{21 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin^{2}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((9*a**3*x*sin(c + d*x)**10/256 + 45*a**3*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 5*a**3*x*sin(c + d*x)**8/128 + 45*a**3*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 5*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 45*a**3*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 15*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 45*a**3*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 5*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 9*a**3*x*cos(c + d*x)**10/256 + 5*a**3*x*cos(c + d*x)**8/128 + 9*a**3*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 21*a**3*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 5*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 3*a**3*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 55*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) - a**3*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 21*a**3*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) + 73*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) - 4*a**3*sin(c + d*x)**2*cos(c + d*x)**9/(63*d) - 3*a**3*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 9*a**3*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 5*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 8*a**3*cos(c + d*x)**11/(693*d) - 2*a**3*cos(c + d*x)**9/(21*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)**2*cos(c)**6, True))","A",0
608,1,542,0,26.982396," ","integrate(cos(d*x+c)**6*sin(d*x+c)*(a+a*sin(d*x+c))**3,x)","\begin{cases} \frac{3 a^{3} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{15 a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{15 a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{45 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{15 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a^{3} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{15 a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a^{3} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 a^{3} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{15 a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{a^{3} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{55 a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{7 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{73 a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{3 a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{3 a^{3} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{15 a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{2 a^{3} \cos^{9}{\left(c + d x \right)}}{21 d} - \frac{a^{3} \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right)^{3} \sin{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**3*x*sin(c + d*x)**10/256 + 15*a**3*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 15*a**3*x*sin(c + d*x)**8/128 + 15*a**3*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 15*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*a**3*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 45*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 15*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a**3*x*cos(c + d*x)**10/256 + 15*a**3*x*cos(c + d*x)**8/128 + 3*a**3*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*a**3*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 15*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + a**3*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 55*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 7*a**3*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) + 73*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 3*a**3*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 3*a**3*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 15*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 2*a**3*cos(c + d*x)**9/(21*d) - a**3*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(a*sin(c) + a)**3*sin(c)*cos(c)**6, True))","A",0
609,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
610,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
611,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
612,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
613,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
614,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
615,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**7*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
616,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**8*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
617,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**9*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
618,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**10*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
619,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**11*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
620,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**12*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
621,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**13*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
622,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**14*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
623,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
624,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
625,1,3580,0,122.265903," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{105 d x \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{840 d x \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{2940 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{5880 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{7350 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{5880 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{2940 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{840 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{105 d x}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{210 \tan^{15}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{1610 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{17920 \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} + \frac{23310 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{46970 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{17920 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} + \frac{46970 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{28672 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{23310 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} + \frac{3584 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} + \frac{1610 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{4096 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} + \frac{210 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} - \frac{512}{4480 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 313600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 250880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 125440 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4480 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{6}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-105*d*x*tan(c/2 + d*x/2)**16/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 840*d*x*tan(c/2 + d*x/2)**14/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 2940*d*x*tan(c/2 + d*x/2)**12/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 5880*d*x*tan(c/2 + d*x/2)**10/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 7350*d*x*tan(c/2 + d*x/2)**8/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 5880*d*x*tan(c/2 + d*x/2)**6/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 2940*d*x*tan(c/2 + d*x/2)**4/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 840*d*x*tan(c/2 + d*x/2)**2/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 105*d*x/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 210*tan(c/2 + d*x/2)**15/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 1610*tan(c/2 + d*x/2)**13/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 17920*tan(c/2 + d*x/2)**12/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) + 23310*tan(c/2 + d*x/2)**11/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 46970*tan(c/2 + d*x/2)**9/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 17920*tan(c/2 + d*x/2)**8/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) + 46970*tan(c/2 + d*x/2)**7/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 28672*tan(c/2 + d*x/2)**6/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 23310*tan(c/2 + d*x/2)**5/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) + 3584*tan(c/2 + d*x/2)**4/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) + 1610*tan(c/2 + d*x/2)**3/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 4096*tan(c/2 + d*x/2)**2/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) + 210*tan(c/2 + d*x/2)/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d) - 512/(4480*a*d*tan(c/2 + d*x/2)**16 + 35840*a*d*tan(c/2 + d*x/2)**14 + 125440*a*d*tan(c/2 + d*x/2)**12 + 250880*a*d*tan(c/2 + d*x/2)**10 + 313600*a*d*tan(c/2 + d*x/2)**8 + 250880*a*d*tan(c/2 + d*x/2)**6 + 125440*a*d*tan(c/2 + d*x/2)**4 + 35840*a*d*tan(c/2 + d*x/2)**2 + 4480*a*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**6/(a*sin(c) + a), True))","A",0
626,1,2773,0,78.793419," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{105 d x \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{735 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{2205 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{3675 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{3675 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{2205 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{735 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{105 d x}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{210 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{3080 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{6720 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{2170 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{6720 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{13440 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{2170 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{2688 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{3080 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{1344 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} - \frac{210 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} + \frac{192}{1680 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 58800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 35280 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11760 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1680 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{6}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((105*d*x*tan(c/2 + d*x/2)**14/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 735*d*x*tan(c/2 + d*x/2)**12/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 2205*d*x*tan(c/2 + d*x/2)**10/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 3675*d*x*tan(c/2 + d*x/2)**8/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 3675*d*x*tan(c/2 + d*x/2)**6/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 2205*d*x*tan(c/2 + d*x/2)**4/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 735*d*x*tan(c/2 + d*x/2)**2/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 105*d*x/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 210*tan(c/2 + d*x/2)**13/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 3080*tan(c/2 + d*x/2)**11/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 6720*tan(c/2 + d*x/2)**10/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 2170*tan(c/2 + d*x/2)**9/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 6720*tan(c/2 + d*x/2)**8/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 13440*tan(c/2 + d*x/2)**6/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 2170*tan(c/2 + d*x/2)**5/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 2688*tan(c/2 + d*x/2)**4/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 3080*tan(c/2 + d*x/2)**3/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 1344*tan(c/2 + d*x/2)**2/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) - 210*tan(c/2 + d*x/2)/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d) + 192/(1680*a*d*tan(c/2 + d*x/2)**14 + 11760*a*d*tan(c/2 + d*x/2)**12 + 35280*a*d*tan(c/2 + d*x/2)**10 + 58800*a*d*tan(c/2 + d*x/2)**8 + 58800*a*d*tan(c/2 + d*x/2)**6 + 35280*a*d*tan(c/2 + d*x/2)**4 + 11760*a*d*tan(c/2 + d*x/2)**2 + 1680*a*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**6/(a*sin(c) + a), True))","A",0
627,1,2307,0,49.685967," ","integrate(cos(d*x+c)**6*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{15 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{90 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{225 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{300 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{225 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{90 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{15 d x}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{30 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{480 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} + \frac{470 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{480 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{780 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{960 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} + \frac{780 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{960 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{470 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{96 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} + \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} - \frac{96}{240 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{6}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*d*x*tan(c/2 + d*x/2)**12/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 90*d*x*tan(c/2 + d*x/2)**10/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 225*d*x*tan(c/2 + d*x/2)**8/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 300*d*x*tan(c/2 + d*x/2)**6/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 225*d*x*tan(c/2 + d*x/2)**4/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 90*d*x*tan(c/2 + d*x/2)**2/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 15*d*x/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 30*tan(c/2 + d*x/2)**11/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 480*tan(c/2 + d*x/2)**10/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) + 470*tan(c/2 + d*x/2)**9/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 480*tan(c/2 + d*x/2)**8/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 780*tan(c/2 + d*x/2)**7/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 960*tan(c/2 + d*x/2)**6/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) + 780*tan(c/2 + d*x/2)**5/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 960*tan(c/2 + d*x/2)**4/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 470*tan(c/2 + d*x/2)**3/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 96*tan(c/2 + d*x/2)**2/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) + 30*tan(c/2 + d*x/2)/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d) - 96/(240*a*d*tan(c/2 + d*x/2)**12 + 1440*a*d*tan(c/2 + d*x/2)**10 + 3600*a*d*tan(c/2 + d*x/2)**8 + 4800*a*d*tan(c/2 + d*x/2)**6 + 3600*a*d*tan(c/2 + d*x/2)**4 + 1440*a*d*tan(c/2 + d*x/2)**2 + 240*a*d), Ne(d, 0)), (x*sin(c)*cos(c)**6/(a*sin(c) + a), True))","A",0
628,0,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\cos^{6}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(cos(c + d*x)**6*csc(c + d*x)/(sin(c + d*x) + 1), x)/a","F",0
629,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
630,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
631,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
632,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
633,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
634,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
635,1,2271,0,139.913553," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{45 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{270 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{675 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{900 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{675 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{270 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{45 d x}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{90 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{130 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{1920 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{1500 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{1280 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{1500 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{130 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{768 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} - \frac{90 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} + \frac{128}{240 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 4800 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1440 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 240 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{6}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((45*d*x*tan(c/2 + d*x/2)**12/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 270*d*x*tan(c/2 + d*x/2)**10/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 675*d*x*tan(c/2 + d*x/2)**8/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 900*d*x*tan(c/2 + d*x/2)**6/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 675*d*x*tan(c/2 + d*x/2)**4/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 270*d*x*tan(c/2 + d*x/2)**2/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 45*d*x/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 90*tan(c/2 + d*x/2)**11/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 130*tan(c/2 + d*x/2)**9/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 1920*tan(c/2 + d*x/2)**8/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 1500*tan(c/2 + d*x/2)**7/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 1280*tan(c/2 + d*x/2)**6/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 1500*tan(c/2 + d*x/2)**5/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 130*tan(c/2 + d*x/2)**3/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 768*tan(c/2 + d*x/2)**2/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) - 90*tan(c/2 + d*x/2)/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d) + 128/(240*a**2*d*tan(c/2 + d*x/2)**12 + 1440*a**2*d*tan(c/2 + d*x/2)**10 + 3600*a**2*d*tan(c/2 + d*x/2)**8 + 4800*a**2*d*tan(c/2 + d*x/2)**6 + 3600*a**2*d*tan(c/2 + d*x/2)**4 + 1440*a**2*d*tan(c/2 + d*x/2)**2 + 240*a**2*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**6/(a*sin(c) + a)**2, True))","A",0
636,1,1720,0,87.469756," ","integrate(cos(d*x+c)**6*sin(d*x+c)/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{15 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{75 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{150 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{150 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{75 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{15 d x}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{30 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{120 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} + \frac{180 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{480 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{80 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{180 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{160 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} + \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} - \frac{56}{60 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 600 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 60 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{6}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*d*x*tan(c/2 + d*x/2)**10/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 75*d*x*tan(c/2 + d*x/2)**8/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 150*d*x*tan(c/2 + d*x/2)**6/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 150*d*x*tan(c/2 + d*x/2)**4/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 75*d*x*tan(c/2 + d*x/2)**2/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 15*d*x/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 30*tan(c/2 + d*x/2)**9/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 120*tan(c/2 + d*x/2)**8/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) + 180*tan(c/2 + d*x/2)**7/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 480*tan(c/2 + d*x/2)**6/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 80*tan(c/2 + d*x/2)**4/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 180*tan(c/2 + d*x/2)**3/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 160*tan(c/2 + d*x/2)**2/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) + 30*tan(c/2 + d*x/2)/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d) - 56/(60*a**2*d*tan(c/2 + d*x/2)**10 + 300*a**2*d*tan(c/2 + d*x/2)**8 + 600*a**2*d*tan(c/2 + d*x/2)**6 + 600*a**2*d*tan(c/2 + d*x/2)**4 + 300*a**2*d*tan(c/2 + d*x/2)**2 + 60*a**2*d), Ne(d, 0)), (x*sin(c)*cos(c)**6/(a*sin(c) + a)**2, True))","A",0
637,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
638,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
639,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
640,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
641,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
642,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
643,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**7/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
644,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
645,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
646,1,1246,0,166.361170," ","integrate(cos(d*x+c)**6*sin(d*x+c)/(a+a*sin(d*x+c))**3,x)","\begin{cases} - \frac{15 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{60 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{90 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{60 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{15 d x}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{30 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{16 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{46 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{144 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{46 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{176 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} + \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} - \frac{48}{8 a^{3} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 a^{3} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 32 a^{3} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8 a^{3} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{6}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{3}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-15*d*x*tan(c/2 + d*x/2)**8/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 60*d*x*tan(c/2 + d*x/2)**6/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 90*d*x*tan(c/2 + d*x/2)**4/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 60*d*x*tan(c/2 + d*x/2)**2/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 15*d*x/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 30*tan(c/2 + d*x/2)**7/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 16*tan(c/2 + d*x/2)**6/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 46*tan(c/2 + d*x/2)**5/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 144*tan(c/2 + d*x/2)**4/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) + 46*tan(c/2 + d*x/2)**3/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 176*tan(c/2 + d*x/2)**2/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) + 30*tan(c/2 + d*x/2)/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d) - 48/(8*a**3*d*tan(c/2 + d*x/2)**8 + 32*a**3*d*tan(c/2 + d*x/2)**6 + 48*a**3*d*tan(c/2 + d*x/2)**4 + 32*a**3*d*tan(c/2 + d*x/2)**2 + 8*a**3*d), Ne(d, 0)), (x*sin(c)*cos(c)**6/(a*sin(c) + a)**3, True))","A",0
647,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
648,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
649,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
650,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
651,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
652,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
653,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**n*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
654,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**n*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
655,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**n*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
656,1,184,0,117.153853," ","integrate(cos(d*x+c)**7*sin(d*x+c)**6*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{16 a \sin^{13}{\left(c + d x \right)}}{3003 d} + \frac{8 a \sin^{11}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{231 d} + \frac{2 a \sin^{9}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{21 d} + \frac{a \sin^{7}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{7 d} - \frac{a \sin^{6}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{8 d} - \frac{3 a \sin^{4}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{40 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{12}{\left(c + d x \right)}}{40 d} - \frac{a \cos^{14}{\left(c + d x \right)}}{280 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{6}{\left(c \right)} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a*sin(c + d*x)**13/(3003*d) + 8*a*sin(c + d*x)**11*cos(c + d*x)**2/(231*d) + 2*a*sin(c + d*x)**9*cos(c + d*x)**4/(21*d) + a*sin(c + d*x)**7*cos(c + d*x)**6/(7*d) - a*sin(c + d*x)**6*cos(c + d*x)**8/(8*d) - 3*a*sin(c + d*x)**4*cos(c + d*x)**10/(40*d) - a*sin(c + d*x)**2*cos(c + d*x)**12/(40*d) - a*cos(c + d*x)**14/(280*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**6*cos(c)**7, True))","A",0
657,1,160,0,83.455603," ","integrate(cos(d*x+c)**7*sin(d*x+c)**5*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{16 a \sin^{13}{\left(c + d x \right)}}{3003 d} + \frac{8 a \sin^{11}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{231 d} + \frac{2 a \sin^{9}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{21 d} + \frac{a \sin^{7}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{7 d} - \frac{a \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{8 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{20 d} - \frac{a \cos^{12}{\left(c + d x \right)}}{120 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{5}{\left(c \right)} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a*sin(c + d*x)**13/(3003*d) + 8*a*sin(c + d*x)**11*cos(c + d*x)**2/(231*d) + 2*a*sin(c + d*x)**9*cos(c + d*x)**4/(21*d) + a*sin(c + d*x)**7*cos(c + d*x)**6/(7*d) - a*sin(c + d*x)**4*cos(c + d*x)**8/(8*d) - a*sin(c + d*x)**2*cos(c + d*x)**10/(20*d) - a*cos(c + d*x)**12/(120*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**5*cos(c)**7, True))","A",0
658,1,160,0,56.203711," ","integrate(cos(d*x+c)**7*sin(d*x+c)**4*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{16 a \sin^{11}{\left(c + d x \right)}}{1155 d} + \frac{8 a \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{105 d} + \frac{6 a \sin^{7}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{35 d} + \frac{a \sin^{5}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{5 d} - \frac{a \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{8 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{20 d} - \frac{a \cos^{12}{\left(c + d x \right)}}{120 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{4}{\left(c \right)} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a*sin(c + d*x)**11/(1155*d) + 8*a*sin(c + d*x)**9*cos(c + d*x)**2/(105*d) + 6*a*sin(c + d*x)**7*cos(c + d*x)**4/(35*d) + a*sin(c + d*x)**5*cos(c + d*x)**6/(5*d) - a*sin(c + d*x)**4*cos(c + d*x)**8/(8*d) - a*sin(c + d*x)**2*cos(c + d*x)**10/(20*d) - a*cos(c + d*x)**12/(120*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**4*cos(c)**7, True))","A",0
659,1,138,0,37.468482," ","integrate(cos(d*x+c)**7*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{16 a \sin^{11}{\left(c + d x \right)}}{1155 d} + \frac{8 a \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{105 d} + \frac{6 a \sin^{7}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{35 d} + \frac{a \sin^{5}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{5 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{8 d} - \frac{a \cos^{10}{\left(c + d x \right)}}{40 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{3}{\left(c \right)} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a*sin(c + d*x)**11/(1155*d) + 8*a*sin(c + d*x)**9*cos(c + d*x)**2/(105*d) + 6*a*sin(c + d*x)**7*cos(c + d*x)**4/(35*d) + a*sin(c + d*x)**5*cos(c + d*x)**6/(5*d) - a*sin(c + d*x)**2*cos(c + d*x)**8/(8*d) - a*cos(c + d*x)**10/(40*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**3*cos(c)**7, True))","A",0
660,1,138,0,24.119084," ","integrate(cos(d*x+c)**7*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{16 a \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{8 a \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{2 a \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{8 d} - \frac{a \cos^{10}{\left(c + d x \right)}}{40 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin^{2}{\left(c \right)} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a*sin(c + d*x)**9/(315*d) + 8*a*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 2*a*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + a*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) - a*sin(c + d*x)**2*cos(c + d*x)**8/(8*d) - a*cos(c + d*x)**10/(40*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)**2*cos(c)**7, True))","A",0
661,1,114,0,15.732203," ","integrate(cos(d*x+c)**7*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\begin{cases} \frac{16 a \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{8 a \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{2 a \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{a \cos^{8}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a \sin{\left(c \right)} + a\right) \sin{\left(c \right)} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*a*sin(c + d*x)**9/(315*d) + 8*a*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 2*a*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + a*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) - a*cos(c + d*x)**8/(8*d), Ne(d, 0)), (x*(a*sin(c) + a)*sin(c)*cos(c)**7, True))","A",0
662,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
663,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
664,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**3*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
665,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
666,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
667,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**6*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
668,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**7*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
669,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**8*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
670,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**9*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
671,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**10*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
672,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**11*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
673,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**12*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
674,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**13*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
675,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**14*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
676,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**15*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
677,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
678,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
679,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
680,1,1906,0,169.579411," ","integrate(cos(d*x+c)**7*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{1260 \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} - \frac{2016 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} - \frac{420 \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} + \frac{3456 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} + \frac{2520 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} - \frac{6976 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} + \frac{2520 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} + \frac{3456 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} - \frac{420 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} - \frac{2016 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} + \frac{1260 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{315 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 39690 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 26460 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 11340 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2835 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 315 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{3}{\left(c \right)} \cos^{7}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((1260*tan(c/2 + d*x/2)**14/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) - 2016*tan(c/2 + d*x/2)**13/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) - 420*tan(c/2 + d*x/2)**12/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) + 3456*tan(c/2 + d*x/2)**11/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) + 2520*tan(c/2 + d*x/2)**10/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) - 6976*tan(c/2 + d*x/2)**9/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) + 2520*tan(c/2 + d*x/2)**8/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) + 3456*tan(c/2 + d*x/2)**7/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) - 420*tan(c/2 + d*x/2)**6/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) - 2016*tan(c/2 + d*x/2)**5/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d) + 1260*tan(c/2 + d*x/2)**4/(315*a*d*tan(c/2 + d*x/2)**18 + 2835*a*d*tan(c/2 + d*x/2)**16 + 11340*a*d*tan(c/2 + d*x/2)**14 + 26460*a*d*tan(c/2 + d*x/2)**12 + 39690*a*d*tan(c/2 + d*x/2)**10 + 39690*a*d*tan(c/2 + d*x/2)**8 + 26460*a*d*tan(c/2 + d*x/2)**6 + 11340*a*d*tan(c/2 + d*x/2)**4 + 2835*a*d*tan(c/2 + d*x/2)**2 + 315*a*d), Ne(d, 0)), (x*sin(c)**3*cos(c)**7/(a*sin(c) + a), True))","A",0
681,1,1719,0,114.128981," ","integrate(cos(d*x+c)**7*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{280 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{420 \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{56 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{560 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{688 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{1400 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{688 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{560 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{56 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{420 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{280 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 7350 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2940 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{7}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((280*tan(c/2 + d*x/2)**13/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 420*tan(c/2 + d*x/2)**12/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 56*tan(c/2 + d*x/2)**11/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 560*tan(c/2 + d*x/2)**10/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 688*tan(c/2 + d*x/2)**9/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 1400*tan(c/2 + d*x/2)**8/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 688*tan(c/2 + d*x/2)**7/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 560*tan(c/2 + d*x/2)**6/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 56*tan(c/2 + d*x/2)**5/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 420*tan(c/2 + d*x/2)**4/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 280*tan(c/2 + d*x/2)**3/(105*a*d*tan(c/2 + d*x/2)**16 + 840*a*d*tan(c/2 + d*x/2)**14 + 2940*a*d*tan(c/2 + d*x/2)**12 + 5880*a*d*tan(c/2 + d*x/2)**10 + 7350*a*d*tan(c/2 + d*x/2)**8 + 5880*a*d*tan(c/2 + d*x/2)**6 + 2940*a*d*tan(c/2 + d*x/2)**4 + 840*a*d*tan(c/2 + d*x/2)**2 + 105*a*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**7/(a*sin(c) + a), True))","A",0
682,1,1530,0,76.743920," ","integrate(cos(d*x+c)**7*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{210 \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{280 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{210 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{224 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{700 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{912 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{700 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{224 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{210 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{280 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{210 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{7}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((210*tan(c/2 + d*x/2)**12/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 280*tan(c/2 + d*x/2)**11/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 210*tan(c/2 + d*x/2)**10/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 224*tan(c/2 + d*x/2)**9/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 700*tan(c/2 + d*x/2)**8/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 912*tan(c/2 + d*x/2)**7/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 700*tan(c/2 + d*x/2)**6/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 224*tan(c/2 + d*x/2)**5/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 210*tan(c/2 + d*x/2)**4/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 280*tan(c/2 + d*x/2)**3/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 210*tan(c/2 + d*x/2)**2/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d), Ne(d, 0)), (x*sin(c)*cos(c)**7/(a*sin(c) + a), True))","A",0
683,1,1096,0,49.954435," ","integrate(cos(d*x+c)**7/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{30 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{30 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{70 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{156 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{100 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{156 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{70 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{30 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} & \text{for}\: d \neq 0 \\\frac{x \cos^{7}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*tan(c/2 + d*x/2)**11/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 30*tan(c/2 + d*x/2)**10/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 70*tan(c/2 + d*x/2)**9/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 156*tan(c/2 + d*x/2)**7/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 100*tan(c/2 + d*x/2)**6/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 156*tan(c/2 + d*x/2)**5/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 70*tan(c/2 + d*x/2)**3/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 30*tan(c/2 + d*x/2)**2/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*tan(c/2 + d*x/2)/(15*a*d*tan(c/2 + d*x/2)**12 + 90*a*d*tan(c/2 + d*x/2)**10 + 225*a*d*tan(c/2 + d*x/2)**8 + 300*a*d*tan(c/2 + d*x/2)**6 + 225*a*d*tan(c/2 + d*x/2)**4 + 90*a*d*tan(c/2 + d*x/2)**2 + 15*a*d), Ne(d, 0)), (x*cos(c)**7/(a*sin(c) + a), True))","A",0
684,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
685,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
686,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
687,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
688,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
689,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
690,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
691,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**8/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
692,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**9/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
693,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**10/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
694,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**11/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
695,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**12/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
696,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*csc(d*x+c)**13/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
697,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**n*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
698,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**n*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
699,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**n*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
700,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**n/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
701,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**n/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
702,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**n/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
703,-2,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**n/(a+a*sin(d*x+c))**4,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
704,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*sin(d*x+c)**n/(a+a*sin(d*x+c))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
705,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
706,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
707,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
708,1,4490,0,170.692711," ","integrate(cos(d*x+c)**8*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{315 d x \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{2835 d x \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{11340 d x \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{26460 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{39690 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{39690 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{26460 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{11340 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{2835 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{315 d x}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{630 \tan^{17}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} - \frac{16044 \tan^{15}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{32256 \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{20916 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} - \frac{53760 \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} - \frac{36540 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{161280 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} - \frac{96768 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{36540 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{96768 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} - \frac{20916 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} - \frac{13824 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{16044 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{4608 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} - \frac{630 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} + \frac{512}{8064 a d \tan^{18}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1016064 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 677376 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 290304 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72576 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 8064 a d} & \text{for}\: d \neq 0 \\\frac{x \sin^{2}{\left(c \right)} \cos^{8}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((315*d*x*tan(c/2 + d*x/2)**18/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 2835*d*x*tan(c/2 + d*x/2)**16/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 11340*d*x*tan(c/2 + d*x/2)**14/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 26460*d*x*tan(c/2 + d*x/2)**12/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 39690*d*x*tan(c/2 + d*x/2)**10/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 39690*d*x*tan(c/2 + d*x/2)**8/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 26460*d*x*tan(c/2 + d*x/2)**6/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 11340*d*x*tan(c/2 + d*x/2)**4/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 2835*d*x*tan(c/2 + d*x/2)**2/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 315*d*x/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 630*tan(c/2 + d*x/2)**17/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) - 16044*tan(c/2 + d*x/2)**15/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 32256*tan(c/2 + d*x/2)**14/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 20916*tan(c/2 + d*x/2)**13/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) - 53760*tan(c/2 + d*x/2)**12/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) - 36540*tan(c/2 + d*x/2)**11/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 161280*tan(c/2 + d*x/2)**10/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) - 96768*tan(c/2 + d*x/2)**8/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 36540*tan(c/2 + d*x/2)**7/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 96768*tan(c/2 + d*x/2)**6/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) - 20916*tan(c/2 + d*x/2)**5/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) - 13824*tan(c/2 + d*x/2)**4/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 16044*tan(c/2 + d*x/2)**3/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 4608*tan(c/2 + d*x/2)**2/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) - 630*tan(c/2 + d*x/2)/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d) + 512/(8064*a*d*tan(c/2 + d*x/2)**18 + 72576*a*d*tan(c/2 + d*x/2)**16 + 290304*a*d*tan(c/2 + d*x/2)**14 + 677376*a*d*tan(c/2 + d*x/2)**12 + 1016064*a*d*tan(c/2 + d*x/2)**10 + 1016064*a*d*tan(c/2 + d*x/2)**8 + 677376*a*d*tan(c/2 + d*x/2)**6 + 290304*a*d*tan(c/2 + d*x/2)**4 + 72576*a*d*tan(c/2 + d*x/2)**2 + 8064*a*d), Ne(d, 0)), (x*sin(c)**2*cos(c)**8/(a*sin(c) + a), True))","A",0
709,1,3888,0,111.637728," ","integrate(cos(d*x+c)**8*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\begin{cases} - \frac{105 d x \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{840 d x \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{2940 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{5880 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{7350 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{5880 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{2940 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{840 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{105 d x}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{210 \tan^{15}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{5376 \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} + \frac{5558 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{5376 \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{12530 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{26880 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} + \frac{24710 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{26880 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{24710 \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{16128 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} + \frac{12530 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{16128 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{5558 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{768 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} + \frac{210 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} - \frac{768}{2688 a d \tan^{16}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 188160 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150528 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75264 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 21504 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2688 a d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{8}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-105*d*x*tan(c/2 + d*x/2)**16/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 840*d*x*tan(c/2 + d*x/2)**14/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 2940*d*x*tan(c/2 + d*x/2)**12/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 5880*d*x*tan(c/2 + d*x/2)**10/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 7350*d*x*tan(c/2 + d*x/2)**8/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 5880*d*x*tan(c/2 + d*x/2)**6/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 2940*d*x*tan(c/2 + d*x/2)**4/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 840*d*x*tan(c/2 + d*x/2)**2/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 105*d*x/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 210*tan(c/2 + d*x/2)**15/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 5376*tan(c/2 + d*x/2)**14/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) + 5558*tan(c/2 + d*x/2)**13/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 5376*tan(c/2 + d*x/2)**12/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 12530*tan(c/2 + d*x/2)**11/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 26880*tan(c/2 + d*x/2)**10/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) + 24710*tan(c/2 + d*x/2)**9/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 26880*tan(c/2 + d*x/2)**8/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 24710*tan(c/2 + d*x/2)**7/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 16128*tan(c/2 + d*x/2)**6/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) + 12530*tan(c/2 + d*x/2)**5/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 16128*tan(c/2 + d*x/2)**4/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 5558*tan(c/2 + d*x/2)**3/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 768*tan(c/2 + d*x/2)**2/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) + 210*tan(c/2 + d*x/2)/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d) - 768/(2688*a*d*tan(c/2 + d*x/2)**16 + 21504*a*d*tan(c/2 + d*x/2)**14 + 75264*a*d*tan(c/2 + d*x/2)**12 + 150528*a*d*tan(c/2 + d*x/2)**10 + 188160*a*d*tan(c/2 + d*x/2)**8 + 150528*a*d*tan(c/2 + d*x/2)**6 + 75264*a*d*tan(c/2 + d*x/2)**4 + 21504*a*d*tan(c/2 + d*x/2)**2 + 2688*a*d), Ne(d, 0)), (x*sin(c)*cos(c)**8/(a*sin(c) + a), True))","A",0
710,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
711,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
712,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
713,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
714,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
715,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
716,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
717,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**8/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
718,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**9/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
719,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**10/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
720,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**11/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
721,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**12/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
722,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
723,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
724,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
725,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
726,1,3196,0,172.039916," ","integrate(cos(d*x+c)**8*sin(d*x+c)/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{105 d x \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{735 d x \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{2205 d x \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{3675 d x \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{3675 d x \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{2205 d x \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{735 d x \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{105 d x}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{210 \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{1680 \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} + \frac{3080 \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{6720 \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{2170 \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{1680 \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{13440 \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} + \frac{2170 \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{2352 \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{3080 \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{1344 \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} + \frac{210 \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} - \frac{432}{840 a^{2} d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 29400 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 17640 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 5880 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 840 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \sin{\left(c \right)} \cos^{8}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-105*d*x*tan(c/2 + d*x/2)**14/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 735*d*x*tan(c/2 + d*x/2)**12/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 2205*d*x*tan(c/2 + d*x/2)**10/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 3675*d*x*tan(c/2 + d*x/2)**8/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 3675*d*x*tan(c/2 + d*x/2)**6/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 2205*d*x*tan(c/2 + d*x/2)**4/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 735*d*x*tan(c/2 + d*x/2)**2/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 105*d*x/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 210*tan(c/2 + d*x/2)**13/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 1680*tan(c/2 + d*x/2)**12/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) + 3080*tan(c/2 + d*x/2)**11/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 6720*tan(c/2 + d*x/2)**10/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 2170*tan(c/2 + d*x/2)**9/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 1680*tan(c/2 + d*x/2)**8/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 13440*tan(c/2 + d*x/2)**6/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) + 2170*tan(c/2 + d*x/2)**5/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 2352*tan(c/2 + d*x/2)**4/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 3080*tan(c/2 + d*x/2)**3/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 1344*tan(c/2 + d*x/2)**2/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) + 210*tan(c/2 + d*x/2)/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d) - 432/(840*a**2*d*tan(c/2 + d*x/2)**14 + 5880*a**2*d*tan(c/2 + d*x/2)**12 + 17640*a**2*d*tan(c/2 + d*x/2)**10 + 29400*a**2*d*tan(c/2 + d*x/2)**8 + 29400*a**2*d*tan(c/2 + d*x/2)**6 + 17640*a**2*d*tan(c/2 + d*x/2)**4 + 5880*a**2*d*tan(c/2 + d*x/2)**2 + 840*a**2*d), Ne(d, 0)), (x*sin(c)*cos(c)**8/(a*sin(c) + a)**2, True))","A",0
727,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
728,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
729,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
730,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
731,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
732,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**6/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
733,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**7/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
734,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**8/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
735,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**9/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
736,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**10/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
737,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**11/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
738,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**12/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
739,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
740,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
741,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*sin(d*x+c)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
742,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
743,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
744,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
745,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
746,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
747,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**6/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
748,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**7/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
749,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**8/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
750,-1,0,0,0.000000," ","integrate(cos(d*x+c)**8*csc(d*x+c)**9/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
751,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
752,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","a \left(\int \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)**3*sec(c + d*x)**2, x) + Integral(sin(c + d*x)**4*sec(c + d*x)**2, x))","F",0
753,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","a \left(\int \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(sin(c + d*x)**3*sec(c + d*x)**2, x))","F",0
754,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)*(a+a*sin(d*x+c)),x)","a \left(\int \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)*sec(c + d*x)**2, x) + Integral(sin(c + d*x)**2*sec(c + d*x)**2, x))","F",0
755,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2*(a+a*sin(d*x+c)),x)","a \left(\int \csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin{\left(c + d x \right)} \csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(csc(c + d*x)*sec(c + d*x)**2, x) + Integral(sin(c + d*x)*csc(c + d*x)*sec(c + d*x)**2, x))","F",0
756,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
757,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
758,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
759,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
760,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 2 \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(2*sin(c + d*x)**3*sec(c + d*x)**2, x) + Integral(sin(c + d*x)**4*sec(c + d*x)**2, x))","F",0
761,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)*(a+a*sin(d*x+c))**2,x)","a^{2} \left(\int \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 2 \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(sin(c + d*x)*sec(c + d*x)**2, x) + Integral(2*sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(sin(c + d*x)**3*sec(c + d*x)**2, x))","F",0
762,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
763,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
764,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
765,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
766,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
767,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)*(a+a*sin(d*x+c))**3,x)","a^{3} \left(\int \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int \sin^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(sin(c + d*x)*sec(c + d*x)**2, x) + Integral(3*sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(3*sin(c + d*x)**3*sec(c + d*x)**2, x) + Integral(sin(c + d*x)**4*sec(c + d*x)**2, x))","F",0
768,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
769,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
770,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
771,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
772,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sin(c + d*x)**4*sec(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
773,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
774,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
775,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
776,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(c + d*x)*sec(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
777,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\csc^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(csc(c + d*x)**2*sec(c + d*x)**2/(sin(c + d*x) + 1), x)/a","F",0
778,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**6/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
779,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
780,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sin^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sin(c + d*x)**4*sec(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
781,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
782,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
783,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
784,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(c + d*x)*sec(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
785,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\csc^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(csc(c + d*x)**2*sec(c + d*x)**2/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
786,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
787,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**6/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
788,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
789,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
790,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
791,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
792,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
793,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(csc(c + d*x)*sec(c + d*x)**2/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
794,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
795,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**6*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
796,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
797,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
798,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
799,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
800,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)*(a+a*sin(d*x+c)),x)","a \left(\int \sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int \sin^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(sin(c + d*x)*sec(c + d*x)**4, x) + Integral(sin(c + d*x)**2*sec(c + d*x)**4, x))","F",0
801,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
802,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
803,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
804,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
805,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
806,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
807,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
808,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
809,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
810,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
811,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
812,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
813,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
814,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
815,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
816,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
817,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
818,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
819,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
820,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2*(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
821,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
822,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
823,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
824,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
825,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**4/(sin(c + d*x) + 1), x)/a","F",0
826,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**4/(sin(c + d*x) + 1), x)/a","F",0
827,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
828,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
829,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**7/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
830,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**6/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
831,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**5/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
832,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
833,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
834,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**4/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
835,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{\sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**4/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x)/a**2","F",0
836,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
837,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
838,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**4/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
839,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**7/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
840,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**6/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
841,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**5/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
842,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
843,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
844,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
845,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)/(a+a*sin(d*x+c))**3,x)","\frac{\int \frac{\sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{\sin^{3}{\left(c + d x \right)} + 3 \sin^{2}{\left(c + d x \right)} + 3 \sin{\left(c + d x \right)} + 1}\, dx}{a^{3}}"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**4/(sin(c + d*x)**3 + 3*sin(c + d*x)**2 + 3*sin(c + d*x) + 1), x)/a**3","F",0
846,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
847,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**4/(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
848,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
849,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**3/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
850,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2/(a+a*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
851,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**6*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
852,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
853,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**4*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
854,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**3*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
855,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**2*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
856,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
857,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
858,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
859,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
860,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**5*(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
861,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
862,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**4*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
863,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
864,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**2*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
865,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
866,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
867,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
868,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
869,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**5*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
870,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
871,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**4*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
872,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**3*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
873,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**2*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
874,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
875,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
876,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
877,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**5*(a+a*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
878,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**11/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
879,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**10/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
880,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**9/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
881,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**8/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
882,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
883,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
884,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
885,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
886,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
887,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
888,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
889,0,0,0,0.000000," ","integrate(sec(d*x+c)**7/(a+a*sin(d*x+c)),x)","\frac{\int \frac{\sec^{7}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"Integral(sec(c + d*x)**7/(sin(c + d*x) + 1), x)/a","F",0
890,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
891,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
892,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
893,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
894,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*sin(d*x+c)**3*(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
895,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**12/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
896,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**11/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
897,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**10/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
898,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**9/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
899,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**8/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
900,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**7/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
901,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**6/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
902,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**5/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
903,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**4/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
904,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**3/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
905,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)**2/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
906,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*sin(d*x+c)/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
907,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
908,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**9/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
909,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**9/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
910,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**9/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
911,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))**p*(d*sin(f*x+e))**n*(a+a*sin(f*x+e))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
912,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
913,1,11900,0,138.036470," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**4*(c+d*sin(f*x+e))**n,x)","\begin{cases} c^{n} \left(\frac{a^{4} \sin^{5}{\left(e + f x \right)}}{5 f} + \frac{a^{4} \sin^{4}{\left(e + f x \right)}}{f} + \frac{2 a^{4} \sin^{3}{\left(e + f x \right)}}{f} + \frac{2 a^{4} \sin^{2}{\left(e + f x \right)}}{f} + \frac{a^{4} \sin{\left(e + f x \right)}}{f}\right) & \text{for}\: d = 0 \\x \left(c + d \sin{\left(e \right)}\right)^{n} \left(a \sin{\left(e \right)} + a\right)^{4} \cos{\left(e \right)} & \text{for}\: f = 0 \\\frac{12 a^{4} c^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} + \frac{25 a^{4} c^{4}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} + \frac{48 a^{4} c^{3} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} + \frac{88 a^{4} c^{3} d \sin{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{12 a^{4} c^{3} d}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} + \frac{72 a^{4} c^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} + \frac{108 a^{4} c^{2} d^{2} \sin^{2}{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{48 a^{4} c^{2} d^{2} \sin{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{6 a^{4} c^{2} d^{2}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} + \frac{48 a^{4} c d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{3}{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} + \frac{48 a^{4} c d^{3} \sin^{3}{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{72 a^{4} c d^{3} \sin^{2}{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{24 a^{4} c d^{3} \sin{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{4 a^{4} c d^{3}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} + \frac{12 a^{4} d^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{4}{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{48 a^{4} d^{4} \sin^{3}{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{36 a^{4} d^{4} \sin^{2}{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{16 a^{4} d^{4} \sin{\left(e + f x \right)}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} - \frac{3 a^{4} d^{4}}{12 c^{4} d^{5} f + 48 c^{3} d^{6} f \sin{\left(e + f x \right)} + 72 c^{2} d^{7} f \sin^{2}{\left(e + f x \right)} + 48 c d^{8} f \sin^{3}{\left(e + f x \right)} + 12 d^{9} f \sin^{4}{\left(e + f x \right)}} & \text{for}\: n = -5 \\- \frac{12 a^{4} c^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{22 a^{4} c^{4}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{36 a^{4} c^{3} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} + \frac{12 a^{4} c^{3} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{54 a^{4} c^{3} d \sin{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} + \frac{22 a^{4} c^{3} d}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{36 a^{4} c^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} + \frac{36 a^{4} c^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{36 a^{4} c^{2} d^{2} \sin^{2}{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} + \frac{54 a^{4} c^{2} d^{2} \sin{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{6 a^{4} c^{2} d^{2}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{12 a^{4} c d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{3}{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} + \frac{36 a^{4} c d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} + \frac{36 a^{4} c d^{3} \sin^{2}{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{18 a^{4} c d^{3} \sin{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{2 a^{4} c d^{3}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} + \frac{12 a^{4} d^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{3}{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} + \frac{3 a^{4} d^{4} \sin^{4}{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{18 a^{4} d^{4} \sin^{2}{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{6 a^{4} d^{4} \sin{\left(e + f x \right)}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} - \frac{a^{4} d^{4}}{3 c^{3} d^{5} f + 9 c^{2} d^{6} f \sin{\left(e + f x \right)} + 9 c d^{7} f \sin^{2}{\left(e + f x \right)} + 3 d^{8} f \sin^{3}{\left(e + f x \right)}} & \text{for}\: n = -4 \\\frac{12 a^{4} c^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{18 a^{4} c^{4}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{24 a^{4} c^{3} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{24 a^{4} c^{3} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{24 a^{4} c^{3} d \sin{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{36 a^{4} c^{3} d}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{12 a^{4} c^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{48 a^{4} c^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{12 a^{4} c^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{48 a^{4} c^{2} d^{2} \sin{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{18 a^{4} c^{2} d^{2}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{24 a^{4} c d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{24 a^{4} c d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{4 a^{4} c d^{3} \sin^{3}{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{24 a^{4} c d^{3} \sin{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{4 a^{4} c d^{3}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{12 a^{4} d^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{a^{4} d^{4} \sin^{4}{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} + \frac{8 a^{4} d^{4} \sin^{3}{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{8 a^{4} d^{4} \sin{\left(e + f x \right)}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} - \frac{a^{4} d^{4}}{2 c^{2} d^{5} f + 4 c d^{6} f \sin{\left(e + f x \right)} + 2 d^{7} f \sin^{2}{\left(e + f x \right)}} & \text{for}\: n = -3 \\- \frac{12 a^{4} c^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} - \frac{12 a^{4} c^{4}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} - \frac{12 a^{4} c^{3} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{36 a^{4} c^{3} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{36 a^{4} c^{3} d}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{36 a^{4} c^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} - \frac{36 a^{4} c^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{6 a^{4} c^{2} d^{2} \sin^{2}{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} - \frac{36 a^{4} c^{2} d^{2}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} - \frac{36 a^{4} c d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{12 a^{4} c d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} - \frac{2 a^{4} c d^{3} \sin^{3}{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} - \frac{18 a^{4} c d^{3} \sin^{2}{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{12 a^{4} c d^{3}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{12 a^{4} d^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{a^{4} d^{4} \sin^{4}{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{6 a^{4} d^{4} \sin^{3}{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} + \frac{18 a^{4} d^{4} \sin^{2}{\left(e + f x \right)}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} - \frac{3 a^{4} d^{4}}{3 c d^{5} f + 3 d^{6} f \sin{\left(e + f x \right)}} & \text{for}\: n = -2 \\\frac{a^{4} c^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{5} f} - \frac{4 a^{4} c^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{4} f} - \frac{a^{4} c^{3} \sin{\left(e + f x \right)}}{d^{4} f} + \frac{6 a^{4} c^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{3} f} + \frac{a^{4} c^{2} \sin^{2}{\left(e + f x \right)}}{2 d^{3} f} + \frac{4 a^{4} c^{2} \sin{\left(e + f x \right)}}{d^{3} f} - \frac{4 a^{4} c \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{2} f} - \frac{a^{4} c \sin^{3}{\left(e + f x \right)}}{3 d^{2} f} - \frac{2 a^{4} c \sin^{2}{\left(e + f x \right)}}{d^{2} f} - \frac{6 a^{4} c \sin{\left(e + f x \right)}}{d^{2} f} + \frac{a^{4} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d f} + \frac{a^{4} \sin^{4}{\left(e + f x \right)}}{4 d f} + \frac{4 a^{4} \sin^{3}{\left(e + f x \right)}}{3 d f} + \frac{3 a^{4} \sin^{2}{\left(e + f x \right)}}{d f} + \frac{4 a^{4} \sin{\left(e + f x \right)}}{d f} & \text{for}\: n = -1 \\\frac{24 a^{4} c^{5} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{24 a^{4} c^{4} d n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{24 a^{4} c^{4} d n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{120 a^{4} c^{4} d \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{12 a^{4} c^{3} d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{24 a^{4} c^{3} d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{12 a^{4} c^{3} d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{12 a^{4} c^{3} d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{120 a^{4} c^{3} d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{108 a^{4} c^{3} d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{240 a^{4} c^{3} d^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{4 a^{4} c^{2} d^{3} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{12 a^{4} c^{2} d^{3} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{12 a^{4} c^{2} d^{3} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{4 a^{4} c^{2} d^{3} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{12 a^{4} c^{2} d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{72 a^{4} c^{2} d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{108 a^{4} c^{2} d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{48 a^{4} c^{2} d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{8 a^{4} c^{2} d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{60 a^{4} c^{2} d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{240 a^{4} c^{2} d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{188 a^{4} c^{2} d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} - \frac{240 a^{4} c^{2} d^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{a^{4} c d^{4} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{4 a^{4} c d^{4} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{6 a^{4} c d^{4} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{4 a^{4} c d^{4} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{a^{4} c d^{4} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{6 a^{4} c d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{32 a^{4} c d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{60 a^{4} c d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{48 a^{4} c d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{14 a^{4} c d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{11 a^{4} c d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{68 a^{4} c d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{174 a^{4} c d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{188 a^{4} c d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{71 a^{4} c d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{6 a^{4} c d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{40 a^{4} c d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{120 a^{4} c d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{240 a^{4} c d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{154 a^{4} c d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{120 a^{4} c d^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{a^{4} d^{5} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{5}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{4 a^{4} d^{5} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{6 a^{4} d^{5} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{4 a^{4} d^{5} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{a^{4} d^{5} n^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{10 a^{4} d^{5} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{5}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{44 a^{4} d^{5} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{72 a^{4} d^{5} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{52 a^{4} d^{5} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{14 a^{4} d^{5} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{35 a^{4} d^{5} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{5}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{164 a^{4} d^{5} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{294 a^{4} d^{5} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{236 a^{4} d^{5} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{71 a^{4} d^{5} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{50 a^{4} d^{5} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{5}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{244 a^{4} d^{5} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{468 a^{4} d^{5} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{428 a^{4} d^{5} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{154 a^{4} d^{5} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{24 a^{4} d^{5} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{5}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{120 a^{4} d^{5} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{240 a^{4} d^{5} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{240 a^{4} d^{5} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} + \frac{120 a^{4} d^{5} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{5} f n^{5} + 15 d^{5} f n^{4} + 85 d^{5} f n^{3} + 225 d^{5} f n^{2} + 274 d^{5} f n + 120 d^{5} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(a**4*sin(e + f*x)**5/(5*f) + a**4*sin(e + f*x)**4/f + 2*a**4*sin(e + f*x)**3/f + 2*a**4*sin(e + f*x)**2/f + a**4*sin(e + f*x)/f), Eq(d, 0)), (x*(c + d*sin(e))**n*(a*sin(e) + a)**4*cos(e), Eq(f, 0)), (12*a**4*c**4*log(c/d + sin(e + f*x))/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) + 25*a**4*c**4/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) + 48*a**4*c**3*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) + 88*a**4*c**3*d*sin(e + f*x)/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 12*a**4*c**3*d/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) + 72*a**4*c**2*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) + 108*a**4*c**2*d**2*sin(e + f*x)**2/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 48*a**4*c**2*d**2*sin(e + f*x)/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 6*a**4*c**2*d**2/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) + 48*a**4*c*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)**3/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) + 48*a**4*c*d**3*sin(e + f*x)**3/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 72*a**4*c*d**3*sin(e + f*x)**2/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 24*a**4*c*d**3*sin(e + f*x)/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 4*a**4*c*d**3/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) + 12*a**4*d**4*log(c/d + sin(e + f*x))*sin(e + f*x)**4/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 48*a**4*d**4*sin(e + f*x)**3/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 36*a**4*d**4*sin(e + f*x)**2/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 16*a**4*d**4*sin(e + f*x)/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4) - 3*a**4*d**4/(12*c**4*d**5*f + 48*c**3*d**6*f*sin(e + f*x) + 72*c**2*d**7*f*sin(e + f*x)**2 + 48*c*d**8*f*sin(e + f*x)**3 + 12*d**9*f*sin(e + f*x)**4), Eq(n, -5)), (-12*a**4*c**4*log(c/d + sin(e + f*x))/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 22*a**4*c**4/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 36*a**4*c**3*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) + 12*a**4*c**3*d*log(c/d + sin(e + f*x))/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 54*a**4*c**3*d*sin(e + f*x)/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) + 22*a**4*c**3*d/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 36*a**4*c**2*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) + 36*a**4*c**2*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 36*a**4*c**2*d**2*sin(e + f*x)**2/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) + 54*a**4*c**2*d**2*sin(e + f*x)/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 6*a**4*c**2*d**2/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 12*a**4*c*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)**3/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) + 36*a**4*c*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) + 36*a**4*c*d**3*sin(e + f*x)**2/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 18*a**4*c*d**3*sin(e + f*x)/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 2*a**4*c*d**3/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) + 12*a**4*d**4*log(c/d + sin(e + f*x))*sin(e + f*x)**3/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) + 3*a**4*d**4*sin(e + f*x)**4/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 18*a**4*d**4*sin(e + f*x)**2/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - 6*a**4*d**4*sin(e + f*x)/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3) - a**4*d**4/(3*c**3*d**5*f + 9*c**2*d**6*f*sin(e + f*x) + 9*c*d**7*f*sin(e + f*x)**2 + 3*d**8*f*sin(e + f*x)**3), Eq(n, -4)), (12*a**4*c**4*log(c/d + sin(e + f*x))/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 18*a**4*c**4/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 24*a**4*c**3*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - 24*a**4*c**3*d*log(c/d + sin(e + f*x))/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 24*a**4*c**3*d*sin(e + f*x)/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - 36*a**4*c**3*d/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 12*a**4*c**2*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - 48*a**4*c**2*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 12*a**4*c**2*d**2*log(c/d + sin(e + f*x))/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - 48*a**4*c**2*d**2*sin(e + f*x)/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 18*a**4*c**2*d**2/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - 24*a**4*c*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 24*a**4*c*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - 4*a**4*c*d**3*sin(e + f*x)**3/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 24*a**4*c*d**3*sin(e + f*x)/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - 4*a**4*c*d**3/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 12*a**4*d**4*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + a**4*d**4*sin(e + f*x)**4/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) + 8*a**4*d**4*sin(e + f*x)**3/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - 8*a**4*d**4*sin(e + f*x)/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2) - a**4*d**4/(2*c**2*d**5*f + 4*c*d**6*f*sin(e + f*x) + 2*d**7*f*sin(e + f*x)**2), Eq(n, -3)), (-12*a**4*c**4*log(c/d + sin(e + f*x))/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) - 12*a**4*c**4/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) - 12*a**4*c**3*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 36*a**4*c**3*d*log(c/d + sin(e + f*x))/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 36*a**4*c**3*d/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 36*a**4*c**2*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) - 36*a**4*c**2*d**2*log(c/d + sin(e + f*x))/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 6*a**4*c**2*d**2*sin(e + f*x)**2/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) - 36*a**4*c**2*d**2/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) - 36*a**4*c*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 12*a**4*c*d**3*log(c/d + sin(e + f*x))/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) - 2*a**4*c*d**3*sin(e + f*x)**3/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) - 18*a**4*c*d**3*sin(e + f*x)**2/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 12*a**4*c*d**3/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 12*a**4*d**4*log(c/d + sin(e + f*x))*sin(e + f*x)/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + a**4*d**4*sin(e + f*x)**4/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 6*a**4*d**4*sin(e + f*x)**3/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) + 18*a**4*d**4*sin(e + f*x)**2/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)) - 3*a**4*d**4/(3*c*d**5*f + 3*d**6*f*sin(e + f*x)), Eq(n, -2)), (a**4*c**4*log(c/d + sin(e + f*x))/(d**5*f) - 4*a**4*c**3*log(c/d + sin(e + f*x))/(d**4*f) - a**4*c**3*sin(e + f*x)/(d**4*f) + 6*a**4*c**2*log(c/d + sin(e + f*x))/(d**3*f) + a**4*c**2*sin(e + f*x)**2/(2*d**3*f) + 4*a**4*c**2*sin(e + f*x)/(d**3*f) - 4*a**4*c*log(c/d + sin(e + f*x))/(d**2*f) - a**4*c*sin(e + f*x)**3/(3*d**2*f) - 2*a**4*c*sin(e + f*x)**2/(d**2*f) - 6*a**4*c*sin(e + f*x)/(d**2*f) + a**4*log(c/d + sin(e + f*x))/(d*f) + a**4*sin(e + f*x)**4/(4*d*f) + 4*a**4*sin(e + f*x)**3/(3*d*f) + 3*a**4*sin(e + f*x)**2/(d*f) + 4*a**4*sin(e + f*x)/(d*f), Eq(n, -1)), (24*a**4*c**5*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 24*a**4*c**4*d*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 24*a**4*c**4*d*n*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 120*a**4*c**4*d*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 12*a**4*c**3*d**2*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 24*a**4*c**3*d**2*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 12*a**4*c**3*d**2*n**2*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 12*a**4*c**3*d**2*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 120*a**4*c**3*d**2*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 108*a**4*c**3*d**2*n*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 240*a**4*c**3*d**2*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 4*a**4*c**2*d**3*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 12*a**4*c**2*d**3*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 12*a**4*c**2*d**3*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 4*a**4*c**2*d**3*n**3*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 12*a**4*c**2*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 72*a**4*c**2*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 108*a**4*c**2*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 48*a**4*c**2*d**3*n**2*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 8*a**4*c**2*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 60*a**4*c**2*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 240*a**4*c**2*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 188*a**4*c**2*d**3*n*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) - 240*a**4*c**2*d**3*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + a**4*c*d**4*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 4*a**4*c*d**4*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 6*a**4*c*d**4*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 4*a**4*c*d**4*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + a**4*c*d**4*n**4*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 6*a**4*c*d**4*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 32*a**4*c*d**4*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 60*a**4*c*d**4*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 48*a**4*c*d**4*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 14*a**4*c*d**4*n**3*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 11*a**4*c*d**4*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 68*a**4*c*d**4*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 174*a**4*c*d**4*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 188*a**4*c*d**4*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 71*a**4*c*d**4*n**2*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 6*a**4*c*d**4*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 40*a**4*c*d**4*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 120*a**4*c*d**4*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 240*a**4*c*d**4*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 154*a**4*c*d**4*n*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 120*a**4*c*d**4*(c + d*sin(e + f*x))**n/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + a**4*d**5*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**5/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 4*a**4*d**5*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 6*a**4*d**5*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 4*a**4*d**5*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + a**4*d**5*n**4*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 10*a**4*d**5*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**5/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 44*a**4*d**5*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 72*a**4*d**5*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 52*a**4*d**5*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 14*a**4*d**5*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 35*a**4*d**5*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**5/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 164*a**4*d**5*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 294*a**4*d**5*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 236*a**4*d**5*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 71*a**4*d**5*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 50*a**4*d**5*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**5/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 244*a**4*d**5*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 468*a**4*d**5*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 428*a**4*d**5*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 154*a**4*d**5*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 24*a**4*d**5*(c + d*sin(e + f*x))**n*sin(e + f*x)**5/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 120*a**4*d**5*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 240*a**4*d**5*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 240*a**4*d**5*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f) + 120*a**4*d**5*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**5*f*n**5 + 15*d**5*f*n**4 + 85*d**5*f*n**3 + 225*d**5*f*n**2 + 274*d**5*f*n + 120*d**5*f), True))","A",0
914,1,5596,0,54.770114," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**3*(c+d*sin(f*x+e))**n,x)","\begin{cases} c^{n} \left(\frac{a^{3} \sin^{4}{\left(e + f x \right)}}{4 f} + \frac{a^{3} \sin^{3}{\left(e + f x \right)}}{f} + \frac{3 a^{3} \sin^{2}{\left(e + f x \right)}}{2 f} + \frac{a^{3} \sin{\left(e + f x \right)}}{f}\right) & \text{for}\: d = 0 \\x \left(c + d \sin{\left(e \right)}\right)^{n} \left(a \sin{\left(e \right)} + a\right)^{3} \cos{\left(e \right)} & \text{for}\: f = 0 \\\frac{6 a^{3} c^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} + \frac{11 a^{3} c^{3}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} + \frac{18 a^{3} c^{2} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} + \frac{27 a^{3} c^{2} d \sin{\left(e + f x \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} - \frac{6 a^{3} c^{2} d}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} + \frac{18 a^{3} c d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} + \frac{18 a^{3} c d^{2} \sin^{2}{\left(e + f x \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} - \frac{18 a^{3} c d^{2} \sin{\left(e + f x \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} - \frac{3 a^{3} c d^{2}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} + \frac{6 a^{3} d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{3}{\left(e + f x \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} - \frac{18 a^{3} d^{3} \sin^{2}{\left(e + f x \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} - \frac{9 a^{3} d^{3} \sin{\left(e + f x \right)}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} - \frac{2 a^{3} d^{3}}{6 c^{3} d^{4} f + 18 c^{2} d^{5} f \sin{\left(e + f x \right)} + 18 c d^{6} f \sin^{2}{\left(e + f x \right)} + 6 d^{7} f \sin^{3}{\left(e + f x \right)}} & \text{for}\: n = -4 \\- \frac{6 a^{3} c^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} - \frac{9 a^{3} c^{3}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} - \frac{12 a^{3} c^{2} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} + \frac{6 a^{3} c^{2} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} - \frac{12 a^{3} c^{2} d \sin{\left(e + f x \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} + \frac{9 a^{3} c^{2} d}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} - \frac{6 a^{3} c d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} + \frac{12 a^{3} c d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} + \frac{12 a^{3} c d^{2} \sin{\left(e + f x \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} - \frac{3 a^{3} c d^{2}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} + \frac{6 a^{3} d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} + \frac{2 a^{3} d^{3} \sin^{3}{\left(e + f x \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} - \frac{6 a^{3} d^{3} \sin{\left(e + f x \right)}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} - \frac{a^{3} d^{3}}{2 c^{2} d^{4} f + 4 c d^{5} f \sin{\left(e + f x \right)} + 2 d^{6} f \sin^{2}{\left(e + f x \right)}} & \text{for}\: n = -3 \\\frac{6 a^{3} c^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} + \frac{6 a^{3} c^{3}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} + \frac{6 a^{3} c^{2} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} - \frac{12 a^{3} c^{2} d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} - \frac{12 a^{3} c^{2} d}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} - \frac{12 a^{3} c d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} + \frac{6 a^{3} c d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} - \frac{3 a^{3} c d^{2} \sin^{2}{\left(e + f x \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} + \frac{6 a^{3} c d^{2}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} + \frac{6 a^{3} d^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} + \frac{a^{3} d^{3} \sin^{3}{\left(e + f x \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} + \frac{6 a^{3} d^{3} \sin^{2}{\left(e + f x \right)}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} - \frac{2 a^{3} d^{3}}{2 c d^{4} f + 2 d^{5} f \sin{\left(e + f x \right)}} & \text{for}\: n = -2 \\- \frac{a^{3} c^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{4} f} + \frac{3 a^{3} c^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{3} f} + \frac{a^{3} c^{2} \sin{\left(e + f x \right)}}{d^{3} f} - \frac{3 a^{3} c \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{2} f} - \frac{a^{3} c \sin^{2}{\left(e + f x \right)}}{2 d^{2} f} - \frac{3 a^{3} c \sin{\left(e + f x \right)}}{d^{2} f} + \frac{a^{3} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d f} + \frac{a^{3} \sin^{3}{\left(e + f x \right)}}{3 d f} + \frac{3 a^{3} \sin^{2}{\left(e + f x \right)}}{2 d f} + \frac{3 a^{3} \sin{\left(e + f x \right)}}{d f} & \text{for}\: n = -1 \\- \frac{6 a^{3} c^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{6 a^{3} c^{3} d n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{6 a^{3} c^{3} d n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{24 a^{3} c^{3} d \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} - \frac{3 a^{3} c^{2} d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} - \frac{6 a^{3} c^{2} d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} - \frac{3 a^{3} c^{2} d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} - \frac{3 a^{3} c^{2} d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} - \frac{24 a^{3} c^{2} d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} - \frac{21 a^{3} c^{2} d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} - \frac{36 a^{3} c^{2} d^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{a^{3} c d^{3} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{3 a^{3} c d^{3} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{3 a^{3} c d^{3} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{a^{3} c d^{3} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{3 a^{3} c d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{15 a^{3} c d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{21 a^{3} c d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{9 a^{3} c d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{2 a^{3} c d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{12 a^{3} c d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{36 a^{3} c d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{26 a^{3} c d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{24 a^{3} c d^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{a^{3} d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{3 a^{3} d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{3 a^{3} d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{a^{3} d^{4} n^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{6 a^{3} d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{21 a^{3} d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{24 a^{3} d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{9 a^{3} d^{4} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{11 a^{3} d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{42 a^{3} d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{57 a^{3} d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{26 a^{3} d^{4} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{6 a^{3} d^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{4}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{24 a^{3} d^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{36 a^{3} d^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} + \frac{24 a^{3} d^{4} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{4} f n^{4} + 10 d^{4} f n^{3} + 35 d^{4} f n^{2} + 50 d^{4} f n + 24 d^{4} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(a**3*sin(e + f*x)**4/(4*f) + a**3*sin(e + f*x)**3/f + 3*a**3*sin(e + f*x)**2/(2*f) + a**3*sin(e + f*x)/f), Eq(d, 0)), (x*(c + d*sin(e))**n*(a*sin(e) + a)**3*cos(e), Eq(f, 0)), (6*a**3*c**3*log(c/d + sin(e + f*x))/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) + 11*a**3*c**3/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) + 18*a**3*c**2*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) + 27*a**3*c**2*d*sin(e + f*x)/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) - 6*a**3*c**2*d/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) + 18*a**3*c*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) + 18*a**3*c*d**2*sin(e + f*x)**2/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) - 18*a**3*c*d**2*sin(e + f*x)/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) - 3*a**3*c*d**2/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) + 6*a**3*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)**3/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) - 18*a**3*d**3*sin(e + f*x)**2/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) - 9*a**3*d**3*sin(e + f*x)/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3) - 2*a**3*d**3/(6*c**3*d**4*f + 18*c**2*d**5*f*sin(e + f*x) + 18*c*d**6*f*sin(e + f*x)**2 + 6*d**7*f*sin(e + f*x)**3), Eq(n, -4)), (-6*a**3*c**3*log(c/d + sin(e + f*x))/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) - 9*a**3*c**3/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) - 12*a**3*c**2*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) + 6*a**3*c**2*d*log(c/d + sin(e + f*x))/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) - 12*a**3*c**2*d*sin(e + f*x)/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) + 9*a**3*c**2*d/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) - 6*a**3*c*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) + 12*a**3*c*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) + 12*a**3*c*d**2*sin(e + f*x)/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) - 3*a**3*c*d**2/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) + 6*a**3*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) + 2*a**3*d**3*sin(e + f*x)**3/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) - 6*a**3*d**3*sin(e + f*x)/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2) - a**3*d**3/(2*c**2*d**4*f + 4*c*d**5*f*sin(e + f*x) + 2*d**6*f*sin(e + f*x)**2), Eq(n, -3)), (6*a**3*c**3*log(c/d + sin(e + f*x))/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) + 6*a**3*c**3/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) + 6*a**3*c**2*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) - 12*a**3*c**2*d*log(c/d + sin(e + f*x))/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) - 12*a**3*c**2*d/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) - 12*a**3*c*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) + 6*a**3*c*d**2*log(c/d + sin(e + f*x))/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) - 3*a**3*c*d**2*sin(e + f*x)**2/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) + 6*a**3*c*d**2/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) + 6*a**3*d**3*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) + a**3*d**3*sin(e + f*x)**3/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) + 6*a**3*d**3*sin(e + f*x)**2/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)) - 2*a**3*d**3/(2*c*d**4*f + 2*d**5*f*sin(e + f*x)), Eq(n, -2)), (-a**3*c**3*log(c/d + sin(e + f*x))/(d**4*f) + 3*a**3*c**2*log(c/d + sin(e + f*x))/(d**3*f) + a**3*c**2*sin(e + f*x)/(d**3*f) - 3*a**3*c*log(c/d + sin(e + f*x))/(d**2*f) - a**3*c*sin(e + f*x)**2/(2*d**2*f) - 3*a**3*c*sin(e + f*x)/(d**2*f) + a**3*log(c/d + sin(e + f*x))/(d*f) + a**3*sin(e + f*x)**3/(3*d*f) + 3*a**3*sin(e + f*x)**2/(2*d*f) + 3*a**3*sin(e + f*x)/(d*f), Eq(n, -1)), (-6*a**3*c**4*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 6*a**3*c**3*d*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 6*a**3*c**3*d*n*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 24*a**3*c**3*d*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) - 3*a**3*c**2*d**2*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) - 6*a**3*c**2*d**2*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) - 3*a**3*c**2*d**2*n**2*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) - 3*a**3*c**2*d**2*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) - 24*a**3*c**2*d**2*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) - 21*a**3*c**2*d**2*n*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) - 36*a**3*c**2*d**2*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + a**3*c*d**3*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 3*a**3*c*d**3*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 3*a**3*c*d**3*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + a**3*c*d**3*n**3*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 3*a**3*c*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 15*a**3*c*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 21*a**3*c*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 9*a**3*c*d**3*n**2*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 2*a**3*c*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 12*a**3*c*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 36*a**3*c*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 26*a**3*c*d**3*n*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 24*a**3*c*d**3*(c + d*sin(e + f*x))**n/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + a**3*d**4*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 3*a**3*d**4*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 3*a**3*d**4*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + a**3*d**4*n**3*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 6*a**3*d**4*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 21*a**3*d**4*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 24*a**3*d**4*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 9*a**3*d**4*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 11*a**3*d**4*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 42*a**3*d**4*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 57*a**3*d**4*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 26*a**3*d**4*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 6*a**3*d**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**4/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 24*a**3*d**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 36*a**3*d**4*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f) + 24*a**3*d**4*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**4*f*n**4 + 10*d**4*f*n**3 + 35*d**4*f*n**2 + 50*d**4*f*n + 24*d**4*f), True))","A",0
915,1,2159,0,20.586658," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**n,x)","\begin{cases} c^{n} \left(\frac{a^{2} \sin^{3}{\left(e + f x \right)}}{3 f} + \frac{a^{2} \sin^{2}{\left(e + f x \right)}}{f} + \frac{a^{2} \sin{\left(e + f x \right)}}{f}\right) & \text{for}\: d = 0 \\x \left(c + d \sin{\left(e \right)}\right)^{n} \left(a \sin{\left(e \right)} + a\right)^{2} \cos{\left(e \right)} & \text{for}\: f = 0 \\\frac{2 a^{2} c^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{2 c^{2} d^{3} f + 4 c d^{4} f \sin{\left(e + f x \right)} + 2 d^{5} f \sin^{2}{\left(e + f x \right)}} + \frac{3 a^{2} c^{2}}{2 c^{2} d^{3} f + 4 c d^{4} f \sin{\left(e + f x \right)} + 2 d^{5} f \sin^{2}{\left(e + f x \right)}} + \frac{4 a^{2} c d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{2 c^{2} d^{3} f + 4 c d^{4} f \sin{\left(e + f x \right)} + 2 d^{5} f \sin^{2}{\left(e + f x \right)}} + \frac{4 a^{2} c d \sin{\left(e + f x \right)}}{2 c^{2} d^{3} f + 4 c d^{4} f \sin{\left(e + f x \right)} + 2 d^{5} f \sin^{2}{\left(e + f x \right)}} - \frac{2 a^{2} c d}{2 c^{2} d^{3} f + 4 c d^{4} f \sin{\left(e + f x \right)} + 2 d^{5} f \sin^{2}{\left(e + f x \right)}} + \frac{2 a^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin^{2}{\left(e + f x \right)}}{2 c^{2} d^{3} f + 4 c d^{4} f \sin{\left(e + f x \right)} + 2 d^{5} f \sin^{2}{\left(e + f x \right)}} - \frac{4 a^{2} d^{2} \sin{\left(e + f x \right)}}{2 c^{2} d^{3} f + 4 c d^{4} f \sin{\left(e + f x \right)} + 2 d^{5} f \sin^{2}{\left(e + f x \right)}} - \frac{a^{2} d^{2}}{2 c^{2} d^{3} f + 4 c d^{4} f \sin{\left(e + f x \right)} + 2 d^{5} f \sin^{2}{\left(e + f x \right)}} & \text{for}\: n = -3 \\- \frac{2 a^{2} c^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{c d^{3} f + d^{4} f \sin{\left(e + f x \right)}} - \frac{2 a^{2} c^{2}}{c d^{3} f + d^{4} f \sin{\left(e + f x \right)}} - \frac{2 a^{2} c d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{c d^{3} f + d^{4} f \sin{\left(e + f x \right)}} + \frac{2 a^{2} c d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{c d^{3} f + d^{4} f \sin{\left(e + f x \right)}} + \frac{2 a^{2} c d}{c d^{3} f + d^{4} f \sin{\left(e + f x \right)}} + \frac{2 a^{2} d^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{c d^{3} f + d^{4} f \sin{\left(e + f x \right)}} + \frac{a^{2} d^{2} \sin^{2}{\left(e + f x \right)}}{c d^{3} f + d^{4} f \sin{\left(e + f x \right)}} - \frac{a^{2} d^{2}}{c d^{3} f + d^{4} f \sin{\left(e + f x \right)}} & \text{for}\: n = -2 \\\frac{a^{2} c^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{3} f} - \frac{2 a^{2} c \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{2} f} - \frac{a^{2} c \sin{\left(e + f x \right)}}{d^{2} f} + \frac{a^{2} \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d f} + \frac{a^{2} \sin^{2}{\left(e + f x \right)}}{2 d f} + \frac{2 a^{2} \sin{\left(e + f x \right)}}{d f} & \text{for}\: n = -1 \\\frac{2 a^{2} c^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} - \frac{2 a^{2} c^{2} d n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} - \frac{2 a^{2} c^{2} d n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} - \frac{6 a^{2} c^{2} d \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{a^{2} c d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{2 a^{2} c d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{a^{2} c d^{2} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{a^{2} c d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{6 a^{2} c d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{5 a^{2} c d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{6 a^{2} c d^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{a^{2} d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{2 a^{2} d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{a^{2} d^{3} n^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{3 a^{2} d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{8 a^{2} d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{5 a^{2} d^{3} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{2 a^{2} d^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{3}{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{6 a^{2} d^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} + \frac{6 a^{2} d^{3} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{3} f n^{3} + 6 d^{3} f n^{2} + 11 d^{3} f n + 6 d^{3} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(a**2*sin(e + f*x)**3/(3*f) + a**2*sin(e + f*x)**2/f + a**2*sin(e + f*x)/f), Eq(d, 0)), (x*(c + d*sin(e))**n*(a*sin(e) + a)**2*cos(e), Eq(f, 0)), (2*a**2*c**2*log(c/d + sin(e + f*x))/(2*c**2*d**3*f + 4*c*d**4*f*sin(e + f*x) + 2*d**5*f*sin(e + f*x)**2) + 3*a**2*c**2/(2*c**2*d**3*f + 4*c*d**4*f*sin(e + f*x) + 2*d**5*f*sin(e + f*x)**2) + 4*a**2*c*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(2*c**2*d**3*f + 4*c*d**4*f*sin(e + f*x) + 2*d**5*f*sin(e + f*x)**2) + 4*a**2*c*d*sin(e + f*x)/(2*c**2*d**3*f + 4*c*d**4*f*sin(e + f*x) + 2*d**5*f*sin(e + f*x)**2) - 2*a**2*c*d/(2*c**2*d**3*f + 4*c*d**4*f*sin(e + f*x) + 2*d**5*f*sin(e + f*x)**2) + 2*a**2*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)**2/(2*c**2*d**3*f + 4*c*d**4*f*sin(e + f*x) + 2*d**5*f*sin(e + f*x)**2) - 4*a**2*d**2*sin(e + f*x)/(2*c**2*d**3*f + 4*c*d**4*f*sin(e + f*x) + 2*d**5*f*sin(e + f*x)**2) - a**2*d**2/(2*c**2*d**3*f + 4*c*d**4*f*sin(e + f*x) + 2*d**5*f*sin(e + f*x)**2), Eq(n, -3)), (-2*a**2*c**2*log(c/d + sin(e + f*x))/(c*d**3*f + d**4*f*sin(e + f*x)) - 2*a**2*c**2/(c*d**3*f + d**4*f*sin(e + f*x)) - 2*a**2*c*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(c*d**3*f + d**4*f*sin(e + f*x)) + 2*a**2*c*d*log(c/d + sin(e + f*x))/(c*d**3*f + d**4*f*sin(e + f*x)) + 2*a**2*c*d/(c*d**3*f + d**4*f*sin(e + f*x)) + 2*a**2*d**2*log(c/d + sin(e + f*x))*sin(e + f*x)/(c*d**3*f + d**4*f*sin(e + f*x)) + a**2*d**2*sin(e + f*x)**2/(c*d**3*f + d**4*f*sin(e + f*x)) - a**2*d**2/(c*d**3*f + d**4*f*sin(e + f*x)), Eq(n, -2)), (a**2*c**2*log(c/d + sin(e + f*x))/(d**3*f) - 2*a**2*c*log(c/d + sin(e + f*x))/(d**2*f) - a**2*c*sin(e + f*x)/(d**2*f) + a**2*log(c/d + sin(e + f*x))/(d*f) + a**2*sin(e + f*x)**2/(2*d*f) + 2*a**2*sin(e + f*x)/(d*f), Eq(n, -1)), (2*a**2*c**3*(c + d*sin(e + f*x))**n/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) - 2*a**2*c**2*d*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) - 2*a**2*c**2*d*n*(c + d*sin(e + f*x))**n/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) - 6*a**2*c**2*d*(c + d*sin(e + f*x))**n/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + a**2*c*d**2*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 2*a**2*c*d**2*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + a**2*c*d**2*n**2*(c + d*sin(e + f*x))**n/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + a**2*c*d**2*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 6*a**2*c*d**2*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 5*a**2*c*d**2*n*(c + d*sin(e + f*x))**n/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 6*a**2*c*d**2*(c + d*sin(e + f*x))**n/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + a**2*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 2*a**2*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + a**2*d**3*n**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 3*a**2*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 8*a**2*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 5*a**2*d**3*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 2*a**2*d**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**3/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 6*a**2*d**3*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f) + 6*a**2*d**3*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**3*f*n**3 + 6*d**3*f*n**2 + 11*d**3*f*n + 6*d**3*f), True))","A",0
916,1,586,0,7.129148," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\begin{cases} c^{n} \left(\frac{a \sin^{2}{\left(e + f x \right)}}{2 f} + \frac{a \sin{\left(e + f x \right)}}{f}\right) & \text{for}\: d = 0 \\x \left(c + d \sin{\left(e \right)}\right)^{n} \left(a \sin{\left(e \right)} + a\right) \cos{\left(e \right)} & \text{for}\: f = 0 \\\frac{a c \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{c d^{2} f + d^{3} f \sin{\left(e + f x \right)}} + \frac{a c}{c d^{2} f + d^{3} f \sin{\left(e + f x \right)}} + \frac{a d \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)} \sin{\left(e + f x \right)}}{c d^{2} f + d^{3} f \sin{\left(e + f x \right)}} - \frac{a d}{c d^{2} f + d^{3} f \sin{\left(e + f x \right)}} & \text{for}\: n = -2 \\- \frac{a c \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d^{2} f} + \frac{a \log{\left(\frac{c}{d} + \sin{\left(e + f x \right)} \right)}}{d f} + \frac{a \sin{\left(e + f x \right)}}{d f} & \text{for}\: n = -1 \\- \frac{a c^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{2} f n^{2} + 3 d^{2} f n + 2 d^{2} f} + \frac{a c d n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{2} f n^{2} + 3 d^{2} f n + 2 d^{2} f} + \frac{a c d n \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{2} f n^{2} + 3 d^{2} f n + 2 d^{2} f} + \frac{2 a c d \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{d^{2} f n^{2} + 3 d^{2} f n + 2 d^{2} f} + \frac{a d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{2} f n^{2} + 3 d^{2} f n + 2 d^{2} f} + \frac{a d^{2} n \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{2} f n^{2} + 3 d^{2} f n + 2 d^{2} f} + \frac{a d^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin^{2}{\left(e + f x \right)}}{d^{2} f n^{2} + 3 d^{2} f n + 2 d^{2} f} + \frac{2 a d^{2} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}}{d^{2} f n^{2} + 3 d^{2} f n + 2 d^{2} f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((c**n*(a*sin(e + f*x)**2/(2*f) + a*sin(e + f*x)/f), Eq(d, 0)), (x*(c + d*sin(e))**n*(a*sin(e) + a)*cos(e), Eq(f, 0)), (a*c*log(c/d + sin(e + f*x))/(c*d**2*f + d**3*f*sin(e + f*x)) + a*c/(c*d**2*f + d**3*f*sin(e + f*x)) + a*d*log(c/d + sin(e + f*x))*sin(e + f*x)/(c*d**2*f + d**3*f*sin(e + f*x)) - a*d/(c*d**2*f + d**3*f*sin(e + f*x)), Eq(n, -2)), (-a*c*log(c/d + sin(e + f*x))/(d**2*f) + a*log(c/d + sin(e + f*x))/(d*f) + a*sin(e + f*x)/(d*f), Eq(n, -1)), (-a*c**2*(c + d*sin(e + f*x))**n/(d**2*f*n**2 + 3*d**2*f*n + 2*d**2*f) + a*c*d*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**2*f*n**2 + 3*d**2*f*n + 2*d**2*f) + a*c*d*n*(c + d*sin(e + f*x))**n/(d**2*f*n**2 + 3*d**2*f*n + 2*d**2*f) + 2*a*c*d*(c + d*sin(e + f*x))**n/(d**2*f*n**2 + 3*d**2*f*n + 2*d**2*f) + a*d**2*n*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**2*f*n**2 + 3*d**2*f*n + 2*d**2*f) + a*d**2*n*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**2*f*n**2 + 3*d**2*f*n + 2*d**2*f) + a*d**2*(c + d*sin(e + f*x))**n*sin(e + f*x)**2/(d**2*f*n**2 + 3*d**2*f*n + 2*d**2*f) + 2*a*d**2*(c + d*sin(e + f*x))**n*sin(e + f*x)/(d**2*f*n**2 + 3*d**2*f*n + 2*d**2*f), True))","A",0
917,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
918,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
919,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
920,1,9238,0,102.309420," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**4,x)","\begin{cases} x \left(c + d \sin{\left(e \right)}\right)^{4} \left(a \sin{\left(e \right)} + a\right)^{m} \cos{\left(e \right)} & \text{for}\: f = 0 \\- \frac{3 c^{4}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{16 c^{3} d \sin{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{4 c^{3} d}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{36 c^{2} d^{2} \sin^{2}{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{24 c^{2} d^{2} \sin{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{6 c^{2} d^{2}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{48 c d^{3} \sin^{3}{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{72 c d^{3} \sin^{2}{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{48 c d^{3} \sin{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} - \frac{12 c d^{3}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{12 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{4}{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{48 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{3}{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{72 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{48 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{12 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{48 d^{4} \sin^{3}{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{108 d^{4} \sin^{2}{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{88 d^{4} \sin{\left(e + f x \right)}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} + \frac{25 d^{4}}{12 a^{5} f \sin^{4}{\left(e + f x \right)} + 48 a^{5} f \sin^{3}{\left(e + f x \right)} + 72 a^{5} f \sin^{2}{\left(e + f x \right)} + 48 a^{5} f \sin{\left(e + f x \right)} + 12 a^{5} f} & \text{for}\: m = -5 \\- \frac{c^{4}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{6 c^{3} d \sin{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{2 c^{3} d}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{18 c^{2} d^{2} \sin^{2}{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{18 c^{2} d^{2} \sin{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{6 c^{2} d^{2}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} + \frac{12 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{3}{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} + \frac{36 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} + \frac{36 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} + \frac{12 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} + \frac{36 c d^{3} \sin^{2}{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} + \frac{54 c d^{3} \sin{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} + \frac{22 c d^{3}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{12 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{3}{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{36 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{36 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{12 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} + \frac{3 d^{4} \sin^{4}{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{36 d^{4} \sin^{2}{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{54 d^{4} \sin{\left(e + f x \right)}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} - \frac{22 d^{4}}{3 a^{4} f \sin^{3}{\left(e + f x \right)} + 9 a^{4} f \sin^{2}{\left(e + f x \right)} + 9 a^{4} f \sin{\left(e + f x \right)} + 3 a^{4} f} & \text{for}\: m = -4 \\- \frac{c^{4}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{8 c^{3} d \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{4 c^{3} d}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{12 c^{2} d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{24 c^{2} d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{12 c^{2} d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{24 c^{2} d^{2} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{18 c^{2} d^{2}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{24 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{48 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{24 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{8 c d^{3} \sin^{3}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{48 c d^{3} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{36 c d^{3}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{12 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{24 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{12 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{d^{4} \sin^{4}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{4 d^{4} \sin^{3}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{24 d^{4} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{18 d^{4}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} & \text{for}\: m = -3 \\- \frac{3 c^{4}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{12 c^{3} d \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{12 c^{3} d \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{12 c^{3} d}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} - \frac{36 c^{2} d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} - \frac{36 c^{2} d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{18 c^{2} d^{2} \sin^{2}{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} - \frac{36 c^{2} d^{2}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{36 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{36 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{6 c d^{3} \sin^{3}{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} - \frac{18 c d^{3} \sin^{2}{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{36 c d^{3}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} - \frac{12 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} - \frac{12 d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{d^{4} \sin^{4}{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} - \frac{2 d^{4} \sin^{3}{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} + \frac{6 d^{4} \sin^{2}{\left(e + f x \right)}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} - \frac{12 d^{4}}{3 a^{2} f \sin{\left(e + f x \right)} + 3 a^{2} f} & \text{for}\: m = -2 \\\frac{c^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} - \frac{4 c^{3} d \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{4 c^{3} d \sin{\left(e + f x \right)}}{a f} + \frac{6 c^{2} d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{3 c^{2} d^{2} \sin^{2}{\left(e + f x \right)}}{a f} - \frac{6 c^{2} d^{2} \sin{\left(e + f x \right)}}{a f} - \frac{4 c d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{4 c d^{3} \sin^{3}{\left(e + f x \right)}}{3 a f} - \frac{2 c d^{3} \sin^{2}{\left(e + f x \right)}}{a f} + \frac{4 c d^{3} \sin{\left(e + f x \right)}}{a f} + \frac{d^{4} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{d^{4} \sin^{4}{\left(e + f x \right)}}{4 a f} - \frac{d^{4} \sin^{3}{\left(e + f x \right)}}{3 a f} + \frac{d^{4} \sin^{2}{\left(e + f x \right)}}{2 a f} - \frac{d^{4} \sin{\left(e + f x \right)}}{a f} & \text{for}\: m = -1 \\\frac{c^{4} m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{c^{4} m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{14 c^{4} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{14 c^{4} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{71 c^{4} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{71 c^{4} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{154 c^{4} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{154 c^{4} m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{120 c^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{120 c^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{4 c^{3} d m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{4 c^{3} d m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{52 c^{3} d m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{48 c^{3} d m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{4 c^{3} d m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{236 c^{3} d m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{188 c^{3} d m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{48 c^{3} d m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{428 c^{3} d m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{240 c^{3} d m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{188 c^{3} d m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{240 c^{3} d \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{240 c^{3} d \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{6 c^{2} d^{2} m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{6 c^{2} d^{2} m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{72 c^{2} d^{2} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{60 c^{2} d^{2} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{12 c^{2} d^{2} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{294 c^{2} d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{174 c^{2} d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{108 c^{2} d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{12 c^{2} d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{468 c^{2} d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{120 c^{2} d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{240 c^{2} d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{108 c^{2} d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{240 c^{2} d^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{240 c^{2} d^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{4 c d^{3} m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{4 c d^{3} m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{44 c d^{3} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{32 c d^{3} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{12 c d^{3} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{164 c d^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{68 c d^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{72 c d^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{24 c d^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{244 c d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{40 c d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{60 c d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{120 c d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{24 c d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{120 c d^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{120 c d^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{d^{4} m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{5}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{d^{4} m^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{10 d^{4} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{5}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{6 d^{4} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{4 d^{4} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{35 d^{4} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{5}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{11 d^{4} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{12 d^{4} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{12 d^{4} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{50 d^{4} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{5}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{6 d^{4} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{8 d^{4} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{12 d^{4} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} - \frac{24 d^{4} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{24 d^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{5}{\left(e + f x \right)}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} + \frac{24 d^{4} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{5} + 15 f m^{4} + 85 f m^{3} + 225 f m^{2} + 274 f m + 120 f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(c + d*sin(e))**4*(a*sin(e) + a)**m*cos(e), Eq(f, 0)), (-3*c**4/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 16*c**3*d*sin(e + f*x)/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 4*c**3*d/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 36*c**2*d**2*sin(e + f*x)**2/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 24*c**2*d**2*sin(e + f*x)/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 6*c**2*d**2/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 48*c*d**3*sin(e + f*x)**3/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 72*c*d**3*sin(e + f*x)**2/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 48*c*d**3*sin(e + f*x)/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) - 12*c*d**3/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 12*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)**4/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 48*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)**3/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 72*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 48*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 12*d**4*log(sin(e + f*x) + 1)/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 48*d**4*sin(e + f*x)**3/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 108*d**4*sin(e + f*x)**2/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 88*d**4*sin(e + f*x)/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f) + 25*d**4/(12*a**5*f*sin(e + f*x)**4 + 48*a**5*f*sin(e + f*x)**3 + 72*a**5*f*sin(e + f*x)**2 + 48*a**5*f*sin(e + f*x) + 12*a**5*f), Eq(m, -5)), (-c**4/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 6*c**3*d*sin(e + f*x)/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 2*c**3*d/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 18*c**2*d**2*sin(e + f*x)**2/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 18*c**2*d**2*sin(e + f*x)/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 6*c**2*d**2/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) + 12*c*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)**3/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) + 36*c*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) + 36*c*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) + 12*c*d**3*log(sin(e + f*x) + 1)/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) + 36*c*d**3*sin(e + f*x)**2/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) + 54*c*d**3*sin(e + f*x)/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) + 22*c*d**3/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 12*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)**3/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 36*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 36*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 12*d**4*log(sin(e + f*x) + 1)/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) + 3*d**4*sin(e + f*x)**4/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 36*d**4*sin(e + f*x)**2/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 54*d**4*sin(e + f*x)/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f) - 22*d**4/(3*a**4*f*sin(e + f*x)**3 + 9*a**4*f*sin(e + f*x)**2 + 9*a**4*f*sin(e + f*x) + 3*a**4*f), Eq(m, -4)), (-c**4/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 8*c**3*d*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 4*c**3*d/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 12*c**2*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 24*c**2*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 12*c**2*d**2*log(sin(e + f*x) + 1)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 24*c**2*d**2*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 18*c**2*d**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 24*c*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 48*c*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 24*c*d**3*log(sin(e + f*x) + 1)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 8*c*d**3*sin(e + f*x)**3/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 48*c*d**3*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 36*c*d**3/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 12*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 24*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 12*d**4*log(sin(e + f*x) + 1)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + d**4*sin(e + f*x)**4/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 4*d**4*sin(e + f*x)**3/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 24*d**4*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 18*d**4/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f), Eq(m, -3)), (-3*c**4/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 12*c**3*d*log(sin(e + f*x) + 1)*sin(e + f*x)/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 12*c**3*d*log(sin(e + f*x) + 1)/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 12*c**3*d/(3*a**2*f*sin(e + f*x) + 3*a**2*f) - 36*c**2*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)/(3*a**2*f*sin(e + f*x) + 3*a**2*f) - 36*c**2*d**2*log(sin(e + f*x) + 1)/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 18*c**2*d**2*sin(e + f*x)**2/(3*a**2*f*sin(e + f*x) + 3*a**2*f) - 36*c**2*d**2/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 36*c*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 36*c*d**3*log(sin(e + f*x) + 1)/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 6*c*d**3*sin(e + f*x)**3/(3*a**2*f*sin(e + f*x) + 3*a**2*f) - 18*c*d**3*sin(e + f*x)**2/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 36*c*d**3/(3*a**2*f*sin(e + f*x) + 3*a**2*f) - 12*d**4*log(sin(e + f*x) + 1)*sin(e + f*x)/(3*a**2*f*sin(e + f*x) + 3*a**2*f) - 12*d**4*log(sin(e + f*x) + 1)/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + d**4*sin(e + f*x)**4/(3*a**2*f*sin(e + f*x) + 3*a**2*f) - 2*d**4*sin(e + f*x)**3/(3*a**2*f*sin(e + f*x) + 3*a**2*f) + 6*d**4*sin(e + f*x)**2/(3*a**2*f*sin(e + f*x) + 3*a**2*f) - 12*d**4/(3*a**2*f*sin(e + f*x) + 3*a**2*f), Eq(m, -2)), (c**4*log(sin(e + f*x) + 1)/(a*f) - 4*c**3*d*log(sin(e + f*x) + 1)/(a*f) + 4*c**3*d*sin(e + f*x)/(a*f) + 6*c**2*d**2*log(sin(e + f*x) + 1)/(a*f) + 3*c**2*d**2*sin(e + f*x)**2/(a*f) - 6*c**2*d**2*sin(e + f*x)/(a*f) - 4*c*d**3*log(sin(e + f*x) + 1)/(a*f) + 4*c*d**3*sin(e + f*x)**3/(3*a*f) - 2*c*d**3*sin(e + f*x)**2/(a*f) + 4*c*d**3*sin(e + f*x)/(a*f) + d**4*log(sin(e + f*x) + 1)/(a*f) + d**4*sin(e + f*x)**4/(4*a*f) - d**4*sin(e + f*x)**3/(3*a*f) + d**4*sin(e + f*x)**2/(2*a*f) - d**4*sin(e + f*x)/(a*f), Eq(m, -1)), (c**4*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + c**4*m**4*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 14*c**4*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 14*c**4*m**3*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 71*c**4*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 71*c**4*m**2*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 154*c**4*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 154*c**4*m*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 120*c**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 120*c**4*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 4*c**3*d*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 4*c**3*d*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 52*c**3*d*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 48*c**3*d*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 4*c**3*d*m**3*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 236*c**3*d*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 188*c**3*d*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 48*c**3*d*m**2*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 428*c**3*d*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 240*c**3*d*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 188*c**3*d*m*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 240*c**3*d*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 240*c**3*d*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 6*c**2*d**2*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 6*c**2*d**2*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 72*c**2*d**2*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 60*c**2*d**2*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 12*c**2*d**2*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 294*c**2*d**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 174*c**2*d**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 108*c**2*d**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 12*c**2*d**2*m**2*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 468*c**2*d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 120*c**2*d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 240*c**2*d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 108*c**2*d**2*m*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 240*c**2*d**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 240*c**2*d**2*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 4*c*d**3*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 4*c*d**3*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 44*c*d**3*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 32*c*d**3*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 12*c*d**3*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 164*c*d**3*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 68*c*d**3*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 72*c*d**3*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 24*c*d**3*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 244*c*d**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 40*c*d**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 60*c*d**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 120*c*d**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 24*c*d**3*m*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 120*c*d**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 120*c*d**3*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + d**4*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)**5/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + d**4*m**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 10*d**4*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**5/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 6*d**4*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 4*d**4*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 35*d**4*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**5/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 11*d**4*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 12*d**4*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 12*d**4*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 50*d**4*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**5/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 6*d**4*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 8*d**4*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 12*d**4*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) - 24*d**4*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 24*d**4*(a*sin(e + f*x) + a)**m*sin(e + f*x)**5/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f) + 24*d**4*(a*sin(e + f*x) + a)**m/(f*m**5 + 15*f*m**4 + 85*f*m**3 + 225*f*m**2 + 274*f*m + 120*f), True))","A",0
921,1,4310,0,41.430172," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**3,x)","\begin{cases} x \left(c + d \sin{\left(e \right)}\right)^{3} \left(a \sin{\left(e \right)} + a\right)^{m} \cos{\left(e \right)} & \text{for}\: f = 0 \\- \frac{2 c^{3}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{9 c^{2} d \sin{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{3 c^{2} d}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{18 c d^{2} \sin^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{18 c d^{2} \sin{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{6 c d^{2}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{6 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{3}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{18 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{18 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{6 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{18 d^{3} \sin^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{27 d^{3} \sin{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{11 d^{3}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} & \text{for}\: m = -4 \\- \frac{c^{3}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{6 c^{2} d \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{3 c^{2} d}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{6 c d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{12 c d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{6 c d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{12 c d^{2} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{9 c d^{2}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{6 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{12 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{6 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{2 d^{3} \sin^{3}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{12 d^{3} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{9 d^{3}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} & \text{for}\: m = -3 \\- \frac{2 c^{3}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} + \frac{6 c^{2} d \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} + \frac{6 c^{2} d \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} + \frac{6 c^{2} d}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} - \frac{12 c d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} - \frac{12 c d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} + \frac{6 c d^{2} \sin^{2}{\left(e + f x \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} - \frac{12 c d^{2}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} + \frac{6 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} + \frac{6 d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} + \frac{d^{3} \sin^{3}{\left(e + f x \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} - \frac{3 d^{3} \sin^{2}{\left(e + f x \right)}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} + \frac{6 d^{3}}{2 a^{2} f \sin{\left(e + f x \right)} + 2 a^{2} f} & \text{for}\: m = -2 \\\frac{c^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} - \frac{3 c^{2} d \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{3 c^{2} d \sin{\left(e + f x \right)}}{a f} + \frac{3 c d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{3 c d^{2} \sin^{2}{\left(e + f x \right)}}{2 a f} - \frac{3 c d^{2} \sin{\left(e + f x \right)}}{a f} - \frac{d^{3} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{d^{3} \sin^{3}{\left(e + f x \right)}}{3 a f} - \frac{d^{3} \sin^{2}{\left(e + f x \right)}}{2 a f} + \frac{d^{3} \sin{\left(e + f x \right)}}{a f} & \text{for}\: m = -1 \\\frac{c^{3} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{c^{3} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{9 c^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{9 c^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{26 c^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{26 c^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{24 c^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{24 c^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{3 c^{2} d m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{3 c^{2} d m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{24 c^{2} d m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{21 c^{2} d m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{3 c^{2} d m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{57 c^{2} d m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{36 c^{2} d m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{21 c^{2} d m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{36 c^{2} d \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{36 c^{2} d \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{3 c d^{2} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{3 c d^{2} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{21 c d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{15 c d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{6 c d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{42 c d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{12 c d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{24 c d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{6 c d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{24 c d^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{24 c d^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{d^{3} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{d^{3} m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{6 d^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{3 d^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{3 d^{3} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{11 d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{2 d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{3 d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{6 d^{3} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{6 d^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{6 d^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(c + d*sin(e))**3*(a*sin(e) + a)**m*cos(e), Eq(f, 0)), (-2*c**3/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 9*c**2*d*sin(e + f*x)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 3*c**2*d/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 18*c*d**2*sin(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 18*c*d**2*sin(e + f*x)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 6*c*d**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 6*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)**3/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 18*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 18*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 6*d**3*log(sin(e + f*x) + 1)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 18*d**3*sin(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 27*d**3*sin(e + f*x)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 11*d**3/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f), Eq(m, -4)), (-c**3/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 6*c**2*d*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 3*c**2*d/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 6*c*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 12*c*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 6*c*d**2*log(sin(e + f*x) + 1)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 12*c*d**2*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 9*c*d**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 6*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 12*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 6*d**3*log(sin(e + f*x) + 1)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 2*d**3*sin(e + f*x)**3/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 12*d**3*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 9*d**3/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f), Eq(m, -3)), (-2*c**3/(2*a**2*f*sin(e + f*x) + 2*a**2*f) + 6*c**2*d*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**2*f*sin(e + f*x) + 2*a**2*f) + 6*c**2*d*log(sin(e + f*x) + 1)/(2*a**2*f*sin(e + f*x) + 2*a**2*f) + 6*c**2*d/(2*a**2*f*sin(e + f*x) + 2*a**2*f) - 12*c*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**2*f*sin(e + f*x) + 2*a**2*f) - 12*c*d**2*log(sin(e + f*x) + 1)/(2*a**2*f*sin(e + f*x) + 2*a**2*f) + 6*c*d**2*sin(e + f*x)**2/(2*a**2*f*sin(e + f*x) + 2*a**2*f) - 12*c*d**2/(2*a**2*f*sin(e + f*x) + 2*a**2*f) + 6*d**3*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**2*f*sin(e + f*x) + 2*a**2*f) + 6*d**3*log(sin(e + f*x) + 1)/(2*a**2*f*sin(e + f*x) + 2*a**2*f) + d**3*sin(e + f*x)**3/(2*a**2*f*sin(e + f*x) + 2*a**2*f) - 3*d**3*sin(e + f*x)**2/(2*a**2*f*sin(e + f*x) + 2*a**2*f) + 6*d**3/(2*a**2*f*sin(e + f*x) + 2*a**2*f), Eq(m, -2)), (c**3*log(sin(e + f*x) + 1)/(a*f) - 3*c**2*d*log(sin(e + f*x) + 1)/(a*f) + 3*c**2*d*sin(e + f*x)/(a*f) + 3*c*d**2*log(sin(e + f*x) + 1)/(a*f) + 3*c*d**2*sin(e + f*x)**2/(2*a*f) - 3*c*d**2*sin(e + f*x)/(a*f) - d**3*log(sin(e + f*x) + 1)/(a*f) + d**3*sin(e + f*x)**3/(3*a*f) - d**3*sin(e + f*x)**2/(2*a*f) + d**3*sin(e + f*x)/(a*f), Eq(m, -1)), (c**3*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + c**3*m**3*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 9*c**3*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 9*c**3*m**2*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 26*c**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 26*c**3*m*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 24*c**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 24*c**3*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 3*c**2*d*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 3*c**2*d*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 24*c**2*d*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 21*c**2*d*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 3*c**2*d*m**2*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 57*c**2*d*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 36*c**2*d*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 21*c**2*d*m*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 36*c**2*d*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 36*c**2*d*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 3*c*d**2*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 3*c*d**2*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 21*c*d**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 15*c*d**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 6*c*d**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 42*c*d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 12*c*d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 24*c*d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 6*c*d**2*m*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 24*c*d**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 24*c*d**2*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + d**3*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + d**3*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 6*d**3*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 3*d**3*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 3*d**3*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 11*d**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 2*d**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 3*d**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 6*d**3*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 6*d**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 6*d**3*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f), True))","A",0
922,1,1622,0,15.950913," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**2,x)","\begin{cases} x \left(c + d \sin{\left(e \right)}\right)^{2} \left(a \sin{\left(e \right)} + a\right)^{m} \cos{\left(e \right)} & \text{for}\: f = 0 \\- \frac{c^{2}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{4 c d \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{2 c d}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{2 d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{4 d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{2 d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{4 d^{2} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{3 d^{2}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} & \text{for}\: m = -3 \\- \frac{c^{2}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{2 c d \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{2 c d \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{2 c d}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} - \frac{2 d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} - \frac{2 d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{d^{2} \sin^{2}{\left(e + f x \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} - \frac{2 d^{2}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} & \text{for}\: m = -2 \\\frac{c^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} - \frac{2 c d \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{2 c d \sin{\left(e + f x \right)}}{a f} + \frac{d^{2} \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{d^{2} \sin^{2}{\left(e + f x \right)}}{2 a f} - \frac{d^{2} \sin{\left(e + f x \right)}}{a f} & \text{for}\: m = -1 \\\frac{c^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{c^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{5 c^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{5 c^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{6 c^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{6 c^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{2 c d m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{2 c d m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{8 c d m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{6 c d m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} - \frac{2 c d m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{6 c d \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} - \frac{6 c d \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{d^{2} m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{3 d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} - \frac{2 d^{2} m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{2 d^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} + \frac{2 d^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{3} + 6 f m^{2} + 11 f m + 6 f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(c + d*sin(e))**2*(a*sin(e) + a)**m*cos(e), Eq(f, 0)), (-c**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 4*c*d*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 2*c*d/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 2*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 4*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 2*d**2*log(sin(e + f*x) + 1)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 4*d**2*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 3*d**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f), Eq(m, -3)), (-c**2/(a**2*f*sin(e + f*x) + a**2*f) + 2*c*d*log(sin(e + f*x) + 1)*sin(e + f*x)/(a**2*f*sin(e + f*x) + a**2*f) + 2*c*d*log(sin(e + f*x) + 1)/(a**2*f*sin(e + f*x) + a**2*f) + 2*c*d/(a**2*f*sin(e + f*x) + a**2*f) - 2*d**2*log(sin(e + f*x) + 1)*sin(e + f*x)/(a**2*f*sin(e + f*x) + a**2*f) - 2*d**2*log(sin(e + f*x) + 1)/(a**2*f*sin(e + f*x) + a**2*f) + d**2*sin(e + f*x)**2/(a**2*f*sin(e + f*x) + a**2*f) - 2*d**2/(a**2*f*sin(e + f*x) + a**2*f), Eq(m, -2)), (c**2*log(sin(e + f*x) + 1)/(a*f) - 2*c*d*log(sin(e + f*x) + 1)/(a*f) + 2*c*d*sin(e + f*x)/(a*f) + d**2*log(sin(e + f*x) + 1)/(a*f) + d**2*sin(e + f*x)**2/(2*a*f) - d**2*sin(e + f*x)/(a*f), Eq(m, -1)), (c**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + c**2*m**2*(a*sin(e + f*x) + a)**m/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 5*c**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 5*c**2*m*(a*sin(e + f*x) + a)**m/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 6*c**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 6*c**2*(a*sin(e + f*x) + a)**m/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 2*c*d*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 2*c*d*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 8*c*d*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 6*c*d*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) - 2*c*d*m*(a*sin(e + f*x) + a)**m/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 6*c*d*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) - 6*c*d*(a*sin(e + f*x) + a)**m/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + d**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + d**2*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 3*d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) - 2*d**2*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 2*d**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f) + 2*d**2*(a*sin(e + f*x) + a)**m/(f*m**3 + 6*f*m**2 + 11*f*m + 6*f), True))","A",0
923,1,428,0,5.591954," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e)),x)","\begin{cases} x \left(c + d \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{m} \cos{\left(e \right)} & \text{for}\: f = 0 \\- \frac{c}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{d \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{d \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{d}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} & \text{for}\: m = -2 \\\frac{c \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} - \frac{d \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{d \sin{\left(e + f x \right)}}{a f} & \text{for}\: m = -1 \\\frac{c m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} + \frac{c m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{2} + 3 f m + 2 f} + \frac{2 c \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} + \frac{2 c \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{2} + 3 f m + 2 f} + \frac{d m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} + \frac{d m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} + \frac{d \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} - \frac{d \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{2} + 3 f m + 2 f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(c + d*sin(e))*(a*sin(e) + a)**m*cos(e), Eq(f, 0)), (-c/(a**2*f*sin(e + f*x) + a**2*f) + d*log(sin(e + f*x) + 1)*sin(e + f*x)/(a**2*f*sin(e + f*x) + a**2*f) + d*log(sin(e + f*x) + 1)/(a**2*f*sin(e + f*x) + a**2*f) + d/(a**2*f*sin(e + f*x) + a**2*f), Eq(m, -2)), (c*log(sin(e + f*x) + 1)/(a*f) - d*log(sin(e + f*x) + 1)/(a*f) + d*sin(e + f*x)/(a*f), Eq(m, -1)), (c*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**2 + 3*f*m + 2*f) + c*m*(a*sin(e + f*x) + a)**m/(f*m**2 + 3*f*m + 2*f) + 2*c*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**2 + 3*f*m + 2*f) + 2*c*(a*sin(e + f*x) + a)**m/(f*m**2 + 3*f*m + 2*f) + d*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**2 + 3*f*m + 2*f) + d*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**2 + 3*f*m + 2*f) + d*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**2 + 3*f*m + 2*f) - d*(a*sin(e + f*x) + a)**m/(f*m**2 + 3*f*m + 2*f), True))","A",0
924,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
925,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
926,-1,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m/(c+d*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
927,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)**n*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \sin^{n}{\left(c + d x \right)} \cos{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*sin(c + d*x)**n*cos(c + d*x), x)","F",0
928,1,2747,0,67.343822," ","integrate(cos(d*x+c)*sin(d*x+c)**4*(a+a*sin(d*x+c))**m,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{m} \sin^{4}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{4}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{48 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{3}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{72 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{48 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{48 \sin^{3}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{108 \sin^{2}{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{88 \sin{\left(c + d x \right)}}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} + \frac{25}{12 a^{5} d \sin^{4}{\left(c + d x \right)} + 48 a^{5} d \sin^{3}{\left(c + d x \right)} + 72 a^{5} d \sin^{2}{\left(c + d x \right)} + 48 a^{5} d \sin{\left(c + d x \right)} + 12 a^{5} d} & \text{for}\: m = -5 \\- \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{3}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{36 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{36 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} + \frac{3 \sin^{4}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{36 \sin^{2}{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{54 \sin{\left(c + d x \right)}}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} - \frac{22}{3 a^{4} d \sin^{3}{\left(c + d x \right)} + 9 a^{4} d \sin^{2}{\left(c + d x \right)} + 9 a^{4} d \sin{\left(c + d x \right)} + 3 a^{4} d} & \text{for}\: m = -4 \\\frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{24 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{\sin^{4}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{4 \sin^{3}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{24 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{18}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: m = -3 \\- \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} + \frac{\sin^{4}{\left(c + d x \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} - \frac{2 \sin^{3}{\left(c + d x \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} + \frac{6 \sin^{2}{\left(c + d x \right)}}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} - \frac{12}{3 a^{2} d \sin{\left(c + d x \right)} + 3 a^{2} d} & \text{for}\: m = -2 \\\frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} + \frac{\sin^{4}{\left(c + d x \right)}}{4 a d} - \frac{\sin^{3}{\left(c + d x \right)}}{3 a d} - \frac{\sin{\left(c + d x \right)}}{a d} - \frac{\cos^{2}{\left(c + d x \right)}}{2 a d} & \text{for}\: m = -1 \\\frac{m^{4} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{5}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{m^{4} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{10 m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{5}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{6 m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{4 m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{35 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{5}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{11 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{12 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{12 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{50 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{5}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{6 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{8 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{12 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} - \frac{24 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{24 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{5}{\left(c + d x \right)}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} + \frac{24 \left(a \sin{\left(c + d x \right)} + a\right)^{m}}{d m^{5} + 15 d m^{4} + 85 d m^{3} + 225 d m^{2} + 274 d m + 120 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**m*sin(c)**4*cos(c), Eq(d, 0)), (12*log(sin(c + d*x) + 1)*sin(c + d*x)**4/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 48*log(sin(c + d*x) + 1)*sin(c + d*x)**3/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 72*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 48*log(sin(c + d*x) + 1)*sin(c + d*x)/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 12*log(sin(c + d*x) + 1)/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 48*sin(c + d*x)**3/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 108*sin(c + d*x)**2/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 88*sin(c + d*x)/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d) + 25/(12*a**5*d*sin(c + d*x)**4 + 48*a**5*d*sin(c + d*x)**3 + 72*a**5*d*sin(c + d*x)**2 + 48*a**5*d*sin(c + d*x) + 12*a**5*d), Eq(m, -5)), (-12*log(sin(c + d*x) + 1)*sin(c + d*x)**3/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 36*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 36*log(sin(c + d*x) + 1)*sin(c + d*x)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 12*log(sin(c + d*x) + 1)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) + 3*sin(c + d*x)**4/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 36*sin(c + d*x)**2/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 54*sin(c + d*x)/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d) - 22/(3*a**4*d*sin(c + d*x)**3 + 9*a**4*d*sin(c + d*x)**2 + 9*a**4*d*sin(c + d*x) + 3*a**4*d), Eq(m, -4)), (12*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 24*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 12*log(sin(c + d*x) + 1)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + sin(c + d*x)**4/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 4*sin(c + d*x)**3/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 24*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 18/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Eq(m, -3)), (-12*log(sin(c + d*x) + 1)*sin(c + d*x)/(3*a**2*d*sin(c + d*x) + 3*a**2*d) - 12*log(sin(c + d*x) + 1)/(3*a**2*d*sin(c + d*x) + 3*a**2*d) + sin(c + d*x)**4/(3*a**2*d*sin(c + d*x) + 3*a**2*d) - 2*sin(c + d*x)**3/(3*a**2*d*sin(c + d*x) + 3*a**2*d) + 6*sin(c + d*x)**2/(3*a**2*d*sin(c + d*x) + 3*a**2*d) - 12/(3*a**2*d*sin(c + d*x) + 3*a**2*d), Eq(m, -2)), (log(sin(c + d*x) + 1)/(a*d) + sin(c + d*x)**4/(4*a*d) - sin(c + d*x)**3/(3*a*d) - sin(c + d*x)/(a*d) - cos(c + d*x)**2/(2*a*d), Eq(m, -1)), (m**4*(a*sin(c + d*x) + a)**m*sin(c + d*x)**5/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + m**4*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 10*m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)**5/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 6*m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 4*m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 35*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**5/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 11*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 12*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 12*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 50*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**5/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 6*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 8*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 12*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) - 24*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 24*(a*sin(c + d*x) + a)**m*sin(c + d*x)**5/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d) + 24*(a*sin(c + d*x) + a)**m/(d*m**5 + 15*d*m**4 + 85*d*m**3 + 225*d*m**2 + 274*d*m + 120*d), True))","A",0
929,1,1508,0,28.582713," ","integrate(cos(d*x+c)*sin(d*x+c)**3*(a+a*sin(d*x+c))**m,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{m} \sin^{3}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{3}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{18 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{18 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{18 \sin^{2}{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{27 \sin{\left(c + d x \right)}}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} + \frac{11}{6 a^{4} d \sin^{3}{\left(c + d x \right)} + 18 a^{4} d \sin^{2}{\left(c + d x \right)} + 18 a^{4} d \sin{\left(c + d x \right)} + 6 a^{4} d} & \text{for}\: m = -4 \\- \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{12 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{2 \sin^{3}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{12 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} - \frac{9}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: m = -3 \\\frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} + \frac{6 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} + \frac{\sin^{3}{\left(c + d x \right)}}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} - \frac{3 \sin^{2}{\left(c + d x \right)}}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} + \frac{6}{2 a^{2} d \sin{\left(c + d x \right)} + 2 a^{2} d} & \text{for}\: m = -2 \\- \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} + \frac{\sin^{3}{\left(c + d x \right)}}{3 a d} + \frac{\sin{\left(c + d x \right)}}{a d} + \frac{\cos^{2}{\left(c + d x \right)}}{2 a d} & \text{for}\: m = -1 \\\frac{m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} + \frac{m^{3} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} + \frac{6 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} + \frac{3 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} - \frac{3 m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} + \frac{11 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} + \frac{2 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} - \frac{3 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} + \frac{6 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} + \frac{6 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{4}{\left(c + d x \right)}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} - \frac{6 \left(a \sin{\left(c + d x \right)} + a\right)^{m}}{d m^{4} + 10 d m^{3} + 35 d m^{2} + 50 d m + 24 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**m*sin(c)**3*cos(c), Eq(d, 0)), (6*log(sin(c + d*x) + 1)*sin(c + d*x)**3/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 18*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 18*log(sin(c + d*x) + 1)*sin(c + d*x)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 6*log(sin(c + d*x) + 1)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 18*sin(c + d*x)**2/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 27*sin(c + d*x)/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d) + 11/(6*a**4*d*sin(c + d*x)**3 + 18*a**4*d*sin(c + d*x)**2 + 18*a**4*d*sin(c + d*x) + 6*a**4*d), Eq(m, -4)), (-6*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 12*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 6*log(sin(c + d*x) + 1)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 2*sin(c + d*x)**3/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 12*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) - 9/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Eq(m, -3)), (6*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**2*d*sin(c + d*x) + 2*a**2*d) + 6*log(sin(c + d*x) + 1)/(2*a**2*d*sin(c + d*x) + 2*a**2*d) + sin(c + d*x)**3/(2*a**2*d*sin(c + d*x) + 2*a**2*d) - 3*sin(c + d*x)**2/(2*a**2*d*sin(c + d*x) + 2*a**2*d) + 6/(2*a**2*d*sin(c + d*x) + 2*a**2*d), Eq(m, -2)), (-log(sin(c + d*x) + 1)/(a*d) + sin(c + d*x)**3/(3*a*d) + sin(c + d*x)/(a*d) + cos(c + d*x)**2/(2*a*d), Eq(m, -1)), (m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) + m**3*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) + 6*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) + 3*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) - 3*m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) + 11*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) + 2*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) - 3*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) + 6*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) + 6*(a*sin(c + d*x) + a)**m*sin(c + d*x)**4/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d) - 6*(a*sin(c + d*x) + a)**m/(d*m**4 + 10*d*m**3 + 35*d*m**2 + 50*d*m + 24*d), True))","A",0
930,1,697,0,11.846521," ","integrate(cos(d*x+c)*sin(d*x+c)**2*(a+a*sin(d*x+c))**m,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{m} \sin^{2}{\left(c \right)} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin^{2}{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{4 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{4 \sin{\left(c + d x \right)}}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} + \frac{3}{2 a^{3} d \sin^{2}{\left(c + d x \right)} + 4 a^{3} d \sin{\left(c + d x \right)} + 2 a^{3} d} & \text{for}\: m = -3 \\- \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} - \frac{2 \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{\sin^{2}{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} - \frac{2}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} & \text{for}\: m = -2 \\\frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} - \frac{\sin{\left(c + d x \right)}}{a d} - \frac{\cos^{2}{\left(c + d x \right)}}{2 a d} & \text{for}\: m = -1 \\\frac{m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{m^{2} \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{3 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} - \frac{2 m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{2 \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{3}{\left(c + d x \right)}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} + \frac{2 \left(a \sin{\left(c + d x \right)} + a\right)^{m}}{d m^{3} + 6 d m^{2} + 11 d m + 6 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**m*sin(c)**2*cos(c), Eq(d, 0)), (2*log(sin(c + d*x) + 1)*sin(c + d*x)**2/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 4*log(sin(c + d*x) + 1)*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 2*log(sin(c + d*x) + 1)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 4*sin(c + d*x)/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d) + 3/(2*a**3*d*sin(c + d*x)**2 + 4*a**3*d*sin(c + d*x) + 2*a**3*d), Eq(m, -3)), (-2*log(sin(c + d*x) + 1)*sin(c + d*x)/(a**2*d*sin(c + d*x) + a**2*d) - 2*log(sin(c + d*x) + 1)/(a**2*d*sin(c + d*x) + a**2*d) + sin(c + d*x)**2/(a**2*d*sin(c + d*x) + a**2*d) - 2/(a**2*d*sin(c + d*x) + a**2*d), Eq(m, -2)), (log(sin(c + d*x) + 1)/(a*d) - sin(c + d*x)/(a*d) - cos(c + d*x)**2/(2*a*d), Eq(m, -1)), (m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + m**2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 3*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) - 2*m*(a*sin(c + d*x) + a)**m*sin(c + d*x)/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 2*(a*sin(c + d*x) + a)**m*sin(c + d*x)**3/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d) + 2*(a*sin(c + d*x) + a)**m/(d*m**3 + 6*d*m**2 + 11*d*m + 6*d), True))","A",0
931,1,248,0,4.802187," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))**m,x)","\begin{cases} x \left(a \sin{\left(c \right)} + a\right)^{m} \sin{\left(c \right)} \cos{\left(c \right)} & \text{for}\: d = 0 \\\frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{1}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} & \text{for}\: m = -2 \\- \frac{\log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} + \frac{\sin{\left(c + d x \right)}}{a d} & \text{for}\: m = -1 \\\frac{m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{2} + 3 d m + 2 d} + \frac{m \left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin{\left(c + d x \right)}}{d m^{2} + 3 d m + 2 d} + \frac{\left(a \sin{\left(c + d x \right)} + a\right)^{m} \sin^{2}{\left(c + d x \right)}}{d m^{2} + 3 d m + 2 d} - \frac{\left(a \sin{\left(c + d x \right)} + a\right)^{m}}{d m^{2} + 3 d m + 2 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a*sin(c) + a)**m*sin(c)*cos(c), Eq(d, 0)), (log(sin(c + d*x) + 1)*sin(c + d*x)/(a**2*d*sin(c + d*x) + a**2*d) + log(sin(c + d*x) + 1)/(a**2*d*sin(c + d*x) + a**2*d) + 1/(a**2*d*sin(c + d*x) + a**2*d), Eq(m, -2)), (-log(sin(c + d*x) + 1)/(a*d) + sin(c + d*x)/(a*d), Eq(m, -1)), (m*(a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**2 + 3*d*m + 2*d) + m*(a*sin(c + d*x) + a)**m*sin(c + d*x)/(d*m**2 + 3*d*m + 2*d) + (a*sin(c + d*x) + a)**m*sin(c + d*x)**2/(d*m**2 + 3*d*m + 2*d) - (a*sin(c + d*x) + a)**m/(d*m**2 + 3*d*m + 2*d), True))","A",0
932,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \cos{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*cos(c + d*x)*csc(c + d*x), x)","F",0
933,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2*(a+a*sin(d*x+c))**m,x)","\int \left(a \left(\sin{\left(c + d x \right)} + 1\right)\right)^{m} \cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a*(sin(c + d*x) + 1))**m*cos(c + d*x)*csc(c + d*x)**2, x)","F",0
934,-1,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3*(a+a*sin(d*x+c))**m,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
935,1,199,0,0.988912," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x)","\begin{cases} \frac{a c x \sin^{2}{\left(e + f x \right)}}{2} + \frac{a c x \cos^{2}{\left(e + f x \right)}}{2} + \frac{a c \sin{\left(e + f x \right)} \cos{\left(e + f x \right)}}{2 f} - \frac{a c \cos^{3}{\left(e + f x \right)}}{3 f} + \frac{a d x \sin^{4}{\left(e + f x \right)}}{8} + \frac{a d x \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{4} + \frac{a d x \cos^{4}{\left(e + f x \right)}}{8} + \frac{a d \sin^{3}{\left(e + f x \right)} \cos{\left(e + f x \right)}}{8 f} - \frac{a d \sin{\left(e + f x \right)} \cos^{3}{\left(e + f x \right)}}{8 f} - \frac{a d \cos^{3}{\left(e + f x \right)}}{3 f} & \text{for}\: f \neq 0 \\x \left(c + d \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right) \cos^{2}{\left(e \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*c*x*sin(e + f*x)**2/2 + a*c*x*cos(e + f*x)**2/2 + a*c*sin(e + f*x)*cos(e + f*x)/(2*f) - a*c*cos(e + f*x)**3/(3*f) + a*d*x*sin(e + f*x)**4/8 + a*d*x*sin(e + f*x)**2*cos(e + f*x)**2/4 + a*d*x*cos(e + f*x)**4/8 + a*d*sin(e + f*x)**3*cos(e + f*x)/(8*f) - a*d*sin(e + f*x)*cos(e + f*x)**3/(8*f) - a*d*cos(e + f*x)**3/(3*f), Ne(f, 0)), (x*(c + d*sin(e))*(a*sin(e) + a)*cos(e)**2, True))","A",0
936,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
937,0,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+a*sin(f*x+e))**(3/2)/(c+d*sin(f*x+e))**(1/2),x)","\int \frac{\cos^{2}{\left(e + f x \right)}}{\left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{\frac{3}{2}} \sqrt{c + d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(cos(e + f*x)**2/((a*(sin(e + f*x) + 1))**(3/2)*sqrt(c + d*sin(e + f*x))), x)","F",0
938,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
939,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**3*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
940,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
941,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
942,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
943,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
944,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
945,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
946,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
947,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
948,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
949,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
950,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
951,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
952,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
953,1,228,0,13.879743," ","integrate(cos(d*x+c)**7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{16 A a \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 A a \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 A a \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{A a \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{A a \cos^{8}{\left(c + d x \right)}}{8 d} + \frac{16 B a \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{8 B a \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{2 B a \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{B a \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{B a \cos^{8}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right) \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*A*a*sin(c + d*x)**7/(35*d) + 8*A*a*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*A*a*sin(c + d*x)**3*cos(c + d*x)**4/d + A*a*sin(c + d*x)*cos(c + d*x)**6/d - A*a*cos(c + d*x)**8/(8*d) + 16*B*a*sin(c + d*x)**9/(315*d) + 8*B*a*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 2*B*a*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + B*a*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) - B*a*cos(c + d*x)**8/(8*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)*cos(c)**7, True))","A",0
954,1,178,0,5.331831," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{8 A a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{A a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{A a \cos^{6}{\left(c + d x \right)}}{6 d} + \frac{8 B a \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 B a \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{B a \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{B a \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right) \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a*sin(c + d*x)**5/(15*d) + 4*A*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + A*a*sin(c + d*x)*cos(c + d*x)**4/d - A*a*cos(c + d*x)**6/(6*d) + 8*B*a*sin(c + d*x)**7/(105*d) + 4*B*a*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + B*a*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - B*a*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)*cos(c)**5, True))","A",0
955,1,128,0,1.765047," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{2 A a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{A a \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{2 B a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{B a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{B a \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right) \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*a*sin(c + d*x)**3/(3*d) + A*a*sin(c + d*x)*cos(c + d*x)**2/d - A*a*cos(c + d*x)**4/(4*d) + 2*B*a*sin(c + d*x)**5/(15*d) + B*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - B*a*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)*cos(c)**3, True))","A",0
956,1,75,0,0.438132," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a \sin{\left(c + d x \right)}}{d} - \frac{A a \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{B a \sin^{3}{\left(c + d x \right)}}{3 d} - \frac{B a \cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*sin(c + d*x)/d - A*a*cos(c + d*x)**2/(2*d) + B*a*sin(c + d*x)**3/(3*d) - B*a*cos(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)*cos(c), True))","A",0
957,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","a \left(\int A \sec{\left(c + d x \right)}\, dx + \int A \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x), x) + Integral(A*sin(c + d*x)*sec(c + d*x), x) + Integral(B*sin(c + d*x)*sec(c + d*x), x) + Integral(B*sin(c + d*x)**2*sec(c + d*x), x))","F",0
958,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","a \left(\int A \sec^{3}{\left(c + d x \right)}\, dx + \int A \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int B \sin^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x)**3, x) + Integral(A*sin(c + d*x)*sec(c + d*x)**3, x) + Integral(B*sin(c + d*x)*sec(c + d*x)**3, x) + Integral(B*sin(c + d*x)**2*sec(c + d*x)**3, x))","F",0
959,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
960,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
961,1,416,0,9.703894," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{5 A a x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 A a x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 A a x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 A a x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 A a \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{5 A a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{11 A a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{A a \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{5 B a x \sin^{8}{\left(c + d x \right)}}{128} + \frac{5 B a x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 B a x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{5 B a x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{5 B a x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 B a \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 B a \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{73 B a \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} - \frac{5 B a \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{B a \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right) \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*A*a*x*sin(c + d*x)**6/16 + 15*A*a*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*A*a*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*A*a*x*cos(c + d*x)**6/16 + 5*A*a*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 5*A*a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 11*A*a*sin(c + d*x)*cos(c + d*x)**5/(16*d) - A*a*cos(c + d*x)**7/(7*d) + 5*B*a*x*sin(c + d*x)**8/128 + 5*B*a*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*B*a*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 5*B*a*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 5*B*a*x*cos(c + d*x)**8/128 + 5*B*a*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*B*a*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 73*B*a*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) - 5*B*a*sin(c + d*x)*cos(c + d*x)**7/(128*d) - B*a*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)*cos(c)**6, True))","A",0
962,1,306,0,3.503596," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{3 A a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{5 A a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{A a \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{B a x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 B a x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 B a x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{B a x \cos^{6}{\left(c + d x \right)}}{16} + \frac{B a \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{B a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{B a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{B a \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right) \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a*x*sin(c + d*x)**4/8 + 3*A*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*a*x*cos(c + d*x)**4/8 + 3*A*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) + 5*A*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) - A*a*cos(c + d*x)**5/(5*d) + B*a*x*sin(c + d*x)**6/16 + 3*B*a*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*B*a*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + B*a*x*cos(c + d*x)**6/16 + B*a*sin(c + d*x)**5*cos(c + d*x)/(16*d) + B*a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - B*a*sin(c + d*x)*cos(c + d*x)**5/(16*d) - B*a*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)*cos(c)**4, True))","A",0
963,1,199,0,1.006358," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{A a \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{B a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{B a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{B a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{B a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{B a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{B a \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right) \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*x*sin(c + d*x)**2/2 + A*a*x*cos(c + d*x)**2/2 + A*a*sin(c + d*x)*cos(c + d*x)/(2*d) - A*a*cos(c + d*x)**3/(3*d) + B*a*x*sin(c + d*x)**4/8 + B*a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + B*a*x*cos(c + d*x)**4/8 + B*a*sin(c + d*x)**3*cos(c + d*x)/(8*d) - B*a*sin(c + d*x)*cos(c + d*x)**3/(8*d) - B*a*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)*cos(c)**2, True))","A",0
964,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","a \left(\int A \sec^{2}{\left(c + d x \right)}\, dx + \int A \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x)**2, x) + Integral(A*sin(c + d*x)*sec(c + d*x)**2, x) + Integral(B*sin(c + d*x)*sec(c + d*x)**2, x) + Integral(B*sin(c + d*x)**2*sec(c + d*x)**2, x))","F",0
965,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","a \left(\int A \sec^{4}{\left(c + d x \right)}\, dx + \int A \sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx + \int B \sin^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}\, dx\right)"," ",0,"a*(Integral(A*sec(c + d*x)**4, x) + Integral(A*sin(c + d*x)*sec(c + d*x)**4, x) + Integral(B*sin(c + d*x)*sec(c + d*x)**4, x) + Integral(B*sin(c + d*x)**2*sec(c + d*x)**4, x))","F",0
966,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
967,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
968,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
969,1,440,0,24.904766," ","integrate(cos(d*x+c)**7*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{16 A a^{2} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{8 A a^{2} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{16 A a^{2} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{2 A a^{2} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{8 A a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{2 A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{A a^{2} \cos^{8}{\left(c + d x \right)}}{4 d} + \frac{B a^{2} \sin^{10}{\left(c + d x \right)}}{40 d} + \frac{32 B a^{2} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{B a^{2} \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8 d} + \frac{16 B a^{2} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{B a^{2} \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{4 B a^{2} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{B a^{2} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{4 d} + \frac{2 B a^{2} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \cos^{8}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*A*a**2*sin(c + d*x)**9/(315*d) + 8*A*a**2*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 16*A*a**2*sin(c + d*x)**7/(35*d) + 2*A*a**2*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 8*A*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + A*a**2*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) + 2*A*a**2*sin(c + d*x)**3*cos(c + d*x)**4/d + A*a**2*sin(c + d*x)*cos(c + d*x)**6/d - A*a**2*cos(c + d*x)**8/(4*d) + B*a**2*sin(c + d*x)**10/(40*d) + 32*B*a**2*sin(c + d*x)**9/(315*d) + B*a**2*sin(c + d*x)**8*cos(c + d*x)**2/(8*d) + 16*B*a**2*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + B*a**2*sin(c + d*x)**6*cos(c + d*x)**4/(4*d) + 4*B*a**2*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + B*a**2*sin(c + d*x)**4*cos(c + d*x)**6/(4*d) + 2*B*a**2*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) - B*a**2*cos(c + d*x)**8/(8*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**2*cos(c)**7, True))","A",0
970,1,335,0,10.168748," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{8 A a^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 A a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{8 A a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} + \frac{4 A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{A a^{2} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{B a^{2} \sin^{8}{\left(c + d x \right)}}{24 d} + \frac{16 B a^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{B a^{2} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{6 d} + \frac{8 B a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{B a^{2} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{2 B a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a**2*sin(c + d*x)**7/(105*d) + 4*A*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + 8*A*a**2*sin(c + d*x)**5/(15*d) + A*a**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) + 4*A*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + A*a**2*sin(c + d*x)*cos(c + d*x)**4/d - A*a**2*cos(c + d*x)**6/(3*d) + B*a**2*sin(c + d*x)**8/(24*d) + 16*B*a**2*sin(c + d*x)**7/(105*d) + B*a**2*sin(c + d*x)**6*cos(c + d*x)**2/(6*d) + 8*B*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + B*a**2*sin(c + d*x)**4*cos(c + d*x)**4/(4*d) + 2*B*a**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - B*a**2*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**2*cos(c)**5, True))","A",0
971,1,228,0,3.511275," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{2 A a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{2 A a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{A a^{2} \cos^{4}{\left(c + d x \right)}}{2 d} + \frac{B a^{2} \sin^{6}{\left(c + d x \right)}}{12 d} + \frac{4 B a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{B a^{2} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{2 B a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*a**2*sin(c + d*x)**5/(15*d) + A*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + 2*A*a**2*sin(c + d*x)**3/(3*d) + A*a**2*sin(c + d*x)*cos(c + d*x)**2/d - A*a**2*cos(c + d*x)**4/(2*d) + B*a**2*sin(c + d*x)**6/(12*d) + 4*B*a**2*sin(c + d*x)**5/(15*d) + B*a**2*sin(c + d*x)**4*cos(c + d*x)**2/(4*d) + 2*B*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - B*a**2*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**2*cos(c)**3, True))","A",0
972,1,117,0,0.986731," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a^{2} \sin{\left(c + d x \right)}}{d} - \frac{A a^{2} \cos^{2}{\left(c + d x \right)}}{d} + \frac{B a^{2} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{2 B a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*sin(c + d*x)**3/(3*d) + A*a**2*sin(c + d*x)/d - A*a**2*cos(c + d*x)**2/d + B*a**2*sin(c + d*x)**4/(4*d) + 2*B*a**2*sin(c + d*x)**3/(3*d) - B*a**2*cos(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**2*cos(c), True))","A",0
973,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","a^{2} \left(\int A \sec{\left(c + d x \right)}\, dx + \int 2 A \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int A \sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 2 B \sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \sin^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sec(c + d*x), x) + Integral(2*A*sin(c + d*x)*sec(c + d*x), x) + Integral(A*sin(c + d*x)**2*sec(c + d*x), x) + Integral(B*sin(c + d*x)*sec(c + d*x), x) + Integral(2*B*sin(c + d*x)**2*sec(c + d*x), x) + Integral(B*sin(c + d*x)**3*sec(c + d*x), x))","F",0
974,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","a^{2} \left(\int A \sec^{3}{\left(c + d x \right)}\, dx + \int 2 A \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int A \sin^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int 2 B \sin^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx + \int B \sin^{3}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sec(c + d*x)**3, x) + Integral(2*A*sin(c + d*x)*sec(c + d*x)**3, x) + Integral(A*sin(c + d*x)**2*sec(c + d*x)**3, x) + Integral(B*sin(c + d*x)*sec(c + d*x)**3, x) + Integral(2*B*sin(c + d*x)**2*sec(c + d*x)**3, x) + Integral(B*sin(c + d*x)**3*sec(c + d*x)**3, x))","F",0
975,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
976,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
977,1,719,0,17.401211," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{5 A a^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{5 A a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{5 A a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{15 A a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 A a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{5 A a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{15 A a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{5 A a^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 A a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 A a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 A a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{5 A a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{73 A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} + \frac{5 A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{5 A a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{11 A a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 A a^{2} \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{5 B a^{2} x \sin^{8}{\left(c + d x \right)}}{64} + \frac{5 B a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 B a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{5 B a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 B a^{2} x \cos^{8}{\left(c + d x \right)}}{64} + \frac{5 B a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} + \frac{55 B a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{192 d} + \frac{73 B a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{192 d} - \frac{B a^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{5 B a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{2 B a^{2} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{B a^{2} \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*A*a**2*x*sin(c + d*x)**8/128 + 5*A*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 5*A*a**2*x*sin(c + d*x)**6/16 + 15*A*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*A*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 5*A*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 15*A*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 5*A*a**2*x*cos(c + d*x)**8/128 + 5*A*a**2*x*cos(c + d*x)**6/16 + 5*A*a**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*A*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 5*A*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 73*A*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) + 5*A*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - 5*A*a**2*sin(c + d*x)*cos(c + d*x)**7/(128*d) + 11*A*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*A*a**2*cos(c + d*x)**7/(7*d) + 5*B*a**2*x*sin(c + d*x)**8/64 + 5*B*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + 15*B*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 5*B*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 5*B*a**2*x*cos(c + d*x)**8/64 + 5*B*a**2*sin(c + d*x)**7*cos(c + d*x)/(64*d) + 55*B*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(192*d) + 73*B*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(192*d) - B*a**2*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 5*B*a**2*sin(c + d*x)*cos(c + d*x)**7/(64*d) - 2*B*a**2*cos(c + d*x)**9/(63*d) - B*a**2*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**2*cos(c)**6, True))","A",0
978,1,539,0,6.699311," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 A a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 A a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 A a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{A a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 A a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{A a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{3 A a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{5 A a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 A a^{2} \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{B a^{2} x \sin^{6}{\left(c + d x \right)}}{8} + \frac{3 B a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 B a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{B a^{2} x \cos^{6}{\left(c + d x \right)}}{8} + \frac{B a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{B a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{B a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{2 B a^{2} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{B a^{2} \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x*sin(c + d*x)**6/16 + 3*A*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*A*a**2*x*sin(c + d*x)**4/8 + 3*A*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*A*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + A*a**2*x*cos(c + d*x)**6/16 + 3*A*a**2*x*cos(c + d*x)**4/8 + A*a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + A*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 3*A*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - A*a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 5*A*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*A*a**2*cos(c + d*x)**5/(5*d) + B*a**2*x*sin(c + d*x)**6/8 + 3*B*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 3*B*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + B*a**2*x*cos(c + d*x)**6/8 + B*a**2*sin(c + d*x)**5*cos(c + d*x)/(8*d) + B*a**2*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - B*a**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - B*a**2*sin(c + d*x)*cos(c + d*x)**5/(8*d) - 2*B*a**2*cos(c + d*x)**7/(35*d) - B*a**2*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**2*cos(c)**4, True))","A",0
979,1,371,0,2.425931," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{A a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{A a^{2} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{A a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{A a^{2} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{A a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{2 A a^{2} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{B a^{2} x \sin^{4}{\left(c + d x \right)}}{4} + \frac{B a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{B a^{2} x \cos^{4}{\left(c + d x \right)}}{4} + \frac{B a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{B a^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} - \frac{2 B a^{2} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{B a^{2} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{2} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*x*sin(c + d*x)**4/8 + A*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + A*a**2*x*sin(c + d*x)**2/2 + A*a**2*x*cos(c + d*x)**4/8 + A*a**2*x*cos(c + d*x)**2/2 + A*a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - A*a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) + A*a**2*sin(c + d*x)*cos(c + d*x)/(2*d) - 2*A*a**2*cos(c + d*x)**3/(3*d) + B*a**2*x*sin(c + d*x)**4/4 + B*a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + B*a**2*x*cos(c + d*x)**4/4 + B*a**2*sin(c + d*x)**3*cos(c + d*x)/(4*d) - B*a**2*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - B*a**2*sin(c + d*x)*cos(c + d*x)**3/(4*d) - 2*B*a**2*cos(c + d*x)**5/(15*d) - B*a**2*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**2*cos(c)**2, True))","A",0
980,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","a^{2} \left(\int A \sec^{2}{\left(c + d x \right)}\, dx + \int 2 A \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int A \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 2 B \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**2*(Integral(A*sec(c + d*x)**2, x) + Integral(2*A*sin(c + d*x)*sec(c + d*x)**2, x) + Integral(A*sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(B*sin(c + d*x)*sec(c + d*x)**2, x) + Integral(2*B*sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(B*sin(c + d*x)**3*sec(c + d*x)**2, x))","F",0
981,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
982,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
983,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
984,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
985,-1,0,0,0.000000," ","integrate(sec(d*x+c)**12*(a+a*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
986,1,636,0,38.222896," ","integrate(cos(d*x+c)**7*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a^{3} \sin^{10}{\left(c + d x \right)}}{40 d} + \frac{16 A a^{3} \sin^{9}{\left(c + d x \right)}}{105 d} + \frac{A a^{3} \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8 d} + \frac{24 A a^{3} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{16 A a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{A a^{3} \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{6 A a^{3} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{8 A a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{A a^{3} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{4 d} + \frac{A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} + \frac{2 A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{3 A a^{3} \cos^{8}{\left(c + d x \right)}}{8 d} + \frac{16 B a^{3} \sin^{11}{\left(c + d x \right)}}{1155 d} + \frac{3 B a^{3} \sin^{10}{\left(c + d x \right)}}{40 d} + \frac{8 B a^{3} \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{105 d} + \frac{16 B a^{3} \sin^{9}{\left(c + d x \right)}}{105 d} + \frac{3 B a^{3} \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8 d} + \frac{6 B a^{3} \sin^{7}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{35 d} + \frac{24 B a^{3} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{3 B a^{3} \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{B a^{3} \sin^{5}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{5 d} + \frac{6 B a^{3} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{3 B a^{3} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{4 d} + \frac{B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{B a^{3} \cos^{8}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*sin(c + d*x)**10/(40*d) + 16*A*a**3*sin(c + d*x)**9/(105*d) + A*a**3*sin(c + d*x)**8*cos(c + d*x)**2/(8*d) + 24*A*a**3*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 16*A*a**3*sin(c + d*x)**7/(35*d) + A*a**3*sin(c + d*x)**6*cos(c + d*x)**4/(4*d) + 6*A*a**3*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 8*A*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + A*a**3*sin(c + d*x)**4*cos(c + d*x)**6/(4*d) + A*a**3*sin(c + d*x)**3*cos(c + d*x)**6/d + 2*A*a**3*sin(c + d*x)**3*cos(c + d*x)**4/d + A*a**3*sin(c + d*x)*cos(c + d*x)**6/d - 3*A*a**3*cos(c + d*x)**8/(8*d) + 16*B*a**3*sin(c + d*x)**11/(1155*d) + 3*B*a**3*sin(c + d*x)**10/(40*d) + 8*B*a**3*sin(c + d*x)**9*cos(c + d*x)**2/(105*d) + 16*B*a**3*sin(c + d*x)**9/(105*d) + 3*B*a**3*sin(c + d*x)**8*cos(c + d*x)**2/(8*d) + 6*B*a**3*sin(c + d*x)**7*cos(c + d*x)**4/(35*d) + 24*B*a**3*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 3*B*a**3*sin(c + d*x)**6*cos(c + d*x)**4/(4*d) + B*a**3*sin(c + d*x)**5*cos(c + d*x)**6/(5*d) + 6*B*a**3*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 3*B*a**3*sin(c + d*x)**4*cos(c + d*x)**6/(4*d) + B*a**3*sin(c + d*x)**3*cos(c + d*x)**6/d - B*a**3*cos(c + d*x)**8/(8*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**3*cos(c)**7, True))","A",0
987,1,471,0,16.659625," ","integrate(cos(d*x+c)**5*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a^{3} \sin^{8}{\left(c + d x \right)}}{24 d} + \frac{8 A a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{A a^{3} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{6 d} + \frac{4 A a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{8 A a^{3} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{A a^{3} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{4 A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{A a^{3} \cos^{6}{\left(c + d x \right)}}{2 d} + \frac{8 B a^{3} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{B a^{3} \sin^{8}{\left(c + d x \right)}}{8 d} + \frac{4 B a^{3} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{8 B a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{B a^{3} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{B a^{3} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{4 B a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{3 B a^{3} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{B a^{3} \cos^{6}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*sin(c + d*x)**8/(24*d) + 8*A*a**3*sin(c + d*x)**7/(35*d) + A*a**3*sin(c + d*x)**6*cos(c + d*x)**2/(6*d) + 4*A*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 8*A*a**3*sin(c + d*x)**5/(15*d) + A*a**3*sin(c + d*x)**4*cos(c + d*x)**4/(4*d) + A*a**3*sin(c + d*x)**3*cos(c + d*x)**4/d + 4*A*a**3*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + A*a**3*sin(c + d*x)*cos(c + d*x)**4/d - A*a**3*cos(c + d*x)**6/(2*d) + 8*B*a**3*sin(c + d*x)**9/(315*d) + B*a**3*sin(c + d*x)**8/(8*d) + 4*B*a**3*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 8*B*a**3*sin(c + d*x)**7/(35*d) + B*a**3*sin(c + d*x)**6*cos(c + d*x)**2/(2*d) + B*a**3*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 4*B*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 3*B*a**3*sin(c + d*x)**4*cos(c + d*x)**4/(4*d) + B*a**3*sin(c + d*x)**3*cos(c + d*x)**4/d - B*a**3*cos(c + d*x)**6/(6*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**3*cos(c)**5, True))","A",0
988,1,313,0,6.340543," ","integrate(cos(d*x+c)**3*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a^{3} \sin^{6}{\left(c + d x \right)}}{12 d} + \frac{2 A a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{A a^{3} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} + \frac{2 A a^{3} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{3 A a^{3} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{2 B a^{3} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{B a^{3} \sin^{6}{\left(c + d x \right)}}{4 d} + \frac{B a^{3} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 B a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{3 B a^{3} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} + \frac{B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{B a^{3} \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*sin(c + d*x)**6/(12*d) + 2*A*a**3*sin(c + d*x)**5/(5*d) + A*a**3*sin(c + d*x)**4*cos(c + d*x)**2/(4*d) + A*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d + 2*A*a**3*sin(c + d*x)**3/(3*d) + A*a**3*sin(c + d*x)*cos(c + d*x)**2/d - 3*A*a**3*cos(c + d*x)**4/(4*d) + 2*B*a**3*sin(c + d*x)**7/(35*d) + B*a**3*sin(c + d*x)**6/(4*d) + B*a**3*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*B*a**3*sin(c + d*x)**5/(5*d) + 3*B*a**3*sin(c + d*x)**4*cos(c + d*x)**2/(4*d) + B*a**3*sin(c + d*x)**3*cos(c + d*x)**2/d - B*a**3*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**3*cos(c)**3, True))","A",0
989,1,151,0,2.015568," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a^{3} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{A a^{3} \sin^{3}{\left(c + d x \right)}}{d} + \frac{A a^{3} \sin{\left(c + d x \right)}}{d} - \frac{3 A a^{3} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{B a^{3} \sin^{5}{\left(c + d x \right)}}{5 d} + \frac{3 B a^{3} \sin^{4}{\left(c + d x \right)}}{4 d} + \frac{B a^{3} \sin^{3}{\left(c + d x \right)}}{d} - \frac{B a^{3} \cos^{2}{\left(c + d x \right)}}{2 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{3} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**3*sin(c + d*x)**4/(4*d) + A*a**3*sin(c + d*x)**3/d + A*a**3*sin(c + d*x)/d - 3*A*a**3*cos(c + d*x)**2/(2*d) + B*a**3*sin(c + d*x)**5/(5*d) + 3*B*a**3*sin(c + d*x)**4/(4*d) + B*a**3*sin(c + d*x)**3/d - B*a**3*cos(c + d*x)**2/(2*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**3*cos(c), True))","A",0
990,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","a^{3} \left(\int A \sec{\left(c + d x \right)}\, dx + \int 3 A \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 A \sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int A \sin^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 B \sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int 3 B \sin^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx + \int B \sin^{4}{\left(c + d x \right)} \sec{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(A*sec(c + d*x), x) + Integral(3*A*sin(c + d*x)*sec(c + d*x), x) + Integral(3*A*sin(c + d*x)**2*sec(c + d*x), x) + Integral(A*sin(c + d*x)**3*sec(c + d*x), x) + Integral(B*sin(c + d*x)*sec(c + d*x), x) + Integral(3*B*sin(c + d*x)**2*sec(c + d*x), x) + Integral(3*B*sin(c + d*x)**3*sec(c + d*x), x) + Integral(B*sin(c + d*x)**4*sec(c + d*x), x))","F",0
991,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
992,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
993,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
994,-1,0,0,0.000000," ","integrate(sec(d*x+c)**9*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
995,1,1042,0,27.745885," ","integrate(cos(d*x+c)**6*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{15 A a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 A a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{5 A a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{45 A a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 A a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{15 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{15 A a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 A a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{15 A a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 A a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{5 A a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{73 A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} + \frac{5 A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{A a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{15 A a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{11 A a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 A a^{3} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{3 A a^{3} \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{3 B a^{3} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 B a^{3} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{15 B a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{15 B a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{15 B a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 B a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{45 B a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{15 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 B a^{3} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{15 B a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 B a^{3} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 B a^{3} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{15 B a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{B a^{3} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} + \frac{55 B a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{7 B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} + \frac{73 B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{3 B a^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{15 B a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{2 B a^{3} \cos^{9}{\left(c + d x \right)}}{21 d} - \frac{B a^{3} \cos^{7}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((15*A*a**3*x*sin(c + d*x)**8/128 + 15*A*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 5*A*a**3*x*sin(c + d*x)**6/16 + 45*A*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*A*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 15*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 15*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 15*A*a**3*x*cos(c + d*x)**8/128 + 5*A*a**3*x*cos(c + d*x)**6/16 + 15*A*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*A*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) + 5*A*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + 73*A*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) + 5*A*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - A*a**3*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 15*A*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) + 11*A*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*A*a**3*cos(c + d*x)**9/(63*d) - 3*A*a**3*cos(c + d*x)**7/(7*d) + 3*B*a**3*x*sin(c + d*x)**10/256 + 15*B*a**3*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 15*B*a**3*x*sin(c + d*x)**8/128 + 15*B*a**3*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 15*B*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*B*a**3*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 45*B*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 15*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 15*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*B*a**3*x*cos(c + d*x)**10/256 + 15*B*a**3*x*cos(c + d*x)**8/128 + 3*B*a**3*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*B*a**3*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + 15*B*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + B*a**3*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) + 55*B*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 7*B*a**3*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) + 73*B*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 3*B*a**3*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 3*B*a**3*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 15*B*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 2*B*a**3*cos(c + d*x)**9/(21*d) - B*a**3*cos(c + d*x)**7/(7*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**3*cos(c)**6, True))","A",0
996,1,823,0,11.667055," ","integrate(cos(d*x+c)**4*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{3 A a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 A a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 A a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{9 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 A a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 A a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{A a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} + \frac{3 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{A a^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} + \frac{5 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 A a^{3} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{3 A a^{3} \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{3 B a^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 B a^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{3 B a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 B a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{9 B a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{9 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 B a^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 B a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 B a^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 B a^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{3 B a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{11 B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} + \frac{B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} - \frac{3 B a^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{6 B a^{3} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{B a^{3} \cos^{5}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*x*sin(c + d*x)**6/16 + 9*A*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*A*a**3*x*sin(c + d*x)**4/8 + 9*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*A*a**3*x*cos(c + d*x)**6/16 + 3*A*a**3*x*cos(c + d*x)**4/8 + 3*A*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + A*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) + 3*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) - A*a**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*A*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) + 5*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*A*a**3*cos(c + d*x)**7/(35*d) - 3*A*a**3*cos(c + d*x)**5/(5*d) + 3*B*a**3*x*sin(c + d*x)**8/128 + 3*B*a**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 3*B*a**3*x*sin(c + d*x)**6/16 + 9*B*a**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 9*B*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 9*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*B*a**3*x*cos(c + d*x)**8/128 + 3*B*a**3*x*cos(c + d*x)**6/16 + 3*B*a**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*B*a**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) + 3*B*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) - 11*B*a**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) + B*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) - 3*B*a**3*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 3*B*a**3*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 3*B*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 6*B*a**3*cos(c + d*x)**7/(35*d) - B*a**3*cos(c + d*x)**5/(5*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**3*cos(c)**4, True))","A",0
997,1,588,0,4.381025," ","integrate(cos(d*x+c)**2*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{3 A a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 A a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{A a^{3} x \sin^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{A a^{3} x \cos^{2}{\left(c + d x \right)}}{2} + \frac{3 A a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{A a^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{3 A a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} + \frac{A a^{3} \sin{\left(c + d x \right)} \cos{\left(c + d x \right)}}{2 d} - \frac{2 A a^{3} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{A a^{3} \cos^{3}{\left(c + d x \right)}}{d} + \frac{B a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 B a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 B a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 B a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{B a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 B a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{B a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{B a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} + \frac{3 B a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{B a^{3} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{B a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{3 B a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 B a^{3} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{B a^{3} \cos^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a \sin{\left(c \right)} + a\right)^{3} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*A*a**3*x*sin(c + d*x)**4/8 + 3*A*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + A*a**3*x*sin(c + d*x)**2/2 + 3*A*a**3*x*cos(c + d*x)**4/8 + A*a**3*x*cos(c + d*x)**2/2 + 3*A*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) - A*a**3*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 3*A*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) + A*a**3*sin(c + d*x)*cos(c + d*x)/(2*d) - 2*A*a**3*cos(c + d*x)**5/(15*d) - A*a**3*cos(c + d*x)**3/d + B*a**3*x*sin(c + d*x)**6/16 + 3*B*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*B*a**3*x*sin(c + d*x)**4/8 + 3*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*B*a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + B*a**3*x*cos(c + d*x)**6/16 + 3*B*a**3*x*cos(c + d*x)**4/8 + B*a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) - B*a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) + 3*B*a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) - B*a**3*sin(c + d*x)**2*cos(c + d*x)**3/d - B*a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 3*B*a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*B*a**3*cos(c + d*x)**5/(5*d) - B*a**3*cos(c + d*x)**3/(3*d), Ne(d, 0)), (x*(A + B*sin(c))*(a*sin(c) + a)**3*cos(c)**2, True))","A",0
998,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","a^{3} \left(\int A \sec^{2}{\left(c + d x \right)}\, dx + \int 3 A \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 A \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int A \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 B \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int 3 B \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx + \int B \sin^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx\right)"," ",0,"a**3*(Integral(A*sec(c + d*x)**2, x) + Integral(3*A*sin(c + d*x)*sec(c + d*x)**2, x) + Integral(3*A*sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(A*sin(c + d*x)**3*sec(c + d*x)**2, x) + Integral(B*sin(c + d*x)*sec(c + d*x)**2, x) + Integral(3*B*sin(c + d*x)**2*sec(c + d*x)**2, x) + Integral(3*B*sin(c + d*x)**3*sec(c + d*x)**2, x) + Integral(B*sin(c + d*x)**4*sec(c + d*x)**2, x))","F",0
999,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1000,-1,0,0,0.000000," ","integrate(sec(d*x+c)**6*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1001,-1,0,0,0.000000," ","integrate(sec(d*x+c)**8*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1002,-1,0,0,0.000000," ","integrate(sec(d*x+c)**10*(a+a*sin(d*x+c))**3*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1003,1,3363,0,83.075934," ","integrate(cos(d*x+c)**7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{210 A \tan^{13}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{210 A \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{700 A \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{210 A \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{1582 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{700 A \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{2184 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{700 A \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{1582 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{210 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{700 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{210 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{210 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{210 B \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{280 B \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{210 B \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{224 B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{700 B \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{912 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{700 B \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{224 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{210 B \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} - \frac{280 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} + \frac{210 B \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{105 a d \tan^{14}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3675 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2205 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 735 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 105 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos^{7}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((210*A*tan(c/2 + d*x/2)**13/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 210*A*tan(c/2 + d*x/2)**12/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 700*A*tan(c/2 + d*x/2)**11/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 210*A*tan(c/2 + d*x/2)**10/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 1582*A*tan(c/2 + d*x/2)**9/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 700*A*tan(c/2 + d*x/2)**8/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 2184*A*tan(c/2 + d*x/2)**7/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 700*A*tan(c/2 + d*x/2)**6/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 1582*A*tan(c/2 + d*x/2)**5/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 210*A*tan(c/2 + d*x/2)**4/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 700*A*tan(c/2 + d*x/2)**3/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 210*A*tan(c/2 + d*x/2)**2/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 210*A*tan(c/2 + d*x/2)/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 210*B*tan(c/2 + d*x/2)**12/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 280*B*tan(c/2 + d*x/2)**11/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 210*B*tan(c/2 + d*x/2)**10/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 224*B*tan(c/2 + d*x/2)**9/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 700*B*tan(c/2 + d*x/2)**8/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 912*B*tan(c/2 + d*x/2)**7/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 700*B*tan(c/2 + d*x/2)**6/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 224*B*tan(c/2 + d*x/2)**5/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 210*B*tan(c/2 + d*x/2)**4/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) - 280*B*tan(c/2 + d*x/2)**3/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d) + 210*B*tan(c/2 + d*x/2)**2/(105*a*d*tan(c/2 + d*x/2)**14 + 735*a*d*tan(c/2 + d*x/2)**12 + 2205*a*d*tan(c/2 + d*x/2)**10 + 3675*a*d*tan(c/2 + d*x/2)**8 + 3675*a*d*tan(c/2 + d*x/2)**6 + 2205*a*d*tan(c/2 + d*x/2)**4 + 735*a*d*tan(c/2 + d*x/2)**2 + 105*a*d), Ne(d, 0)), (x*(A + B*sin(c))*cos(c)**7/(a*sin(c) + a), True))","A",0
1004,1,1703,0,30.974910," ","integrate(cos(d*x+c)**5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{30 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{30 A \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{80 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{30 A \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{100 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{30 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{80 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{30 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 B \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{40 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 B \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{16 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 B \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} - \frac{40 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} + \frac{30 B \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos^{5}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*A*tan(c/2 + d*x/2)**9/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 30*A*tan(c/2 + d*x/2)**8/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 80*A*tan(c/2 + d*x/2)**7/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 30*A*tan(c/2 + d*x/2)**6/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 100*A*tan(c/2 + d*x/2)**5/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 30*A*tan(c/2 + d*x/2)**4/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 80*A*tan(c/2 + d*x/2)**3/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 30*A*tan(c/2 + d*x/2)**2/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*A*tan(c/2 + d*x/2)/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*B*tan(c/2 + d*x/2)**8/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 40*B*tan(c/2 + d*x/2)**7/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*B*tan(c/2 + d*x/2)**6/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 16*B*tan(c/2 + d*x/2)**5/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*B*tan(c/2 + d*x/2)**4/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) - 40*B*tan(c/2 + d*x/2)**3/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d) + 30*B*tan(c/2 + d*x/2)**2/(15*a*d*tan(c/2 + d*x/2)**10 + 75*a*d*tan(c/2 + d*x/2)**8 + 150*a*d*tan(c/2 + d*x/2)**6 + 150*a*d*tan(c/2 + d*x/2)**4 + 75*a*d*tan(c/2 + d*x/2)**2 + 15*a*d), Ne(d, 0)), (x*(A + B*sin(c))*cos(c)**5/(a*sin(c) + a), True))","A",0
1005,1,588,0,9.860930," ","integrate(cos(d*x+c)**3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{6 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{6 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{12 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{6 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{6 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{6 B \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} - \frac{8 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} + \frac{6 B \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 9 a d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*A*tan(c/2 + d*x/2)**5/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 6*A*tan(c/2 + d*x/2)**4/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 12*A*tan(c/2 + d*x/2)**3/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 6*A*tan(c/2 + d*x/2)**2/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 6*A*tan(c/2 + d*x/2)/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 6*B*tan(c/2 + d*x/2)**4/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) - 8*B*tan(c/2 + d*x/2)**3/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d) + 6*B*tan(c/2 + d*x/2)**2/(3*a*d*tan(c/2 + d*x/2)**6 + 9*a*d*tan(c/2 + d*x/2)**4 + 9*a*d*tan(c/2 + d*x/2)**2 + 3*a*d), Ne(d, 0)), (x*(A + B*sin(c))*cos(c)**3/(a*sin(c) + a), True))","A",0
1006,1,60,0,0.582342," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\begin{cases} \frac{A \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} - \frac{B \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a d} + \frac{B \sin{\left(c + d x \right)}}{a d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos{\left(c \right)}}{a \sin{\left(c \right)} + a} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*log(sin(c + d*x) + 1)/(a*d) - B*log(sin(c + d*x) + 1)/(a*d) + B*sin(c + d*x)/(a*d), Ne(d, 0)), (x*(A + B*sin(c))*cos(c)/(a*sin(c) + a), True))","A",0
1007,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\frac{\int \frac{A \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{B \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)/(sin(c + d*x) + 1), x) + Integral(B*sin(c + d*x)*sec(c + d*x)/(sin(c + d*x) + 1), x))/a","F",0
1008,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\frac{\int \frac{A \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{B \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)**3/(sin(c + d*x) + 1), x) + Integral(B*sin(c + d*x)*sec(c + d*x)**3/(sin(c + d*x) + 1), x))/a","F",0
1009,0,0,0,0.000000," ","integrate(sec(d*x+c)**5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\frac{\int \frac{A \sec^{5}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx + \int \frac{B \sin{\left(c + d x \right)} \sec^{5}{\left(c + d x \right)}}{\sin{\left(c + d x \right)} + 1}\, dx}{a}"," ",0,"(Integral(A*sec(c + d*x)**5/(sin(c + d*x) + 1), x) + Integral(B*sin(c + d*x)*sec(c + d*x)**5/(sin(c + d*x) + 1), x))/a","F",0
1010,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1011,1,2705,0,132.037987," ","integrate(cos(d*x+c)**7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{30 A \tan^{11}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{60 A \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{150 A \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{120 A \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{204 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{120 A \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{204 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{120 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{150 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{60 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{30 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{30 B \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{80 B \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{120 B \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{48 B \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{20 B \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{48 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{120 B \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} - \frac{80 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} + \frac{30 B \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 a^{2} d \tan^{12}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 300 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 225 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 90 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos^{7}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((30*A*tan(c/2 + d*x/2)**11/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 60*A*tan(c/2 + d*x/2)**10/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 150*A*tan(c/2 + d*x/2)**9/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 120*A*tan(c/2 + d*x/2)**8/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 204*A*tan(c/2 + d*x/2)**7/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 120*A*tan(c/2 + d*x/2)**6/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 204*A*tan(c/2 + d*x/2)**5/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 120*A*tan(c/2 + d*x/2)**4/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 150*A*tan(c/2 + d*x/2)**3/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 60*A*tan(c/2 + d*x/2)**2/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 30*A*tan(c/2 + d*x/2)/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 30*B*tan(c/2 + d*x/2)**10/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 80*B*tan(c/2 + d*x/2)**9/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 120*B*tan(c/2 + d*x/2)**8/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 48*B*tan(c/2 + d*x/2)**7/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 20*B*tan(c/2 + d*x/2)**6/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 48*B*tan(c/2 + d*x/2)**5/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 120*B*tan(c/2 + d*x/2)**4/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) - 80*B*tan(c/2 + d*x/2)**3/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d) + 30*B*tan(c/2 + d*x/2)**2/(15*a**2*d*tan(c/2 + d*x/2)**12 + 90*a**2*d*tan(c/2 + d*x/2)**10 + 225*a**2*d*tan(c/2 + d*x/2)**8 + 300*a**2*d*tan(c/2 + d*x/2)**6 + 225*a**2*d*tan(c/2 + d*x/2)**4 + 90*a**2*d*tan(c/2 + d*x/2)**2 + 15*a**2*d), Ne(d, 0)), (x*(A + B*sin(c))*cos(c)**7/(a*sin(c) + a)**2, True))","A",0
1012,1,1182,0,53.393838," ","integrate(cos(d*x+c)**5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{6 A \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{12 A \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{26 A \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{24 A \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{26 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{12 A \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{6 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{6 B \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{16 B \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{24 B \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} - \frac{16 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} + \frac{6 B \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{3 a^{2} d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 18 a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 12 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 3 a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos^{5}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((6*A*tan(c/2 + d*x/2)**7/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 12*A*tan(c/2 + d*x/2)**6/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 26*A*tan(c/2 + d*x/2)**5/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 24*A*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 26*A*tan(c/2 + d*x/2)**3/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 12*A*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 6*A*tan(c/2 + d*x/2)/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 6*B*tan(c/2 + d*x/2)**6/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 16*B*tan(c/2 + d*x/2)**5/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 24*B*tan(c/2 + d*x/2)**4/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) - 16*B*tan(c/2 + d*x/2)**3/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d) + 6*B*tan(c/2 + d*x/2)**2/(3*a**2*d*tan(c/2 + d*x/2)**8 + 12*a**2*d*tan(c/2 + d*x/2)**6 + 18*a**2*d*tan(c/2 + d*x/2)**4 + 12*a**2*d*tan(c/2 + d*x/2)**2 + 3*a**2*d), Ne(d, 0)), (x*(A + B*sin(c))*cos(c)**5/(a*sin(c) + a)**2, True))","A",0
1013,1,1096,0,19.006835," ","integrate(cos(d*x+c)**3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))**2,x)","\begin{cases} \frac{4 A \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{8 A \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{4 A \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{2 A \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{4 A \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{2 A \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{2 A \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{2 A \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{4 B \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{8 B \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{4 B \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{2 B \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{4 B \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{2 B \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{4 B \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} - \frac{2 B \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} + \frac{4 B \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{a^{2} d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 2 a^{2} d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos^{3}{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((4*A*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**4/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) + 8*A*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**2/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) + 4*A*log(tan(c/2 + d*x/2) + 1)/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 2*A*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 4*A*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 2*A*log(tan(c/2 + d*x/2)**2 + 1)/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 2*A*tan(c/2 + d*x/2)**3/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 2*A*tan(c/2 + d*x/2)/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 4*B*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**4/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 8*B*log(tan(c/2 + d*x/2) + 1)*tan(c/2 + d*x/2)**2/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 4*B*log(tan(c/2 + d*x/2) + 1)/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) + 2*B*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) + 4*B*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) + 2*B*log(tan(c/2 + d*x/2)**2 + 1)/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) + 4*B*tan(c/2 + d*x/2)**3/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) - 2*B*tan(c/2 + d*x/2)**2/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d) + 4*B*tan(c/2 + d*x/2)/(a**2*d*tan(c/2 + d*x/2)**4 + 2*a**2*d*tan(c/2 + d*x/2)**2 + a**2*d), Ne(d, 0)), (x*(A + B*sin(c))*cos(c)**3/(a*sin(c) + a)**2, True))","A",0
1014,1,121,0,0.837474," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))**2,x)","\begin{cases} - \frac{A}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{B \log{\left(\sin{\left(c + d x \right)} + 1 \right)} \sin{\left(c + d x \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{B \log{\left(\sin{\left(c + d x \right)} + 1 \right)}}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} + \frac{B}{a^{2} d \sin{\left(c + d x \right)} + a^{2} d} & \text{for}\: d \neq 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a \sin{\left(c \right)} + a\right)^{2}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-A/(a**2*d*sin(c + d*x) + a**2*d) + B*log(sin(c + d*x) + 1)*sin(c + d*x)/(a**2*d*sin(c + d*x) + a**2*d) + B*log(sin(c + d*x) + 1)/(a**2*d*sin(c + d*x) + a**2*d) + B/(a**2*d*sin(c + d*x) + a**2*d), Ne(d, 0)), (x*(A + B*sin(c))*cos(c)/(a*sin(c) + a)**2, True))","A",0
1015,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{A \sec{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx + \int \frac{B \sin{\left(c + d x \right)} \sec{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sec(c + d*x)/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x) + Integral(B*sin(c + d*x)*sec(c + d*x)/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x))/a**2","F",0
1016,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))**2,x)","\frac{\int \frac{A \sec^{3}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx + \int \frac{B \sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{\sin^{2}{\left(c + d x \right)} + 2 \sin{\left(c + d x \right)} + 1}\, dx}{a^{2}}"," ",0,"(Integral(A*sec(c + d*x)**3/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x) + Integral(B*sin(c + d*x)*sec(c + d*x)**3/(sin(c + d*x)**2 + 2*sin(c + d*x) + 1), x))/a**2","F",0
1017,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1018,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1019,0,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(g \cos{\left(e + f x \right)}\right)^{p} \left(A + B \sin{\left(e + f x \right)}\right)\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(g*cos(e + f*x))**p*(A + B*sin(e + f*x)), x)","F",0
1020,-1,0,0,0.000000," ","integrate(cos(f*x+e)**7*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1021,-1,0,0,0.000000," ","integrate(cos(f*x+e)**5*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1022,1,5243,0,54.477592," ","integrate(cos(f*x+e)**3*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\begin{cases} x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{m} \cos^{3}{\left(e \right)} & \text{for}\: f = 0 \\\frac{4 A \sin^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{6 A \sin{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{2 A \cos^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} + \frac{2 A}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{6 B \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{3}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{18 B \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{18 B \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{6 B \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{10 B \sin^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{3 B \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{18 B \sin{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{B \cos^{2}{\left(e + f x \right)}}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} - \frac{8 B}{6 a^{4} f \sin^{3}{\left(e + f x \right)} + 18 a^{4} f \sin^{2}{\left(e + f x \right)} + 18 a^{4} f \sin{\left(e + f x \right)} + 6 a^{4} f} & \text{for}\: m = -4 \\- \frac{2 A \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{4 A \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{2 A \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{2 A \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{A \cos^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{2 A}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{6 B \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{12 B \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{6 B \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{4 B \sin^{3}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{2 B \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{14 B \sin{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} - \frac{B \cos^{2}{\left(e + f x \right)}}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} + \frac{10 B}{2 a^{3} f \sin^{2}{\left(e + f x \right)} + 4 a^{3} f \sin{\left(e + f x \right)} + 2 a^{3} f} & \text{for}\: m = -3 \\\frac{4 A \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} + \frac{8 A \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} + \frac{4 A \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{2 A \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{4 A \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{2 A \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{2 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{2 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{4 B \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{8 B \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{4 B \log{\left(\tan{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} + \frac{2 B \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} + \frac{4 B \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} + \frac{2 B \log{\left(\tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 1 \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} + \frac{4 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} - \frac{2 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} + \frac{4 B \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{a^{2} f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 2 a^{2} f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + a^{2} f} & \text{for}\: m = -2 \\\frac{6 A \tan^{5}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a f} - \frac{6 A \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a f} + \frac{12 A \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a f} - \frac{6 A \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a f} + \frac{6 A \tan{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a f} + \frac{6 B \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a f} - \frac{8 B \tan^{3}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a f} + \frac{6 B \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)}}{3 a f \tan^{6}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{4}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 9 a f \tan^{2}{\left(\frac{e}{2} + \frac{f x}{2} \right)} + 3 a f} & \text{for}\: m = -1 \\\frac{A m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{A m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{2 A m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{4 A m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{9 A m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{2 A m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{9 A m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{12 A m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{22 A m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{26 A m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{8 A m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{26 A m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{2 A m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{16 A \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{24 A \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{24 A \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{24 A \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{8 A \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{B m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{B m^{3} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{2 B m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{4 B m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{8 B m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{2 B m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{7 B m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{B m^{2} \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{8 B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{10 B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{3}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{19 B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{4 B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{12 B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{6 B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{7 B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{6 B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{4}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{12 B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{12 B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} - \frac{12 B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \cos^{2}{\left(e + f x \right)}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} + \frac{6 B \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{4} + 10 f m^{3} + 35 f m^{2} + 50 f m + 24 f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(A + B*sin(e))*(a*sin(e) + a)**m*cos(e)**3, Eq(f, 0)), (4*A*sin(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 6*A*sin(e + f*x)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 2*A*cos(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) + 2*A/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 6*B*log(sin(e + f*x) + 1)*sin(e + f*x)**3/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 18*B*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 18*B*log(sin(e + f*x) + 1)*sin(e + f*x)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 6*B*log(sin(e + f*x) + 1)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 10*B*sin(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 3*B*sin(e + f*x)*cos(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 18*B*sin(e + f*x)/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - B*cos(e + f*x)**2/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f) - 8*B/(6*a**4*f*sin(e + f*x)**3 + 18*a**4*f*sin(e + f*x)**2 + 18*a**4*f*sin(e + f*x) + 6*a**4*f), Eq(m, -4)), (-2*A*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 4*A*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 2*A*log(sin(e + f*x) + 1)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 2*A*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - A*cos(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 2*A/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 6*B*log(sin(e + f*x) + 1)*sin(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 12*B*log(sin(e + f*x) + 1)*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 6*B*log(sin(e + f*x) + 1)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 4*B*sin(e + f*x)**3/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - 2*B*sin(e + f*x)*cos(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 14*B*sin(e + f*x)/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) - B*cos(e + f*x)**2/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f) + 10*B/(2*a**3*f*sin(e + f*x)**2 + 4*a**3*f*sin(e + f*x) + 2*a**3*f), Eq(m, -3)), (4*A*log(tan(e/2 + f*x/2) + 1)*tan(e/2 + f*x/2)**4/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) + 8*A*log(tan(e/2 + f*x/2) + 1)*tan(e/2 + f*x/2)**2/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) + 4*A*log(tan(e/2 + f*x/2) + 1)/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 2*A*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)**4/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 4*A*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)**2/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 2*A*log(tan(e/2 + f*x/2)**2 + 1)/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 2*A*tan(e/2 + f*x/2)**3/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 2*A*tan(e/2 + f*x/2)/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 4*B*log(tan(e/2 + f*x/2) + 1)*tan(e/2 + f*x/2)**4/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 8*B*log(tan(e/2 + f*x/2) + 1)*tan(e/2 + f*x/2)**2/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 4*B*log(tan(e/2 + f*x/2) + 1)/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) + 2*B*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)**4/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) + 4*B*log(tan(e/2 + f*x/2)**2 + 1)*tan(e/2 + f*x/2)**2/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) + 2*B*log(tan(e/2 + f*x/2)**2 + 1)/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) + 4*B*tan(e/2 + f*x/2)**3/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) - 2*B*tan(e/2 + f*x/2)**2/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f) + 4*B*tan(e/2 + f*x/2)/(a**2*f*tan(e/2 + f*x/2)**4 + 2*a**2*f*tan(e/2 + f*x/2)**2 + a**2*f), Eq(m, -2)), (6*A*tan(e/2 + f*x/2)**5/(3*a*f*tan(e/2 + f*x/2)**6 + 9*a*f*tan(e/2 + f*x/2)**4 + 9*a*f*tan(e/2 + f*x/2)**2 + 3*a*f) - 6*A*tan(e/2 + f*x/2)**4/(3*a*f*tan(e/2 + f*x/2)**6 + 9*a*f*tan(e/2 + f*x/2)**4 + 9*a*f*tan(e/2 + f*x/2)**2 + 3*a*f) + 12*A*tan(e/2 + f*x/2)**3/(3*a*f*tan(e/2 + f*x/2)**6 + 9*a*f*tan(e/2 + f*x/2)**4 + 9*a*f*tan(e/2 + f*x/2)**2 + 3*a*f) - 6*A*tan(e/2 + f*x/2)**2/(3*a*f*tan(e/2 + f*x/2)**6 + 9*a*f*tan(e/2 + f*x/2)**4 + 9*a*f*tan(e/2 + f*x/2)**2 + 3*a*f) + 6*A*tan(e/2 + f*x/2)/(3*a*f*tan(e/2 + f*x/2)**6 + 9*a*f*tan(e/2 + f*x/2)**4 + 9*a*f*tan(e/2 + f*x/2)**2 + 3*a*f) + 6*B*tan(e/2 + f*x/2)**4/(3*a*f*tan(e/2 + f*x/2)**6 + 9*a*f*tan(e/2 + f*x/2)**4 + 9*a*f*tan(e/2 + f*x/2)**2 + 3*a*f) - 8*B*tan(e/2 + f*x/2)**3/(3*a*f*tan(e/2 + f*x/2)**6 + 9*a*f*tan(e/2 + f*x/2)**4 + 9*a*f*tan(e/2 + f*x/2)**2 + 3*a*f) + 6*B*tan(e/2 + f*x/2)**2/(3*a*f*tan(e/2 + f*x/2)**6 + 9*a*f*tan(e/2 + f*x/2)**4 + 9*a*f*tan(e/2 + f*x/2)**2 + 3*a*f), Eq(m, -1)), (A*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + A*m**3*(a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 2*A*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 4*A*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 9*A*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 2*A*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 9*A*m**2*(a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 12*A*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 22*A*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 26*A*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 8*A*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 26*A*m*(a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 2*A*m*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 16*A*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 24*A*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 24*A*(a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 24*A*(a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 8*A*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + B*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + B*m**3*(a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 2*B*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 4*B*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 8*B*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 2*B*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 7*B*m**2*(a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - B*m**2*(a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 8*B*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 10*B*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**3/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 19*B*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 4*B*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 12*B*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 6*B*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 7*B*m*(a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 6*B*(a*sin(e + f*x) + a)**m*sin(e + f*x)**4/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 12*B*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 12*B*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) - 12*B*(a*sin(e + f*x) + a)**m*cos(e + f*x)**2/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f) + 6*B*(a*sin(e + f*x) + a)**m/(f*m**4 + 10*f*m**3 + 35*f*m**2 + 50*f*m + 24*f), True))","A",0
1023,1,428,0,5.819367," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\begin{cases} x \left(A + B \sin{\left(e \right)}\right) \left(a \sin{\left(e \right)} + a\right)^{m} \cos{\left(e \right)} & \text{for}\: f = 0 \\- \frac{A}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{B \log{\left(\sin{\left(e + f x \right)} + 1 \right)} \sin{\left(e + f x \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{B \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} + \frac{B}{a^{2} f \sin{\left(e + f x \right)} + a^{2} f} & \text{for}\: m = -2 \\\frac{A \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} - \frac{B \log{\left(\sin{\left(e + f x \right)} + 1 \right)}}{a f} + \frac{B \sin{\left(e + f x \right)}}{a f} & \text{for}\: m = -1 \\\frac{A m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} + \frac{A m \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{2} + 3 f m + 2 f} + \frac{2 A \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} + \frac{2 A \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{2} + 3 f m + 2 f} + \frac{B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} + \frac{B m \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} + \frac{B \left(a \sin{\left(e + f x \right)} + a\right)^{m} \sin^{2}{\left(e + f x \right)}}{f m^{2} + 3 f m + 2 f} - \frac{B \left(a \sin{\left(e + f x \right)} + a\right)^{m}}{f m^{2} + 3 f m + 2 f} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(A + B*sin(e))*(a*sin(e) + a)**m*cos(e), Eq(f, 0)), (-A/(a**2*f*sin(e + f*x) + a**2*f) + B*log(sin(e + f*x) + 1)*sin(e + f*x)/(a**2*f*sin(e + f*x) + a**2*f) + B*log(sin(e + f*x) + 1)/(a**2*f*sin(e + f*x) + a**2*f) + B/(a**2*f*sin(e + f*x) + a**2*f), Eq(m, -2)), (A*log(sin(e + f*x) + 1)/(a*f) - B*log(sin(e + f*x) + 1)/(a*f) + B*sin(e + f*x)/(a*f), Eq(m, -1)), (A*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**2 + 3*f*m + 2*f) + A*m*(a*sin(e + f*x) + a)**m/(f*m**2 + 3*f*m + 2*f) + 2*A*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**2 + 3*f*m + 2*f) + 2*A*(a*sin(e + f*x) + a)**m/(f*m**2 + 3*f*m + 2*f) + B*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**2 + 3*f*m + 2*f) + B*m*(a*sin(e + f*x) + a)**m*sin(e + f*x)/(f*m**2 + 3*f*m + 2*f) + B*(a*sin(e + f*x) + a)**m*sin(e + f*x)**2/(f*m**2 + 3*f*m + 2*f) - B*(a*sin(e + f*x) + a)**m/(f*m**2 + 3*f*m + 2*f), True))","A",0
1024,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right) \sec{\left(e + f x \right)}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))*sec(e + f*x), x)","F",0
1025,-1,0,0,0.000000," ","integrate(sec(f*x+e)**3*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1026,-1,0,0,0.000000," ","integrate(sec(f*x+e)**5*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1027,-1,0,0,0.000000," ","integrate(cos(f*x+e)**6*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1028,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1029,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\int \left(a \left(\sin{\left(e + f x \right)} + 1\right)\right)^{m} \left(A + B \sin{\left(e + f x \right)}\right) \cos^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((a*(sin(e + f*x) + 1))**m*(A + B*sin(e + f*x))*cos(e + f*x)**2, x)","F",0
1030,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1031,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1032,-1,0,0,0.000000," ","integrate(sec(f*x+e)**6*(a+a*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1033,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(-4-p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1034,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(-3-p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1035,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(-2-p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1036,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(-1-p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1037,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))**p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1038,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(1-p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1039,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))**(2-p),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1040,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(a+a*sin(f*x+e))**m*(A*m-A*(1+m+p)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1041,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(a-a*sin(f*x+e))**m*(A*m+A*(1+m+p)*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1042,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1043,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(a+a*sin(f*x+e))**2*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1044,0,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","a \left(\int \left(g \cos{\left(e + f x \right)}\right)^{p} \left(c + d \sin{\left(e + f x \right)}\right)^{n}\, dx + \int \left(g \cos{\left(e + f x \right)}\right)^{p} \left(c + d \sin{\left(e + f x \right)}\right)^{n} \sin{\left(e + f x \right)}\, dx\right)"," ",0,"a*(Integral((g*cos(e + f*x))**p*(c + d*sin(e + f*x))**n, x) + Integral((g*cos(e + f*x))**p*(c + d*sin(e + f*x))**n*sin(e + f*x), x))","F",0
1045,0,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e)),x)","\frac{\int \frac{\left(g \cos{\left(e + f x \right)}\right)^{p} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{\sin{\left(e + f x \right)} + 1}\, dx}{a}"," ",0,"Integral((g*cos(e + f*x))**p*(c + d*sin(e + f*x))**n/(sin(e + f*x) + 1), x)/a","F",0
1046,0,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**2,x)","\frac{\int \frac{\left(g \cos{\left(e + f x \right)}\right)^{p} \left(c + d \sin{\left(e + f x \right)}\right)^{n}}{\sin^{2}{\left(e + f x \right)} + 2 \sin{\left(e + f x \right)} + 1}\, dx}{a^{2}}"," ",0,"Integral((g*cos(e + f*x))**p*(c + d*sin(e + f*x))**n/(sin(e + f*x)**2 + 2*sin(e + f*x) + 1), x)/a**2","F",0
1047,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1048,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p*(c+d*sin(f*x+e))**n/(a+a*sin(f*x+e))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1049,-1,0,0,0.000000," ","integrate((g*sec(f*x+e))**p*(a+a*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1050,1,192,0,3.567517," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3*(a+b*sin(d*x+c)),x)","\begin{cases} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{2 a \cos^{5}{\left(c + d x \right)}}{15 d} + \frac{b x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 b x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 b x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{b x \cos^{6}{\left(c + d x \right)}}{16} + \frac{b \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{b \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{b \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{3}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 2*a*cos(c + d*x)**5/(15*d) + b*x*sin(c + d*x)**6/16 + 3*b*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*b*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + b*x*cos(c + d*x)**6/16 + b*sin(c + d*x)**5*cos(c + d*x)/(16*d) - b*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - b*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**3*cos(c)**2, True))","A",0
1051,1,144,0,1.808317," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{a x \sin^{4}{\left(c + d x \right)}}{8} + \frac{a x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{b \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{2 b \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**4/8 + a*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a*x*cos(c + d*x)**4/8 + a*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a*sin(c + d*x)*cos(c + d*x)**3/(8*d) - b*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 2*b*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**2*cos(c)**2, True))","A",0
1052,1,119,0,0.903347," ","integrate(cos(d*x+c)**2*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\begin{cases} - \frac{a \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*cos(c + d*x)**3/(3*d) + b*x*sin(c + d*x)**4/8 + b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + b*x*cos(c + d*x)**4/8 + b*sin(c + d*x)**3*cos(c + d*x)/(8*d) - b*sin(c + d*x)*cos(c + d*x)**3/(8*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)*cos(c)**2, True))","A",0
1053,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*cos(c + d*x)**2*csc(c + d*x), x)","F",0
1054,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*cos(c + d*x)**2*csc(c + d*x)**2, x)","F",0
1055,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*cos(c + d*x)**2*csc(c + d*x)**3, x)","F",0
1056,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \cos^{2}{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*cos(c + d*x)**2*csc(c + d*x)**4, x)","F",0
1057,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**5*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1058,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**6*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1059,1,275,0,5.910844," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{2 a^{2} \cos^{5}{\left(c + d x \right)}}{15 d} + \frac{a b x \sin^{6}{\left(c + d x \right)}}{8} + \frac{3 a b x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 a b x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{a b x \cos^{6}{\left(c + d x \right)}}{8} + \frac{a b \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a b \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a b \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{b^{2} \sin^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{4 b^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{8 b^{2} \cos^{7}{\left(c + d x \right)}}{105 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin^{3}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 2*a**2*cos(c + d*x)**5/(15*d) + a*b*x*sin(c + d*x)**6/8 + 3*a*b*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 3*a*b*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + a*b*x*cos(c + d*x)**6/8 + a*b*sin(c + d*x)**5*cos(c + d*x)/(8*d) - a*b*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - a*b*sin(c + d*x)*cos(c + d*x)**5/(8*d) - b**2*sin(c + d*x)**4*cos(c + d*x)**3/(3*d) - 4*b**2*sin(c + d*x)**2*cos(c + d*x)**5/(15*d) - 8*b**2*cos(c + d*x)**7/(105*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)**3*cos(c)**2, True))","A",0
1060,1,309,0,3.568981," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a^{2} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{2 a b \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{4 a b \cos^{5}{\left(c + d x \right)}}{15 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 + b \sin{\left(c \right)}\right)^{2} \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**4/8 + a**2*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a**2*x*cos(c + d*x)**4/8 + a**2*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a**2*sin(c + d*x)*cos(c + d*x)**3/(8*d) - 2*a*b*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 4*a*b*cos(c + d*x)**5/(15*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 + b*sin(c))**2*sin(c)**2*cos(c)**2, True))","A",0
1061,1,172,0,1.961698," ","integrate(cos(d*x+c)**2*sin(d*x+c)*(a+b*sin(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{a b x \sin^{4}{\left(c + d x \right)}}{4} + \frac{a b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{2} + \frac{a b x \cos^{4}{\left(c + d x \right)}}{4} + \frac{a b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{4 d} - \frac{a b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{4 d} - \frac{b^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{2 b^{2} \cos^{5}{\left(c + d x \right)}}{15 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*cos(c + d*x)**3/(3*d) + a*b*x*sin(c + d*x)**4/4 + a*b*x*sin(c + d*x)**2*cos(c + d*x)**2/2 + a*b*x*cos(c + d*x)**4/4 + a*b*sin(c + d*x)**3*cos(c + d*x)/(4*d) - a*b*sin(c + d*x)*cos(c + d*x)**3/(4*d) - b**2*sin(c + d*x)**2*cos(c + d*x)**3/(3*d) - 2*b**2*cos(c + d*x)**5/(15*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)*cos(c)**2, True))","A",0
1062,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*cos(c + d*x)**2*csc(c + d*x), x)","F",0
1063,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*cos(c + d*x)**2*csc(c + d*x)**2, x)","F",0
1064,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1065,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1066,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1067,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**6*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1068,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**7*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1069,1,394,0,6.285127," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} x \sin^{4}{\left(c + d x \right)}}{8} + \frac{a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{a^{3} x \cos^{4}{\left(c + d x \right)}}{8} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{a^{3} \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{a^{2} b \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{2 a^{2} b \cos^{5}{\left(c + d x \right)}}{5 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^{4}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{4 b^{3} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{15 d} - \frac{8 b^{3} \cos^{7}{\left(c + d x \right)}}{105 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \sin^{2}{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x*sin(c + d*x)**4/8 + a**3*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + a**3*x*cos(c + d*x)**4/8 + a**3*sin(c + d*x)**3*cos(c + d*x)/(8*d) - a**3*sin(c + d*x)*cos(c + d*x)**3/(8*d) - a**2*b*sin(c + d*x)**2*cos(c + d*x)**3/d - 2*a**2*b*cos(c + d*x)**5/(5*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)**4*cos(c + d*x)**3/(3*d) - 4*b**3*sin(c + d*x)**2*cos(c + d*x)**5/(15*d) - 8*b**3*cos(c + d*x)**7/(105*d), Ne(d, 0)), (x*(a + b*sin(c))**3*sin(c)**2*cos(c)**2, True))","A",0
1070,1,340,0,3.608516," ","integrate(cos(d*x+c)**2*sin(d*x+c)*(a+b*sin(d*x+c))**3,x)","\begin{cases} - \frac{a^{3} \cos^{3}{\left(c + d x \right)}}{3 d} + \frac{3 a^{2} b x \sin^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} b x \sin^{2}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4} + \frac{3 a^{2} b x \cos^{4}{\left(c + d x \right)}}{8} + \frac{3 a^{2} b \sin^{3}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} - \frac{3 a^{2} b \sin{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{8 d} - \frac{a b^{2} \sin^{2}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{d} - \frac{2 a b^{2} \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{b^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{b^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{b^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} - \frac{b^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{b^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \sin{\left(c \right)} \cos^{2}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*cos(c + d*x)**3/(3*d) + 3*a**2*b*x*sin(c + d*x)**4/8 + 3*a**2*b*x*sin(c + d*x)**2*cos(c + d*x)**2/4 + 3*a**2*b*x*cos(c + d*x)**4/8 + 3*a**2*b*sin(c + d*x)**3*cos(c + d*x)/(8*d) - 3*a**2*b*sin(c + d*x)*cos(c + d*x)**3/(8*d) - a*b**2*sin(c + d*x)**2*cos(c + d*x)**3/d - 2*a*b**2*cos(c + d*x)**5/(5*d) + b**3*x*sin(c + d*x)**6/16 + 3*b**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*b**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + b**3*x*cos(c + d*x)**6/16 + b**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) - b**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - b**3*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*sin(c))**3*sin(c)*cos(c)**2, True))","A",0
1071,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)*(a+b*sin(d*x+c))**3,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{3} \cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**3*cos(c + d*x)**2*csc(c + d*x), x)","F",0
1072,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1073,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1074,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1075,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**5*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1076,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**6*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1077,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**7*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1078,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1079,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1080,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1081,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)/(a+b*sin(d*x+c))**2,x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)/(a + b*sin(c + d*x))**2, x)","F",0
1082,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**2/(a + b*sin(c + d*x))**2, x)","F",0
1083,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**3/(a + b*sin(c + d*x))**2, x)","F",0
1084,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4/(a+b*sin(d*x+c))**2,x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**4/(a + b*sin(c + d*x))**2, x)","F",0
1085,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1086,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1087,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1088,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)/(a+b*sin(d*x+c))**3,x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)/(a + b*sin(c + d*x))**3, x)","F",0
1089,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**2/(a + b*sin(c + d*x))**3, x)","F",0
1090,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**3/(a + b*sin(c + d*x))**3, x)","F",0
1091,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2/(a+b*sin(f*x+e))**(5/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1092,1,272,0,15.147127," ","integrate(cos(d*x+c)**4*sin(d*x+c)**4*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{3 a x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 a x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{9 a x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 a x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 a \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{11 a \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{3 a \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{b \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{4 b \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{8 b \cos^{9}{\left(c + d x \right)}}{315 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{4}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a*x*sin(c + d*x)**8/128 + 3*a*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 9*a*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*a*x*cos(c + d*x)**8/128 + 3*a*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*a*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 11*a*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 3*a*sin(c + d*x)*cos(c + d*x)**7/(128*d) - b*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 4*b*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 8*b*cos(c + d*x)**9/(315*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**4*cos(c)**4, True))","A",0
1093,1,248,0,9.162693," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3*(a+b*sin(d*x+c)),x)","\begin{cases} - \frac{a \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{2 a \cos^{7}{\left(c + d x \right)}}{35 d} + \frac{3 b x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 b x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{9 b x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 b x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 b x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 b \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 b \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{11 b \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{3 b \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{3}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 2*a*cos(c + d*x)**7/(35*d) + 3*b*x*sin(c + d*x)**8/128 + 3*b*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 9*b*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*b*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*b*x*cos(c + d*x)**8/128 + 3*b*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*b*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 11*b*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 3*b*sin(c + d*x)*cos(c + d*x)**7/(128*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**3*cos(c)**4, True))","A",0
1094,1,192,0,5.494145," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{a x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{a x \cos^{6}{\left(c + d x \right)}}{16} + \frac{a \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{a \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{b \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{2 b \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*x*sin(c + d*x)**6/16 + 3*a*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + a*x*cos(c + d*x)**6/16 + a*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - a*sin(c + d*x)*cos(c + d*x)**5/(16*d) - b*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 2*b*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**2*cos(c)**4, True))","A",0
1095,1,167,0,3.241004," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\begin{cases} - \frac{a \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{b x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 b x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 b x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{b x \cos^{6}{\left(c + d x \right)}}{16} + \frac{b \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{b \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{b \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*cos(c + d*x)**5/(5*d) + b*x*sin(c + d*x)**6/16 + 3*b*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*b*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + b*x*cos(c + d*x)**6/16 + b*sin(c + d*x)**5*cos(c + d*x)/(16*d) + b*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - b*sin(c + d*x)*cos(c + d*x)**5/(16*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)*cos(c)**4, True))","A",0
1096,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*cos(c + d*x)**4*csc(c + d*x), x)","F",0
1097,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \cos^{4}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*cos(c + d*x)**4*csc(c + d*x)**2, x)","F",0
1098,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1099,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1100,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1101,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1102,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1103,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**8*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1104,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**9*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1105,1,335,0,15.575409," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{2 a^{2} \cos^{7}{\left(c + d x \right)}}{35 d} + \frac{3 a b x \sin^{8}{\left(c + d x \right)}}{64} + \frac{3 a b x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 a b x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{3 a b x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a b x \cos^{8}{\left(c + d x \right)}}{64} + \frac{3 a b \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} + \frac{11 a b \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{64 d} - \frac{11 a b \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{64 d} - \frac{3 a b \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{b^{2} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{4 b^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{8 b^{2} \cos^{9}{\left(c + d x \right)}}{315 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin^{3}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 2*a**2*cos(c + d*x)**7/(35*d) + 3*a*b*x*sin(c + d*x)**8/64 + 3*a*b*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + 9*a*b*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 3*a*b*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 3*a*b*x*cos(c + d*x)**8/64 + 3*a*b*sin(c + d*x)**7*cos(c + d*x)/(64*d) + 11*a*b*sin(c + d*x)**5*cos(c + d*x)**3/(64*d) - 11*a*b*sin(c + d*x)**3*cos(c + d*x)**5/(64*d) - 3*a*b*sin(c + d*x)*cos(c + d*x)**7/(64*d) - b**2*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 4*b**2*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 8*b**2*cos(c + d*x)**9/(315*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)**3*cos(c)**4, True))","A",0
1106,1,420,0,9.874981," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{a^{2} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{a^{2} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{a^{2} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{2 a b \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{4 a b \cos^{7}{\left(c + d x \right)}}{35 d} + \frac{3 b^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{9 b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 b^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 b^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 b^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{11 b^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{3 b^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**2*x*sin(c + d*x)**6/16 + 3*a**2*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a**2*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + a**2*x*cos(c + d*x)**6/16 + a**2*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a**2*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - a**2*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 2*a*b*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 4*a*b*cos(c + d*x)**7/(35*d) + 3*b**2*x*sin(c + d*x)**8/128 + 3*b**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 9*b**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*b**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*b**2*x*cos(c + d*x)**8/128 + 3*b**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*b**2*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 11*b**2*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 3*b**2*sin(c + d*x)*cos(c + d*x)**7/(128*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)**2*cos(c)**4, True))","A",0
1107,1,223,0,5.768298," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+b*sin(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{a b x \sin^{6}{\left(c + d x \right)}}{8} + \frac{3 a b x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8} + \frac{3 a b x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{8} + \frac{a b x \cos^{6}{\left(c + d x \right)}}{8} + \frac{a b \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{8 d} + \frac{a b \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3 d} - \frac{a b \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{8 d} - \frac{b^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{2 b^{2} \cos^{7}{\left(c + d x \right)}}{35 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*cos(c + d*x)**5/(5*d) + a*b*x*sin(c + d*x)**6/8 + 3*a*b*x*sin(c + d*x)**4*cos(c + d*x)**2/8 + 3*a*b*x*sin(c + d*x)**2*cos(c + d*x)**4/8 + a*b*x*cos(c + d*x)**6/8 + a*b*sin(c + d*x)**5*cos(c + d*x)/(8*d) + a*b*sin(c + d*x)**3*cos(c + d*x)**3/(3*d) - a*b*sin(c + d*x)*cos(c + d*x)**5/(8*d) - b**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 2*b**2*cos(c + d*x)**7/(35*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)*cos(c)**4, True))","A",0
1108,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*cos(c + d*x)**4*csc(c + d*x), x)","F",0
1109,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1110,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1111,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1112,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1113,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1114,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1115,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**8*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1116,1,505,0,16.181242," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\begin{cases} \frac{a^{3} x \sin^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{3 a^{3} x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{a^{3} x \cos^{6}{\left(c + d x \right)}}{16} + \frac{a^{3} \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a^{3} \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{6 d} - \frac{a^{3} \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{3 a^{2} b \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{6 a^{2} b \cos^{7}{\left(c + d x \right)}}{35 d} + \frac{9 a b^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{9 a b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{27 a b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{9 a b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{9 a b^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{9 a b^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{33 a b^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{33 a b^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{9 a b^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{b^{3} \sin^{4}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{4 b^{3} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{35 d} - \frac{8 b^{3} \cos^{9}{\left(c + d x \right)}}{315 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \sin^{2}{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a**3*x*sin(c + d*x)**6/16 + 3*a**3*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 3*a**3*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + a**3*x*cos(c + d*x)**6/16 + a**3*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a**3*sin(c + d*x)**3*cos(c + d*x)**3/(6*d) - a**3*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 3*a**2*b*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 6*a**2*b*cos(c + d*x)**7/(35*d) + 9*a*b**2*x*sin(c + d*x)**8/128 + 9*a*b**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 27*a*b**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 9*a*b**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 9*a*b**2*x*cos(c + d*x)**8/128 + 9*a*b**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 33*a*b**2*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 33*a*b**2*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 9*a*b**2*sin(c + d*x)*cos(c + d*x)**7/(128*d) - b**3*sin(c + d*x)**4*cos(c + d*x)**5/(5*d) - 4*b**3*sin(c + d*x)**2*cos(c + d*x)**7/(35*d) - 8*b**3*cos(c + d*x)**9/(315*d), Ne(d, 0)), (x*(a + b*sin(c))**3*sin(c)**2*cos(c)**4, True))","A",0
1117,1,456,0,10.058502," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+b*sin(d*x+c))**3,x)","\begin{cases} - \frac{a^{3} \cos^{5}{\left(c + d x \right)}}{5 d} + \frac{3 a^{2} b x \sin^{6}{\left(c + d x \right)}}{16} + \frac{9 a^{2} b x \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{9 a^{2} b x \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{16} + \frac{3 a^{2} b x \cos^{6}{\left(c + d x \right)}}{16} + \frac{3 a^{2} b \sin^{5}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{16 d} + \frac{a^{2} b \sin^{3}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{2 d} - \frac{3 a^{2} b \sin{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{16 d} - \frac{3 a b^{2} \sin^{2}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{6 a b^{2} \cos^{7}{\left(c + d x \right)}}{35 d} + \frac{3 b^{3} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{3 b^{3} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{9 b^{3} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{3 b^{3} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{3 b^{3} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 b^{3} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{11 b^{3} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} - \frac{11 b^{3} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{128 d} - \frac{3 b^{3} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{3} \sin{\left(c \right)} \cos^{4}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**3*cos(c + d*x)**5/(5*d) + 3*a**2*b*x*sin(c + d*x)**6/16 + 9*a**2*b*x*sin(c + d*x)**4*cos(c + d*x)**2/16 + 9*a**2*b*x*sin(c + d*x)**2*cos(c + d*x)**4/16 + 3*a**2*b*x*cos(c + d*x)**6/16 + 3*a**2*b*sin(c + d*x)**5*cos(c + d*x)/(16*d) + a**2*b*sin(c + d*x)**3*cos(c + d*x)**3/(2*d) - 3*a**2*b*sin(c + d*x)*cos(c + d*x)**5/(16*d) - 3*a*b**2*sin(c + d*x)**2*cos(c + d*x)**5/(5*d) - 6*a*b**2*cos(c + d*x)**7/(35*d) + 3*b**3*x*sin(c + d*x)**8/128 + 3*b**3*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 9*b**3*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 3*b**3*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 3*b**3*x*cos(c + d*x)**8/128 + 3*b**3*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 11*b**3*sin(c + d*x)**5*cos(c + d*x)**3/(128*d) - 11*b**3*sin(c + d*x)**3*cos(c + d*x)**5/(128*d) - 3*b**3*sin(c + d*x)*cos(c + d*x)**7/(128*d), Ne(d, 0)), (x*(a + b*sin(c))**3*sin(c)*cos(c)**4, True))","A",0
1118,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1119,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1120,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1121,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1122,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1123,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1124,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**7*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1125,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**8*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1126,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**9*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1127,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1128,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1129,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1130,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+b*sin(d*x+c))**2,x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)/(a + b*sin(c + d*x))**2, x)","F",0
1131,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)**2/(a + b*sin(c + d*x))**2, x)","F",0
1132,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1133,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1134,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1135,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1136,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1137,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1138,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+b*sin(d*x+c))**3,x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)/(a + b*sin(c + d*x))**3, x)","F",0
1139,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)**2/(a + b*sin(c + d*x))**3, x)","F",0
1140,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1141,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1142,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1143,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*sin(c + d*x)**2*cos(c + d*x)**4, x)","F",0
1144,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1145,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*cot(d*x+c)*(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1146,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*cot(d*x+c)**2*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \cos^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*cos(c + d*x)**2*cot(c + d*x)**2, x)","F",0
1147,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)**3*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \cos{\left(c + d x \right)} \cot^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*cos(c + d*x)*cot(c + d*x)**3, x)","F",0
1148,0,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \cot^{4}{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*cot(c + d*x)**4, x)","F",0
1149,0,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)*(a+b*sin(d*x+c))**(1/2),x)","\int \sqrt{a + b \sin{\left(c + d x \right)}} \cot^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral(sqrt(a + b*sin(c + d*x))*cot(c + d*x)**4*csc(c + d*x), x)","F",0
1150,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)**2*(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1151,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1152,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1153,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*cot(d*x+c)*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1154,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*cot(d*x+c)**2*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1155,-1,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)**3*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1156,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1157,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1158,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)**2*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1159,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)**3*(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1160,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1161,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*cot(d*x+c)*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1162,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*cot(d*x+c)**2*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1163,-1,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)**3*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1164,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1165,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1166,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)**2*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1167,-1,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)**3*(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1169,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sin(c + d*x)**2*cos(c + d*x)**4/sqrt(a + b*sin(c + d*x)), x)","F",0
1170,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1171,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*cot(d*x+c)/(a+b*sin(d*x+c))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1172,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*cot(d*x+c)**2/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)**2*cot(c + d*x)**2/sqrt(a + b*sin(c + d*x)), x)","F",0
1173,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)**3/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\cos{\left(c + d x \right)} \cot^{3}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cos(c + d*x)*cot(c + d*x)**3/sqrt(a + b*sin(c + d*x)), x)","F",0
1174,0,0,0,0.000000," ","integrate(cot(d*x+c)**4/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\cot^{4}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)**4/sqrt(a + b*sin(c + d*x)), x)","F",0
1175,0,0,0,0.000000," ","integrate(cot(d*x+c)**4*csc(d*x+c)/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\cot^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(cot(c + d*x)**4*csc(c + d*x)/sqrt(a + b*sin(c + d*x)), x)","F",0
1176,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1177,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1178,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1179,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*cot(d*x+c)/(a+b*sin(d*x+c))**(3/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1180,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*cot(d*x+c)**2/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2*cot(c + d*x)**2/(a + b*sin(c + d*x))**(3/2), x)","F",0
1181,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)**3/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\cos{\left(c + d x \right)} \cot^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)*cot(c + d*x)**3/(a + b*sin(c + d*x))**(3/2), x)","F",0
1182,0,0,0,0.000000," ","integrate(cot(d*x+c)**4/(a+b*sin(d*x+c))**(3/2),x)","\int \frac{\cot^{4}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(cot(c + d*x)**4/(a + b*sin(c + d*x))**(3/2), x)","F",0
1183,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1184,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1185,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1186,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*cot(d*x+c)/(a+b*sin(d*x+c))**(5/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1187,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*cot(d*x+c)**2/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \cot^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)**2*cot(c + d*x)**2/(a + b*sin(c + d*x))**(5/2), x)","F",0
1188,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)**3/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\cos{\left(c + d x \right)} \cot^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cos(c + d*x)*cot(c + d*x)**3/(a + b*sin(c + d*x))**(5/2), x)","F",0
1189,0,0,0,0.000000," ","integrate(cot(d*x+c)**4/(a+b*sin(d*x+c))**(5/2),x)","\int \frac{\cot^{4}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(cot(c + d*x)**4/(a + b*sin(c + d*x))**(5/2), x)","F",0
1190,-1,0,0,0.000000," ","integrate(cos(f*x+e)**4/(a+b*sin(f*x+e))**(9/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1191,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**(1/3)/(a+b*sin(d*x+c))**(1/2),x)","\int \frac{\sqrt[3]{\sin{\left(c + d x \right)}} \cos^{4}{\left(c + d x \right)}}{\sqrt{a + b \sin{\left(c + d x \right)}}}\, dx"," ",0,"Integral(sin(c + d*x)**(1/3)*cos(c + d*x)**4/sqrt(a + b*sin(c + d*x)), x)","F",0
1192,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**n*(a+b*sin(d*x+c))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1193,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**(-3-p)*(a+b*sin(d*x+c))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1194,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**(-4-p)*(a+b*sin(d*x+c))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1195,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**n*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1196,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**n*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1197,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**n*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1198,1,136,0,32.617182," ","integrate(cos(d*x+c)**5*sin(d*x+c)**5*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{a \sin^{10}{\left(c + d x \right)}}{60 d} + \frac{a \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{12 d} + \frac{a \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{6 d} + \frac{8 b \sin^{11}{\left(c + d x \right)}}{693 d} + \frac{4 b \sin^{9}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{63 d} + \frac{b \sin^{7}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{7 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{5}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sin(c + d*x)**10/(60*d) + a*sin(c + d*x)**8*cos(c + d*x)**2/(12*d) + a*sin(c + d*x)**6*cos(c + d*x)**4/(6*d) + 8*b*sin(c + d*x)**11/(693*d) + 4*b*sin(c + d*x)**9*cos(c + d*x)**2/(63*d) + b*sin(c + d*x)**7*cos(c + d*x)**4/(7*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**5*cos(c)**5, True))","A",0
1199,1,136,0,20.994775," ","integrate(cos(d*x+c)**5*sin(d*x+c)**4*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{4 a \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{a \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{b \sin^{10}{\left(c + d x \right)}}{60 d} + \frac{b \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{12 d} + \frac{b \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{6 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{4}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**9/(315*d) + 4*a*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + a*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + b*sin(c + d*x)**10/(60*d) + b*sin(c + d*x)**8*cos(c + d*x)**2/(12*d) + b*sin(c + d*x)**6*cos(c + d*x)**4/(6*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**4*cos(c)**5, True))","A",0
1200,1,136,0,13.677018," ","integrate(cos(d*x+c)**5*sin(d*x+c)**3*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{a \sin^{8}{\left(c + d x \right)}}{24 d} + \frac{a \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{6 d} + \frac{a \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{8 b \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{4 b \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{b \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{3}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((a*sin(c + d*x)**8/(24*d) + a*sin(c + d*x)**6*cos(c + d*x)**2/(6*d) + a*sin(c + d*x)**4*cos(c + d*x)**4/(4*d) + 8*b*sin(c + d*x)**9/(315*d) + 4*b*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + b*sin(c + d*x)**5*cos(c + d*x)**4/(5*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**3*cos(c)**5, True))","A",0
1201,1,136,0,8.394157," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2*(a+b*sin(d*x+c)),x)","\begin{cases} \frac{8 a \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 a \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{a \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} + \frac{b \sin^{8}{\left(c + d x \right)}}{24 d} + \frac{b \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{6 d} + \frac{b \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin^{2}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a*sin(c + d*x)**7/(105*d) + 4*a*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + a*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) + b*sin(c + d*x)**8/(24*d) + b*sin(c + d*x)**6*cos(c + d*x)**2/(6*d) + b*sin(c + d*x)**4*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)**2*cos(c)**5, True))","A",0
1202,1,90,0,5.067719," ","integrate(cos(d*x+c)**5*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\begin{cases} - \frac{a \cos^{6}{\left(c + d x \right)}}{6 d} + \frac{8 b \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 b \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{b \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right) \sin{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a*cos(c + d*x)**6/(6*d) + 8*b*sin(c + d*x)**7/(105*d) + 4*b*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + b*sin(c + d*x)**3*cos(c + d*x)**4/(3*d), Ne(d, 0)), (x*(a + b*sin(c))*sin(c)*cos(c)**5, True))","A",0
1203,0,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \cos^{5}{\left(c + d x \right)} \csc{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*cos(c + d*x)**5*csc(c + d*x), x)","F",0
1204,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1205,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1206,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1207,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1208,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1209,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**7*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1210,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**8*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1211,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**9*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1212,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**10*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1213,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**11*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1214,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**12*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1215,1,214,0,14.269780," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{8 a^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} + \frac{a b \sin^{8}{\left(c + d x \right)}}{12 d} + \frac{a b \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{a b \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{2 d} + \frac{8 b^{2} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{4 b^{2} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{b^{2} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin^{2}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*a**2*sin(c + d*x)**7/(105*d) + 4*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + a**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) + a*b*sin(c + d*x)**8/(12*d) + a*b*sin(c + d*x)**6*cos(c + d*x)**2/(3*d) + a*b*sin(c + d*x)**4*cos(c + d*x)**4/(2*d) + 8*b**2*sin(c + d*x)**9/(315*d) + 4*b**2*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + b**2*sin(c + d*x)**5*cos(c + d*x)**4/(5*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)**2*cos(c)**5, True))","A",0
1216,1,163,0,8.695669," ","integrate(cos(d*x+c)**5*sin(d*x+c)*(a+b*sin(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \cos^{6}{\left(c + d x \right)}}{6 d} + \frac{16 a b \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{8 a b \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{2 a b \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} + \frac{b^{2} \sin^{8}{\left(c + d x \right)}}{24 d} + \frac{b^{2} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{6 d} + \frac{b^{2} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin{\left(c \right)} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*cos(c + d*x)**6/(6*d) + 16*a*b*sin(c + d*x)**7/(105*d) + 8*a*b*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + 2*a*b*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) + b**2*sin(c + d*x)**8/(24*d) + b**2*sin(c + d*x)**6*cos(c + d*x)**2/(6*d) + b**2*sin(c + d*x)**4*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)*cos(c)**5, True))","A",0
1217,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1218,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1219,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1220,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1221,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1222,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1223,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**7*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1224,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**8*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1225,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**9*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1226,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1227,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1228,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1229,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1230,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1231,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1232,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1233,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1234,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1235,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1236,1,8675,0,100.867566," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n*(a+b*sin(d*x+c)),x)","\begin{cases} x \left(a + b \sin{\left(c \right)}\right) \sin^{n}{\left(c \right)} \cos^{5}{\left(c \right)} & \text{for}\: d = 0 \\- \frac{8 a}{15 d \sin{\left(c + d x \right)}} + \frac{4 a \cos^{2}{\left(c + d x \right)}}{15 d \sin^{3}{\left(c + d x \right)}} - \frac{a \cos^{4}{\left(c + d x \right)}}{5 d \sin^{5}{\left(c + d x \right)}} + \frac{b \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{b \cos^{2}{\left(c + d x \right)}}{2 d \sin^{2}{\left(c + d x \right)}} - \frac{b \cos^{4}{\left(c + d x \right)}}{4 d \sin^{4}{\left(c + d x \right)}} & \text{for}\: n = -6 \\\frac{a \log{\left(\sin{\left(c + d x \right)} \right)}}{d} + \frac{a \cos^{2}{\left(c + d x \right)}}{2 d \sin^{2}{\left(c + d x \right)}} - \frac{a \cos^{4}{\left(c + d x \right)}}{4 d \sin^{4}{\left(c + d x \right)}} + \frac{8 b \sin{\left(c + d x \right)}}{3 d} + \frac{4 b \cos^{2}{\left(c + d x \right)}}{3 d \sin{\left(c + d x \right)}} - \frac{b \cos^{4}{\left(c + d x \right)}}{3 d \sin^{3}{\left(c + d x \right)}} & \text{for}\: n = -5 \\- \frac{a \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{19 a \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{110 a \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{110 a \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{19 a \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{a}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{48 b \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{96 b \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{48 b \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{48 b \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{96 b \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{48 b \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{3 b \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{54 b \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{3 b \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 48 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} & \text{for}\: n = -4 \\\frac{48 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{144 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{144 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{48 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{48 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{144 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{144 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{48 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{3 a \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{63 a \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{63 a \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{3 a}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{12 b \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{144 b \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{200 b \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{144 b \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{12 b \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{24 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 72 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}} & \text{for}\: n = -3 \\- \frac{3 a \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{39 a \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{86 a \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{86 a \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{39 a \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{3 a}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{6 b \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{24 b \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{36 b \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{24 b \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{6 b \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{6 b \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{24 b \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{36 b \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{24 b \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} + \frac{6 b \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{24 b \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{24 b \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} - \frac{24 b \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{6 d \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 36 d \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 24 d \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 6 d \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}} & \text{for}\: n = -2 \\- \frac{15 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{75 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{150 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{150 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{75 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{15 a \log{\left(\tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 1 \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{15 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{75 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{150 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{150 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{75 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)} \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{15 a \log{\left(\tan{\left(\frac{c}{2} + \frac{d x}{2} \right)} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{60 a \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{120 a \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{120 a \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} - \frac{60 a \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{30 b \tan^{9}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{40 b \tan^{7}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{116 b \tan^{5}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{40 b \tan^{3}{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} + \frac{30 b \tan{\left(\frac{c}{2} + \frac{d x}{2} \right)}}{15 d \tan^{10}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{8}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{6}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 150 d \tan^{4}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 75 d \tan^{2}{\left(\frac{c}{2} + \frac{d x}{2} \right)} + 15 d} & \text{for}\: n = -1 \\\frac{a n^{5} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{4 a n^{4} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{20 a n^{4} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{8 a n^{3} \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{68 a n^{3} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{155 a n^{3} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{96 a n^{2} \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{416 a n^{2} \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{580 a n^{2} \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{352 a n \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{1072 a n \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{1044 a n \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{384 a \sin^{5}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{960 a \sin^{3}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{720 a \sin{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{b n^{5} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{4 b n^{4} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{19 b n^{4} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{8 b n^{3} \sin^{6}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{60 b n^{3} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{137 b n^{3} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{72 b n^{2} \sin^{6}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{308 b n^{2} \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{461 b n^{2} \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{184 b n \sin^{6}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{612 b n \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{702 b n \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{120 b \sin^{6}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{360 b \sin^{4}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} + \frac{360 b \sin^{2}{\left(c + d x \right)} \sin^{n}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d n^{6} + 21 d n^{5} + 175 d n^{4} + 735 d n^{3} + 1624 d n^{2} + 1764 d n + 720 d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(a + b*sin(c))*sin(c)**n*cos(c)**5, Eq(d, 0)), (-8*a/(15*d*sin(c + d*x)) + 4*a*cos(c + d*x)**2/(15*d*sin(c + d*x)**3) - a*cos(c + d*x)**4/(5*d*sin(c + d*x)**5) + b*log(sin(c + d*x))/d + b*cos(c + d*x)**2/(2*d*sin(c + d*x)**2) - b*cos(c + d*x)**4/(4*d*sin(c + d*x)**4), Eq(n, -6)), (a*log(sin(c + d*x))/d + a*cos(c + d*x)**2/(2*d*sin(c + d*x)**2) - a*cos(c + d*x)**4/(4*d*sin(c + d*x)**4) + 8*b*sin(c + d*x)/(3*d) + 4*b*cos(c + d*x)**2/(3*d*sin(c + d*x)) - b*cos(c + d*x)**4/(3*d*sin(c + d*x)**3), Eq(n, -5)), (-a*tan(c/2 + d*x/2)**10/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) + 19*a*tan(c/2 + d*x/2)**8/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) + 110*a*tan(c/2 + d*x/2)**6/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) + 110*a*tan(c/2 + d*x/2)**4/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) + 19*a*tan(c/2 + d*x/2)**2/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) - a/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) + 48*b*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**7/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) + 96*b*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**5/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) + 48*b*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**3/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) - 48*b*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**7/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) - 96*b*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**5/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) - 48*b*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**3/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) - 3*b*tan(c/2 + d*x/2)**9/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) + 54*b*tan(c/2 + d*x/2)**5/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3) - 3*b*tan(c/2 + d*x/2)/(24*d*tan(c/2 + d*x/2)**7 + 48*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3), Eq(n, -4)), (48*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**8/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) + 144*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**6/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) + 144*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) + 48*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 48*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**8/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 144*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**6/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 144*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**4/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 48*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 3*a*tan(c/2 + d*x/2)**10/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) + 63*a*tan(c/2 + d*x/2)**6/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) + 63*a*tan(c/2 + d*x/2)**4/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 3*a/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 12*b*tan(c/2 + d*x/2)**9/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 144*b*tan(c/2 + d*x/2)**7/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 200*b*tan(c/2 + d*x/2)**5/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 144*b*tan(c/2 + d*x/2)**3/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2) - 12*b*tan(c/2 + d*x/2)/(24*d*tan(c/2 + d*x/2)**8 + 72*d*tan(c/2 + d*x/2)**6 + 72*d*tan(c/2 + d*x/2)**4 + 24*d*tan(c/2 + d*x/2)**2), Eq(n, -3)), (-3*a*tan(c/2 + d*x/2)**10/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 39*a*tan(c/2 + d*x/2)**8/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 86*a*tan(c/2 + d*x/2)**6/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 86*a*tan(c/2 + d*x/2)**4/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 39*a*tan(c/2 + d*x/2)**2/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 3*a/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 6*b*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**9/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 24*b*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**7/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 36*b*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**5/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 24*b*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**3/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 6*b*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) + 6*b*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**9/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) + 24*b*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**7/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) + 36*b*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**5/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) + 24*b*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**3/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) + 6*b*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 24*b*tan(c/2 + d*x/2)**7/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 24*b*tan(c/2 + d*x/2)**5/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)) - 24*b*tan(c/2 + d*x/2)**3/(6*d*tan(c/2 + d*x/2)**9 + 24*d*tan(c/2 + d*x/2)**7 + 36*d*tan(c/2 + d*x/2)**5 + 24*d*tan(c/2 + d*x/2)**3 + 6*d*tan(c/2 + d*x/2)), Eq(n, -2)), (-15*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**10/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 75*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**8/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 150*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**6/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 150*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**4/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 75*a*log(tan(c/2 + d*x/2)**2 + 1)*tan(c/2 + d*x/2)**2/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 15*a*log(tan(c/2 + d*x/2)**2 + 1)/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 15*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**10/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 75*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**8/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 150*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**6/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 150*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**4/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 75*a*log(tan(c/2 + d*x/2))*tan(c/2 + d*x/2)**2/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 15*a*log(tan(c/2 + d*x/2))/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 60*a*tan(c/2 + d*x/2)**8/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 120*a*tan(c/2 + d*x/2)**6/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 120*a*tan(c/2 + d*x/2)**4/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) - 60*a*tan(c/2 + d*x/2)**2/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 30*b*tan(c/2 + d*x/2)**9/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 40*b*tan(c/2 + d*x/2)**7/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 116*b*tan(c/2 + d*x/2)**5/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 40*b*tan(c/2 + d*x/2)**3/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d) + 30*b*tan(c/2 + d*x/2)/(15*d*tan(c/2 + d*x/2)**10 + 75*d*tan(c/2 + d*x/2)**8 + 150*d*tan(c/2 + d*x/2)**6 + 150*d*tan(c/2 + d*x/2)**4 + 75*d*tan(c/2 + d*x/2)**2 + 15*d), Eq(n, -1)), (a*n**5*sin(c + d*x)*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 4*a*n**4*sin(c + d*x)**3*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 20*a*n**4*sin(c + d*x)*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 8*a*n**3*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 68*a*n**3*sin(c + d*x)**3*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 155*a*n**3*sin(c + d*x)*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 96*a*n**2*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 416*a*n**2*sin(c + d*x)**3*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 580*a*n**2*sin(c + d*x)*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 352*a*n*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 1072*a*n*sin(c + d*x)**3*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 1044*a*n*sin(c + d*x)*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 384*a*sin(c + d*x)**5*sin(c + d*x)**n/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 960*a*sin(c + d*x)**3*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 720*a*sin(c + d*x)*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + b*n**5*sin(c + d*x)**2*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 4*b*n**4*sin(c + d*x)**4*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 19*b*n**4*sin(c + d*x)**2*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 8*b*n**3*sin(c + d*x)**6*sin(c + d*x)**n/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 60*b*n**3*sin(c + d*x)**4*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 137*b*n**3*sin(c + d*x)**2*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 72*b*n**2*sin(c + d*x)**6*sin(c + d*x)**n/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 308*b*n**2*sin(c + d*x)**4*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 461*b*n**2*sin(c + d*x)**2*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 184*b*n*sin(c + d*x)**6*sin(c + d*x)**n/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 612*b*n*sin(c + d*x)**4*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 702*b*n*sin(c + d*x)**2*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 120*b*sin(c + d*x)**6*sin(c + d*x)**n/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 360*b*sin(c + d*x)**4*sin(c + d*x)**n*cos(c + d*x)**2/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d) + 360*b*sin(c + d*x)**2*sin(c + d*x)**n*cos(c + d*x)**4/(d*n**6 + 21*d*n**5 + 175*d*n**4 + 735*d*n**3 + 1624*d*n**2 + 1764*d*n + 720*d), True))","A",0
1237,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1238,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**n/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1239,1,488,0,77.817177," ","integrate(cos(d*x+c)**6*sin(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{4 a^{2} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{8 a^{2} \cos^{11}{\left(c + d x \right)}}{693 d} + \frac{5 a b x \sin^{12}{\left(c + d x \right)}}{512} + \frac{15 a b x \sin^{10}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{75 a b x \sin^{8}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{512} + \frac{25 a b x \sin^{6}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{75 a b x \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{512} + \frac{15 a b x \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{256} + \frac{5 a b x \cos^{12}{\left(c + d x \right)}}{512} + \frac{5 a b \sin^{11}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{512 d} + \frac{85 a b \sin^{9}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{1536 d} + \frac{33 a b \sin^{7}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{256 d} - \frac{33 a b \sin^{5}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{256 d} - \frac{85 a b \sin^{3}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{1536 d} - \frac{5 a b \sin{\left(c + d x \right)} \cos^{11}{\left(c + d x \right)}}{512 d} - \frac{b^{2} \sin^{6}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{2 b^{2} \sin^{4}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{21 d} - \frac{8 b^{2} \sin^{2}{\left(c + d x \right)} \cos^{11}{\left(c + d x \right)}}{231 d} - \frac{16 b^{2} \cos^{13}{\left(c + d x \right)}}{3003 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin^{5}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 4*a**2*sin(c + d*x)**2*cos(c + d*x)**9/(63*d) - 8*a**2*cos(c + d*x)**11/(693*d) + 5*a*b*x*sin(c + d*x)**12/512 + 15*a*b*x*sin(c + d*x)**10*cos(c + d*x)**2/256 + 75*a*b*x*sin(c + d*x)**8*cos(c + d*x)**4/512 + 25*a*b*x*sin(c + d*x)**6*cos(c + d*x)**6/128 + 75*a*b*x*sin(c + d*x)**4*cos(c + d*x)**8/512 + 15*a*b*x*sin(c + d*x)**2*cos(c + d*x)**10/256 + 5*a*b*x*cos(c + d*x)**12/512 + 5*a*b*sin(c + d*x)**11*cos(c + d*x)/(512*d) + 85*a*b*sin(c + d*x)**9*cos(c + d*x)**3/(1536*d) + 33*a*b*sin(c + d*x)**7*cos(c + d*x)**5/(256*d) - 33*a*b*sin(c + d*x)**5*cos(c + d*x)**7/(256*d) - 85*a*b*sin(c + d*x)**3*cos(c + d*x)**9/(1536*d) - 5*a*b*sin(c + d*x)*cos(c + d*x)**11/(512*d) - b**2*sin(c + d*x)**6*cos(c + d*x)**7/(7*d) - 2*b**2*sin(c + d*x)**4*cos(c + d*x)**9/(21*d) - 8*b**2*sin(c + d*x)**2*cos(c + d*x)**11/(231*d) - 16*b**2*cos(c + d*x)**13/(3003*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)**5*cos(c)**6, True))","A",0
1240,1,656,0,54.310364," ","integrate(cos(d*x+c)**6*sin(d*x+c)**4*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{3 a^{2} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 a^{2} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{15 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{15 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{3 a^{2} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{3 a^{2} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 a^{2} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{a^{2} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} - \frac{7 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{3 a^{2} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} - \frac{2 a b \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{8 a b \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{16 a b \cos^{11}{\left(c + d x \right)}}{693 d} + \frac{5 b^{2} x \sin^{12}{\left(c + d x \right)}}{1024} + \frac{15 b^{2} x \sin^{10}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{512} + \frac{75 b^{2} x \sin^{8}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{1024} + \frac{25 b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{256} + \frac{75 b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{1024} + \frac{15 b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{10}{\left(c + d x \right)}}{512} + \frac{5 b^{2} x \cos^{12}{\left(c + d x \right)}}{1024} + \frac{5 b^{2} \sin^{11}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{1024 d} + \frac{85 b^{2} \sin^{9}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{3072 d} + \frac{33 b^{2} \sin^{7}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{512 d} - \frac{33 b^{2} \sin^{5}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{512 d} - \frac{85 b^{2} \sin^{3}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{3072 d} - \frac{5 b^{2} \sin{\left(c + d x \right)} \cos^{11}{\left(c + d x \right)}}{1024 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin^{4}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((3*a**2*x*sin(c + d*x)**10/256 + 15*a**2*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 15*a**2*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 15*a**2*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 3*a**2*x*cos(c + d*x)**10/256 + 3*a**2*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*a**2*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + a**2*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) - 7*a**2*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 3*a**2*sin(c + d*x)*cos(c + d*x)**9/(256*d) - 2*a*b*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 8*a*b*sin(c + d*x)**2*cos(c + d*x)**9/(63*d) - 16*a*b*cos(c + d*x)**11/(693*d) + 5*b**2*x*sin(c + d*x)**12/1024 + 15*b**2*x*sin(c + d*x)**10*cos(c + d*x)**2/512 + 75*b**2*x*sin(c + d*x)**8*cos(c + d*x)**4/1024 + 25*b**2*x*sin(c + d*x)**6*cos(c + d*x)**6/256 + 75*b**2*x*sin(c + d*x)**4*cos(c + d*x)**8/1024 + 15*b**2*x*sin(c + d*x)**2*cos(c + d*x)**10/512 + 5*b**2*x*cos(c + d*x)**12/1024 + 5*b**2*sin(c + d*x)**11*cos(c + d*x)/(1024*d) + 85*b**2*sin(c + d*x)**9*cos(c + d*x)**3/(3072*d) + 33*b**2*sin(c + d*x)**7*cos(c + d*x)**5/(512*d) - 33*b**2*sin(c + d*x)**5*cos(c + d*x)**7/(512*d) - 85*b**2*sin(c + d*x)**3*cos(c + d*x)**9/(3072*d) - 5*b**2*sin(c + d*x)*cos(c + d*x)**11/(1024*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)**4*cos(c)**6, True))","A",0
1241,1,384,0,35.401198," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{2 a^{2} \cos^{9}{\left(c + d x \right)}}{63 d} + \frac{3 a b x \sin^{10}{\left(c + d x \right)}}{128} + \frac{15 a b x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{128} + \frac{15 a b x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{15 a b x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{64} + \frac{15 a b x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{128} + \frac{3 a b x \cos^{10}{\left(c + d x \right)}}{128} + \frac{3 a b \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{7 a b \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{64 d} + \frac{a b \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{5 d} - \frac{7 a b \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{3 a b \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{128 d} - \frac{b^{2} \sin^{4}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{4 b^{2} \sin^{2}{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{63 d} - \frac{8 b^{2} \cos^{11}{\left(c + d x \right)}}{693 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin^{3}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 2*a**2*cos(c + d*x)**9/(63*d) + 3*a*b*x*sin(c + d*x)**10/128 + 15*a*b*x*sin(c + d*x)**8*cos(c + d*x)**2/128 + 15*a*b*x*sin(c + d*x)**6*cos(c + d*x)**4/64 + 15*a*b*x*sin(c + d*x)**4*cos(c + d*x)**6/64 + 15*a*b*x*sin(c + d*x)**2*cos(c + d*x)**8/128 + 3*a*b*x*cos(c + d*x)**10/128 + 3*a*b*sin(c + d*x)**9*cos(c + d*x)/(128*d) + 7*a*b*sin(c + d*x)**7*cos(c + d*x)**3/(64*d) + a*b*sin(c + d*x)**5*cos(c + d*x)**5/(5*d) - 7*a*b*sin(c + d*x)**3*cos(c + d*x)**7/(64*d) - 3*a*b*sin(c + d*x)*cos(c + d*x)**9/(128*d) - b**2*sin(c + d*x)**4*cos(c + d*x)**7/(7*d) - 4*b**2*sin(c + d*x)**2*cos(c + d*x)**9/(63*d) - 8*b**2*cos(c + d*x)**11/(693*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)**3*cos(c)**6, True))","A",0
1242,1,529,0,23.774714," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{5 a^{2} x \sin^{8}{\left(c + d x \right)}}{128} + \frac{5 a^{2} x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{32} + \frac{15 a^{2} x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{64} + \frac{5 a^{2} x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{32} + \frac{5 a^{2} x \cos^{8}{\left(c + d x \right)}}{128} + \frac{5 a^{2} \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{128 d} + \frac{55 a^{2} \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{384 d} + \frac{73 a^{2} \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{384 d} - \frac{5 a^{2} \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{2 a b \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{4 a b \cos^{9}{\left(c + d x \right)}}{63 d} + \frac{3 b^{2} x \sin^{10}{\left(c + d x \right)}}{256} + \frac{15 b^{2} x \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{256} + \frac{15 b^{2} x \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{128} + \frac{15 b^{2} x \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{128} + \frac{15 b^{2} x \sin^{2}{\left(c + d x \right)} \cos^{8}{\left(c + d x \right)}}{256} + \frac{3 b^{2} x \cos^{10}{\left(c + d x \right)}}{256} + \frac{3 b^{2} \sin^{9}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{256 d} + \frac{7 b^{2} \sin^{7}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{128 d} + \frac{b^{2} \sin^{5}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{10 d} - \frac{7 b^{2} \sin^{3}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{128 d} - \frac{3 b^{2} \sin{\left(c + d x \right)} \cos^{9}{\left(c + d x \right)}}{256 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin^{2}{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((5*a**2*x*sin(c + d*x)**8/128 + 5*a**2*x*sin(c + d*x)**6*cos(c + d*x)**2/32 + 15*a**2*x*sin(c + d*x)**4*cos(c + d*x)**4/64 + 5*a**2*x*sin(c + d*x)**2*cos(c + d*x)**6/32 + 5*a**2*x*cos(c + d*x)**8/128 + 5*a**2*sin(c + d*x)**7*cos(c + d*x)/(128*d) + 55*a**2*sin(c + d*x)**5*cos(c + d*x)**3/(384*d) + 73*a**2*sin(c + d*x)**3*cos(c + d*x)**5/(384*d) - 5*a**2*sin(c + d*x)*cos(c + d*x)**7/(128*d) - 2*a*b*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 4*a*b*cos(c + d*x)**9/(63*d) + 3*b**2*x*sin(c + d*x)**10/256 + 15*b**2*x*sin(c + d*x)**8*cos(c + d*x)**2/256 + 15*b**2*x*sin(c + d*x)**6*cos(c + d*x)**4/128 + 15*b**2*x*sin(c + d*x)**4*cos(c + d*x)**6/128 + 15*b**2*x*sin(c + d*x)**2*cos(c + d*x)**8/256 + 3*b**2*x*cos(c + d*x)**10/256 + 3*b**2*sin(c + d*x)**9*cos(c + d*x)/(256*d) + 7*b**2*sin(c + d*x)**7*cos(c + d*x)**3/(128*d) + b**2*sin(c + d*x)**5*cos(c + d*x)**5/(10*d) - 7*b**2*sin(c + d*x)**3*cos(c + d*x)**7/(128*d) - 3*b**2*sin(c + d*x)*cos(c + d*x)**9/(256*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)**2*cos(c)**6, True))","A",0
1243,1,282,0,14.944491," ","integrate(cos(d*x+c)**6*sin(d*x+c)*(a+b*sin(d*x+c))**2,x)","\begin{cases} - \frac{a^{2} \cos^{7}{\left(c + d x \right)}}{7 d} + \frac{5 a b x \sin^{8}{\left(c + d x \right)}}{64} + \frac{5 a b x \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{16} + \frac{15 a b x \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{32} + \frac{5 a b x \sin^{2}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{16} + \frac{5 a b x \cos^{8}{\left(c + d x \right)}}{64} + \frac{5 a b \sin^{7}{\left(c + d x \right)} \cos{\left(c + d x \right)}}{64 d} + \frac{55 a b \sin^{5}{\left(c + d x \right)} \cos^{3}{\left(c + d x \right)}}{192 d} + \frac{73 a b \sin^{3}{\left(c + d x \right)} \cos^{5}{\left(c + d x \right)}}{192 d} - \frac{5 a b \sin{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{64 d} - \frac{b^{2} \sin^{2}{\left(c + d x \right)} \cos^{7}{\left(c + d x \right)}}{7 d} - \frac{2 b^{2} \cos^{9}{\left(c + d x \right)}}{63 d} & \text{for}\: d \neq 0 \\x \left(a + b \sin{\left(c \right)}\right)^{2} \sin{\left(c \right)} \cos^{6}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((-a**2*cos(c + d*x)**7/(7*d) + 5*a*b*x*sin(c + d*x)**8/64 + 5*a*b*x*sin(c + d*x)**6*cos(c + d*x)**2/16 + 15*a*b*x*sin(c + d*x)**4*cos(c + d*x)**4/32 + 5*a*b*x*sin(c + d*x)**2*cos(c + d*x)**6/16 + 5*a*b*x*cos(c + d*x)**8/64 + 5*a*b*sin(c + d*x)**7*cos(c + d*x)/(64*d) + 55*a*b*sin(c + d*x)**5*cos(c + d*x)**3/(192*d) + 73*a*b*sin(c + d*x)**3*cos(c + d*x)**5/(192*d) - 5*a*b*sin(c + d*x)*cos(c + d*x)**7/(64*d) - b**2*sin(c + d*x)**2*cos(c + d*x)**7/(7*d) - 2*b**2*cos(c + d*x)**9/(63*d), Ne(d, 0)), (x*(a + b*sin(c))**2*sin(c)*cos(c)**6, True))","A",0
1244,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1245,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1246,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1247,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1248,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1249,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1250,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**7*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1251,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**8*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1252,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**9*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1253,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**10*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1254,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**11*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1255,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**12*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1256,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1257,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1258,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1259,0,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)/(a+b*sin(d*x+c))**2,x)","\int \frac{\cos^{6}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(cos(c + d*x)**6*csc(c + d*x)/(a + b*sin(c + d*x))**2, x)","F",0
1260,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1261,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1262,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1263,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1264,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1265,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**7/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1266,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1267,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1268,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1269,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1270,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1271,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1272,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1273,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1274,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1275,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**8/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1276,-1,0,0,0.000000," ","integrate(cos(f*x+e)**6/(a+b*sin(f*x+e))**(13/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1277,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(g*cos(f*x+e))**(5/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1278,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))**2/(g*cos(f*x+e))**(7/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1279,1,105,0,1.714260," ","integrate(cos(d*x+c)*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\begin{cases} \frac{x \sin^{3}{\left(c \right)} \cos{\left(c \right)}}{a} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin^{4}{\left(c + d x \right)}}{4 a d} & \text{for}\: b = 0 \\\frac{x \sin^{3}{\left(c \right)} \cos{\left(c \right)}}{a + b \sin{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{a^{3} \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{b^{4} d} + \frac{a^{2} \sin{\left(c + d x \right)}}{b^{3} d} + \frac{a \cos^{2}{\left(c + d x \right)}}{2 b^{2} d} + \frac{\sin^{3}{\left(c + d x \right)}}{3 b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(c)**3*cos(c)/a, Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)**4/(4*a*d), Eq(b, 0)), (x*sin(c)**3*cos(c)/(a + b*sin(c)), Eq(d, 0)), (-a**3*log(a/b + sin(c + d*x))/(b**4*d) + a**2*sin(c + d*x)/(b**3*d) + a*cos(c + d*x)**2/(2*b**2*d) + sin(c + d*x)**3/(3*b*d), True))","A",0
1280,1,87,0,1.051375," ","integrate(cos(d*x+c)*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\begin{cases} \frac{x \sin^{2}{\left(c \right)} \cos{\left(c \right)}}{a} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\sin^{3}{\left(c + d x \right)}}{3 a d} & \text{for}\: b = 0 \\\frac{x \sin^{2}{\left(c \right)} \cos{\left(c \right)}}{a + b \sin{\left(c \right)}} & \text{for}\: d = 0 \\\frac{a^{2} \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{b^{3} d} - \frac{a \sin{\left(c + d x \right)}}{b^{2} d} - \frac{\cos^{2}{\left(c + d x \right)}}{2 b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(c)**2*cos(c)/a, Eq(b, 0) & Eq(d, 0)), (sin(c + d*x)**3/(3*a*d), Eq(b, 0)), (x*sin(c)**2*cos(c)/(a + b*sin(c)), Eq(d, 0)), (a**2*log(a/b + sin(c + d*x))/(b**3*d) - a*sin(c + d*x)/(b**2*d) - cos(c + d*x)**2/(2*b*d), True))","A",0
1281,1,66,0,0.667158," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\begin{cases} \frac{x \sin{\left(c \right)} \cos{\left(c \right)}}{a} & \text{for}\: b = 0 \wedge d = 0 \\- \frac{\cos^{2}{\left(c + d x \right)}}{2 a d} & \text{for}\: b = 0 \\\frac{x \sin{\left(c \right)} \cos{\left(c \right)}}{a + b \sin{\left(c \right)}} & \text{for}\: d = 0 \\- \frac{a \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{b^{2} d} + \frac{\sin{\left(c + d x \right)}}{b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*sin(c)*cos(c)/a, Eq(b, 0) & Eq(d, 0)), (-cos(c + d*x)**2/(2*a*d), Eq(b, 0)), (x*sin(c)*cos(c)/(a + b*sin(c)), Eq(d, 0)), (-a*log(a/b + sin(c + d*x))/(b**2*d) + sin(c + d*x)/(b*d), True))","A",0
1282,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\cos{\left(c + d x \right)} \csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1283,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\cos{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
1284,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)**3/(a+b*sin(d*x+c)),x)","\int \frac{\cos{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)*csc(c + d*x)**3/(a + b*sin(c + d*x)), x)","F",0
1285,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1286,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1287,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1288,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1289,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1290,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
1291,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**3/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**3/(a + b*sin(c + d*x)), x)","F",0
1292,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**4/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{4}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**4/(a + b*sin(c + d*x)), x)","F",0
1293,0,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**5/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{2}{\left(c + d x \right)} \csc^{5}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**2*csc(c + d*x)**5/(a + b*sin(c + d*x)), x)","F",0
1294,-1,0,0,0.000000," ","integrate(cos(d*x+c)**2*csc(d*x+c)**6/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1295,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1296,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1297,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1298,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1299,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1300,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*csc(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1301,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1302,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1303,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1304,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1305,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
1306,0,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**3/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{4}{\left(c + d x \right)} \csc^{3}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**4*csc(c + d*x)**3/(a + b*sin(c + d*x)), x)","F",0
1307,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1308,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1309,-1,0,0,0.000000," ","integrate(cos(d*x+c)**4*csc(d*x+c)**6/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1310,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1311,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1312,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1313,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1314,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1315,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1316,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1317,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1318,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**6/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1319,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*csc(d*x+c)**7/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1320,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1321,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1322,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1323,0,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\cos^{6}{\left(c + d x \right)} \csc{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(cos(c + d*x)**6*csc(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1324,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1325,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1326,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1327,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1328,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**6/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1329,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**7/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1330,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**8/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1331,-1,0,0,0.000000," ","integrate(cos(d*x+c)**6*csc(d*x+c)**9/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1332,-1,0,0,0.000000," ","integrate(sec(d*x+c)*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1333,0,0,0,0.000000," ","integrate(sec(d*x+c)*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1334,0,0,0,0.000000," ","integrate(sec(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\sin{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1335,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\csc{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1336,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\csc^{2}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**2*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1337,0,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\csc^{3}{\left(c + d x \right)} \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**3*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1338,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1339,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**4/(a+b*sin(d*x+c)),x)","\int \frac{\sin^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**4*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
1340,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1341,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
1342,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
1343,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
1344,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\csc^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)**2*sec(c + d*x)**2/(a + b*sin(c + d*x)), x)","F",0
1345,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1346,-1,0,0,0.000000," ","integrate(sec(d*x+c)**3*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1347,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**3/(a + b*sin(c + d*x)), x)","F",0
1348,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\sin{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**3/(a + b*sin(c + d*x)), x)","F",0
1349,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**3/(a+b*sin(d*x+c)),x)","\int \frac{\csc{\left(c + d x \right)} \sec^{3}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(csc(c + d*x)*sec(c + d*x)**3/(a + b*sin(c + d*x)), x)","F",0
1350,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1351,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1352,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1353,-1,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1354,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**4/(a + b*sin(c + d*x)), x)","F",0
1355,0,0,0,0.000000," ","integrate(sec(d*x+c)**4*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\sin{\left(c + d x \right)} \sec^{4}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**4/(a + b*sin(c + d*x)), x)","F",0
1356,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1357,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1358,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1359,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**8/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1360,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**7/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1361,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**6/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1362,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1363,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**4/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1364,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**3/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1365,0,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**2/(a+b*sin(d*x+c)),x)","\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{5}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**5/(a + b*sin(c + d*x)), x)","F",0
1366,0,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)/(a+b*sin(d*x+c)),x)","\int \frac{\sin{\left(c + d x \right)} \sec^{5}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**5/(a + b*sin(c + d*x)), x)","F",0
1367,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1368,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1369,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**5/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1370,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1371,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1372,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1373,-1,0,0,0.000000," ","integrate(sin(f*x+e)*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1374,0,0,0,0.000000," ","integrate(csc(f*x+e)*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{g \cos{\left(e + f x \right)}} \csc{\left(e + f x \right)}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(g*cos(e + f*x))*csc(e + f*x)/(a + b*sin(e + f*x)), x)","F",0
1375,0,0,0,0.000000," ","integrate(csc(f*x+e)**2*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{g \cos{\left(e + f x \right)}} \csc^{2}{\left(e + f x \right)}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(g*cos(e + f*x))*csc(e + f*x)**2/(a + b*sin(e + f*x)), x)","F",0
1376,0,0,0,0.000000," ","integrate(csc(f*x+e)**3*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{g \cos{\left(e + f x \right)}} \csc^{3}{\left(e + f x \right)}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(g*cos(e + f*x))*csc(e + f*x)**3/(a + b*sin(e + f*x)), x)","F",0
1377,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*sin(f*x+e)**3/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1378,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*sin(f*x+e)**2/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1379,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1380,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1381,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*csc(f*x+e)**2/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1382,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*csc(f*x+e)**3/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1383,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)*sin(f*x+e)**3/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1384,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)*sin(f*x+e)**2/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1385,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1386,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1387,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)*csc(f*x+e)**2/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1388,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)*csc(f*x+e)**3/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1389,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1390,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1391,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1392,-1,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1393,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\int \frac{\csc{\left(e + f x \right)}}{\sqrt{g \cos{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(csc(e + f*x)/(sqrt(g*cos(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1394,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\sqrt{g \cos{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(csc(e + f*x)**2/(sqrt(g*cos(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1395,0,0,0,0.000000," ","integrate(csc(f*x+e)**3/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\int \frac{\csc^{3}{\left(e + f x \right)}}{\sqrt{g \cos{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(csc(e + f*x)**3/(sqrt(g*cos(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1396,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1397,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1398,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1399,-1,0,0,0.000000," ","integrate(sin(f*x+e)/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1400,0,0,0,0.000000," ","integrate(csc(f*x+e)/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\int \frac{\csc{\left(e + f x \right)}}{\left(g \cos{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(csc(e + f*x)/((g*cos(e + f*x))**(3/2)*(a + b*sin(e + f*x))), x)","F",0
1401,0,0,0,0.000000," ","integrate(csc(f*x+e)**2/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\int \frac{\csc^{2}{\left(e + f x \right)}}{\left(g \cos{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(csc(e + f*x)**2/((g*cos(e + f*x))**(3/2)*(a + b*sin(e + f*x))), x)","F",0
1402,-1,0,0,0.000000," ","integrate(sin(f*x+e)**4/(g*cos(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1403,-1,0,0,0.000000," ","integrate(sin(f*x+e)**3/(g*cos(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1404,-1,0,0,0.000000," ","integrate(sin(f*x+e)**2/(g*cos(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1405,-1,0,0,0.000000," ","integrate(sin(f*x+e)/(g*cos(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1406,-1,0,0,0.000000," ","integrate(csc(f*x+e)/(g*cos(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1407,-1,0,0,0.000000," ","integrate(csc(f*x+e)**2/(g*cos(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1408,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**(5/2)*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1409,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**(3/2)*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1410,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**(1/2)*(g*cos(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{d \sin{\left(e + f x \right)}} \sqrt{g \cos{\left(e + f x \right)}}}{a + b \sin{\left(e + f x \right)}}\, dx"," ",0,"Integral(sqrt(d*sin(e + f*x))*sqrt(g*cos(e + f*x))/(a + b*sin(e + f*x)), x)","F",0
1411,0,0,0,0.000000," ","integrate((g*cos(f*x+e))**(1/2)/(d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{g \cos{\left(e + f x \right)}}}{\sqrt{d \sin{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(sqrt(g*cos(e + f*x))/(sqrt(d*sin(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1412,0,0,0,0.000000," ","integrate((g*cos(f*x+e))**(1/2)/(d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{g \cos{\left(e + f x \right)}}}{\left(d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(sqrt(g*cos(e + f*x))/((d*sin(e + f*x))**(3/2)*(a + b*sin(e + f*x))), x)","F",0
1413,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(1/2)/(d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1414,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(1/2)/(d*sin(f*x+e))**(7/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1415,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(1/2)/(d*sin(f*x+e))**(9/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1416,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1417,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)*(d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1418,0,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{\left(g \cos{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\sqrt{d \sin{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral((g*cos(e + f*x))**(3/2)/(sqrt(d*sin(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1419,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1420,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1421,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(d*sin(f*x+e))**(7/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1422,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(d*sin(f*x+e))**(9/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1423,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)*(d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1424,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)/(d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1425,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)/(d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1426,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)/(d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1427,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)/(d*sin(f*x+e))**(7/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1428,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)/(d*sin(f*x+e))**(9/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1429,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(5/2)/(d*sin(f*x+e))**(11/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1430,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1431,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\int \frac{\left(d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}}}{\sqrt{g \cos{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral((d*sin(e + f*x))**(3/2)/(sqrt(g*cos(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1432,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\int \frac{\sqrt{d \sin{\left(e + f x \right)}}}{\sqrt{g \cos{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(sqrt(d*sin(e + f*x))/(sqrt(g*cos(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1433,0,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\int \frac{1}{\sqrt{d \sin{\left(e + f x \right)}} \sqrt{g \cos{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(1/(sqrt(d*sin(e + f*x))*sqrt(g*cos(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1434,0,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\int \frac{1}{\left(d \sin{\left(e + f x \right)}\right)^{\frac{3}{2}} \sqrt{g \cos{\left(e + f x \right)}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(1/((d*sin(e + f*x))**(3/2)*sqrt(g*cos(e + f*x))*(a + b*sin(e + f*x))), x)","F",0
1435,-1,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1436,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**(5/2)/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1437,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))**(3/2)/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1438,0,0,0,0.000000," ","integrate((d*sin(f*x+e))**(1/2)/(g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\int \frac{\sqrt{d \sin{\left(e + f x \right)}}}{\left(g \cos{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(sqrt(d*sin(e + f*x))/((g*cos(e + f*x))**(3/2)*(a + b*sin(e + f*x))), x)","F",0
1439,0,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))**(3/2)/(d*sin(f*x+e))**(1/2)/(a+b*sin(f*x+e)),x)","\int \frac{1}{\sqrt{d \sin{\left(e + f x \right)}} \left(g \cos{\left(e + f x \right)}\right)^{\frac{3}{2}} \left(a + b \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral(1/(sqrt(d*sin(e + f*x))*(g*cos(e + f*x))**(3/2)*(a + b*sin(e + f*x))), x)","F",0
1440,-1,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))**(3/2)/(d*sin(f*x+e))**(3/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1441,-1,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))**(3/2)/(d*sin(f*x+e))**(5/2)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1442,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(3/2)/(a+b*sin(f*x+e))**2/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1443,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**4*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1444,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \sin^{3}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*sin(c + d*x)**3*sec(c + d*x)**2, x)","F",0
1445,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*sin(c + d*x)**2*sec(c + d*x)**2, x)","F",0
1446,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*sin(c + d*x)*sec(c + d*x)**2, x)","F",0
1447,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2*(a+b*sin(d*x+c)),x)","\int \left(a + b \sin{\left(c + d x \right)}\right) \csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))*csc(c + d*x)*sec(c + d*x)**2, x)","F",0
1448,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1449,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1450,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1451,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*sin(c + d*x)**2*sec(c + d*x)**2, x)","F",0
1452,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)*(a+b*sin(d*x+c))**2,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**2*sin(c + d*x)*sec(c + d*x)**2, x)","F",0
1453,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1454,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1455,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1456,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1457,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1458,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1459,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)*(a+b*sin(d*x+c))**3,x)","\int \left(a + b \sin{\left(c + d x \right)}\right)^{3} \sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}\, dx"," ",0,"Integral((a + b*sin(c + d*x))**3*sin(c + d*x)*sec(c + d*x)**2, x)","F",0
1460,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1461,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1462,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1463,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1464,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**4/(a+b*sin(d*x+c))**2,x)","\int \frac{\sin^{4}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sin(c + d*x)**4*sec(c + d*x)**2/(a + b*sin(c + d*x))**2, x)","F",0
1465,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1466,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**2/(a + b*sin(c + d*x))**2, x)","F",0
1467,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)/(a+b*sin(d*x+c))**2,x)","\int \frac{\sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**2/(a + b*sin(c + d*x))**2, x)","F",0
1468,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\int \frac{\csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(csc(c + d*x)*sec(c + d*x)**2/(a + b*sin(c + d*x))**2, x)","F",0
1469,0,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\int \frac{\csc^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral(csc(c + d*x)**2*sec(c + d*x)**2/(a + b*sin(c + d*x))**2, x)","F",0
1470,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1471,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**4/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1472,-1,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**3/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1473,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\int \frac{\sin^{2}{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sin(c + d*x)**2*sec(c + d*x)**2/(a + b*sin(c + d*x))**3, x)","F",0
1474,0,0,0,0.000000," ","integrate(sec(d*x+c)**2*sin(d*x+c)/(a+b*sin(d*x+c))**3,x)","\int \frac{\sin{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(sin(c + d*x)*sec(c + d*x)**2/(a + b*sin(c + d*x))**3, x)","F",0
1475,0,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\int \frac{\csc{\left(c + d x \right)} \sec^{2}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{3}}\, dx"," ",0,"Integral(csc(c + d*x)*sec(c + d*x)**2/(a + b*sin(c + d*x))**3, x)","F",0
1476,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1477,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**2/(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1478,0,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e))**(1/2)/(d*sin(f*x+e))**(1/2),x)","\int \frac{\sqrt{a + b \sin{\left(e + f x \right)}} \sec^{2}{\left(e + f x \right)}}{\sqrt{d \sin{\left(e + f x \right)}}}\, dx"," ",0,"Integral(sqrt(a + b*sin(e + f*x))*sec(e + f*x)**2/sqrt(d*sin(e + f*x)), x)","F",0
1479,-1,0,0,0.000000," ","integrate(sec(f*x+e)**2*(a+b*sin(f*x+e))**(3/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1480,-1,0,0,0.000000," ","integrate(sec(f*x+e)**4*(a+b*sin(f*x+e))**(5/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1481,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**7*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1482,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**6*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1483,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**5*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1484,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**4*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1485,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**3*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1486,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**2*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1487,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1488,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**5*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1489,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**5*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1490,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**5*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1491,-1,0,0,0.000000," ","integrate(csc(d*x+c)**4*sec(d*x+c)**5*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1492,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**6*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1493,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1494,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**4*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1495,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**3*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1496,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**2*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1497,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1498,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1499,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1500,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**5*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1501,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**5*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1502,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**4*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1503,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**3*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1504,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**2*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1505,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1506,-1,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)**5*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1507,-1,0,0,0.000000," ","integrate(csc(d*x+c)**2*sec(d*x+c)**5*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1508,-1,0,0,0.000000," ","integrate(csc(d*x+c)**3*sec(d*x+c)**5*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1509,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**n*(a+b*sin(d*x+c))**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1510,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**n*(a+b*sin(d*x+c))**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1511,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**n*(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1512,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**n*(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1513,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**n/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1514,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*sin(d*x+c)**n*(a+b*sin(d*x+c))**p,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1515,-1,0,0,0.000000," ","integrate(sec(f*x+e)**6*(a+b*sin(f*x+e))**(9/2)/(d*sin(f*x+e))**(1/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1516,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e))**2*(c+d*sin(f*x+e))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1517,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1518,0,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**(4/3),x)","\int \left(c + d \sin{\left(e + f x \right)}\right)^{\frac{4}{3}} \cos^{2}{\left(e + f x \right)}\, dx"," ",0,"Integral((c + d*sin(e + f*x))**(4/3)*cos(e + f*x)**2, x)","F",0
1519,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**(4/3)/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1520,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**(4/3)/(a+b*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1521,-2,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e))**m*(c+d*sin(f*x+e))**n,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1522,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e))**m*(c+d*sin(f*x+e))**(4/3),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1523,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e))**2*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1524,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1525,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**n,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1526,-1,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**n/(a+b*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1527,-2,0,0,0.000000," ","integrate(cos(f*x+e)**2*(c+d*sin(f*x+e))**n/(a+b*sin(f*x+e))**2,x)","\text{Exception raised: HeuristicGCDFailed}"," ",0,"Exception raised: HeuristicGCDFailed","F(-2)",0
1528,1,228,0,15.626609," ","integrate(cos(d*x+c)**7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{16 A a \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 A a \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 A a \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{A a \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{A b \cos^{8}{\left(c + d x \right)}}{8 d} - \frac{B a \cos^{8}{\left(c + d x \right)}}{8 d} + \frac{16 B b \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{8 B b \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{2 B b \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{B b \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a + b \sin{\left(c \right)}\right) \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*A*a*sin(c + d*x)**7/(35*d) + 8*A*a*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*A*a*sin(c + d*x)**3*cos(c + d*x)**4/d + A*a*sin(c + d*x)*cos(c + d*x)**6/d - A*b*cos(c + d*x)**8/(8*d) - B*a*cos(c + d*x)**8/(8*d) + 16*B*b*sin(c + d*x)**9/(315*d) + 8*B*b*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 2*B*b*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + B*b*sin(c + d*x)**3*cos(c + d*x)**6/(3*d), Ne(d, 0)), (x*(A + B*sin(c))*(a + b*sin(c))*cos(c)**7, True))","A",0
1529,1,178,0,5.837380," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{8 A a \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A a \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{A a \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{A b \cos^{6}{\left(c + d x \right)}}{6 d} - \frac{B a \cos^{6}{\left(c + d x \right)}}{6 d} + \frac{8 B b \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 B b \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{B b \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a + b \sin{\left(c \right)}\right) \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a*sin(c + d*x)**5/(15*d) + 4*A*a*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + A*a*sin(c + d*x)*cos(c + d*x)**4/d - A*b*cos(c + d*x)**6/(6*d) - B*a*cos(c + d*x)**6/(6*d) + 8*B*b*sin(c + d*x)**7/(105*d) + 4*B*b*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + B*b*sin(c + d*x)**3*cos(c + d*x)**4/(3*d), Ne(d, 0)), (x*(A + B*sin(c))*(a + b*sin(c))*cos(c)**5, True))","A",0
1530,1,128,0,1.897840," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{2 A a \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{A b \cos^{4}{\left(c + d x \right)}}{4 d} - \frac{B a \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{2 B b \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{B b \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a + b \sin{\left(c \right)}\right) \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*a*sin(c + d*x)**3/(3*d) + A*a*sin(c + d*x)*cos(c + d*x)**2/d - A*b*cos(c + d*x)**4/(4*d) - B*a*cos(c + d*x)**4/(4*d) + 2*B*b*sin(c + d*x)**5/(15*d) + B*b*sin(c + d*x)**3*cos(c + d*x)**2/(3*d), Ne(d, 0)), (x*(A + B*sin(c))*(a + b*sin(c))*cos(c)**3, True))","A",0
1531,1,75,0,0.475468," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a \sin{\left(c + d x \right)}}{d} - \frac{A b \cos^{2}{\left(c + d x \right)}}{2 d} - \frac{B a \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{B b \sin^{3}{\left(c + d x \right)}}{3 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a + b \sin{\left(c \right)}\right) \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a*sin(c + d*x)/d - A*b*cos(c + d*x)**2/(2*d) - B*a*cos(c + d*x)**2/(2*d) + B*b*sin(c + d*x)**3/(3*d), Ne(d, 0)), (x*(A + B*sin(c))*(a + b*sin(c))*cos(c), True))","A",0
1532,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\int \left(A + B \sin{\left(c + d x \right)}\right) \left(a + b \sin{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*(a + b*sin(c + d*x))*sec(c + d*x), x)","F",0
1533,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\int \left(A + B \sin{\left(c + d x \right)}\right) \left(a + b \sin{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*(a + b*sin(c + d*x))*sec(c + d*x)**3, x)","F",0
1534,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1535,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1536,1,440,0,25.922829," ","integrate(cos(d*x+c)**7*(a+b*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{16 A a^{2} \sin^{7}{\left(c + d x \right)}}{35 d} + \frac{8 A a^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{5 d} + \frac{2 A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{d} - \frac{A a b \cos^{8}{\left(c + d x \right)}}{4 d} + \frac{16 A b^{2} \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{8 A b^{2} \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{2 A b^{2} \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{A b^{2} \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \cos^{8}{\left(c + d x \right)}}{8 d} + \frac{32 B a b \sin^{9}{\left(c + d x \right)}}{315 d} + \frac{16 B a b \sin^{7}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{35 d} + \frac{4 B a b \sin^{5}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{5 d} + \frac{2 B a b \sin^{3}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{B b^{2} \sin^{10}{\left(c + d x \right)}}{40 d} + \frac{B b^{2} \sin^{8}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{8 d} + \frac{B b^{2} \sin^{6}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{B b^{2} \sin^{4}{\left(c + d x \right)} \cos^{6}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a + b \sin{\left(c \right)}\right)^{2} \cos^{7}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((16*A*a**2*sin(c + d*x)**7/(35*d) + 8*A*a**2*sin(c + d*x)**5*cos(c + d*x)**2/(5*d) + 2*A*a**2*sin(c + d*x)**3*cos(c + d*x)**4/d + A*a**2*sin(c + d*x)*cos(c + d*x)**6/d - A*a*b*cos(c + d*x)**8/(4*d) + 16*A*b**2*sin(c + d*x)**9/(315*d) + 8*A*b**2*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 2*A*b**2*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + A*b**2*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) - B*a**2*cos(c + d*x)**8/(8*d) + 32*B*a*b*sin(c + d*x)**9/(315*d) + 16*B*a*b*sin(c + d*x)**7*cos(c + d*x)**2/(35*d) + 4*B*a*b*sin(c + d*x)**5*cos(c + d*x)**4/(5*d) + 2*B*a*b*sin(c + d*x)**3*cos(c + d*x)**6/(3*d) + B*b**2*sin(c + d*x)**10/(40*d) + B*b**2*sin(c + d*x)**8*cos(c + d*x)**2/(8*d) + B*b**2*sin(c + d*x)**6*cos(c + d*x)**4/(4*d) + B*b**2*sin(c + d*x)**4*cos(c + d*x)**6/(4*d), Ne(d, 0)), (x*(A + B*sin(c))*(a + b*sin(c))**2*cos(c)**7, True))","A",0
1537,1,335,0,10.359816," ","integrate(cos(d*x+c)**5*(a+b*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{8 A a^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{4 A a^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{d} - \frac{A a b \cos^{6}{\left(c + d x \right)}}{3 d} + \frac{8 A b^{2} \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{4 A b^{2} \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{A b^{2} \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \cos^{6}{\left(c + d x \right)}}{6 d} + \frac{16 B a b \sin^{7}{\left(c + d x \right)}}{105 d} + \frac{8 B a b \sin^{5}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{15 d} + \frac{2 B a b \sin^{3}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{3 d} + \frac{B b^{2} \sin^{8}{\left(c + d x \right)}}{24 d} + \frac{B b^{2} \sin^{6}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{6 d} + \frac{B b^{2} \sin^{4}{\left(c + d x \right)} \cos^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a + b \sin{\left(c \right)}\right)^{2} \cos^{5}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((8*A*a**2*sin(c + d*x)**5/(15*d) + 4*A*a**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + A*a**2*sin(c + d*x)*cos(c + d*x)**4/d - A*a*b*cos(c + d*x)**6/(3*d) + 8*A*b**2*sin(c + d*x)**7/(105*d) + 4*A*b**2*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + A*b**2*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) - B*a**2*cos(c + d*x)**6/(6*d) + 16*B*a*b*sin(c + d*x)**7/(105*d) + 8*B*a*b*sin(c + d*x)**5*cos(c + d*x)**2/(15*d) + 2*B*a*b*sin(c + d*x)**3*cos(c + d*x)**4/(3*d) + B*b**2*sin(c + d*x)**8/(24*d) + B*b**2*sin(c + d*x)**6*cos(c + d*x)**2/(6*d) + B*b**2*sin(c + d*x)**4*cos(c + d*x)**4/(4*d), Ne(d, 0)), (x*(A + B*sin(c))*(a + b*sin(c))**2*cos(c)**5, True))","A",0
1538,1,228,0,3.676871," ","integrate(cos(d*x+c)**3*(a+b*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{2 A a^{2} \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{A a^{2} \sin{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{d} - \frac{A a b \cos^{4}{\left(c + d x \right)}}{2 d} + \frac{2 A b^{2} \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{A b^{2} \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \cos^{4}{\left(c + d x \right)}}{4 d} + \frac{4 B a b \sin^{5}{\left(c + d x \right)}}{15 d} + \frac{2 B a b \sin^{3}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{3 d} + \frac{B b^{2} \sin^{6}{\left(c + d x \right)}}{12 d} + \frac{B b^{2} \sin^{4}{\left(c + d x \right)} \cos^{2}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a + b \sin{\left(c \right)}\right)^{2} \cos^{3}{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((2*A*a**2*sin(c + d*x)**3/(3*d) + A*a**2*sin(c + d*x)*cos(c + d*x)**2/d - A*a*b*cos(c + d*x)**4/(2*d) + 2*A*b**2*sin(c + d*x)**5/(15*d) + A*b**2*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) - B*a**2*cos(c + d*x)**4/(4*d) + 4*B*a*b*sin(c + d*x)**5/(15*d) + 2*B*a*b*sin(c + d*x)**3*cos(c + d*x)**2/(3*d) + B*b**2*sin(c + d*x)**6/(12*d) + B*b**2*sin(c + d*x)**4*cos(c + d*x)**2/(4*d), Ne(d, 0)), (x*(A + B*sin(c))*(a + b*sin(c))**2*cos(c)**3, True))","A",0
1539,1,117,0,1.015876," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\begin{cases} \frac{A a^{2} \sin{\left(c + d x \right)}}{d} - \frac{A a b \cos^{2}{\left(c + d x \right)}}{d} + \frac{A b^{2} \sin^{3}{\left(c + d x \right)}}{3 d} - \frac{B a^{2} \cos^{2}{\left(c + d x \right)}}{2 d} + \frac{2 B a b \sin^{3}{\left(c + d x \right)}}{3 d} + \frac{B b^{2} \sin^{4}{\left(c + d x \right)}}{4 d} & \text{for}\: d \neq 0 \\x \left(A + B \sin{\left(c \right)}\right) \left(a + b \sin{\left(c \right)}\right)^{2} \cos{\left(c \right)} & \text{otherwise} \end{cases}"," ",0,"Piecewise((A*a**2*sin(c + d*x)/d - A*a*b*cos(c + d*x)**2/d + A*b**2*sin(c + d*x)**3/(3*d) - B*a**2*cos(c + d*x)**2/(2*d) + 2*B*a*b*sin(c + d*x)**3/(3*d) + B*b**2*sin(c + d*x)**4/(4*d), Ne(d, 0)), (x*(A + B*sin(c))*(a + b*sin(c))**2*cos(c), True))","A",0
1540,0,0,0,0.000000," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\int \left(A + B \sin{\left(c + d x \right)}\right) \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sec{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*(a + b*sin(c + d*x))**2*sec(c + d*x), x)","F",0
1541,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(a+b*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\int \left(A + B \sin{\left(c + d x \right)}\right) \left(a + b \sin{\left(c + d x \right)}\right)^{2} \sec^{3}{\left(c + d x \right)}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*(a + b*sin(c + d*x))**2*sec(c + d*x)**3, x)","F",0
1542,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(a+b*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1543,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(a+b*sin(d*x+c))**2*(A+B*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1544,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1545,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1546,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1547,1,104,0,0.712685," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\begin{cases} \frac{x \left(A + B \sin{\left(c \right)}\right) \cos{\left(c \right)}}{a} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\frac{A \sin{\left(c + d x \right)}}{d} - \frac{B \cos^{2}{\left(c + d x \right)}}{2 d}}{a} & \text{for}\: b = 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos{\left(c \right)}}{a + b \sin{\left(c \right)}} & \text{for}\: d = 0 \\\frac{A \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{b d} - \frac{B a \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{b^{2} d} + \frac{B \sin{\left(c + d x \right)}}{b d} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(A + B*sin(c))*cos(c)/a, Eq(b, 0) & Eq(d, 0)), ((A*sin(c + d*x)/d - B*cos(c + d*x)**2/(2*d))/a, Eq(b, 0)), (x*(A + B*sin(c))*cos(c)/(a + b*sin(c)), Eq(d, 0)), (A*log(a/b + sin(c + d*x))/(b*d) - B*a*log(a/b + sin(c + d*x))/(b**2*d) + B*sin(c + d*x)/(b*d), True))","A",0
1548,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\int \frac{\left(A + B \sin{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*sec(c + d*x)/(a + b*sin(c + d*x)), x)","F",0
1549,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\int \frac{\left(A + B \sin{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*sec(c + d*x)**3/(a + b*sin(c + d*x)), x)","F",0
1550,0,0,0,0.000000," ","integrate(sec(d*x+c)**5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\int \frac{\left(A + B \sin{\left(c + d x \right)}\right) \sec^{5}{\left(c + d x \right)}}{a + b \sin{\left(c + d x \right)}}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*sec(c + d*x)**5/(a + b*sin(c + d*x)), x)","F",0
1551,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1552,-1,0,0,0.000000," ","integrate(cos(d*x+c)**7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1553,-1,0,0,0.000000," ","integrate(cos(d*x+c)**5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1554,-1,0,0,0.000000," ","integrate(cos(d*x+c)**3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1555,1,178,0,1.360288," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))**2,x)","\begin{cases} \frac{x \left(A + B \sin{\left(c \right)}\right) \cos{\left(c \right)}}{a^{2}} & \text{for}\: b = 0 \wedge d = 0 \\\frac{\frac{A \sin{\left(c + d x \right)}}{d} - \frac{B \cos^{2}{\left(c + d x \right)}}{2 d}}{a^{2}} & \text{for}\: b = 0 \\\frac{x \left(A + B \sin{\left(c \right)}\right) \cos{\left(c \right)}}{\left(a + b \sin{\left(c \right)}\right)^{2}} & \text{for}\: d = 0 \\- \frac{A b}{a b^{2} d + b^{3} d \sin{\left(c + d x \right)}} + \frac{B a \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)}}{a b^{2} d + b^{3} d \sin{\left(c + d x \right)}} + \frac{B a}{a b^{2} d + b^{3} d \sin{\left(c + d x \right)}} + \frac{B b \log{\left(\frac{a}{b} + \sin{\left(c + d x \right)} \right)} \sin{\left(c + d x \right)}}{a b^{2} d + b^{3} d \sin{\left(c + d x \right)}} & \text{otherwise} \end{cases}"," ",0,"Piecewise((x*(A + B*sin(c))*cos(c)/a**2, Eq(b, 0) & Eq(d, 0)), ((A*sin(c + d*x)/d - B*cos(c + d*x)**2/(2*d))/a**2, Eq(b, 0)), (x*(A + B*sin(c))*cos(c)/(a + b*sin(c))**2, Eq(d, 0)), (-A*b/(a*b**2*d + b**3*d*sin(c + d*x)) + B*a*log(a/b + sin(c + d*x))/(a*b**2*d + b**3*d*sin(c + d*x)) + B*a/(a*b**2*d + b**3*d*sin(c + d*x)) + B*b*log(a/b + sin(c + d*x))*sin(c + d*x)/(a*b**2*d + b**3*d*sin(c + d*x)), True))","A",0
1556,0,0,0,0.000000," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))**2,x)","\int \frac{\left(A + B \sin{\left(c + d x \right)}\right) \sec{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*sec(c + d*x)/(a + b*sin(c + d*x))**2, x)","F",0
1557,0,0,0,0.000000," ","integrate(sec(d*x+c)**3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))**2,x)","\int \frac{\left(A + B \sin{\left(c + d x \right)}\right) \sec^{3}{\left(c + d x \right)}}{\left(a + b \sin{\left(c + d x \right)}\right)^{2}}\, dx"," ",0,"Integral((A + B*sin(c + d*x))*sec(c + d*x)**3/(a + b*sin(c + d*x))**2, x)","F",0
1558,-1,0,0,0.000000," ","integrate(sec(d*x+c)**5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1559,-1,0,0,0.000000," ","integrate(sec(d*x+c)**7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1560,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**(-1-m)*(a+b*sin(f*x+e))**m*(A+B*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1561,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1562,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))**p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1563,0,0,0,0.000000," ","integrate((g*sec(f*x+e))**p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x)","\int \frac{\left(g \sec{\left(e + f x \right)}\right)^{p}}{\left(a + b \sin{\left(e + f x \right)}\right) \left(c + d \sin{\left(e + f x \right)}\right)}\, dx"," ",0,"Integral((g*sec(e + f*x))**p/((a + b*sin(e + f*x))*(c + d*sin(e + f*x))), x)","F",0