1,1,110,0,1.344300," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(5 \, c^{3} \cos\left(f x + e\right)^{6} - 30 \, c^{3} \cos\left(f x + e\right)^{4} + 25 \, c^{3} + 2 \, {\left(9 \, c^{3} \cos\left(f x + e\right)^{4} - 8 \, c^{3} \cos\left(f x + e\right)^{2} - 16 \, c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, f \cos\left(f x + e\right)}"," ",0,"-1/30*(5*c^3*cos(f*x + e)^6 - 30*c^3*cos(f*x + e)^4 + 25*c^3 + 2*(9*c^3*cos(f*x + e)^4 - 8*c^3*cos(f*x + e)^2 - 16*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
2,1,96,0,1.222476," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(5 \, c^{2} \cos\left(f x + e\right)^{4} - 5 \, c^{2} - 2 \, {\left(c^{2} \cos\left(f x + e\right)^{4} - 2 \, c^{2} \cos\left(f x + e\right)^{2} - 4 \, c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{10 \, f \cos\left(f x + e\right)}"," ",0,"1/10*(5*c^2*cos(f*x + e)^4 - 5*c^2 - 2*(c^2*cos(f*x + e)^4 - 2*c^2*cos(f*x + e)^2 - 4*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
3,1,75,0,1.288759," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, c \cos\left(f x + e\right)^{4} + 4 \, {\left(c \cos\left(f x + e\right)^{2} + 2 \, c\right)} \sin\left(f x + e\right) - 3 \, c\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{12 \, f \cos\left(f x + e\right)}"," ",0,"1/12*(3*c*cos(f*x + e)^4 + 4*(c*cos(f*x + e)^2 + 2*c)*sin(f*x + e) - 3*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
4,1,54,0,1.406022," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\cos\left(f x + e\right)^{2} + 2\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{3 \, f \cos\left(f x + e\right)}"," ",0,"1/3*(cos(f*x + e)^2 + 2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e)/(f*cos(f*x + e))","A",0
5,1,59,0,1.380028," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(f x + e\right)^{2} - 2 \, \sin\left(f x + e\right) - 1\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, c f \cos\left(f x + e\right)}"," ",0,"-1/2*(cos(f*x + e)^2 - 2*sin(f*x + e) - 1)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*f*cos(f*x + e))","A",0
6,0,0,0,2.250937," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
7,0,0,0,2.827279," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
8,1,79,0,1.224857," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{c^{4} f \cos\left(f x + e\right)^{3} + 2 \, c^{4} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c^{4} f \cos\left(f x + e\right)}"," ",0,"-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e)/(c^4*f*cos(f*x + e)^3 + 2*c^4*f*cos(f*x + e)*sin(f*x + e) - 2*c^4*f*cos(f*x + e))","A",0
9,1,116,0,1.359553," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(35 \, a c^{3} \cos\left(f x + e\right)^{6} - 35 \, a c^{3} - {\left(15 \, a c^{3} \cos\left(f x + e\right)^{6} - 24 \, a c^{3} \cos\left(f x + e\right)^{4} - 32 \, a c^{3} \cos\left(f x + e\right)^{2} - 64 \, a c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{105 \, f \cos\left(f x + e\right)}"," ",0,"1/105*(35*a*c^3*cos(f*x + e)^6 - 35*a*c^3 - (15*a*c^3*cos(f*x + e)^6 - 24*a*c^3*cos(f*x + e)^4 - 32*a*c^3*cos(f*x + e)^2 - 64*a*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
10,1,102,0,1.439626," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a c^{2} \cos\left(f x + e\right)^{6} - 5 \, a c^{2} + 2 \, {\left(3 \, a c^{2} \cos\left(f x + e\right)^{4} + 4 \, a c^{2} \cos\left(f x + e\right)^{2} + 8 \, a c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, f \cos\left(f x + e\right)}"," ",0,"1/30*(5*a*c^2*cos(f*x + e)^6 - 5*a*c^2 + 2*(3*a*c^2*cos(f*x + e)^4 + 4*a*c^2*cos(f*x + e)^2 + 8*a*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
11,1,73,0,1.399541," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a c \cos\left(f x + e\right)^{4} + 4 \, a c \cos\left(f x + e\right)^{2} + 8 \, a c\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{15 \, f \cos\left(f x + e\right)}"," ",0,"1/15*(3*a*c*cos(f*x + e)^4 + 4*a*c*cos(f*x + e)^2 + 8*a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e)/(f*cos(f*x + e))","A",0
12,1,75,0,1.423885," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a \cos\left(f x + e\right)^{4} - 4 \, {\left(a \cos\left(f x + e\right)^{2} + 2 \, a\right)} \sin\left(f x + e\right) - 3 \, a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{12 \, f \cos\left(f x + e\right)}"," ",0,"-1/12*(3*a*cos(f*x + e)^4 - 4*(a*cos(f*x + e)^2 + 2*a)*sin(f*x + e) - 3*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
13,1,77,0,1.261669," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a \cos\left(f x + e\right)^{2} + {\left(a \cos\left(f x + e\right)^{2} - 4 \, a\right)} \sin\left(f x + e\right) - 3 \, a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c f \cos\left(f x + e\right)}"," ",0,"-1/3*(3*a*cos(f*x + e)^2 + (a*cos(f*x + e)^2 - 4*a)*sin(f*x + e) - 3*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*f*cos(f*x + e))","A",0
14,0,0,0,2.360123," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) + a \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-(a*cos(f*x + e)^2*sin(f*x + e) + a*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
15,0,0,0,3.169548," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) + a \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a*cos(f*x + e)^2*sin(f*x + e) + a*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
16,0,0,0,3.868494," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) + a \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((a*cos(f*x + e)^2*sin(f*x + e) + a*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
17,1,105,0,0.627115," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left(3 \, a \cos\left(f x + e\right)^{2} - 4 \, a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, {\left(3 \, c^{5} f \cos\left(f x + e\right)^{3} - 4 \, c^{5} f \cos\left(f x + e\right) - {\left(c^{5} f \cos\left(f x + e\right)^{3} - 4 \, c^{5} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/3*(3*a*cos(f*x + e)^2 - 4*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^5*f*cos(f*x + e)^3 - 4*c^5*f*cos(f*x + e) - (c^5*f*cos(f*x + e)^3 - 4*c^5*f*cos(f*x + e))*sin(f*x + e))","B",0
18,1,127,0,0.985484," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, a \cos\left(f x + e\right)^{2} - 2 \, a \sin\left(f x + e\right) - 4 \, a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{6 \, {\left(c^{6} f \cos\left(f x + e\right)^{5} - 8 \, c^{6} f \cos\left(f x + e\right)^{3} + 8 \, c^{6} f \cos\left(f x + e\right) + 4 \, {\left(c^{6} f \cos\left(f x + e\right)^{3} - 2 \, c^{6} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/6*(3*a*cos(f*x + e)^2 - 2*a*sin(f*x + e) - 4*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^6*f*cos(f*x + e)^5 - 8*c^6*f*cos(f*x + e)^3 + 8*c^6*f*cos(f*x + e) + 4*(c^6*f*cos(f*x + e)^3 - 2*c^6*f*cos(f*x + e))*sin(f*x + e))","A",0
19,1,128,0,0.940942," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(35 \, a^{2} c^{3} \cos\left(f x + e\right)^{8} - 35 \, a^{2} c^{3} + 8 \, {\left(5 \, a^{2} c^{3} \cos\left(f x + e\right)^{6} + 6 \, a^{2} c^{3} \cos\left(f x + e\right)^{4} + 8 \, a^{2} c^{3} \cos\left(f x + e\right)^{2} + 16 \, a^{2} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{280 \, f \cos\left(f x + e\right)}"," ",0,"1/280*(35*a^2*c^3*cos(f*x + e)^8 - 35*a^2*c^3 + 8*(5*a^2*c^3*cos(f*x + e)^6 + 6*a^2*c^3*cos(f*x + e)^4 + 8*a^2*c^3*cos(f*x + e)^2 + 16*a^2*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
20,1,101,0,0.870857," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a^{2} c^{2} \cos\left(f x + e\right)^{6} + 6 \, a^{2} c^{2} \cos\left(f x + e\right)^{4} + 8 \, a^{2} c^{2} \cos\left(f x + e\right)^{2} + 16 \, a^{2} c^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{35 \, f \cos\left(f x + e\right)}"," ",0,"1/35*(5*a^2*c^2*cos(f*x + e)^6 + 6*a^2*c^2*cos(f*x + e)^4 + 8*a^2*c^2*cos(f*x + e)^2 + 16*a^2*c^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e)/(f*cos(f*x + e))","A",0
21,1,102,0,0.860904," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(5 \, a^{2} c \cos\left(f x + e\right)^{6} - 5 \, a^{2} c - 2 \, {\left(3 \, a^{2} c \cos\left(f x + e\right)^{4} + 4 \, a^{2} c \cos\left(f x + e\right)^{2} + 8 \, a^{2} c\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, f \cos\left(f x + e\right)}"," ",0,"-1/30*(5*a^2*c*cos(f*x + e)^6 - 5*a^2*c - 2*(3*a^2*c*cos(f*x + e)^4 + 4*a^2*c*cos(f*x + e)^2 + 8*a^2*c)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
22,1,96,0,0.923788," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(5 \, a^{2} \cos\left(f x + e\right)^{4} - 5 \, a^{2} + 2 \, {\left(a^{2} \cos\left(f x + e\right)^{4} - 2 \, a^{2} \cos\left(f x + e\right)^{2} - 4 \, a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{10 \, f \cos\left(f x + e\right)}"," ",0,"-1/10*(5*a^2*cos(f*x + e)^4 - 5*a^2 + 2*(a^2*cos(f*x + e)^4 - 2*a^2*cos(f*x + e)^2 - 4*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
23,1,98,0,0.882196," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(a^{2} \cos\left(f x + e\right)^{4} - 8 \, a^{2} \cos\left(f x + e\right)^{2} + 7 \, a^{2} - 4 \, {\left(a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{4 \, c f \cos\left(f x + e\right)}"," ",0,"1/4*(a^2*cos(f*x + e)^4 - 8*a^2*cos(f*x + e)^2 + 7*a^2 - 4*(a^2*cos(f*x + e)^2 - 2*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*f*cos(f*x + e))","B",0
24,0,0,0,1.203709," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \cos\left(f x + e\right)^{4} - 2 \, a^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - 2 \, a^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral((a^2*cos(f*x + e)^4 - 2*a^2*cos(f*x + e)^2*sin(f*x + e) - 2*a^2*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
25,0,0,0,2.440087," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} \cos\left(f x + e\right)^{4} - 2 \, a^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - 2 \, a^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((a^2*cos(f*x + e)^4 - 2*a^2*cos(f*x + e)^2*sin(f*x + e) - 2*a^2*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
26,0,0,0,3.246085," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(f x + e\right)^{4} - 2 \, a^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - 2 \, a^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a^2*cos(f*x + e)^4 - 2*a^2*cos(f*x + e)^2*sin(f*x + e) - 2*a^2*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
27,0,0,0,5.141629," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} \cos\left(f x + e\right)^{4} - 2 \, a^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - 2 \, a^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{5 \, c^{5} \cos\left(f x + e\right)^{4} - 20 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5} - {\left(c^{5} \cos\left(f x + e\right)^{4} - 12 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a^2*cos(f*x + e)^4 - 2*a^2*cos(f*x + e)^2*sin(f*x + e) - 2*a^2*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^5*cos(f*x + e)^4 - 20*c^5*cos(f*x + e)^2 + 16*c^5 - (c^5*cos(f*x + e)^4 - 12*c^5*cos(f*x + e)^2 + 16*c^5)*sin(f*x + e)), x)","F",0
28,1,127,0,0.967789," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""fricas"")","-\frac{{\left(a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{c^{6} f \cos\left(f x + e\right)^{5} - 8 \, c^{6} f \cos\left(f x + e\right)^{3} + 8 \, c^{6} f \cos\left(f x + e\right) + 4 \, {\left(c^{6} f \cos\left(f x + e\right)^{3} - 2 \, c^{6} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}"," ",0,"-(a^2*cos(f*x + e)^2 - 2*a^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e)/(c^6*f*cos(f*x + e)^5 - 8*c^6*f*cos(f*x + e)^3 + 8*c^6*f*cos(f*x + e) + 4*(c^6*f*cos(f*x + e)^3 - 2*c^6*f*cos(f*x + e))*sin(f*x + e))","B",0
29,1,163,0,1.150573," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""fricas"")","-\frac{{\left(5 \, a^{2} \cos\left(f x + e\right)^{2} - 6 \, a^{2} + 5 \, {\left(a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{10 \, {\left(5 \, c^{7} f \cos\left(f x + e\right)^{5} - 20 \, c^{7} f \cos\left(f x + e\right)^{3} + 16 \, c^{7} f \cos\left(f x + e\right) - {\left(c^{7} f \cos\left(f x + e\right)^{5} - 12 \, c^{7} f \cos\left(f x + e\right)^{3} + 16 \, c^{7} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/10*(5*a^2*cos(f*x + e)^2 - 6*a^2 + 5*(a^2*cos(f*x + e)^2 - 2*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^7*f*cos(f*x + e)^5 - 20*c^7*f*cos(f*x + e)^3 + 16*c^7*f*cos(f*x + e) - (c^7*f*cos(f*x + e)^5 - 12*c^7*f*cos(f*x + e)^3 + 16*c^7*f*cos(f*x + e))*sin(f*x + e))","A",0
30,1,144,0,1.054820," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left(63 \, a^{3} c^{4} \cos\left(f x + e\right)^{10} - 63 \, a^{3} c^{4} + 2 \, {\left(35 \, a^{3} c^{4} \cos\left(f x + e\right)^{8} + 40 \, a^{3} c^{4} \cos\left(f x + e\right)^{6} + 48 \, a^{3} c^{4} \cos\left(f x + e\right)^{4} + 64 \, a^{3} c^{4} \cos\left(f x + e\right)^{2} + 128 \, a^{3} c^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{630 \, f \cos\left(f x + e\right)}"," ",0,"1/630*(63*a^3*c^4*cos(f*x + e)^10 - 63*a^3*c^4 + 2*(35*a^3*c^4*cos(f*x + e)^8 + 40*a^3*c^4*cos(f*x + e)^6 + 48*a^3*c^4*cos(f*x + e)^4 + 64*a^3*c^4*cos(f*x + e)^2 + 128*a^3*c^4)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
31,1,117,0,0.993160," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(35 \, a^{3} c^{3} \cos\left(f x + e\right)^{8} + 40 \, a^{3} c^{3} \cos\left(f x + e\right)^{6} + 48 \, a^{3} c^{3} \cos\left(f x + e\right)^{4} + 64 \, a^{3} c^{3} \cos\left(f x + e\right)^{2} + 128 \, a^{3} c^{3}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{315 \, f \cos\left(f x + e\right)}"," ",0,"1/315*(35*a^3*c^3*cos(f*x + e)^8 + 40*a^3*c^3*cos(f*x + e)^6 + 48*a^3*c^3*cos(f*x + e)^4 + 64*a^3*c^3*cos(f*x + e)^2 + 128*a^3*c^3)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e)/(f*cos(f*x + e))","A",0
32,1,128,0,0.934199," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(35 \, a^{3} c^{2} \cos\left(f x + e\right)^{8} - 35 \, a^{3} c^{2} - 8 \, {\left(5 \, a^{3} c^{2} \cos\left(f x + e\right)^{6} + 6 \, a^{3} c^{2} \cos\left(f x + e\right)^{4} + 8 \, a^{3} c^{2} \cos\left(f x + e\right)^{2} + 16 \, a^{3} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{280 \, f \cos\left(f x + e\right)}"," ",0,"-1/280*(35*a^3*c^2*cos(f*x + e)^8 - 35*a^3*c^2 - 8*(5*a^3*c^2*cos(f*x + e)^6 + 6*a^3*c^2*cos(f*x + e)^4 + 8*a^3*c^2*cos(f*x + e)^2 + 16*a^3*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
33,1,115,0,0.865299," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(35 \, a^{3} c \cos\left(f x + e\right)^{6} - 35 \, a^{3} c + {\left(15 \, a^{3} c \cos\left(f x + e\right)^{6} - 24 \, a^{3} c \cos\left(f x + e\right)^{4} - 32 \, a^{3} c \cos\left(f x + e\right)^{2} - 64 \, a^{3} c\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{105 \, f \cos\left(f x + e\right)}"," ",0,"-1/105*(35*a^3*c*cos(f*x + e)^6 - 35*a^3*c + (15*a^3*c*cos(f*x + e)^6 - 24*a^3*c*cos(f*x + e)^4 - 32*a^3*c*cos(f*x + e)^2 - 64*a^3*c)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
34,1,110,0,1.043505," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a^{3} \cos\left(f x + e\right)^{6} - 30 \, a^{3} \cos\left(f x + e\right)^{4} + 25 \, a^{3} - 2 \, {\left(9 \, a^{3} \cos\left(f x + e\right)^{4} - 8 \, a^{3} \cos\left(f x + e\right)^{2} - 16 \, a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, f \cos\left(f x + e\right)}"," ",0,"1/30*(5*a^3*cos(f*x + e)^6 - 30*a^3*cos(f*x + e)^4 + 25*a^3 - 2*(9*a^3*cos(f*x + e)^4 - 8*a^3*cos(f*x + e)^2 - 16*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
35,1,111,0,0.938858," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a^{3} \cos\left(f x + e\right)^{4} - 20 \, a^{3} \cos\left(f x + e\right)^{2} + 15 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{4} - 12 \, a^{3} \cos\left(f x + e\right)^{2} + 16 \, a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{5 \, c f \cos\left(f x + e\right)}"," ",0,"1/5*(5*a^3*cos(f*x + e)^4 - 20*a^3*cos(f*x + e)^2 + 15*a^3 + (a^3*cos(f*x + e)^4 - 12*a^3*cos(f*x + e)^2 + 16*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*f*cos(f*x + e))","B",0
36,0,0,0,2.026627," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2} + {\left(a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral((3*a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2 + (a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
37,0,0,0,3.427814," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2} + {\left(a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((3*a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2 + (a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
38,0,0,0,4.429239," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2} + {\left(a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(3*a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2 + (a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
39,0,0,0,7.099479," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2} + {\left(a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{5 \, c^{5} \cos\left(f x + e\right)^{4} - 20 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5} - {\left(c^{5} \cos\left(f x + e\right)^{4} - 12 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(3*a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2 + (a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^5*cos(f*x + e)^4 - 20*c^5*cos(f*x + e)^2 + 16*c^5 - (c^5*cos(f*x + e)^4 - 12*c^5*cos(f*x + e)^2 + 16*c^5)*sin(f*x + e)), x)","F",0
40,0,0,0,10.220538," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2} + {\left(a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{6} \cos\left(f x + e\right)^{6} - 18 \, c^{6} \cos\left(f x + e\right)^{4} + 48 \, c^{6} \cos\left(f x + e\right)^{2} - 32 \, c^{6} + 2 \, {\left(3 \, c^{6} \cos\left(f x + e\right)^{4} - 16 \, c^{6} \cos\left(f x + e\right)^{2} + 16 \, c^{6}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((3*a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2 + (a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^6*cos(f*x + e)^6 - 18*c^6*cos(f*x + e)^4 + 48*c^6*cos(f*x + e)^2 - 32*c^6 + 2*(3*c^6*cos(f*x + e)^4 - 16*c^6*cos(f*x + e)^2 + 16*c^6)*sin(f*x + e)), x)","F",0
41,1,150,0,1.148622," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""fricas"")","\frac{{\left(5 \, a^{3} \cos\left(f x + e\right)^{4} - 20 \, a^{3} \cos\left(f x + e\right)^{2} + 16 \, a^{3}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{5 \, {\left(5 \, c^{7} f \cos\left(f x + e\right)^{5} - 20 \, c^{7} f \cos\left(f x + e\right)^{3} + 16 \, c^{7} f \cos\left(f x + e\right) - {\left(c^{7} f \cos\left(f x + e\right)^{5} - 12 \, c^{7} f \cos\left(f x + e\right)^{3} + 16 \, c^{7} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/5*(5*a^3*cos(f*x + e)^4 - 20*a^3*cos(f*x + e)^2 + 16*a^3)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^7*f*cos(f*x + e)^5 - 20*c^7*f*cos(f*x + e)^3 + 16*c^7*f*cos(f*x + e) - (c^7*f*cos(f*x + e)^5 - 12*c^7*f*cos(f*x + e)^3 + 16*c^7*f*cos(f*x + e))*sin(f*x + e))","B",0
42,1,191,0,0.885573," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x, algorithm=""fricas"")","-\frac{{\left(15 \, a^{3} \cos\left(f x + e\right)^{4} - 60 \, a^{3} \cos\left(f x + e\right)^{2} + 48 \, a^{3} - 4 \, {\left(5 \, a^{3} \cos\left(f x + e\right)^{2} - 8 \, a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, {\left(c^{8} f \cos\left(f x + e\right)^{7} - 18 \, c^{8} f \cos\left(f x + e\right)^{5} + 48 \, c^{8} f \cos\left(f x + e\right)^{3} - 32 \, c^{8} f \cos\left(f x + e\right) + 2 \, {\left(3 \, c^{8} f \cos\left(f x + e\right)^{5} - 16 \, c^{8} f \cos\left(f x + e\right)^{3} + 16 \, c^{8} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/30*(15*a^3*cos(f*x + e)^4 - 60*a^3*cos(f*x + e)^2 + 48*a^3 - 4*(5*a^3*cos(f*x + e)^2 - 8*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^8*f*cos(f*x + e)^7 - 18*c^8*f*cos(f*x + e)^5 + 48*c^8*f*cos(f*x + e)^3 - 32*c^8*f*cos(f*x + e) + 2*(3*c^8*f*cos(f*x + e)^5 - 16*c^8*f*cos(f*x + e)^3 + 16*c^8*f*cos(f*x + e))*sin(f*x + e))","B",0
43,1,205,0,0.922791," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(17/2),x, algorithm=""fricas"")","-\frac{{\left(35 \, a^{3} \cos\left(f x + e\right)^{4} - 154 \, a^{3} \cos\left(f x + e\right)^{2} + 128 \, a^{3} - 14 \, {\left(5 \, a^{3} \cos\left(f x + e\right)^{2} - 8 \, a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{105 \, {\left(7 \, c^{9} f \cos\left(f x + e\right)^{7} - 56 \, c^{9} f \cos\left(f x + e\right)^{5} + 112 \, c^{9} f \cos\left(f x + e\right)^{3} - 64 \, c^{9} f \cos\left(f x + e\right) - {\left(c^{9} f \cos\left(f x + e\right)^{7} - 24 \, c^{9} f \cos\left(f x + e\right)^{5} + 80 \, c^{9} f \cos\left(f x + e\right)^{3} - 64 \, c^{9} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/105*(35*a^3*cos(f*x + e)^4 - 154*a^3*cos(f*x + e)^2 + 128*a^3 - 14*(5*a^3*cos(f*x + e)^2 - 8*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(7*c^9*f*cos(f*x + e)^7 - 56*c^9*f*cos(f*x + e)^5 + 112*c^9*f*cos(f*x + e)^3 - 64*c^9*f*cos(f*x + e) - (c^9*f*cos(f*x + e)^7 - 24*c^9*f*cos(f*x + e)^5 + 80*c^9*f*cos(f*x + e)^3 - 64*c^9*f*cos(f*x + e))*sin(f*x + e))","A",0
44,1,98,0,0.889794," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(c^{2} \cos\left(f x + e\right)^{4} - 8 \, c^{2} \cos\left(f x + e\right)^{2} + 7 \, c^{2} + 4 \, {\left(c^{2} \cos\left(f x + e\right)^{2} - 2 \, c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{4 \, a f \cos\left(f x + e\right)}"," ",0,"-1/4*(c^2*cos(f*x + e)^4 - 8*c^2*cos(f*x + e)^2 + 7*c^2 + 4*(c^2*cos(f*x + e)^2 - 2*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*f*cos(f*x + e))","B",0
45,1,78,0,0.911792," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, c \cos\left(f x + e\right)^{2} - {\left(c \cos\left(f x + e\right)^{2} - 4 \, c\right)} \sin\left(f x + e\right) - 3 \, c\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a f \cos\left(f x + e\right)}"," ",0,"1/3*(3*c*cos(f*x + e)^2 - (c*cos(f*x + e)^2 - 4*c)*sin(f*x + e) - 3*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*f*cos(f*x + e))","A",0
46,1,59,0,0.949594," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\cos\left(f x + e\right)^{2} + 2 \, \sin\left(f x + e\right) - 1\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, a f \cos\left(f x + e\right)}"," ",0,"1/2*(cos(f*x + e)^2 + 2*sin(f*x + e) - 1)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*f*cos(f*x + e))","A",0
47,1,49,0,0.917562," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{a c f \cos\left(f x + e\right)}"," ",0,"sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e)/(a*c*f*cos(f*x + e))","A",0
48,0,0,0,1.554081," ","integrate(cos(f*x+e)^2/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c^{2} \sin\left(f x + e\right) - a c^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c^2*sin(f*x + e) - a*c^2), x)","F",0
49,1,61,0,0.686957," ","integrate(cos(f*x+e)^2/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - a c^{3} f \cos\left(f x + e\right)}"," ",0,"-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c^3*f*cos(f*x + e)*sin(f*x + e) - a*c^3*f*cos(f*x + e))","A",0
50,0,0,0,2.314131," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, c^{3} \cos\left(f x + e\right)^{4} - 4 \, c^{3} \cos\left(f x + e\right)^{2} - {\left(c^{3} \cos\left(f x + e\right)^{4} - 4 \, c^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral((3*c^3*cos(f*x + e)^4 - 4*c^3*cos(f*x + e)^2 - (c^3*cos(f*x + e)^4 - 4*c^3*cos(f*x + e)^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
51,0,0,0,1.094326," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} \cos\left(f x + e\right)^{4} + 2 \, c^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - 2 \, c^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral((c^2*cos(f*x + e)^4 + 2*c^2*cos(f*x + e)^2*sin(f*x + e) - 2*c^2*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
52,0,0,0,1.592570," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - c \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral((c*cos(f*x + e)^2*sin(f*x + e) - c*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
53,0,0,0,1.046899," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
54,0,0,0,1.625316," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} c \sin\left(f x + e\right) + a^{2} c}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*c*sin(f*x + e) + a^2*c), x)","F",0
55,1,160,0,1.030809," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right)}{2 \, a^{2} c^{2} f}, -\frac{\sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right)}{a^{2} c^{2} f}\right]"," ",0,"[1/2*sqrt(a*c)*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3)/(a^2*c^2*f), -sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e)))/(a^2*c^2*f)]","A",0
56,1,319,0,0.873036," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} {\left(\cos\left(f x + e\right) \sin\left(f x + e\right) - \cos\left(f x + e\right)\right)} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) - 2 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{4 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - a^{2} c^{3} f \cos\left(f x + e\right)\right)}}, -\frac{\sqrt{-a c} {\left(\cos\left(f x + e\right) \sin\left(f x + e\right) - \cos\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) + \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - a^{2} c^{3} f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(sqrt(a*c)*(cos(f*x + e)*sin(f*x + e) - cos(f*x + e))*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) - 2*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^2*c^3*f*cos(f*x + e)*sin(f*x + e) - a^2*c^3*f*cos(f*x + e)), -1/2*(sqrt(-a*c)*(cos(f*x + e)*sin(f*x + e) - cos(f*x + e))*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e))) + sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^2*c^3*f*cos(f*x + e)*sin(f*x + e) - a^2*c^3*f*cos(f*x + e))]","A",0
57,0,0,0,6.284635," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{4} \cos\left(f x + e\right)^{6} - 8 \, c^{4} \cos\left(f x + e\right)^{4} + 8 \, c^{4} \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{4} - 2 \, c^{4} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(c^4*cos(f*x + e)^6 - 8*c^4*cos(f*x + e)^4 + 8*c^4*cos(f*x + e)^2 + 4*(c^4*cos(f*x + e)^4 - 2*c^4*cos(f*x + e)^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
58,0,0,0,4.149435," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, c^{3} \cos\left(f x + e\right)^{4} - 4 \, c^{3} \cos\left(f x + e\right)^{2} - {\left(c^{3} \cos\left(f x + e\right)^{4} - 4 \, c^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((3*c^3*cos(f*x + e)^4 - 4*c^3*cos(f*x + e)^2 - (c^3*cos(f*x + e)^4 - 4*c^3*cos(f*x + e)^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
59,0,0,0,2.361705," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} \cos\left(f x + e\right)^{4} + 2 \, c^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - 2 \, c^{2} \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((c^2*cos(f*x + e)^4 + 2*c^2*cos(f*x + e)^2*sin(f*x + e) - 2*c^2*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
60,0,0,0,2.072278," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - c \cos\left(f x + e\right)^{2}\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((c*cos(f*x + e)^2*sin(f*x + e) - c*cos(f*x + e)^2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
61,0,0,0,1.525758," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
62,1,60,0,0.780550," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{3} c f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{3} c f \cos\left(f x + e\right)}"," ",0,"-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^3*c*f*cos(f*x + e)*sin(f*x + e) + a^3*c*f*cos(f*x + e))","A",0
63,1,313,0,1.044470," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} {\left(\cos\left(f x + e\right) \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) - 2 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{4 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{3} c^{2} f \cos\left(f x + e\right)\right)}}, -\frac{\sqrt{-a c} {\left(\cos\left(f x + e\right) \sin\left(f x + e\right) + \cos\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) + \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{3} c^{2} f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(sqrt(a*c)*(cos(f*x + e)*sin(f*x + e) + cos(f*x + e))*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) - 2*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^3*c^2*f*cos(f*x + e)*sin(f*x + e) + a^3*c^2*f*cos(f*x + e)), -1/2*(sqrt(-a*c)*(cos(f*x + e)*sin(f*x + e) + cos(f*x + e))*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e))) + sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^3*c^2*f*cos(f*x + e)*sin(f*x + e) + a^3*c^2*f*cos(f*x + e))]","A",0
64,1,262,0,1.077320," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} \cos\left(f x + e\right)^{3} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) + 2 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{4 \, a^{3} c^{3} f \cos\left(f x + e\right)^{3}}, -\frac{\sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) \cos\left(f x + e\right)^{3} - \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{2 \, a^{3} c^{3} f \cos\left(f x + e\right)^{3}}\right]"," ",0,"[1/4*(sqrt(a*c)*cos(f*x + e)^3*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) + 2*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/(a^3*c^3*f*cos(f*x + e)^3), -1/2*(sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e)))*cos(f*x + e)^3 - sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/(a^3*c^3*f*cos(f*x + e)^3)]","A",0
65,0,0,0,1.017692," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
66,0,0,0,0.838429," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, c^{3} \cos\left(f x + e\right)^{4} - 4 \, c^{3} \cos\left(f x + e\right)^{2} - {\left(c^{3} \cos\left(f x + e\right)^{4} - 4 \, c^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(3*c^3*cos(f*x + e)^4 - 4*c^3*cos(f*x + e)^2 - (c^3*cos(f*x + e)^4 - 4*c^3*cos(f*x + e)^2)*sin(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
67,0,0,0,0.954813," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} \cos\left(f x + e\right)^{4} + 2 \, c^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - 2 \, c^{2} \cos\left(f x + e\right)^{2}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(c^2*cos(f*x + e)^4 + 2*c^2*cos(f*x + e)^2*sin(f*x + e) - 2*c^2*cos(f*x + e)^2)*(a*sin(f*x + e) + a)^m, x)","F",0
68,0,0,0,0.899708," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - c \cos\left(f x + e\right)^{2}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(c*cos(f*x + e)^2*sin(f*x + e) - c*cos(f*x + e)^2)*(a*sin(f*x + e) + a)^m, x)","F",0
69,0,0,0,0.953904," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
70,0,0,0,0.934367," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c*sin(f*x + e) - c), x)","F",0
71,0,0,0,0.926868," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-(a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
72,0,0,0,0.729996," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
73,1,395,0,0.988697," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(8 \, c^{2} m^{3} + 60 \, c^{2} m^{2} + 142 \, c^{2} m + 105 \, c^{2}\right)} \cos\left(f x + e\right)^{5} - {\left(8 \, c^{2} m^{3} + 108 \, c^{2} m^{2} + 334 \, c^{2} m + 285 \, c^{2}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(8 \, c^{2} m^{3} + 84 \, c^{2} m^{2} + 334 \, c^{2} m + 339 \, c^{2}\right)} \cos\left(f x + e\right)^{3} - 384 \, c^{2} \cos\left(f x + e\right) - 96 \, {\left(2 \, c^{2} m - c^{2}\right)} \cos\left(f x + e\right)^{2} - 768 \, c^{2} + {\left({\left(8 \, c^{2} m^{3} + 60 \, c^{2} m^{2} + 142 \, c^{2} m + 105 \, c^{2}\right)} \cos\left(f x + e\right)^{4} + 2 \, {\left(8 \, c^{2} m^{3} + 84 \, c^{2} m^{2} + 238 \, c^{2} m + 195 \, c^{2}\right)} \cos\left(f x + e\right)^{3} - 384 \, c^{2} \cos\left(f x + e\right) - 96 \, {\left(2 \, c^{2} m + 3 \, c^{2}\right)} \cos\left(f x + e\right)^{2} - 768 \, c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{16 \, f m^{4} + 192 \, f m^{3} + 824 \, f m^{2} + 1488 \, f m + {\left(16 \, f m^{4} + 192 \, f m^{3} + 824 \, f m^{2} + 1488 \, f m + 945 \, f\right)} \cos\left(f x + e\right) - {\left(16 \, f m^{4} + 192 \, f m^{3} + 824 \, f m^{2} + 1488 \, f m + 945 \, f\right)} \sin\left(f x + e\right) + 945 \, f}"," ",0,"-2*((8*c^2*m^3 + 60*c^2*m^2 + 142*c^2*m + 105*c^2)*cos(f*x + e)^5 - (8*c^2*m^3 + 108*c^2*m^2 + 334*c^2*m + 285*c^2)*cos(f*x + e)^4 - 2*(8*c^2*m^3 + 84*c^2*m^2 + 334*c^2*m + 339*c^2)*cos(f*x + e)^3 - 384*c^2*cos(f*x + e) - 96*(2*c^2*m - c^2)*cos(f*x + e)^2 - 768*c^2 + ((8*c^2*m^3 + 60*c^2*m^2 + 142*c^2*m + 105*c^2)*cos(f*x + e)^4 + 2*(8*c^2*m^3 + 84*c^2*m^2 + 238*c^2*m + 195*c^2)*cos(f*x + e)^3 - 384*c^2*cos(f*x + e) - 96*(2*c^2*m + 3*c^2)*cos(f*x + e)^2 - 768*c^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(16*f*m^4 + 192*f*m^3 + 824*f*m^2 + 1488*f*m + (16*f*m^4 + 192*f*m^3 + 824*f*m^2 + 1488*f*m + 945*f)*cos(f*x + e) - (16*f*m^4 + 192*f*m^3 + 824*f*m^2 + 1488*f*m + 945*f)*sin(f*x + e) + 945*f)","A",0
74,1,243,0,0.952015," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(4 \, c m^{2} + 16 \, c m + 15 \, c\right)} \cos\left(f x + e\right)^{4} + {\left(4 \, c m^{2} + 32 \, c m + 39 \, c\right)} \cos\left(f x + e\right)^{3} + 8 \, {\left(2 \, c m - c\right)} \cos\left(f x + e\right)^{2} + 32 \, c \cos\left(f x + e\right) - {\left({\left(4 \, c m^{2} + 16 \, c m + 15 \, c\right)} \cos\left(f x + e\right)^{3} - 8 \, {\left(2 \, c m + 3 \, c\right)} \cos\left(f x + e\right)^{2} - 32 \, c \cos\left(f x + e\right) - 64 \, c\right)} \sin\left(f x + e\right) + 64 \, c\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{8 \, f m^{3} + 60 \, f m^{2} + 142 \, f m + {\left(8 \, f m^{3} + 60 \, f m^{2} + 142 \, f m + 105 \, f\right)} \cos\left(f x + e\right) - {\left(8 \, f m^{3} + 60 \, f m^{2} + 142 \, f m + 105 \, f\right)} \sin\left(f x + e\right) + 105 \, f}"," ",0,"2*((4*c*m^2 + 16*c*m + 15*c)*cos(f*x + e)^4 + (4*c*m^2 + 32*c*m + 39*c)*cos(f*x + e)^3 + 8*(2*c*m - c)*cos(f*x + e)^2 + 32*c*cos(f*x + e) - ((4*c*m^2 + 16*c*m + 15*c)*cos(f*x + e)^3 - 8*(2*c*m + 3*c)*cos(f*x + e)^2 - 32*c*cos(f*x + e) - 64*c)*sin(f*x + e) + 64*c)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(8*f*m^3 + 60*f*m^2 + 142*f*m + (8*f*m^3 + 60*f*m^2 + 142*f*m + 105*f)*cos(f*x + e) - (8*f*m^3 + 60*f*m^2 + 142*f*m + 105*f)*sin(f*x + e) + 105*f)","A",0
75,1,155,0,0.794392," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(2 \, m + 3\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, m - 1\right)} \cos\left(f x + e\right)^{2} + {\left({\left(2 \, m + 3\right)} \cos\left(f x + e\right)^{2} + 4 \, \cos\left(f x + e\right) + 8\right)} \sin\left(f x + e\right) + 4 \, \cos\left(f x + e\right) + 8\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{4 \, f m^{2} + 16 \, f m + {\left(4 \, f m^{2} + 16 \, f m + 15 \, f\right)} \cos\left(f x + e\right) - {\left(4 \, f m^{2} + 16 \, f m + 15 \, f\right)} \sin\left(f x + e\right) + 15 \, f}"," ",0,"2*((2*m + 3)*cos(f*x + e)^3 + (2*m - 1)*cos(f*x + e)^2 + ((2*m + 3)*cos(f*x + e)^2 + 4*cos(f*x + e) + 8)*sin(f*x + e) + 4*cos(f*x + e) + 8)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(4*f*m^2 + 16*f*m + (4*f*m^2 + 16*f*m + 15*f)*cos(f*x + e) - (4*f*m^2 + 16*f*m + 15*f)*sin(f*x + e) + 15*f)","A",0
76,1,108,0,0.834022," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{2 \, c f m + 3 \, c f + {\left(2 \, c f m + 3 \, c f\right)} \cos\left(f x + e\right) - {\left(2 \, c f m + 3 \, c f\right)} \sin\left(f x + e\right)}"," ",0,"-2*(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(2*c*f*m + 3*c*f + (2*c*f*m + 3*c*f)*cos(f*x + e) - (2*c*f*m + 3*c*f)*sin(f*x + e))","B",0
77,0,0,0,0.829617," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
78,0,0,0,0.948889," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
79,1,108,0,0.927331," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{2 \, c f m + 3 \, c f + {\left(2 \, c f m + 3 \, c f\right)} \cos\left(f x + e\right) - {\left(2 \, c f m + 3 \, c f\right)} \sin\left(f x + e\right)}"," ",0,"-2*(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(2*c*f*m + 3*c*f + (2*c*f*m + 3*c*f)*cos(f*x + e) - (2*c*f*m + 3*c*f)*sin(f*x + e))","B",0
80,1,108,0,0.871410," ","integrate(cos(f*x+e)^2*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2\right)} \sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{m}}{2 \, a f m + 3 \, a f + {\left(2 \, a f m + 3 \, a f\right)} \cos\left(f x + e\right) - {\left(2 \, a f m + 3 \, a f\right)} \sin\left(f x + e\right)}"," ",0,"-2*(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)*sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^m/(2*a*f*m + 3*a*f + (2*a*f*m + 3*a*f)*cos(f*x + e) - (2*a*f*m + 3*a*f)*sin(f*x + e))","B",0
81,1,105,0,0.954921," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-5-m),x, algorithm=""fricas"")","-\frac{{\left(2 \, \cos\left(f x + e\right)^{5} + 2 \, {\left(2 \, m + 5\right)} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - {\left(4 \, m^{2} + 20 \, m + 25\right)} \cos\left(f x + e\right)^{3}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 5}}{8 \, f m^{3} + 60 \, f m^{2} + 142 \, f m + 105 \, f}"," ",0,"-(2*cos(f*x + e)^5 + 2*(2*m + 5)*cos(f*x + e)^3*sin(f*x + e) - (4*m^2 + 20*m + 25)*cos(f*x + e)^3)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 5)/(8*f*m^3 + 60*f*m^2 + 142*f*m + 105*f)","A",0
82,1,76,0,0.977533," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-4-m),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(m + 2\right)} \cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)^{3} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 4}}{4 \, f m^{2} + 16 \, f m + 15 \, f}"," ",0,"(2*(m + 2)*cos(f*x + e)^3 - cos(f*x + e)^3*sin(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 4)/(4*f*m^2 + 16*f*m + 15*f)","A",0
83,1,48,0,0.932154," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""fricas"")","\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 3} \cos\left(f x + e\right)^{3}}{2 \, f m + 3 \, f}"," ",0,"(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3)*cos(f*x + e)^3/(2*f*m + 3*f)","A",0
84,0,0,0,0.673708," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2)*cos(f*x + e)^2, x)","F",0
85,0,0,0,0.719248," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 1} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1)*cos(f*x + e)^2, x)","F",0
86,0,0,0,1.007282," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{m}}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^m, x)","F",0
87,0,0,0,1.286908," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 1} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1)*cos(f*x + e)^2, x)","F",0
88,0,0,0,1.887710," ","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, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, c^{3} g \cos\left(f x + e\right)^{3} - 4 \, c^{3} g \cos\left(f x + e\right) - {\left(c^{3} g \cos\left(f x + e\right)^{3} - 4 \, c^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral(-(3*c^3*g*cos(f*x + e)^3 - 4*c^3*g*cos(f*x + e) - (c^3*g*cos(f*x + e)^3 - 4*c^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
89,0,0,0,0.806477," ","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, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} g \cos\left(f x + e\right)^{3} + 2 \, c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral(-(c^2*g*cos(f*x + e)^3 + 2*c^2*g*cos(f*x + e)*sin(f*x + e) - 2*c^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
90,0,0,0,0.937247," ","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, algorithm=""fricas"")","{\rm integral}\left(-{\left(c g \cos\left(f x + e\right) \sin\left(f x + e\right) - c g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral(-(c*g*cos(f*x + e)*sin(f*x + e) - c*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
91,0,0,0,0.928081," ","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, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e), x)","F",0
92,0,0,0,0.906719," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right)}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e)/(c*sin(f*x + e) - c), x)","F",0
93,0,0,0,0.969675," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
94,0,0,0,1.444394," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right)}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
95,0,0,0,0.938478," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right)}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
96,0,0,0,1.024312," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right)}{5 \, c^{5} \cos\left(f x + e\right)^{4} - 20 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5} - {\left(c^{5} \cos\left(f x + e\right)^{4} - 12 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e)/(5*c^5*cos(f*x + e)^4 - 20*c^5*cos(f*x + e)^2 + 16*c^5 - (c^5*cos(f*x + e)^4 - 12*c^5*cos(f*x + e)^2 + 16*c^5)*sin(f*x + e)), x)","F",0
97,0,0,0,0.951485," ","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, algorithm=""fricas"")","{\rm integral}\left(-{\left(a c^{2} g \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - a c^{2} g \cos\left(f x + e\right)^{3}\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral(-(a*c^2*g*cos(f*x + e)^3*sin(f*x + e) - a*c^2*g*cos(f*x + e)^3)*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
98,0,0,0,1.054426," ","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, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} a c g \cos\left(f x + e\right)^{3}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*a*c*g*cos(f*x + e)^3, x)","F",0
99,0,0,0,1.173505," ","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, algorithm=""fricas"")","{\rm integral}\left({\left(a g \cos\left(f x + e\right) \sin\left(f x + e\right) + a g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral((a*g*cos(f*x + e)*sin(f*x + e) + a*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
100,0,0,0,0.941062," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a g \cos\left(f x + e\right) \sin\left(f x + e\right) + a g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(a*g*cos(f*x + e)*sin(f*x + e) + a*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*sin(f*x + e) - c), x)","F",0
101,0,0,0,0.878835," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a g \cos\left(f x + e\right) \sin\left(f x + e\right) + a g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-(a*g*cos(f*x + e)*sin(f*x + e) + a*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
102,0,0,0,0.640428," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a g \cos\left(f x + e\right) \sin\left(f x + e\right) + a g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a*g*cos(f*x + e)*sin(f*x + e) + a*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
103,0,0,0,0.903316," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a g \cos\left(f x + e\right) \sin\left(f x + e\right) + a g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((a*g*cos(f*x + e)*sin(f*x + e) + a*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
104,0,0,0,0.930558," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a g \cos\left(f x + e\right) \sin\left(f x + e\right) + a g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{5 \, c^{5} \cos\left(f x + e\right)^{4} - 20 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5} - {\left(c^{5} \cos\left(f x + e\right)^{4} - 12 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((a*g*cos(f*x + e)*sin(f*x + e) + a*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^5*cos(f*x + e)^4 - 20*c^5*cos(f*x + e)^2 + 16*c^5 - (c^5*cos(f*x + e)^4 - 12*c^5*cos(f*x + e)^2 + 16*c^5)*sin(f*x + e)), x)","F",0
105,0,0,0,1.056561," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a g \cos\left(f x + e\right) \sin\left(f x + e\right) + a g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{6} \cos\left(f x + e\right)^{6} - 18 \, c^{6} \cos\left(f x + e\right)^{4} + 48 \, c^{6} \cos\left(f x + e\right)^{2} - 32 \, c^{6} + 2 \, {\left(3 \, c^{6} \cos\left(f x + e\right)^{4} - 16 \, c^{6} \cos\left(f x + e\right)^{2} + 16 \, c^{6}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a*g*cos(f*x + e)*sin(f*x + e) + a*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^6*cos(f*x + e)^6 - 18*c^6*cos(f*x + e)^4 + 48*c^6*cos(f*x + e)^2 - 32*c^6 + 2*(3*c^6*cos(f*x + e)^4 - 16*c^6*cos(f*x + e)^2 + 16*c^6)*sin(f*x + e)), x)","F",0
106,0,0,0,0.997099," ","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, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} a^{2} c^{2} g \cos\left(f x + e\right)^{5}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*a^2*c^2*g*cos(f*x + e)^5, x)","F",0
107,0,0,0,0.952517," ","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, algorithm=""fricas"")","{\rm integral}\left({\left(a^{2} c g \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + a^{2} c g \cos\left(f x + e\right)^{3}\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral((a^2*c*g*cos(f*x + e)^3*sin(f*x + e) + a^2*c*g*cos(f*x + e)^3)*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
108,0,0,0,0.777833," ","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, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} g \cos\left(f x + e\right)^{3} - 2 \, a^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral(-(a^2*g*cos(f*x + e)^3 - 2*a^2*g*cos(f*x + e)*sin(f*x + e) - 2*a^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
109,0,0,0,1.841121," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} g \cos\left(f x + e\right)^{3} - 2 \, a^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral((a^2*g*cos(f*x + e)^3 - 2*a^2*g*cos(f*x + e)*sin(f*x + e) - 2*a^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*sin(f*x + e) - c), x)","F",0
110,0,0,0,0.875834," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} g \cos\left(f x + e\right)^{3} - 2 \, a^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral((a^2*g*cos(f*x + e)^3 - 2*a^2*g*cos(f*x + e)*sin(f*x + e) - 2*a^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
111,0,0,0,0.882749," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} g \cos\left(f x + e\right)^{3} - 2 \, a^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((a^2*g*cos(f*x + e)^3 - 2*a^2*g*cos(f*x + e)*sin(f*x + e) - 2*a^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
112,0,0,0,0.899138," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} g \cos\left(f x + e\right)^{3} - 2 \, a^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a^2*g*cos(f*x + e)^3 - 2*a^2*g*cos(f*x + e)*sin(f*x + e) - 2*a^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
113,0,0,0,2.101600," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a^{2} g \cos\left(f x + e\right)^{3} - 2 \, a^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{5 \, c^{5} \cos\left(f x + e\right)^{4} - 20 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5} - {\left(c^{5} \cos\left(f x + e\right)^{4} - 12 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a^2*g*cos(f*x + e)^3 - 2*a^2*g*cos(f*x + e)*sin(f*x + e) - 2*a^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^5*cos(f*x + e)^4 - 20*c^5*cos(f*x + e)^2 + 16*c^5 - (c^5*cos(f*x + e)^4 - 12*c^5*cos(f*x + e)^2 + 16*c^5)*sin(f*x + e)), x)","F",0
114,0,0,0,1.255747," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} g \cos\left(f x + e\right)^{3} - 2 \, a^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{6} \cos\left(f x + e\right)^{6} - 18 \, c^{6} \cos\left(f x + e\right)^{4} + 48 \, c^{6} \cos\left(f x + e\right)^{2} - 32 \, c^{6} + 2 \, {\left(3 \, c^{6} \cos\left(f x + e\right)^{4} - 16 \, c^{6} \cos\left(f x + e\right)^{2} + 16 \, c^{6}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((a^2*g*cos(f*x + e)^3 - 2*a^2*g*cos(f*x + e)*sin(f*x + e) - 2*a^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^6*cos(f*x + e)^6 - 18*c^6*cos(f*x + e)^4 + 48*c^6*cos(f*x + e)^2 - 32*c^6 + 2*(3*c^6*cos(f*x + e)^4 - 16*c^6*cos(f*x + e)^2 + 16*c^6)*sin(f*x + e)), x)","F",0
115,0,0,0,1.292569," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a^{2} g \cos\left(f x + e\right)^{3} - 2 \, a^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{7 \, c^{7} \cos\left(f x + e\right)^{6} - 56 \, c^{7} \cos\left(f x + e\right)^{4} + 112 \, c^{7} \cos\left(f x + e\right)^{2} - 64 \, c^{7} - {\left(c^{7} \cos\left(f x + e\right)^{6} - 24 \, c^{7} \cos\left(f x + e\right)^{4} + 80 \, c^{7} \cos\left(f x + e\right)^{2} - 64 \, c^{7}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((a^2*g*cos(f*x + e)^3 - 2*a^2*g*cos(f*x + e)*sin(f*x + e) - 2*a^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(7*c^7*cos(f*x + e)^6 - 56*c^7*cos(f*x + e)^4 + 112*c^7*cos(f*x + e)^2 - 64*c^7 - (c^7*cos(f*x + e)^6 - 24*c^7*cos(f*x + e)^4 + 80*c^7*cos(f*x + e)^2 - 64*c^7)*sin(f*x + e)), x)","F",0
116,0,0,0,1.445106," ","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, algorithm=""fricas"")","{\rm integral}\left({\left(a^{3} c^{2} g \cos\left(f x + e\right)^{5} \sin\left(f x + e\right) + a^{3} c^{2} g \cos\left(f x + e\right)^{5}\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral((a^3*c^2*g*cos(f*x + e)^5*sin(f*x + e) + a^3*c^2*g*cos(f*x + e)^5)*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
117,0,0,0,1.505772," ","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, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{3} c g \cos\left(f x + e\right)^{5} - 2 \, a^{3} c g \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - 2 \, a^{3} c g \cos\left(f x + e\right)^{3}\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral(-(a^3*c*g*cos(f*x + e)^5 - 2*a^3*c*g*cos(f*x + e)^3*sin(f*x + e) - 2*a^3*c*g*cos(f*x + e)^3)*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
118,0,0,0,1.278145," ","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, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral(-(3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
119,0,0,0,0.875668," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral((3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*sin(f*x + e) - c), x)","F",0
120,0,0,0,1.511758," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral((3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
121,0,0,0,1.501348," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
122,0,0,0,1.107065," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
123,0,0,0,1.520793," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{5 \, c^{5} \cos\left(f x + e\right)^{4} - 20 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5} - {\left(c^{5} \cos\left(f x + e\right)^{4} - 12 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^5*cos(f*x + e)^4 - 20*c^5*cos(f*x + e)^2 + 16*c^5 - (c^5*cos(f*x + e)^4 - 12*c^5*cos(f*x + e)^2 + 16*c^5)*sin(f*x + e)), x)","F",0
124,0,0,0,1.588684," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{6} \cos\left(f x + e\right)^{6} - 18 \, c^{6} \cos\left(f x + e\right)^{4} + 48 \, c^{6} \cos\left(f x + e\right)^{2} - 32 \, c^{6} + 2 \, {\left(3 \, c^{6} \cos\left(f x + e\right)^{4} - 16 \, c^{6} \cos\left(f x + e\right)^{2} + 16 \, c^{6}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^6*cos(f*x + e)^6 - 18*c^6*cos(f*x + e)^4 + 48*c^6*cos(f*x + e)^2 - 32*c^6 + 2*(3*c^6*cos(f*x + e)^4 - 16*c^6*cos(f*x + e)^2 + 16*c^6)*sin(f*x + e)), x)","F",0
125,0,0,0,1.845086," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{7 \, c^{7} \cos\left(f x + e\right)^{6} - 56 \, c^{7} \cos\left(f x + e\right)^{4} + 112 \, c^{7} \cos\left(f x + e\right)^{2} - 64 \, c^{7} - {\left(c^{7} \cos\left(f x + e\right)^{6} - 24 \, c^{7} \cos\left(f x + e\right)^{4} + 80 \, c^{7} \cos\left(f x + e\right)^{2} - 64 \, c^{7}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(7*c^7*cos(f*x + e)^6 - 56*c^7*cos(f*x + e)^4 + 112*c^7*cos(f*x + e)^2 - 64*c^7 - (c^7*cos(f*x + e)^6 - 24*c^7*cos(f*x + e)^4 + 80*c^7*cos(f*x + e)^2 - 64*c^7)*sin(f*x + e)), x)","F",0
126,0,0,0,0.880407," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(3 \, a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right) + {\left(a^{3} g \cos\left(f x + e\right)^{3} - 4 \, a^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{8} \cos\left(f x + e\right)^{8} - 32 \, c^{8} \cos\left(f x + e\right)^{6} + 160 \, c^{8} \cos\left(f x + e\right)^{4} - 256 \, c^{8} \cos\left(f x + e\right)^{2} + 128 \, c^{8} + 8 \, {\left(c^{8} \cos\left(f x + e\right)^{6} - 10 \, c^{8} \cos\left(f x + e\right)^{4} + 24 \, c^{8} \cos\left(f x + e\right)^{2} - 16 \, c^{8}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(3*a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e) + (a^3*g*cos(f*x + e)^3 - 4*a^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^8*cos(f*x + e)^8 - 32*c^8*cos(f*x + e)^6 + 160*c^8*cos(f*x + e)^4 - 256*c^8*cos(f*x + e)^2 + 128*c^8 + 8*(c^8*cos(f*x + e)^6 - 10*c^8*cos(f*x + e)^4 + 24*c^8*cos(f*x + e)^2 - 16*c^8)*sin(f*x + e)), x)","F",0
127,0,0,0,1.374525," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{2} g \cos\left(f x + e\right)^{3} + 2 \, c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a}}, x\right)"," ",0,"integral(-(c^2*g*cos(f*x + e)^3 + 2*c^2*g*cos(f*x + e)*sin(f*x + e) - 2*c^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
128,0,0,0,1.418186," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c g \cos\left(f x + e\right) \sin\left(f x + e\right) - c g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a}}, x\right)"," ",0,"integral(-(c*g*cos(f*x + e)*sin(f*x + e) - c*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
129,0,0,0,1.449876," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right)}{\sqrt{a \sin\left(f x + e\right) + a}}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e)/sqrt(a*sin(f*x + e) + a), x)","F",0
130,0,0,0,1.318400," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a c \cos\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a*c*cos(f*x + e)), x)","F",0
131,0,0,0,1.244990," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a c^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - a c^{2} \cos\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a*c^2*cos(f*x + e)*sin(f*x + e) - a*c^2*cos(f*x + e)), x)","F",0
132,0,0,0,1.371505," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a c^{3} \cos\left(f x + e\right)^{3} + 2 \, a c^{3} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a c^{3} \cos\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a*c^3*cos(f*x + e)^3 + 2*a*c^3*cos(f*x + e)*sin(f*x + e) - 2*a*c^3*cos(f*x + e)), x)","F",0
133,0,0,0,1.418308," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{3 \, a c^{4} \cos\left(f x + e\right)^{3} - 4 \, a c^{4} \cos\left(f x + e\right) - {\left(a c^{4} \cos\left(f x + e\right)^{3} - 4 \, a c^{4} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(3*a*c^4*cos(f*x + e)^3 - 4*a*c^4*cos(f*x + e) - (a*c^4*cos(f*x + e)^3 - 4*a*c^4*cos(f*x + e))*sin(f*x + e)), x)","F",0
134,0,0,0,1.427621," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, c^{3} g \cos\left(f x + e\right)^{3} - 4 \, c^{3} g \cos\left(f x + e\right) - {\left(c^{3} g \cos\left(f x + e\right)^{3} - 4 \, c^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral((3*c^3*g*cos(f*x + e)^3 - 4*c^3*g*cos(f*x + e) - (c^3*g*cos(f*x + e)^3 - 4*c^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
135,0,0,0,1.289020," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} g \cos\left(f x + e\right)^{3} + 2 \, c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral((c^2*g*cos(f*x + e)^3 + 2*c^2*g*cos(f*x + e)*sin(f*x + e) - 2*c^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
136,0,0,0,1.217986," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c g \cos\left(f x + e\right) \sin\left(f x + e\right) - c g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral((c*g*cos(f*x + e)*sin(f*x + e) - c*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
137,0,0,0,1.248516," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right)}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
138,0,0,0,1.269872," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a^{2} c \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} c \cos\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a^2*c*cos(f*x + e)*sin(f*x + e) + a^2*c*cos(f*x + e)), x)","F",0
139,0,0,0,1.419430," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a^{2} c^{2} \cos\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a^2*c^2*cos(f*x + e)^3), x)","F",0
140,0,0,0,1.316527," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a^{2} c^{3} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - a^{2} c^{3} \cos\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a^2*c^3*cos(f*x + e)^3*sin(f*x + e) - a^2*c^3*cos(f*x + e)^3), x)","F",0
141,0,0,0,1.405342," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a^{2} c^{4} \cos\left(f x + e\right)^{5} + 2 \, a^{2} c^{4} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - 2 \, a^{2} c^{4} \cos\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a^2*c^4*cos(f*x + e)^5 + 2*a^2*c^4*cos(f*x + e)^3*sin(f*x + e) - 2*a^2*c^4*cos(f*x + e)^3), x)","F",0
142,0,0,0,1.488528," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(c^{4} g \cos\left(f x + e\right)^{5} - 8 \, c^{4} g \cos\left(f x + e\right)^{3} + 8 \, c^{4} g \cos\left(f x + e\right) + 4 \, {\left(c^{4} g \cos\left(f x + e\right)^{3} - 2 \, c^{4} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(c^4*g*cos(f*x + e)^5 - 8*c^4*g*cos(f*x + e)^3 + 8*c^4*g*cos(f*x + e) + 4*(c^4*g*cos(f*x + e)^3 - 2*c^4*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
143,0,0,0,1.361271," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3 \, c^{3} g \cos\left(f x + e\right)^{3} - 4 \, c^{3} g \cos\left(f x + e\right) - {\left(c^{3} g \cos\left(f x + e\right)^{3} - 4 \, c^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((3*c^3*g*cos(f*x + e)^3 - 4*c^3*g*cos(f*x + e) - (c^3*g*cos(f*x + e)^3 - 4*c^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
144,0,0,0,1.412755," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c^{2} g \cos\left(f x + e\right)^{3} + 2 \, c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((c^2*g*cos(f*x + e)^3 + 2*c^2*g*cos(f*x + e)*sin(f*x + e) - 2*c^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
145,0,0,0,1.427788," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c g \cos\left(f x + e\right) \sin\left(f x + e\right) - c g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((c*g*cos(f*x + e)*sin(f*x + e) - c*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
146,0,0,0,1.094755," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g \cos\left(f x + e\right)}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g*cos(f*x + e)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
147,0,0,0,1.344362," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a^{3} c \cos\left(f x + e\right)^{3} - 2 \, a^{3} c \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} c \cos\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a^3*c*cos(f*x + e)^3 - 2*a^3*c*cos(f*x + e)*sin(f*x + e) - 2*a^3*c*cos(f*x + e)), x)","F",0
148,0,0,0,1.359763," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a^{3} c^{2} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + a^{3} c^{2} \cos\left(f x + e\right)^{3}}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a^3*c^2*cos(f*x + e)^3*sin(f*x + e) + a^3*c^2*cos(f*x + e)^3), x)","F",0
149,0,0,0,1.215639," ","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, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a^{3} c^{3} \cos\left(f x + e\right)^{5}}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a^3*c^3*cos(f*x + e)^5), x)","F",0
150,0,0,0,1.385758," ","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, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} g}{a^{3} c^{4} \cos\left(f x + e\right)^{5} \sin\left(f x + e\right) - a^{3} c^{4} \cos\left(f x + e\right)^{5}}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*g/(a^3*c^4*cos(f*x + e)^5*sin(f*x + e) - a^3*c^4*cos(f*x + e)^5), x)","F",0
151,0,0,0,1.317594," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n*g*cos(f*x + e), x)","F",0
152,0,0,0,1.295730," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, c^{3} g \cos\left(f x + e\right)^{3} - 4 \, c^{3} g \cos\left(f x + e\right) - {\left(c^{3} g \cos\left(f x + e\right)^{3} - 4 \, c^{3} g \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(3*c^3*g*cos(f*x + e)^3 - 4*c^3*g*cos(f*x + e) - (c^3*g*cos(f*x + e)^3 - 4*c^3*g*cos(f*x + e))*sin(f*x + e))*sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
153,0,0,0,1.307870," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} g \cos\left(f x + e\right)^{3} + 2 \, c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(c^2*g*cos(f*x + e)^3 + 2*c^2*g*cos(f*x + e)*sin(f*x + e) - 2*c^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
154,0,0,0,0.641914," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c g \cos\left(f x + e\right) \sin\left(f x + e\right) - c g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(c*g*cos(f*x + e)*sin(f*x + e) - c*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
155,0,0,0,1.200804," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*g*cos(f*x + e), x)","F",0
156,0,0,0,1.266183," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right)}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*g*cos(f*x + e)/(c*sin(f*x + e) - c), x)","F",0
157,0,0,0,1.280917," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*g*cos(f*x + e)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
158,0,0,0,1.117195," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right)}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*g*cos(f*x + e)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
159,0,0,0,1.321719," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c^{2} g \cos\left(f x + e\right)^{3} + 2 \, c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c^{2} g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(c^2*g*cos(f*x + e)^3 + 2*c^2*g*cos(f*x + e)*sin(f*x + e) - 2*c^2*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
160,0,0,0,1.454585," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(c g \cos\left(f x + e\right) \sin\left(f x + e\right) - c g \cos\left(f x + e\right)\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(c*g*cos(f*x + e)*sin(f*x + e) - c*g*cos(f*x + e))*sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
161,0,0,0,1.303536," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m*g*cos(f*x + e), x)","F",0
162,0,0,0,1.331505," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right)}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m*g*cos(f*x + e)/(c*sin(f*x + e) - c), x)","F",0
163,0,0,0,1.169010," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right)}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m*g*cos(f*x + e)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
164,0,0,0,1.094845," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right)}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m*g*cos(f*x + e)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
165,0,0,0,1.263695," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right)}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m*g*cos(f*x + e)/(c*sin(f*x + e) - c), x)","F",0
166,0,0,0,1.285968," ","integrate((g*cos(f*x+e))^(3/2)*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{m} g \cos\left(f x + e\right)}{a \sin\left(f x + e\right) - a}, x\right)"," ",0,"integral(-sqrt(g*cos(f*x + e))*sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^m*g*cos(f*x + e)/(a*sin(f*x + e) - a), x)","F",0
167,0,0,0,1.312926," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 3} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3)*g*cos(f*x + e), x)","F",0
168,0,0,0,1.505493," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2)*g*cos(f*x + e), x)","F",0
169,0,0,0,1.478057," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 1} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1)*g*cos(f*x + e), x)","F",0
170,0,0,0,1.429180," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} g \cos\left(f x + e\right)}{{\left(-c \sin\left(f x + e\right) + c\right)}^{m}}, x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*g*cos(f*x + e)/(-c*sin(f*x + e) + c)^m, x)","F",0
171,0,0,0,1.344657," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 1} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1)*g*cos(f*x + e), x)","F",0
172,0,0,0,0.871757," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{g \cos\left(f x + e\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 2} g \cos\left(f x + e\right), x\right)"," ",0,"integral(sqrt(g*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 2)*g*cos(f*x + e), x)","F",0
173,0,0,0,1.156462," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(g \cos\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
174,1,30,0,1.041376," ","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, algorithm=""fricas"")","-\frac{a \left(\frac{a c}{g^{2}}\right)^{m - 1} \log\left(-\sin\left(f x + e\right) + 1\right)}{f g}"," ",0,"-a*(a*c/g^2)^(m - 1)*log(-sin(f*x + e) + 1)/(f*g)","A",0
175,1,651,0,1.060894," ","integrate((g*cos(f*x+e))^(5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","-\frac{{\left({\left(m^{2} - {\left(2 \, m - 7\right)} n + n^{2} - 7 \, m + 12\right)} \cos\left(f x + e\right)^{3} - {\left(m^{2} - {\left(2 \, m - 11\right)} n + n^{2} - 11 \, m + 24\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(m^{2} - {\left(2 \, m - 9\right)} n + n^{2} - 9 \, m + 22\right)} \cos\left(f x + e\right) - {\left({\left(m^{2} - {\left(2 \, m - 7\right)} n + n^{2} - 7 \, m + 12\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(m^{2} - {\left(2 \, m - 9\right)} n + n^{2} - 9 \, m + 18\right)} \cos\left(f x + e\right) - 8\right)} \sin\left(f x + e\right) - 8\right)} \left(g \cos\left(f x + e\right)\right)^{-2 \, m + 5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} e^{\left(2 \, n \log\left(g \cos\left(f x + e\right)\right) - n \log\left(a \sin\left(f x + e\right) + a\right) + n \log\left(\frac{a c}{g^{2}}\right)\right)}}{4 \, f m^{3} - 4 \, f n^{3} - {\left(f m^{3} - f n^{3} - 12 \, f m^{2} + 3 \, {\left(f m - 4 \, f\right)} n^{2} + 47 \, f m - {\left(3 \, f m^{2} - 24 \, f m + 47 \, f\right)} n - 60 \, f\right)} \cos\left(f x + e\right)^{3} - 48 \, f m^{2} + 12 \, {\left(f m - 4 \, f\right)} n^{2} - 3 \, {\left(f m^{3} - f n^{3} - 12 \, f m^{2} + 3 \, {\left(f m - 4 \, f\right)} n^{2} + 47 \, f m - {\left(3 \, f m^{2} - 24 \, f m + 47 \, f\right)} n - 60 \, f\right)} \cos\left(f x + e\right)^{2} + 188 \, f m - 4 \, {\left(3 \, f m^{2} - 24 \, f m + 47 \, f\right)} n + 2 \, {\left(f m^{3} - f n^{3} - 12 \, f m^{2} + 3 \, {\left(f m - 4 \, f\right)} n^{2} + 47 \, f m - {\left(3 \, f m^{2} - 24 \, f m + 47 \, f\right)} n - 60 \, f\right)} \cos\left(f x + e\right) + {\left(4 \, f m^{3} - 4 \, f n^{3} - 48 \, f m^{2} + 12 \, {\left(f m - 4 \, f\right)} n^{2} - {\left(f m^{3} - f n^{3} - 12 \, f m^{2} + 3 \, {\left(f m - 4 \, f\right)} n^{2} + 47 \, f m - {\left(3 \, f m^{2} - 24 \, f m + 47 \, f\right)} n - 60 \, f\right)} \cos\left(f x + e\right)^{2} + 188 \, f m - 4 \, {\left(3 \, f m^{2} - 24 \, f m + 47 \, f\right)} n + 2 \, {\left(f m^{3} - f n^{3} - 12 \, f m^{2} + 3 \, {\left(f m - 4 \, f\right)} n^{2} + 47 \, f m - {\left(3 \, f m^{2} - 24 \, f m + 47 \, f\right)} n - 60 \, f\right)} \cos\left(f x + e\right) - 240 \, f\right)} \sin\left(f x + e\right) - 240 \, f}"," ",0,"-((m^2 - (2*m - 7)*n + n^2 - 7*m + 12)*cos(f*x + e)^3 - (m^2 - (2*m - 11)*n + n^2 - 11*m + 24)*cos(f*x + e)^2 - 2*(m^2 - (2*m - 9)*n + n^2 - 9*m + 22)*cos(f*x + e) - ((m^2 - (2*m - 7)*n + n^2 - 7*m + 12)*cos(f*x + e)^2 + 2*(m^2 - (2*m - 9)*n + n^2 - 9*m + 18)*cos(f*x + e) - 8)*sin(f*x + e) - 8)*(g*cos(f*x + e))^(-2*m + 5)*(a*sin(f*x + e) + a)^m*e^(2*n*log(g*cos(f*x + e)) - n*log(a*sin(f*x + e) + a) + n*log(a*c/g^2))/(4*f*m^3 - 4*f*n^3 - (f*m^3 - f*n^3 - 12*f*m^2 + 3*(f*m - 4*f)*n^2 + 47*f*m - (3*f*m^2 - 24*f*m + 47*f)*n - 60*f)*cos(f*x + e)^3 - 48*f*m^2 + 12*(f*m - 4*f)*n^2 - 3*(f*m^3 - f*n^3 - 12*f*m^2 + 3*(f*m - 4*f)*n^2 + 47*f*m - (3*f*m^2 - 24*f*m + 47*f)*n - 60*f)*cos(f*x + e)^2 + 188*f*m - 4*(3*f*m^2 - 24*f*m + 47*f)*n + 2*(f*m^3 - f*n^3 - 12*f*m^2 + 3*(f*m - 4*f)*n^2 + 47*f*m - (3*f*m^2 - 24*f*m + 47*f)*n - 60*f)*cos(f*x + e) + (4*f*m^3 - 4*f*n^3 - 48*f*m^2 + 12*(f*m - 4*f)*n^2 - (f*m^3 - f*n^3 - 12*f*m^2 + 3*(f*m - 4*f)*n^2 + 47*f*m - (3*f*m^2 - 24*f*m + 47*f)*n - 60*f)*cos(f*x + e)^2 + 188*f*m - 4*(3*f*m^2 - 24*f*m + 47*f)*n + 2*(f*m^3 - f*n^3 - 12*f*m^2 + 3*(f*m - 4*f)*n^2 + 47*f*m - (3*f*m^2 - 24*f*m + 47*f)*n - 60*f)*cos(f*x + e) - 240*f)*sin(f*x + e) - 240*f)","B",0
176,1,298,0,1.233280," ","integrate((g*cos(f*x+e))^(3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left({\left(m - n - 2\right)} \cos\left(f x + e\right)^{2} + {\left(m - n - 4\right)} \cos\left(f x + e\right) + {\left({\left(m - n - 2\right)} \cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - 2\right)} \left(g \cos\left(f x + e\right)\right)^{-2 \, m + 3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} e^{\left(2 \, n \log\left(g \cos\left(f x + e\right)\right) - n \log\left(a \sin\left(f x + e\right) + a\right) + n \log\left(\frac{a c}{g^{2}}\right)\right)}}{2 \, f m^{2} + 2 \, f n^{2} - {\left(f m^{2} + f n^{2} - 5 \, f m - {\left(2 \, f m - 5 \, f\right)} n + 6 \, f\right)} \cos\left(f x + e\right)^{2} - 10 \, f m - 2 \, {\left(2 \, f m - 5 \, f\right)} n + {\left(f m^{2} + f n^{2} - 5 \, f m - {\left(2 \, f m - 5 \, f\right)} n + 6 \, f\right)} \cos\left(f x + e\right) + {\left(2 \, f m^{2} + 2 \, f n^{2} - 10 \, f m - 2 \, {\left(2 \, f m - 5 \, f\right)} n + {\left(f m^{2} + f n^{2} - 5 \, f m - {\left(2 \, f m - 5 \, f\right)} n + 6 \, f\right)} \cos\left(f x + e\right) + 12 \, f\right)} \sin\left(f x + e\right) + 12 \, f}"," ",0,"((m - n - 2)*cos(f*x + e)^2 + (m - n - 4)*cos(f*x + e) + ((m - n - 2)*cos(f*x + e) + 2)*sin(f*x + e) - 2)*(g*cos(f*x + e))^(-2*m + 3)*(a*sin(f*x + e) + a)^m*e^(2*n*log(g*cos(f*x + e)) - n*log(a*sin(f*x + e) + a) + n*log(a*c/g^2))/(2*f*m^2 + 2*f*n^2 - (f*m^2 + f*n^2 - 5*f*m - (2*f*m - 5*f)*n + 6*f)*cos(f*x + e)^2 - 10*f*m - 2*(2*f*m - 5*f)*n + (f*m^2 + f*n^2 - 5*f*m - (2*f*m - 5*f)*n + 6*f)*cos(f*x + e) + (2*f*m^2 + 2*f*n^2 - 10*f*m - 2*(2*f*m - 5*f)*n + (f*m^2 + f*n^2 - 5*f*m - (2*f*m - 5*f)*n + 6*f)*cos(f*x + e) + 12*f)*sin(f*x + e) + 12*f)","B",0
177,1,129,0,1.278681," ","integrate((g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","\frac{\left(g \cos\left(f x + e\right)\right)^{-2 \, m + 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} e^{\left(2 \, n \log\left(g \cos\left(f x + e\right)\right) - n \log\left(a \sin\left(f x + e\right) + a\right) + n \log\left(\frac{a c}{g^{2}}\right)\right)}}{f m - f n + {\left(f m - f n - f\right)} \cos\left(f x + e\right) + {\left(f m - f n - f\right)} \sin\left(f x + e\right) - f}"," ",0,"(g*cos(f*x + e))^(-2*m + 1)*(a*sin(f*x + e) + a)^m*(cos(f*x + e) - sin(f*x + e) + 1)*e^(2*n*log(g*cos(f*x + e)) - n*log(a*sin(f*x + e) + a) + n*log(a*c/g^2))/(f*m - f*n + (f*m - f*n - f)*cos(f*x + e) + (f*m - f*n - f)*sin(f*x + e) - f)","B",0
178,0,0,0,1.044823," ","integrate((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(g \cos\left(f x + e\right)\right)^{-2 \, m - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((g*cos(f*x + e))^(-2*m - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
179,0,0,0,1.266212," ","integrate((g*cos(f*x+e))^(-3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(g \cos\left(f x + e\right)\right)^{-2 \, m - 3} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((g*cos(f*x + e))^(-2*m - 3)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
180,0,0,0,1.145137," ","integrate((g*cos(f*x+e))^(-5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(g \cos\left(f x + e\right)\right)^{-2 \, m - 5} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((g*cos(f*x + e))^(-2*m - 5)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
181,1,48,0,1.155896," ","integrate((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^m,x, algorithm=""fricas"")","\frac{\left(\frac{a c}{g^{2}}\right)^{m} \log\left(\sin\left(f x + e\right) + 1\right) - \left(\frac{a c}{g^{2}}\right)^{m} \log\left(-\sin\left(f x + e\right) + 1\right)}{2 \, f g}"," ",0,"1/2*((a*c/g^2)^m*log(sin(f*x + e) + 1) - (a*c/g^2)^m*log(-sin(f*x + e) + 1))/(f*g)","A",0
182,0,0,0,1.244553," ","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, algorithm=""fricas"")","{\rm integral}\left(\left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n + 3}, x\right)"," ",0,"integral((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n + 3), x)","F",0
183,0,0,0,1.008123," ","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, algorithm=""fricas"")","{\rm integral}\left(\left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n + 2}, x\right)"," ",0,"integral((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n + 2), x)","F",0
184,0,0,0,1.393670," ","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, algorithm=""fricas"")","{\rm integral}\left(\left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n + 1}, x\right)"," ",0,"integral((g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(n + 1), x)","F",0
185,1,83,0,1.515371," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","\frac{\left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right) e^{\left(2 \, n \log\left(g \cos\left(f x + e\right)\right) - n \log\left(a \sin\left(f x + e\right) + a\right) + n \log\left(\frac{a c}{g^{2}}\right)\right)}}{f m - f n}"," ",0,"(g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*cos(f*x + e)*e^(2*n*log(g*cos(f*x + e)) - n*log(a*sin(f*x + e) + a) + n*log(a*c/g^2))/(f*m - f*n)","A",0
186,1,126,0,1.416698," ","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, algorithm=""fricas"")","\frac{{\left({\left(m - n + 1\right)} \cos\left(f x + e\right) - \cos\left(f x + e\right) \sin\left(f x + e\right)\right)} \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} e^{\left(2 \, {\left(n - 1\right)} \log\left(g \cos\left(f x + e\right)\right) - {\left(n - 1\right)} \log\left(a \sin\left(f x + e\right) + a\right) + {\left(n - 1\right)} \log\left(\frac{a c}{g^{2}}\right)\right)}}{f m^{2} + f n^{2} + 2 \, f m - 2 \, {\left(f m + f\right)} n}"," ",0,"((m - n + 1)*cos(f*x + e) - cos(f*x + e)*sin(f*x + e))*(g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*e^(2*(n - 1)*log(g*cos(f*x + e)) - (n - 1)*log(a*sin(f*x + e) + a) + (n - 1)*log(a*c/g^2))/(f*m^2 + f*n^2 + 2*f*m - 2*(f*m + f)*n)","A",0
187,1,183,0,1.414100," ","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, algorithm=""fricas"")","-\frac{{\left(2 \, \cos\left(f x + e\right)^{3} + 2 \, {\left(m - n + 2\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(m^{2} - 2 \, {\left(m + 2\right)} n + n^{2} + 4 \, m + 4\right)} \cos\left(f x + e\right)\right)} \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} e^{\left(2 \, {\left(n - 2\right)} \log\left(g \cos\left(f x + e\right)\right) - {\left(n - 2\right)} \log\left(a \sin\left(f x + e\right) + a\right) + {\left(n - 2\right)} \log\left(\frac{a c}{g^{2}}\right)\right)}}{f m^{3} - f n^{3} + 6 \, f m^{2} + 3 \, {\left(f m + 2 \, f\right)} n^{2} + 8 \, f m - {\left(3 \, f m^{2} + 12 \, f m + 8 \, f\right)} n}"," ",0,"-(2*cos(f*x + e)^3 + 2*(m - n + 2)*cos(f*x + e)*sin(f*x + e) - (m^2 - 2*(m + 2)*n + n^2 + 4*m + 4)*cos(f*x + e))*(g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*e^(2*(n - 2)*log(g*cos(f*x + e)) - (n - 2)*log(a*sin(f*x + e) + a) + (n - 2)*log(a*c/g^2))/(f*m^3 - f*n^3 + 6*f*m^2 + 3*(f*m + 2*f)*n^2 + 8*f*m - (3*f*m^2 + 12*f*m + 8*f)*n)","A",0
188,1,264,0,1.521905," ","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, algorithm=""fricas"")","-\frac{{\left(6 \, {\left(m - n + 3\right)} \cos\left(f x + e\right)^{3} - {\left(m^{3} + 3 \, {\left(m + 3\right)} n^{2} - n^{3} + 9 \, m^{2} - {\left(3 \, m^{2} + 18 \, m + 26\right)} n + 26 \, m + 24\right)} \cos\left(f x + e\right) - 3 \, {\left(2 \, \cos\left(f x + e\right)^{3} - {\left(m^{2} - 2 \, {\left(m + 3\right)} n + n^{2} + 6 \, m + 8\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(g \cos\left(f x + e\right)\right)^{-m - n - 1} {\left(a \sin\left(f x + e\right) + a\right)}^{m} e^{\left(2 \, {\left(n - 3\right)} \log\left(g \cos\left(f x + e\right)\right) - {\left(n - 3\right)} \log\left(a \sin\left(f x + e\right) + a\right) + {\left(n - 3\right)} \log\left(\frac{a c}{g^{2}}\right)\right)}}{f m^{4} + f n^{4} + 12 \, f m^{3} - 4 \, {\left(f m + 3 \, f\right)} n^{3} + 44 \, f m^{2} + 2 \, {\left(3 \, f m^{2} + 18 \, f m + 22 \, f\right)} n^{2} + 48 \, f m - 4 \, {\left(f m^{3} + 9 \, f m^{2} + 22 \, f m + 12 \, f\right)} n}"," ",0,"-(6*(m - n + 3)*cos(f*x + e)^3 - (m^3 + 3*(m + 3)*n^2 - n^3 + 9*m^2 - (3*m^2 + 18*m + 26)*n + 26*m + 24)*cos(f*x + e) - 3*(2*cos(f*x + e)^3 - (m^2 - 2*(m + 3)*n + n^2 + 6*m + 8)*cos(f*x + e))*sin(f*x + e))*(g*cos(f*x + e))^(-m - n - 1)*(a*sin(f*x + e) + a)^m*e^(2*(n - 3)*log(g*cos(f*x + e)) - (n - 3)*log(a*sin(f*x + e) + a) + (n - 3)*log(a*c/g^2))/(f*m^4 + f*n^4 + 12*f*m^3 - 4*(f*m + 3*f)*n^3 + 44*f*m^2 + 2*(3*f*m^2 + 18*f*m + 22*f)*n^2 + 48*f*m - 4*(f*m^3 + 9*f*m^2 + 22*f*m + 12*f)*n)","A",0
189,0,0,0,1.190778," ","integrate((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(g \sec\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
190,1,50,0,1.292096," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right)^{4} - 6 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*a*cos(d*x + c)^4 - 6*a*cos(d*x + c)^2 - 4*(a*cos(d*x + c)^2 - a)*sin(d*x + c))/d","A",0
191,1,39,0,1.242120," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a \cos\left(d x + c\right)^{2} + 2 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(3*a*cos(d*x + c)^2 + 2*(a*cos(d*x + c)^2 - a)*sin(d*x + c))/d","A",0
192,1,24,0,0.748332," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + a \sin\left(d x + c\right)}{d}"," ",0,"(a*log(1/2*sin(d*x + c)) + a*sin(d*x + c))/d","A",0
193,1,33,0,1.762720," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - a}{d \sin\left(d x + c\right)}"," ",0,"(a*log(1/2*sin(d*x + c))*sin(d*x + c) - a)/(d*sin(d*x + c))","A",0
194,1,29,0,1.358900," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \sin\left(d x + c\right) + a}{2 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/2*(2*a*sin(d*x + c) + a)/(d*cos(d*x + c)^2 - d)","A",0
195,1,39,0,1.061972," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \sin\left(d x + c\right) + 2 \, a}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/6*(3*a*sin(d*x + c) + 2*a)/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
196,1,40,0,1.238683," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a \sin\left(d x + c\right) + 3 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/12*(4*a*sin(d*x + c) + 3*a)/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
197,1,72,0,1.328971," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{15 \, a^{2} \cos\left(d x + c\right)^{4} - 30 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{4} - 11 \, a^{2} \cos\left(d x + c\right)^{2} + 8 \, a^{2}\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(15*a^2*cos(d*x + c)^4 - 30*a^2*cos(d*x + c)^2 + 2*(3*a^2*cos(d*x + c)^4 - 11*a^2*cos(d*x + c)^2 + 8*a^2)*sin(d*x + c))/d","A",0
198,1,58,0,1.089289," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} \cos\left(d x + c\right)^{4} - 12 \, a^{2} \cos\left(d x + c\right)^{2} - 8 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*a^2*cos(d*x + c)^4 - 12*a^2*cos(d*x + c)^2 - 8*(a^2*cos(d*x + c)^2 - a^2)*sin(d*x + c))/d","A",0
199,1,43,0,1.419404," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"-1/2*(a^2*cos(d*x + c)^2 - 2*a^2*log(1/2*sin(d*x + c)) - 4*a^2*sin(d*x + c))/d","A",0
200,1,46,0,1.245478," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right)}{d \sin\left(d x + c\right)}"," ",0,"-(a^2*cos(d*x + c)^2 - 2*a^2*log(1/2*sin(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
201,1,62,0,1.020171," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} \sin\left(d x + c\right) + a^{2} + 2 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/2*(4*a^2*sin(d*x + c) + a^2 + 2*(a^2*cos(d*x + c)^2 - a^2)*log(1/2*sin(d*x + c)))/(d*cos(d*x + c)^2 - d)","A",0
202,1,56,0,1.190719," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, a^{2} \cos\left(d x + c\right)^{2} - 3 \, a^{2} \sin\left(d x + c\right) - 4 \, a^{2}}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*(3*a^2*cos(d*x + c)^2 - 3*a^2*sin(d*x + c) - 4*a^2)/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
203,1,57,0,1.179400," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, a^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2} \sin\left(d x + c\right) - 9 \, a^{2}}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/12*(6*a^2*cos(d*x + c)^2 - 8*a^2*sin(d*x + c) - 9*a^2)/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
204,1,65,0,1.226380," ","integrate(cos(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{10 \, a^{2} \cos\left(d x + c\right)^{2} - 15 \, a^{2} \sin\left(d x + c\right) - 16 \, a^{2}}{30 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/30*(10*a^2*cos(d*x + c)^2 - 15*a^2*sin(d*x + c) - 16*a^2)/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
205,1,70,0,1.192226," ","integrate(cos(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{15 \, a^{2} \cos\left(d x + c\right)^{2} - 24 \, a^{2} \sin\left(d x + c\right) - 25 \, a^{2}}{60 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/60*(15*a^2*cos(d*x + c)^2 - 24*a^2*sin(d*x + c) - 25*a^2)/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
206,1,98,0,1.151090," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{70 \, a^{3} \cos\left(d x + c\right)^{6} - 245 \, a^{3} \cos\left(d x + c\right)^{4} + 280 \, a^{3} \cos\left(d x + c\right)^{2} + 4 \, {\left(5 \, a^{3} \cos\left(d x + c\right)^{6} - 36 \, a^{3} \cos\left(d x + c\right)^{4} + 57 \, a^{3} \cos\left(d x + c\right)^{2} - 26 \, a^{3}\right)} \sin\left(d x + c\right)}{140 \, d}"," ",0,"-1/140*(70*a^3*cos(d*x + c)^6 - 245*a^3*cos(d*x + c)^4 + 280*a^3*cos(d*x + c)^2 + 4*(5*a^3*cos(d*x + c)^6 - 36*a^3*cos(d*x + c)^4 + 57*a^3*cos(d*x + c)^2 - 26*a^3)*sin(d*x + c))/d","A",0
207,1,85,0,1.203738," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{10 \, a^{3} \cos\left(d x + c\right)^{6} - 75 \, a^{3} \cos\left(d x + c\right)^{4} + 120 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, {\left(9 \, a^{3} \cos\left(d x + c\right)^{4} - 23 \, a^{3} \cos\left(d x + c\right)^{2} + 14 \, a^{3}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(10*a^3*cos(d*x + c)^6 - 75*a^3*cos(d*x + c)^4 + 120*a^3*cos(d*x + c)^2 - 4*(9*a^3*cos(d*x + c)^4 - 23*a^3*cos(d*x + c)^2 + 14*a^3)*sin(d*x + c))/d","A",0
208,1,71,0,1.094304," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, a^{3} \cos\left(d x + c\right)^{4} - 40 \, a^{3} \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 7 \, a^{3} \cos\left(d x + c\right)^{2} + 6 \, a^{3}\right)} \sin\left(d x + c\right)}{20 \, d}"," ",0,"1/20*(15*a^3*cos(d*x + c)^4 - 40*a^3*cos(d*x + c)^2 + 4*(a^3*cos(d*x + c)^4 - 7*a^3*cos(d*x + c)^2 + 6*a^3)*sin(d*x + c))/d","A",0
209,1,59,0,1.142842," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{9 \, a^{3} \cos\left(d x + c\right)^{2} - 6 \, a^{3} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - 10 \, a^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(9*a^3*cos(d*x + c)^2 - 6*a^3*log(1/2*sin(d*x + c)) + 2*(a^3*cos(d*x + c)^2 - 10*a^3)*sin(d*x + c))/d","A",0
210,1,78,0,1.029212," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{12 \, a^{3} \cos\left(d x + c\right)^{2} - 12 \, a^{3} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 8 \, a^{3} + {\left(2 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \sin\left(d x + c\right)}{4 \, d \sin\left(d x + c\right)}"," ",0,"-1/4*(12*a^3*cos(d*x + c)^2 - 12*a^3*log(1/2*sin(d*x + c))*sin(d*x + c) - 8*a^3 + (2*a^3*cos(d*x + c)^2 - a^3)*sin(d*x + c))/(d*sin(d*x + c))","A",0
211,1,77,0,1.224530," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{3} + 6 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/2*(a^3 + 6*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*sin(d*x + c)) + 2*(a^3*cos(d*x + c)^2 + 2*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
212,1,91,0,1.040216," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{18 \, a^{3} \cos\left(d x + c\right)^{2} - 9 \, a^{3} \sin\left(d x + c\right) - 20 \, a^{3} - 6 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(18*a^3*cos(d*x + c)^2 - 9*a^3*sin(d*x + c) - 20*a^3 - 6*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*sin(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
213,1,72,0,1.292735," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} \cos\left(d x + c\right)^{2} - 7 \, a^{3} + 4 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/4*(6*a^3*cos(d*x + c)^2 - 7*a^3 + 4*(a^3*cos(d*x + c)^2 - 2*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
214,1,81,0,1.273128," ","integrate(cos(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{20 \, a^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{3} + 5 \, {\left(2 \, a^{3} \cos\left(d x + c\right)^{2} - 5 \, a^{3}\right)} \sin\left(d x + c\right)}{20 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/20*(20*a^3*cos(d*x + c)^2 - 24*a^3 + 5*(2*a^3*cos(d*x + c)^2 - 5*a^3)*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
215,1,86,0,0.729048," ","integrate(cos(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{45 \, a^{3} \cos\left(d x + c\right)^{2} - 55 \, a^{3} + 4 \, {\left(5 \, a^{3} \cos\left(d x + c\right)^{2} - 14 \, a^{3}\right)} \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/60*(45*a^3*cos(d*x + c)^2 - 55*a^3 + 4*(5*a^3*cos(d*x + c)^2 - 14*a^3)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
216,1,93,0,1.570702," ","integrate(cos(d*x+c)*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{84 \, a^{3} \cos\left(d x + c\right)^{2} - 104 \, a^{3} + 35 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{3}\right)} \sin\left(d x + c\right)}{140 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/140*(84*a^3*cos(d*x + c)^2 - 104*a^3 + 35*(a^3*cos(d*x + c)^2 - 3*a^3)*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
217,1,124,0,1.469339," ","integrate(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{315 \, a^{4} \cos\left(d x + c\right)^{8} - 1680 \, a^{4} \cos\left(d x + c\right)^{6} + 3150 \, a^{4} \cos\left(d x + c\right)^{4} - 2520 \, a^{4} \cos\left(d x + c\right)^{2} + 2 \, {\left(35 \, a^{4} \cos\left(d x + c\right)^{8} - 410 \, a^{4} \cos\left(d x + c\right)^{6} + 1083 \, a^{4} \cos\left(d x + c\right)^{4} - 1076 \, a^{4} \cos\left(d x + c\right)^{2} + 368 \, a^{4}\right)} \sin\left(d x + c\right)}{630 \, d}"," ",0,"1/630*(315*a^4*cos(d*x + c)^8 - 1680*a^4*cos(d*x + c)^6 + 3150*a^4*cos(d*x + c)^4 - 2520*a^4*cos(d*x + c)^2 + 2*(35*a^4*cos(d*x + c)^8 - 410*a^4*cos(d*x + c)^6 + 1083*a^4*cos(d*x + c)^4 - 1076*a^4*cos(d*x + c)^2 + 368*a^4)*sin(d*x + c))/d","A",0
218,1,111,0,1.342217," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{35 \, a^{4} \cos\left(d x + c\right)^{8} - 420 \, a^{4} \cos\left(d x + c\right)^{6} + 1120 \, a^{4} \cos\left(d x + c\right)^{4} - 1120 \, a^{4} \cos\left(d x + c\right)^{2} - 32 \, {\left(5 \, a^{4} \cos\left(d x + c\right)^{6} - 22 \, a^{4} \cos\left(d x + c\right)^{4} + 29 \, a^{4} \cos\left(d x + c\right)^{2} - 12 \, a^{4}\right)} \sin\left(d x + c\right)}{280 \, d}"," ",0,"1/280*(35*a^4*cos(d*x + c)^8 - 420*a^4*cos(d*x + c)^6 + 1120*a^4*cos(d*x + c)^4 - 1120*a^4*cos(d*x + c)^2 - 32*(5*a^4*cos(d*x + c)^6 - 22*a^4*cos(d*x + c)^4 + 29*a^4*cos(d*x + c)^2 - 12*a^4)*sin(d*x + c))/d","A",0
219,1,97,0,1.432749," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{70 \, a^{4} \cos\left(d x + c\right)^{6} - 315 \, a^{4} \cos\left(d x + c\right)^{4} + 420 \, a^{4} \cos\left(d x + c\right)^{2} + {\left(15 \, a^{4} \cos\left(d x + c\right)^{6} - 171 \, a^{4} \cos\left(d x + c\right)^{4} + 332 \, a^{4} \cos\left(d x + c\right)^{2} - 176 \, a^{4}\right)} \sin\left(d x + c\right)}{105 \, d}"," ",0,"-1/105*(70*a^4*cos(d*x + c)^6 - 315*a^4*cos(d*x + c)^4 + 420*a^4*cos(d*x + c)^2 + (15*a^4*cos(d*x + c)^6 - 171*a^4*cos(d*x + c)^4 + 332*a^4*cos(d*x + c)^2 - 176*a^4)*sin(d*x + c))/d","A",0
220,1,85,0,1.147548," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{5 \, a^{4} \cos\left(d x + c\right)^{6} - 60 \, a^{4} \cos\left(d x + c\right)^{4} + 120 \, a^{4} \cos\left(d x + c\right)^{2} - 8 \, {\left(3 \, a^{4} \cos\left(d x + c\right)^{4} - 11 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4}\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(5*a^4*cos(d*x + c)^6 - 60*a^4*cos(d*x + c)^4 + 120*a^4*cos(d*x + c)^2 - 8*(3*a^4*cos(d*x + c)^4 - 11*a^4*cos(d*x + c)^2 + 8*a^4)*sin(d*x + c))/d","B",0
221,1,72,0,1.656292," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, a^{4} \cos\left(d x + c\right)^{4} - 42 \, a^{4} \cos\left(d x + c\right)^{2} + 12 \, a^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 16 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 4 \, a^{4}\right)} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*a^4*cos(d*x + c)^4 - 42*a^4*cos(d*x + c)^2 + 12*a^4*log(1/2*sin(d*x + c)) - 16*(a^4*cos(d*x + c)^2 - 4*a^4)*sin(d*x + c))/d","A",0
222,1,91,0,1.534270," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{a^{4} \cos\left(d x + c\right)^{4} - 20 \, a^{4} \cos\left(d x + c\right)^{2} + 12 \, a^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 16 \, a^{4} - 3 \, {\left(2 \, a^{4} \cos\left(d x + c\right)^{2} - a^{4}\right)} \sin\left(d x + c\right)}{3 \, d \sin\left(d x + c\right)}"," ",0,"1/3*(a^4*cos(d*x + c)^4 - 20*a^4*cos(d*x + c)^2 + 12*a^4*log(1/2*sin(d*x + c))*sin(d*x + c) + 16*a^4 - 3*(2*a^4*cos(d*x + c)^2 - a^4)*sin(d*x + c))/(d*sin(d*x + c))","A",0
223,1,98,0,1.136615," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{2 \, a^{4} \cos\left(d x + c\right)^{4} - 16 \, a^{4} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 3 \, a^{4} \cos\left(d x + c\right)^{2} - a^{4} - 24 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - a^{4}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(2*a^4*cos(d*x + c)^4 - 16*a^4*cos(d*x + c)^2*sin(d*x + c) - 3*a^4*cos(d*x + c)^2 - a^4 - 24*(a^4*cos(d*x + c)^2 - a^4)*log(1/2*sin(d*x + c)))/(d*cos(d*x + c)^2 - d)","A",0
224,1,58,0,1.114460," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{4} - 12 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) + 12 \, \log\left(\sin\left(d x + c\right) + 1\right)}{12 \, a d}"," ",0,"1/12*(3*cos(d*x + c)^4 - 12*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 4)*sin(d*x + c) + 12*log(sin(d*x + c) + 1))/(a*d)","A",0
225,1,48,0,0.938598," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{6 \, a d}"," ",0,"1/6*(3*cos(d*x + c)^2 - 2*(cos(d*x + c)^2 - 4)*sin(d*x + c) - 6*log(sin(d*x + c) + 1))/(a*d)","A",0
226,1,36,0,1.078637," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} - 2 \, \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(cos(d*x + c)^2 - 2*log(sin(d*x + c) + 1) + 2*sin(d*x + c))/(a*d)","A",0
227,1,26,0,1.152524," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\log\left(\sin\left(d x + c\right) + 1\right) - \sin\left(d x + c\right)}{a d}"," ",0,"-(log(sin(d*x + c) + 1) - sin(d*x + c))/(a*d)","A",0
228,1,28,0,0.840777," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - \log\left(\sin\left(d x + c\right) + 1\right)}{a d}"," ",0,"(log(1/2*sin(d*x + c)) - log(sin(d*x + c) + 1))/(a*d)","A",0
229,1,51,0,0.801862," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 1}{a d \sin\left(d x + c\right)}"," ",0,"-(log(1/2*sin(d*x + c))*sin(d*x + c) - log(sin(d*x + c) + 1)*sin(d*x + c) + 1)/(a*d*sin(d*x + c))","A",0
230,1,72,0,1.083403," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, \sin\left(d x + c\right) + 1}{2 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"1/2*(2*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c)) - 2*(cos(d*x + c)^2 - 1)*log(sin(d*x + c) + 1) - 2*sin(d*x + c) + 1)/(a*d*cos(d*x + c)^2 - a*d)","A",0
231,1,102,0,1.046746," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 6 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 6 \, \cos\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 8}{6 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(6*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c))*sin(d*x + c) - 6*(cos(d*x + c)^2 - 1)*log(sin(d*x + c) + 1)*sin(d*x + c) + 6*cos(d*x + c)^2 + 3*sin(d*x + c) - 8)/((a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
232,1,81,0,1.099119," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{4} - 16 \, \cos\left(d x + c\right)^{2} - 24 \, {\left(\sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(4 \, \cos\left(d x + c\right)^{2} + 17\right)} \sin\left(d x + c\right) + 11}{6 \, {\left(a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(2*cos(d*x + c)^4 - 16*cos(d*x + c)^2 - 24*(sin(d*x + c) + 1)*log(sin(d*x + c) + 1) + (4*cos(d*x + c)^2 + 17)*sin(d*x + c) + 11)/(a^2*d*sin(d*x + c) + a^2*d)","A",0
233,1,72,0,1.081960," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, \cos\left(d x + c\right)^{2} + 12 \, {\left(\sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, \cos\left(d x + c\right)^{2} + 7\right)} \sin\left(d x + c\right) - 3}{4 \, {\left(a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/4*(6*cos(d*x + c)^2 + 12*(sin(d*x + c) + 1)*log(sin(d*x + c) + 1) - (2*cos(d*x + c)^2 + 7)*sin(d*x + c) - 3)/(a^2*d*sin(d*x + c) + a^2*d)","A",0
234,1,57,0,1.169144," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} + 2 \, {\left(\sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - \sin\left(d x + c\right)}{a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"-(cos(d*x + c)^2 + 2*(sin(d*x + c) + 1)*log(sin(d*x + c) + 1) - sin(d*x + c))/(a^2*d*sin(d*x + c) + a^2*d)","A",0
235,1,40,0,0.998213," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(\sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 1}{a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"((sin(d*x + c) + 1)*log(sin(d*x + c) + 1) + 1)/(a^2*d*sin(d*x + c) + a^2*d)","A",0
236,1,59,0,1.018708," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(\sin\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(\sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 1}{a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"((sin(d*x + c) + 1)*log(1/2*sin(d*x + c)) - (sin(d*x + c) + 1)*log(sin(d*x + c) + 1) + 1)/(a^2*d*sin(d*x + c) + a^2*d)","A",0
237,1,104,0,1.084841," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(d x + c\right)^{2} - \sin\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} - \sin\left(d x + c\right) - 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, \sin\left(d x + c\right) - 1}{a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \sin\left(d x + c\right) - a^{2} d}"," ",0,"-(2*(cos(d*x + c)^2 - sin(d*x + c) - 1)*log(1/2*sin(d*x + c)) - 2*(cos(d*x + c)^2 - sin(d*x + c) - 1)*log(sin(d*x + c) + 1) - 2*sin(d*x + c) - 1)/(a^2*d*cos(d*x + c)^2 - a^2*d*sin(d*x + c) - a^2*d)","A",0
238,1,147,0,1.196287," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, \cos\left(d x + c\right)^{2} + 6 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 6 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, \sin\left(d x + c\right) - 5}{2 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d + {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/2*(6*cos(d*x + c)^2 + 6*(cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - 1)*log(1/2*sin(d*x + c)) - 6*(cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - 1)*log(sin(d*x + c) + 1) - 3*sin(d*x + c) - 5)/(a^2*d*cos(d*x + c)^2 - a^2*d + (a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","A",0
239,1,195,0,0.953760," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, \cos\left(d x + c\right)^{2} - 12 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 12 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) - 7}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d - {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/3*(6*cos(d*x + c)^2 - 12*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^2 - 1)*sin(d*x + c) + 1)*log(1/2*sin(d*x + c)) + 12*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^2 - 1)*sin(d*x + c) + 1)*log(sin(d*x + c) + 1) + 2*(6*cos(d*x + c)^2 - 5)*sin(d*x + c) - 7)/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d - (a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","A",0
240,1,117,0,1.095628," ","integrate(cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, \cos\left(d x + c\right)^{4} + 115 \, \cos\left(d x + c\right)^{2} - 120 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, \cos\left(d x + c\right)^{4} - 24 \, \cos\left(d x + c\right)^{2} + 37\right)} \sin\left(d x + c\right) - 80}{12 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"1/12*(10*cos(d*x + c)^4 + 115*cos(d*x + c)^2 - 120*(cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*log(sin(d*x + c) + 1) - 2*(2*cos(d*x + c)^4 - 24*cos(d*x + c)^2 + 37)*sin(d*x + c) - 80)/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","A",0
241,1,107,0,0.984507," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{4} + 19 \, \cos\left(d x + c\right)^{2} - 24 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, \cos\left(d x + c\right)^{2} - 3\right)} \sin\left(d x + c\right) - 8}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"-1/4*(2*cos(d*x + c)^4 + 19*cos(d*x + c)^2 - 24*(cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*log(sin(d*x + c) + 1) + 2*(4*cos(d*x + c)^2 - 3)*sin(d*x + c) - 8)/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","A",0
242,1,95,0,0.924268," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, \cos\left(d x + c\right)^{2} - 6 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(\cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 1}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"1/2*(4*cos(d*x + c)^2 - 6*(cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*log(sin(d*x + c) + 1) + 2*(cos(d*x + c)^2 + 1)*sin(d*x + c) + 1)/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","A",0
243,1,75,0,0.965915," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, \sin\left(d x + c\right) - 3}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"1/2*(2*(cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*log(sin(d*x + c) + 1) - 4*sin(d*x + c) - 3)/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","A",0
244,1,46,0,0.973738," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, \sin\left(d x + c\right) + 1}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"1/2*(2*sin(d*x + c) + 1)/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","A",0
245,1,104,0,0.903942," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) - 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, \sin\left(d x + c\right) - 3}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \sin\left(d x + c\right) - 2 \, a^{3} d\right)}}"," ",0,"1/2*(2*(cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*log(1/2*sin(d*x + c)) - 2*(cos(d*x + c)^2 - 2*sin(d*x + c) - 2)*log(sin(d*x + c) + 1) - 2*sin(d*x + c) - 3)/(a^3*d*cos(d*x + c)^2 - 2*a^3*d*sin(d*x + c) - 2*a^3*d)","A",0
246,1,152,0,1.443096," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{2} + 6 \, {\left(2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) - 2\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 6 \, {\left(2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) - 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, \sin\left(d x + c\right) - 8}{2 \, {\left(2 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(6*cos(d*x + c)^2 + 6*(2*cos(d*x + c)^2 + (cos(d*x + c)^2 - 2)*sin(d*x + c) - 2)*log(1/2*sin(d*x + c)) - 6*(2*cos(d*x + c)^2 + (cos(d*x + c)^2 - 2)*sin(d*x + c) - 2)*log(sin(d*x + c) + 1) - 9*sin(d*x + c) - 8)/(2*a^3*d*cos(d*x + c)^2 - 2*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d)*sin(d*x + c))","A",0
247,1,196,0,1.042110," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{18 \, \cos\left(d x + c\right)^{2} - 12 \, {\left(\cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) + 2\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 12 \, {\left(\cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) + 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 4 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 17}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d - 2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(18*cos(d*x + c)^2 - 12*(cos(d*x + c)^4 - 3*cos(d*x + c)^2 - 2*(cos(d*x + c)^2 - 1)*sin(d*x + c) + 2)*log(1/2*sin(d*x + c)) + 12*(cos(d*x + c)^4 - 3*cos(d*x + c)^2 - 2*(cos(d*x + c)^2 - 1)*sin(d*x + c) + 2)*log(sin(d*x + c) + 1) + 4*(3*cos(d*x + c)^2 - 4)*sin(d*x + c) - 17)/(a^3*d*cos(d*x + c)^4 - 3*a^3*d*cos(d*x + c)^2 + 2*a^3*d - 2*(a^3*d*cos(d*x + c)^2 - a^3*d)*sin(d*x + c))","A",0
248,1,242,0,1.047983," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{60 \, \cos\left(d x + c\right)^{4} - 140 \, \cos\left(d x + c\right)^{2} + 60 \, {\left(2 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right) + 2\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 60 \, {\left(2 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right) + 2\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 5 \, {\left(18 \, \cos\left(d x + c\right)^{2} - 17\right)} \sin\left(d x + c\right) + 82}{6 \, {\left(2 \, a^{3} d \cos\left(d x + c\right)^{4} - 4 \, a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{4} - 3 \, a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/6*(60*cos(d*x + c)^4 - 140*cos(d*x + c)^2 + 60*(2*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + (cos(d*x + c)^4 - 3*cos(d*x + c)^2 + 2)*sin(d*x + c) + 2)*log(1/2*sin(d*x + c)) - 60*(2*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + (cos(d*x + c)^4 - 3*cos(d*x + c)^2 + 2)*sin(d*x + c) + 2)*log(sin(d*x + c) + 1) - 5*(18*cos(d*x + c)^2 - 17)*sin(d*x + c) + 82)/(2*a^3*d*cos(d*x + c)^4 - 4*a^3*d*cos(d*x + c)^2 + 2*a^3*d + (a^3*d*cos(d*x + c)^4 - 3*a^3*d*cos(d*x + c)^2 + 2*a^3*d)*sin(d*x + c))","B",0
249,1,144,0,1.211155," ","integrate(cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{4} - 87 \, \cos\left(d x + c\right)^{2} + 120 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, \cos\left(d x + c\right)^{4} + 39 \, \cos\left(d x + c\right)^{2} + 10\right)} \sin\left(d x + c\right) - 34}{12 \, {\left(3 \, a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d + {\left(a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(30*cos(d*x + c)^4 - 87*cos(d*x + c)^2 + 120*(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)*log(sin(d*x + c) + 1) - 3*(2*cos(d*x + c)^4 + 39*cos(d*x + c)^2 + 10)*sin(d*x + c) - 34)/(3*a^4*d*cos(d*x + c)^2 - 4*a^4*d + (a^4*d*cos(d*x + c)^2 - 4*a^4*d)*sin(d*x + c))","A",0
250,1,132,0,1.067357," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} + 12 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 9 \, {\left(\cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right) - 19}{3 \, {\left(3 \, a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d + {\left(a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 + 12*(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)*log(sin(d*x + c) + 1) - 9*(cos(d*x + c)^2 + 2)*sin(d*x + c) - 19)/(3*a^4*d*cos(d*x + c)^2 - 4*a^4*d + (a^4*d*cos(d*x + c)^2 - 4*a^4*d)*sin(d*x + c))","A",0
251,1,112,0,1.500911," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{18 \, \cos\left(d x + c\right)^{2} + 6 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 27 \, \sin\left(d x + c\right) - 29}{6 \, {\left(3 \, a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d + {\left(a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/6*(18*cos(d*x + c)^2 + 6*(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)*log(sin(d*x + c) + 1) - 27*sin(d*x + c) - 29)/(3*a^4*d*cos(d*x + c)^2 - 4*a^4*d + (a^4*d*cos(d*x + c)^2 - 4*a^4*d)*sin(d*x + c))","A",0
252,1,72,0,1.076997," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) - 4}{3 \, {\left(3 \, a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d + {\left(a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*cos(d*x + c)^2 - 3*sin(d*x + c) - 4)/(3*a^4*d*cos(d*x + c)^2 - 4*a^4*d + (a^4*d*cos(d*x + c)^2 - 4*a^4*d)*sin(d*x + c))","B",0
253,1,62,0,0.797231," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, \sin\left(d x + c\right) + 1}{6 \, {\left(3 \, a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d + {\left(a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/6*(3*sin(d*x + c) + 1)/(3*a^4*d*cos(d*x + c)^2 - 4*a^4*d + (a^4*d*cos(d*x + c)^2 - 4*a^4*d)*sin(d*x + c))","A",0
254,1,152,0,1.167865," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{6 \, \cos\left(d x + c\right)^{2} + 6 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 6 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 4\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, \sin\left(d x + c\right) - 17}{6 \, {\left(3 \, a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d + {\left(a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/6*(6*cos(d*x + c)^2 + 6*(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)*log(1/2*sin(d*x + c)) - 6*(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - 4)*sin(d*x + c) - 4)*log(sin(d*x + c) + 1) - 15*sin(d*x + c) - 17)/(3*a^4*d*cos(d*x + c)^2 - 4*a^4*d + (a^4*d*cos(d*x + c)^2 - 4*a^4*d)*sin(d*x + c))","A",0
255,1,201,0,1.065633," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{2} - 12 \, {\left(\cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) + 4\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 12 \, {\left(\cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) + 4\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6 \, \cos\left(d x + c\right)^{2} - 17\right)} \sin\left(d x + c\right) - 33}{3 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} - 5 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d - {\left(3 \, a^{4} d \cos\left(d x + c\right)^{2} - 4 \, a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/3*(30*cos(d*x + c)^2 - 12*(cos(d*x + c)^4 - 5*cos(d*x + c)^2 - (3*cos(d*x + c)^2 - 4)*sin(d*x + c) + 4)*log(1/2*sin(d*x + c)) + 12*(cos(d*x + c)^4 - 5*cos(d*x + c)^2 - (3*cos(d*x + c)^2 - 4)*sin(d*x + c) + 4)*log(sin(d*x + c) + 1) + 2*(6*cos(d*x + c)^2 - 17)*sin(d*x + c) - 33)/(a^4*d*cos(d*x + c)^4 - 5*a^4*d*cos(d*x + c)^2 + 4*a^4*d - (3*a^4*d*cos(d*x + c)^2 - 4*a^4*d)*sin(d*x + c))","A",0
256,1,242,0,1.109559," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{60 \, \cos\left(d x + c\right)^{4} - 230 \, \cos\left(d x + c\right)^{2} + 60 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 7 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} + 4\right)} \sin\left(d x + c\right) + 4\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 60 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 7 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} + 4\right)} \sin\left(d x + c\right) + 4\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left(10 \, \cos\left(d x + c\right)^{2} - 11\right)} \sin\left(d x + c\right) + 167}{6 \, {\left(3 \, a^{4} d \cos\left(d x + c\right)^{4} - 7 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d + {\left(a^{4} d \cos\left(d x + c\right)^{4} - 5 \, a^{4} d \cos\left(d x + c\right)^{2} + 4 \, a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/6*(60*cos(d*x + c)^4 - 230*cos(d*x + c)^2 + 60*(3*cos(d*x + c)^4 - 7*cos(d*x + c)^2 + (cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 4)*sin(d*x + c) + 4)*log(1/2*sin(d*x + c)) - 60*(3*cos(d*x + c)^4 - 7*cos(d*x + c)^2 + (cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 4)*sin(d*x + c) + 4)*log(sin(d*x + c) + 1) - 15*(10*cos(d*x + c)^2 - 11)*sin(d*x + c) + 167)/(3*a^4*d*cos(d*x + c)^4 - 7*a^4*d*cos(d*x + c)^2 + 4*a^4*d + (a^4*d*cos(d*x + c)^4 - 5*a^4*d*cos(d*x + c)^2 + 4*a^4*d)*sin(d*x + c))","A",0
257,1,86,0,0.986858," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{2} + 4 \, \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} {\left(\sin\left(d x + c\right) + 2\right)} - 8 \, a \sin\left(d x + c\right) - 9 \, a}{\cos\left(d x + c\right)^{2} - 1}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a}}{2 \, d}"," ",0,"1/2*(sqrt(a)*log((a*cos(d*x + c)^2 + 4*sqrt(a*sin(d*x + c) + a)*sqrt(a)*(sin(d*x + c) + 2) - 8*a*sin(d*x + c) - 9*a)/(cos(d*x + c)^2 - 1)) + 4*sqrt(a*sin(d*x + c) + a))/d","A",0
258,1,302,0,1.264059," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{{\left(8 \, a^{4} n^{4} + 96 \, a^{4} n^{3} + 400 \, a^{4} n^{2} + 672 \, a^{4} n + 4 \, {\left(a^{4} n^{4} + 11 \, a^{4} n^{3} + 41 \, a^{4} n^{2} + 61 \, a^{4} n + 30 \, a^{4}\right)} \cos\left(d x + c\right)^{4} + 360 \, a^{4} - 4 \, {\left(3 \, a^{4} n^{4} + 35 \, a^{4} n^{3} + 141 \, a^{4} n^{2} + 229 \, a^{4} n + 120 \, a^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(8 \, a^{4} n^{4} + 96 \, a^{4} n^{3} + 400 \, a^{4} n^{2} + 672 \, a^{4} n + {\left(a^{4} n^{4} + 10 \, a^{4} n^{3} + 35 \, a^{4} n^{2} + 50 \, a^{4} n + 24 \, a^{4}\right)} \cos\left(d x + c\right)^{4} + 384 \, a^{4} - 4 \, {\left(2 \, a^{4} n^{4} + 23 \, a^{4} n^{3} + 91 \, a^{4} n^{2} + 142 \, a^{4} n + 72 \, a^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{d n^{5} + 15 \, d n^{4} + 85 \, d n^{3} + 225 \, d n^{2} + 274 \, d n + 120 \, d}"," ",0,"(8*a^4*n^4 + 96*a^4*n^3 + 400*a^4*n^2 + 672*a^4*n + 4*(a^4*n^4 + 11*a^4*n^3 + 41*a^4*n^2 + 61*a^4*n + 30*a^4)*cos(d*x + c)^4 + 360*a^4 - 4*(3*a^4*n^4 + 35*a^4*n^3 + 141*a^4*n^2 + 229*a^4*n + 120*a^4)*cos(d*x + c)^2 + (8*a^4*n^4 + 96*a^4*n^3 + 400*a^4*n^2 + 672*a^4*n + (a^4*n^4 + 10*a^4*n^3 + 35*a^4*n^2 + 50*a^4*n + 24*a^4)*cos(d*x + c)^4 + 384*a^4 - 4*(2*a^4*n^4 + 23*a^4*n^3 + 91*a^4*n^2 + 142*a^4*n + 72*a^4)*cos(d*x + c)^2)*sin(d*x + c))*sin(d*x + c)^n/(d*n^5 + 15*d*n^4 + 85*d*n^3 + 225*d*n^2 + 274*d*n + 120*d)","B",0
259,1,210,0,0.608893," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(4 \, a^{3} n^{3} + 30 \, a^{3} n^{2} + {\left(a^{3} n^{3} + 6 \, a^{3} n^{2} + 11 \, a^{3} n + 6 \, a^{3}\right)} \cos\left(d x + c\right)^{4} + 68 \, a^{3} n + 42 \, a^{3} - {\left(5 \, a^{3} n^{3} + 36 \, a^{3} n^{2} + 79 \, a^{3} n + 48 \, a^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(4 \, a^{3} n^{3} + 30 \, a^{3} n^{2} + 68 \, a^{3} n + 48 \, a^{3} - 3 \, {\left(a^{3} n^{3} + 7 \, a^{3} n^{2} + 14 \, a^{3} n + 8 \, a^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{d n^{4} + 10 \, d n^{3} + 35 \, d n^{2} + 50 \, d n + 24 \, d}"," ",0,"(4*a^3*n^3 + 30*a^3*n^2 + (a^3*n^3 + 6*a^3*n^2 + 11*a^3*n + 6*a^3)*cos(d*x + c)^4 + 68*a^3*n + 42*a^3 - (5*a^3*n^3 + 36*a^3*n^2 + 79*a^3*n + 48*a^3)*cos(d*x + c)^2 + (4*a^3*n^3 + 30*a^3*n^2 + 68*a^3*n + 48*a^3 - 3*(a^3*n^3 + 7*a^3*n^2 + 14*a^3*n + 8*a^3)*cos(d*x + c)^2)*sin(d*x + c))*sin(d*x + c)^n/(d*n^4 + 10*d*n^3 + 35*d*n^2 + 50*d*n + 24*d)","B",0
260,1,135,0,1.075260," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} n^{2} + 8 \, a^{2} n - 2 \, {\left(a^{2} n^{2} + 4 \, a^{2} n + 3 \, a^{2}\right)} \cos\left(d x + c\right)^{2} + 6 \, a^{2} + {\left(2 \, a^{2} n^{2} + 8 \, a^{2} n - {\left(a^{2} n^{2} + 3 \, a^{2} n + 2 \, a^{2}\right)} \cos\left(d x + c\right)^{2} + 8 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{d n^{3} + 6 \, d n^{2} + 11 \, d n + 6 \, d}"," ",0,"(2*a^2*n^2 + 8*a^2*n - 2*(a^2*n^2 + 4*a^2*n + 3*a^2)*cos(d*x + c)^2 + 6*a^2 + (2*a^2*n^2 + 8*a^2*n - (a^2*n^2 + 3*a^2*n + 2*a^2)*cos(d*x + c)^2 + 8*a^2)*sin(d*x + c))*sin(d*x + c)^n/(d*n^3 + 6*d*n^2 + 11*d*n + 6*d)","A",0
261,1,62,0,0.814392," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left({\left(a n + a\right)} \cos\left(d x + c\right)^{2} - a n - {\left(a n + 2 \, a\right)} \sin\left(d x + c\right) - a\right)} \sin\left(d x + c\right)^{n}}{d n^{2} + 3 \, d n + 2 \, d}"," ",0,"-((a*n + a)*cos(d*x + c)^2 - a*n - (a*n + 2*a)*sin(d*x + c) - a)*sin(d*x + c)^n/(d*n^2 + 3*d*n + 2*d)","A",0
262,0,0,0,0.679424," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
263,0,0,0,0.990233," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sin(d*x + c)^n*cos(d*x + c)/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
264,0,0,0,0.986197," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sin(d*x + c)^n*cos(d*x + c)/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
265,0,0,0,0.808911," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sin(d*x + c)^n*cos(d*x + c)/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
266,1,73,0,0.645422," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, a \cos\left(d x + c\right)^{5} - 80 \, a \cos\left(d x + c\right)^{3} + 15 \, a d x + 5 \, {\left(8 \, a \cos\left(d x + c\right)^{5} - 14 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(48*a*cos(d*x + c)^5 - 80*a*cos(d*x + c)^3 + 15*a*d*x + 5*(8*a*cos(d*x + c)^5 - 14*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
267,1,62,0,0.871509," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{24 \, a \cos\left(d x + c\right)^{5} - 40 \, a \cos\left(d x + c\right)^{3} + 15 \, a d x - 15 \, {\left(2 \, a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(24*a*cos(d*x + c)^5 - 40*a*cos(d*x + c)^3 + 15*a*d*x - 15*(2*a*cos(d*x + c)^3 - a*cos(d*x + c))*sin(d*x + c))/d","A",0
268,1,51,0,0.948504," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, a \cos\left(d x + c\right)^{3} - 3 \, a d x + 3 \, {\left(2 \, a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"-1/24*(8*a*cos(d*x + c)^3 - 3*a*d*x + 3*(2*a*cos(d*x + c)^3 - a*cos(d*x + c))*sin(d*x + c))/d","A",0
269,1,60,0,0.932646," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a d x + a \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, a \cos\left(d x + c\right) - a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, d}"," ",0,"1/2*(a*d*x + a*cos(d*x + c)*sin(d*x + c) + 2*a*cos(d*x + c) - a*log(1/2*cos(d*x + c) + 1/2) + a*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
270,1,84,0,0.910500," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, a \cos\left(d x + c\right) + 2 \, {\left(a d x - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, d \sin\left(d x + c\right)}"," ",0,"-1/2*(a*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - a*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*a*cos(d*x + c) + 2*(a*d*x - a*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","B",0
271,1,114,0,0.931074," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a d x \cos\left(d x + c\right)^{2} - 4 \, a d x - 4 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(4*a*d*x*cos(d*x + c)^2 - 4*a*d*x - 4*a*cos(d*x + c)*sin(d*x + c) - 2*a*cos(d*x + c) - (a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + (a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
272,1,119,0,0.665788," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, a \cos\left(d x + c\right)^{3} + 6 \, a \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(4*a*cos(d*x + c)^3 + 6*a*cos(d*x + c)*sin(d*x + c) + 3*(a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
273,1,137,0,0.742861," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + 6 \, a \cos\left(d x + c\right)^{3} + 6 \, a \cos\left(d x + c\right) - 3 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/48*(16*a*cos(d*x + c)^3*sin(d*x + c) + 6*a*cos(d*x + c)^3 + 6*a*cos(d*x + c) - 3*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 3*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
274,1,169,0,1.001419," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{32 \, a \cos\left(d x + c\right)^{5} - 80 \, a \cos\left(d x + c\right)^{3} + 15 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/240*(32*a*cos(d*x + c)^5 - 80*a*cos(d*x + c)^3 + 15*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*(a*cos(d*x + c)^3 + a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
275,1,98,0,0.972776," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{120 \, a^{2} \cos\left(d x + c\right)^{7} - 504 \, a^{2} \cos\left(d x + c\right)^{5} + 560 \, a^{2} \cos\left(d x + c\right)^{3} - 105 \, a^{2} d x - 35 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{5} - 14 \, a^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"-1/840*(120*a^2*cos(d*x + c)^7 - 504*a^2*cos(d*x + c)^5 + 560*a^2*cos(d*x + c)^3 - 105*a^2*d*x - 35*(8*a^2*cos(d*x + c)^5 - 14*a^2*cos(d*x + c)^3 + 3*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
276,1,85,0,0.898951," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{96 \, a^{2} \cos\left(d x + c\right)^{5} - 160 \, a^{2} \cos\left(d x + c\right)^{3} + 45 \, a^{2} d x + 5 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{5} - 26 \, a^{2} \cos\left(d x + c\right)^{3} + 9 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(96*a^2*cos(d*x + c)^5 - 160*a^2*cos(d*x + c)^3 + 45*a^2*d*x + 5*(8*a^2*cos(d*x + c)^5 - 26*a^2*cos(d*x + c)^3 + 9*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
277,1,72,0,0.755257," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{12 \, a^{2} \cos\left(d x + c\right)^{5} - 40 \, a^{2} \cos\left(d x + c\right)^{3} + 15 \, a^{2} d x - 15 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{3} - a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*a^2*cos(d*x + c)^5 - 40*a^2*cos(d*x + c)^3 + 15*a^2*d*x - 15*(2*a^2*cos(d*x + c)^3 - a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
278,1,86,0,1.224434," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} \cos\left(d x + c\right)^{3} - 6 \, a^{2} d x - 6 \, a^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, a^{2} \cos\left(d x + c\right) + 3 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{6 \, d}"," ",0,"-1/6*(2*a^2*cos(d*x + c)^3 - 6*a^2*d*x - 6*a^2*cos(d*x + c)*sin(d*x + c) - 6*a^2*cos(d*x + c) + 3*a^2*log(1/2*cos(d*x + c) + 1/2) - 3*a^2*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
279,1,105,0,0.622842," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right)^{3} + 2 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + a^{2} \cos\left(d x + c\right) + {\left(a^{2} d x - 4 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, d \sin\left(d x + c\right)}"," ",0,"-1/2*(a^2*cos(d*x + c)^3 + 2*a^2*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*a^2*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + a^2*cos(d*x + c) + (a^2*d*x - 4*a^2*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
280,1,143,0,0.860916," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, a^{2} d x \cos\left(d x + c\right)^{2} - 4 \, a^{2} \cos\left(d x + c\right)^{3} - 8 \, a^{2} d x - 8 \, a^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, a^{2} \cos\left(d x + c\right) + {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(8*a^2*d*x*cos(d*x + c)^2 - 4*a^2*cos(d*x + c)^3 - 8*a^2*d*x - 8*a^2*cos(d*x + c)*sin(d*x + c) + 2*a^2*cos(d*x + c) + (a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2) - (a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
281,1,166,0,0.792801," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, a^{2} \cos\left(d x + c\right)^{3} - 6 \, a^{2} \cos\left(d x + c\right) - 3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, {\left(a^{2} d x \cos\left(d x + c\right)^{2} - a^{2} d x - a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(4*a^2*cos(d*x + c)^3 - 6*a^2*cos(d*x + c) - 3*(a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*(a^2*d*x*cos(d*x + c)^2 - a^2*d*x - a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
282,1,155,0,0.915154," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{32 \, a^{2} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 18 \, a^{2} \cos\left(d x + c\right)^{3} + 30 \, a^{2} \cos\left(d x + c\right) - 15 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/48*(32*a^2*cos(d*x + c)^3*sin(d*x + c) - 18*a^2*cos(d*x + c)^3 + 30*a^2*cos(d*x + c) - 15*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2) + 15*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
283,1,189,0,0.912295," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{56 \, a^{2} \cos\left(d x + c\right)^{5} - 80 \, a^{2} \cos\left(d x + c\right)^{3} + 15 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/120*(56*a^2*cos(d*x + c)^5 - 80*a^2*cos(d*x + c)^3 + 15*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*(a^2*cos(d*x + c)^3 + a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
284,1,227,0,0.896914," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{90 \, a^{2} \cos\left(d x + c\right)^{5} - 80 \, a^{2} \cos\left(d x + c\right)^{3} - 90 \, a^{2} \cos\left(d x + c\right) - 45 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 45 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 64 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{5} - 5 \, a^{2} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/480*(90*a^2*cos(d*x + c)^5 - 80*a^2*cos(d*x + c)^3 - 90*a^2*cos(d*x + c) - 45*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2) + 45*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2) + 64*(2*a^2*cos(d*x + c)^5 - 5*a^2*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
285,1,98,0,0.928535," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{48 \, a^{3} \cos\left(d x + c\right)^{7} - 336 \, a^{3} \cos\left(d x + c\right)^{5} + 448 \, a^{3} \cos\left(d x + c\right)^{3} - 105 \, a^{3} d x - 21 \, {\left(8 \, a^{3} \cos\left(d x + c\right)^{5} - 18 \, a^{3} \cos\left(d x + c\right)^{3} + 5 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{336 \, d}"," ",0,"-1/336*(48*a^3*cos(d*x + c)^7 - 336*a^3*cos(d*x + c)^5 + 448*a^3*cos(d*x + c)^3 - 105*a^3*d*x - 21*(8*a^3*cos(d*x + c)^5 - 18*a^3*cos(d*x + c)^3 + 5*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
286,1,85,0,0.735258," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{144 \, a^{3} \cos\left(d x + c\right)^{5} - 320 \, a^{3} \cos\left(d x + c\right)^{3} + 105 \, a^{3} d x + 5 \, {\left(8 \, a^{3} \cos\left(d x + c\right)^{5} - 50 \, a^{3} \cos\left(d x + c\right)^{3} + 21 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(144*a^3*cos(d*x + c)^5 - 320*a^3*cos(d*x + c)^3 + 105*a^3*d*x + 5*(8*a^3*cos(d*x + c)^5 - 50*a^3*cos(d*x + c)^3 + 21*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
287,1,101,0,0.887580," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, a^{3} \cos\left(d x + c\right)^{3} - 13 \, a^{3} d x - 8 \, a^{3} \cos\left(d x + c\right) + 4 \, a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(2 \, a^{3} \cos\left(d x + c\right)^{3} - 13 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(8*a^3*cos(d*x + c)^3 - 13*a^3*d*x - 8*a^3*cos(d*x + c) + 4*a^3*log(1/2*cos(d*x + c) + 1/2) - 4*a^3*log(-1/2*cos(d*x + c) + 1/2) + (2*a^3*cos(d*x + c)^3 - 13*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
288,1,121,0,0.961951," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{9 \, a^{3} \cos\left(d x + c\right)^{3} + 9 \, a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, a^{3} \cos\left(d x + c\right) + {\left(2 \, a^{3} \cos\left(d x + c\right)^{3} - 3 \, a^{3} d x - 18 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d \sin\left(d x + c\right)}"," ",0,"-1/6*(9*a^3*cos(d*x + c)^3 + 9*a^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*a^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*a^3*cos(d*x + c) + (2*a^3*cos(d*x + c)^3 - 3*a^3*d*x - 18*a^3*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
289,1,159,0,0.833427," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{10 \, a^{3} d x \cos\left(d x + c\right)^{2} - 12 \, a^{3} \cos\left(d x + c\right)^{3} - 10 \, a^{3} d x + 10 \, a^{3} \cos\left(d x + c\right) + 5 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 5 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{3} \cos\left(d x + c\right)^{3} + 5 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(10*a^3*d*x*cos(d*x + c)^2 - 12*a^3*cos(d*x + c)^3 - 10*a^3*d*x + 10*a^3*cos(d*x + c) + 5*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2) - 5*(a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^3*cos(d*x + c)^3 + 5*a^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
290,1,180,0,0.958780," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{32 \, a^{3} \cos\left(d x + c\right)^{3} - 36 \, a^{3} \cos\left(d x + c\right) - 3 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, {\left(6 \, a^{3} d x \cos\left(d x + c\right)^{2} - 2 \, a^{3} \cos\left(d x + c\right)^{3} - 6 \, a^{3} d x - a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(32*a^3*cos(d*x + c)^3 - 36*a^3*cos(d*x + c) - 3*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*(6*a^3*d*x*cos(d*x + c)^2 - 2*a^3*cos(d*x + c)^3 - 6*a^3*d*x - a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
291,1,190,0,1.083603," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{16 \, a^{3} d x \cos\left(d x + c\right)^{4} - 32 \, a^{3} d x \cos\left(d x + c\right)^{2} - 22 \, a^{3} \cos\left(d x + c\right)^{3} + 16 \, a^{3} d x + 16 \, a^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + 26 \, a^{3} \cos\left(d x + c\right) - 13 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 13 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{16 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/16*(16*a^3*d*x*cos(d*x + c)^4 - 32*a^3*d*x*cos(d*x + c)^2 - 22*a^3*cos(d*x + c)^3 + 16*a^3*d*x + 16*a^3*cos(d*x + c)*sin(d*x + c) + 26*a^3*cos(d*x + c) - 13*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2) + 13*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
292,1,190,0,0.959162," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{272 \, a^{3} \cos\left(d x + c\right)^{5} - 320 \, a^{3} \cos\left(d x + c\right)^{3} + 105 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 105 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, {\left(a^{3} \cos\left(d x + c\right)^{3} - 7 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/240*(272*a^3*cos(d*x + c)^5 - 320*a^3*cos(d*x + c)^3 + 105*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 105*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*(a^3*cos(d*x + c)^3 - 7*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
293,1,227,0,1.303617," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{210 \, a^{3} \cos\left(d x + c\right)^{5} - 80 \, a^{3} \cos\left(d x + c\right)^{3} - 210 \, a^{3} \cos\left(d x + c\right) - 105 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 32 \, {\left(11 \, a^{3} \cos\left(d x + c\right)^{5} - 20 \, a^{3} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/480*(210*a^3*cos(d*x + c)^5 - 80*a^3*cos(d*x + c)^3 - 210*a^3*cos(d*x + c) - 105*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2) + 105*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2) + 32*(11*a^3*cos(d*x + c)^5 - 20*a^3*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
294,1,85,0,0.795251," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{192 \, a^{4} \cos\left(d x + c\right)^{5} - 640 \, a^{4} \cos\left(d x + c\right)^{3} + 315 \, a^{4} d x + 5 \, {\left(8 \, a^{4} \cos\left(d x + c\right)^{5} - 86 \, a^{4} \cos\left(d x + c\right)^{3} + 63 \, a^{4} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(192*a^4*cos(d*x + c)^5 - 640*a^4*cos(d*x + c)^3 + 315*a^4*d*x + 5*(8*a^4*cos(d*x + c)^5 - 86*a^4*cos(d*x + c)^3 + 63*a^4*cos(d*x + c))*sin(d*x + c))/d","A",0
295,1,115,0,0.998463," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{6 \, a^{4} \cos\left(d x + c\right)^{5} - 70 \, a^{4} \cos\left(d x + c\right)^{3} + 75 \, a^{4} d x + 30 \, a^{4} \cos\left(d x + c\right) - 15 \, a^{4} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, a^{4} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(2 \, a^{4} \cos\left(d x + c\right)^{3} - 5 \, a^{4} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(6*a^4*cos(d*x + c)^5 - 70*a^4*cos(d*x + c)^3 + 75*a^4*d*x + 30*a^4*cos(d*x + c) - 15*a^4*log(1/2*cos(d*x + c) + 1/2) + 15*a^4*log(-1/2*cos(d*x + c) + 1/2) - 15*(2*a^4*cos(d*x + c)^3 - 5*a^4*cos(d*x + c))*sin(d*x + c))/d","A",0
296,1,135,0,0.615495," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{6 \, a^{4} \cos\left(d x + c\right)^{5} - 81 \, a^{4} \cos\left(d x + c\right)^{3} - 48 \, a^{4} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 48 \, a^{4} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 51 \, a^{4} \cos\left(d x + c\right) - {\left(32 \, a^{4} \cos\left(d x + c\right)^{3} - 51 \, a^{4} d x - 96 \, a^{4} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d \sin\left(d x + c\right)}"," ",0,"1/24*(6*a^4*cos(d*x + c)^5 - 81*a^4*cos(d*x + c)^3 - 48*a^4*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 48*a^4*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 51*a^4*cos(d*x + c) - (32*a^4*cos(d*x + c)^3 - 51*a^4*d*x - 96*a^4*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
297,1,68,0,0.694422," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{24 \, \cos\left(d x + c\right)^{5} - 80 \, \cos\left(d x + c\right)^{3} + 45 \, d x + 15 \, {\left(2 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 120 \, \cos\left(d x + c\right)}{120 \, a d}"," ",0,"1/120*(24*cos(d*x + c)^5 - 80*cos(d*x + c)^3 + 45*d*x + 15*(2*cos(d*x + c)^3 - 5*cos(d*x + c))*sin(d*x + c) + 120*cos(d*x + c))/(a*d)","A",0
298,1,58,0,0.807148," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{3} - 9 \, d x - 3 \, {\left(2 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 24 \, \cos\left(d x + c\right)}{24 \, a d}"," ",0,"1/24*(8*cos(d*x + c)^3 - 9*d*x - 3*(2*cos(d*x + c)^3 - 5*cos(d*x + c))*sin(d*x + c) - 24*cos(d*x + c))/(a*d)","A",0
299,1,45,0,0.939228," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{3} - 3 \, d x + 3 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, \cos\left(d x + c\right)}{6 \, a d}"," ",0,"-1/6*(2*cos(d*x + c)^3 - 3*d*x + 3*cos(d*x + c)*sin(d*x + c) - 6*cos(d*x + c))/(a*d)","A",0
300,1,34,0,0.859433," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d x - \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(d*x - cos(d*x + c)*sin(d*x + c) + 2*cos(d*x + c))/(a*d)","A",0
301,1,37,0,1.041137," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, d x + \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, a d}"," ",0,"-1/2*(2*d*x + log(1/2*cos(d*x + c) + 1/2) - log(-1/2*cos(d*x + c) + 1/2))/(a*d)","A",0
302,1,62,0,0.977213," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)}{2 \, a d \sin\left(d x + c\right)}"," ",0,"1/2*(log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*cos(d*x + c))/(a*d*sin(d*x + c))","B",0
303,1,88,0,1.192238," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)}{4 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"-1/4*((cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) - (cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) + 4*cos(d*x + c)*sin(d*x + c) - 2*cos(d*x + c))/(a*d*cos(d*x + c)^2 - a*d)","A",0
304,1,119,0,0.861894," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{3} - 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 12 \, \cos\left(d x + c\right)}{12 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(8*cos(d*x + c)^3 - 3*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*cos(d*x + c)*sin(d*x + c) - 12*cos(d*x + c))/((a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
305,1,143,0,0.946823," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{18 \, \cos\left(d x + c\right)^{3} - 9 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 30 \, \cos\left(d x + c\right)}{48 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"1/48*(18*cos(d*x + c)^3 - 9*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) + 9*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 16*(2*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c) - 30*cos(d*x + c))/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)","A",0
306,1,173,0,1.050189," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{128 \, \cos\left(d x + c\right)^{5} - 320 \, \cos\left(d x + c\right)^{3} - 45 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 45 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 240 \, \cos\left(d x + c\right)}{240 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/240*(128*cos(d*x + c)^5 - 320*cos(d*x + c)^3 - 45*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 45*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*(3*cos(d*x + c)^3 - 5*cos(d*x + c))*sin(d*x + c) + 240*cos(d*x + c))/((a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","A",0
307,1,144,0,0.869458," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, \cos\left(d x + c\right)^{5} + 16 \, \cos\left(d x + c\right)^{4} - 29 \, \cos\left(d x + c\right)^{3} - 81 \, d x - 3 \, {\left(27 \, d x + 35\right)} \cos\left(d x + c\right) - 96 \, \cos\left(d x + c\right)^{2} - {\left(6 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{3} + 81 \, d x - 39 \, \cos\left(d x + c\right)^{2} + 57 \, \cos\left(d x + c\right) - 48\right)} \sin\left(d x + c\right) - 48}{24 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/24*(6*cos(d*x + c)^5 + 16*cos(d*x + c)^4 - 29*cos(d*x + c)^3 - 81*d*x - 3*(27*d*x + 35)*cos(d*x + c) - 96*cos(d*x + c)^2 - (6*cos(d*x + c)^4 - 10*cos(d*x + c)^3 + 81*d*x - 39*cos(d*x + c)^2 + 57*cos(d*x + c) - 48)*sin(d*x + c) - 48)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
308,1,119,0,1.006249," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 9 \, d x - 3 \, {\left(3 \, d x + 4\right)} \cos\left(d x + c\right) - 9 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{3} - 9 \, d x + 3 \, \cos\left(d x + c\right)^{2} - 6 \, \cos\left(d x + c\right) + 6\right)} \sin\left(d x + c\right) - 6}{3 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/3*(cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 9*d*x - 3*(3*d*x + 4)*cos(d*x + c) - 9*cos(d*x + c)^2 + (cos(d*x + c)^3 - 9*d*x + 3*cos(d*x + c)^2 - 6*cos(d*x + c) + 6)*sin(d*x + c) - 6)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
309,1,100,0,0.916441," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{3} + 5 \, d x + {\left(5 \, d x + 7\right)} \cos\left(d x + c\right) + 4 \, \cos\left(d x + c\right)^{2} + {\left(5 \, d x - \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) + 4}{2 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/2*(cos(d*x + c)^3 + 5*d*x + (5*d*x + 7)*cos(d*x + c) + 4*cos(d*x + c)^2 + (5*d*x - cos(d*x + c)^2 + 3*cos(d*x + c) - 4)*sin(d*x + c) + 4)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
310,1,77,0,0.962907," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, d x + {\left(2 \, d x + 3\right)} \cos\left(d x + c\right) + \cos\left(d x + c\right)^{2} + {\left(2 \, d x + \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 2}{a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"(2*d*x + (2*d*x + 3)*cos(d*x + c) + cos(d*x + c)^2 + (2*d*x + cos(d*x + c) - 2)*sin(d*x + c) + 2)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
311,1,103,0,1.160910," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, \cos\left(d x + c\right) + 4 \, \sin\left(d x + c\right) - 4}{2 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-1/2*((cos(d*x + c) + sin(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) - (cos(d*x + c) + sin(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) - 4*cos(d*x + c) + 4*sin(d*x + c) - 4)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","B",0
312,1,160,0,0.868707," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(3 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) - 2}{a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d - {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"(3*cos(d*x + c)^2 + (cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*log(1/2*cos(d*x + c) + 1/2) - (cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*log(-1/2*cos(d*x + c) + 1/2) + (3*cos(d*x + c) + 2)*sin(d*x + c) + cos(d*x + c) - 2)/(a^2*d*cos(d*x + c)^2 - a^2*d - (a^2*d*cos(d*x + c) + a^2*d)*sin(d*x + c))","B",0
313,1,246,0,0.881807," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{2} - 5 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(8 \, \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right) - 4\right)} \sin\left(d x + c\right) - 14 \, \cos\left(d x + c\right) - 8}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \cos\left(d x + c\right) - a^{2} d + {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*(16*cos(d*x + c)^3 + 10*cos(d*x + c)^2 - 5*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*log(1/2*cos(d*x + c) + 1/2) + 5*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*log(-1/2*cos(d*x + c) + 1/2) - 2*(8*cos(d*x + c)^2 + 3*cos(d*x + c) - 4)*sin(d*x + c) - 14*cos(d*x + c) - 8)/(a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2 - a^2*d*cos(d*x + c) - a^2*d + (a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","B",0
314,1,302,0,0.820315," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{28 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} - 42 \, \cos\left(d x + c\right)^{2} + 9 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 9 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(14 \, \cos\left(d x + c\right)^{3} + 9 \, \cos\left(d x + c\right)^{2} - 12 \, \cos\left(d x + c\right) - 6\right)} \sin\left(d x + c\right) - 12 \, \cos\left(d x + c\right) + 12}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d - {\left(a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/6*(28*cos(d*x + c)^4 + 10*cos(d*x + c)^3 - 42*cos(d*x + c)^2 + 9*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) - 9*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) + 2*(14*cos(d*x + c)^3 + 9*cos(d*x + c)^2 - 12*cos(d*x + c) - 6)*sin(d*x + c) - 12*cos(d*x + c) + 12)/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d - (a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2 - a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))","B",0
315,1,163,0,0.977439," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{4} - {\left(33 \, d x - 53\right)} \cos\left(d x + c\right)^{2} - 12 \, \cos\left(d x + c\right)^{3} + 66 \, d x + {\left(33 \, d x + 64\right)} \cos\left(d x + c\right) + {\left(3 \, \cos\left(d x + c\right)^{3} + 66 \, d x + {\left(33 \, d x + 68\right)} \cos\left(d x + c\right) + 15 \, \cos\left(d x + c\right)^{2} + 4\right)} \sin\left(d x + c\right) - 4}{6 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right) + 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/6*(3*cos(d*x + c)^4 - (33*d*x - 53)*cos(d*x + c)^2 - 12*cos(d*x + c)^3 + 66*d*x + (33*d*x + 64)*cos(d*x + c) + (3*cos(d*x + c)^3 + 66*d*x + (33*d*x + 68)*cos(d*x + c) + 15*cos(d*x + c)^2 + 4)*sin(d*x + c) - 4)/(a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d - (a^3*d*cos(d*x + c) + 2*a^3*d)*sin(d*x + c))","A",0
316,1,144,0,0.760886," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left(9 \, d x - 16\right)} \cos\left(d x + c\right)^{2} + 3 \, \cos\left(d x + c\right)^{3} - 18 \, d x - {\left(9 \, d x + 17\right)} \cos\left(d x + c\right) - {\left(18 \, d x + {\left(9 \, d x + 19\right)} \cos\left(d x + c\right) + 3 \, \cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right) + 2}{3 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right) + 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/3*((9*d*x - 16)*cos(d*x + c)^2 + 3*cos(d*x + c)^3 - 18*d*x - (9*d*x + 17)*cos(d*x + c) - (18*d*x + (9*d*x + 19)*cos(d*x + c) + 3*cos(d*x + c)^2 + 2)*sin(d*x + c) + 2)/(a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d - (a^3*d*cos(d*x + c) + 2*a^3*d)*sin(d*x + c))","A",0
317,1,124,0,0.879918," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, d x - 7\right)} \cos\left(d x + c\right)^{2} - 6 \, d x - {\left(3 \, d x + 5\right)} \cos\left(d x + c\right) - {\left(6 \, d x + {\left(3 \, d x + 7\right)} \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) + 2}{3 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right) + 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3*((3*d*x - 7)*cos(d*x + c)^2 - 6*d*x - (3*d*x + 5)*cos(d*x + c) - (6*d*x + (3*d*x + 7)*cos(d*x + c) + 2)*sin(d*x + c) + 2)/(a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d - (a^3*d*cos(d*x + c) + 2*a^3*d)*sin(d*x + c))","B",0
318,1,194,0,0.680788," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{10 \, \cos\left(d x + c\right)^{2} + 3 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(5 \, \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + 14 \, \cos\left(d x + c\right) + 4}{6 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right) + 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/6*(10*cos(d*x + c)^2 + 3*(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)*log(1/2*cos(d*x + c) + 1/2) - 3*(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)*log(-1/2*cos(d*x + c) + 1/2) + 2*(5*cos(d*x + c) - 2)*sin(d*x + c) + 14*cos(d*x + c) + 4)/(a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d - (a^3*d*cos(d*x + c) + 2*a^3*d)*sin(d*x + c))","B",0
319,1,279,0,0.888646," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{28 \, \cos\left(d x + c\right)^{3} - 10 \, \cos\left(d x + c\right)^{2} - 9 \, {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(14 \, \cos\left(d x + c\right)^{2} + 19 \, \cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - 34 \, \cos\left(d x + c\right) + 4}{6 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 2 \, a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/6*(28*cos(d*x + c)^3 - 10*cos(d*x + c)^2 - 9*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + (cos(d*x + c)^2 - cos(d*x + c) - 2)*sin(d*x + c) - cos(d*x + c) - 2)*log(1/2*cos(d*x + c) + 1/2) + 9*(cos(d*x + c)^3 + 2*cos(d*x + c)^2 + (cos(d*x + c)^2 - cos(d*x + c) - 2)*sin(d*x + c) - cos(d*x + c) - 2)*log(-1/2*cos(d*x + c) + 1/2) - 2*(14*cos(d*x + c)^2 + 19*cos(d*x + c) + 2)*sin(d*x + c) - 34*cos(d*x + c) + 4)/(a^3*d*cos(d*x + c)^3 + 2*a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d + (a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d)*sin(d*x + c))","B",0
320,1,365,0,1.044927," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{104 \, \cos\left(d x + c\right)^{4} + 142 \, \cos\left(d x + c\right)^{3} - 90 \, \cos\left(d x + c\right)^{2} + 33 \, {\left(\cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) + 2\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 33 \, {\left(\cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) + 2\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(52 \, \cos\left(d x + c\right)^{3} - 19 \, \cos\left(d x + c\right)^{2} - 64 \, \cos\left(d x + c\right) + 4\right)} \sin\left(d x + c\right) - 136 \, \cos\left(d x + c\right) - 8}{12 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - a^{3} d \cos\left(d x + c\right)^{3} - 3 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right) + 2 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right)^{3} + 2 \, a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - 2 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/12*(104*cos(d*x + c)^4 + 142*cos(d*x + c)^3 - 90*cos(d*x + c)^2 + 33*(cos(d*x + c)^4 - cos(d*x + c)^3 - 3*cos(d*x + c)^2 - (cos(d*x + c)^3 + 2*cos(d*x + c)^2 - cos(d*x + c) - 2)*sin(d*x + c) + cos(d*x + c) + 2)*log(1/2*cos(d*x + c) + 1/2) - 33*(cos(d*x + c)^4 - cos(d*x + c)^3 - 3*cos(d*x + c)^2 - (cos(d*x + c)^3 + 2*cos(d*x + c)^2 - cos(d*x + c) - 2)*sin(d*x + c) + cos(d*x + c) + 2)*log(-1/2*cos(d*x + c) + 1/2) + 2*(52*cos(d*x + c)^3 - 19*cos(d*x + c)^2 - 64*cos(d*x + c) + 4)*sin(d*x + c) - 136*cos(d*x + c) - 8)/(a^3*d*cos(d*x + c)^4 - a^3*d*cos(d*x + c)^3 - 3*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c) + 2*a^3*d - (a^3*d*cos(d*x + c)^3 + 2*a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - 2*a^3*d)*sin(d*x + c))","B",0
321,1,243,0,0.737640," ","integrate(cos(f*x+e)^2*sin(f*x+e)/(a+a*sin(f*x+e))^6,x, algorithm=""fricas"")","\frac{4 \, \cos\left(f x + e\right)^{5} - 16 \, \cos\left(f x + e\right)^{4} - 50 \, \cos\left(f x + e\right)^{3} - 65 \, \cos\left(f x + e\right)^{2} - {\left(4 \, \cos\left(f x + e\right)^{4} + 20 \, \cos\left(f x + e\right)^{3} - 30 \, \cos\left(f x + e\right)^{2} + 35 \, \cos\left(f x + e\right) + 70\right)} \sin\left(f x + e\right) + 35 \, \cos\left(f x + e\right) + 70}{315 \, {\left(a^{6} f \cos\left(f x + e\right)^{5} + 5 \, a^{6} f \cos\left(f x + e\right)^{4} - 8 \, a^{6} f \cos\left(f x + e\right)^{3} - 20 \, a^{6} f \cos\left(f x + e\right)^{2} + 8 \, a^{6} f \cos\left(f x + e\right) + 16 \, a^{6} f + {\left(a^{6} f \cos\left(f x + e\right)^{4} - 4 \, a^{6} f \cos\left(f x + e\right)^{3} - 12 \, a^{6} f \cos\left(f x + e\right)^{2} + 8 \, a^{6} f \cos\left(f x + e\right) + 16 \, a^{6} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/315*(4*cos(f*x + e)^5 - 16*cos(f*x + e)^4 - 50*cos(f*x + e)^3 - 65*cos(f*x + e)^2 - (4*cos(f*x + e)^4 + 20*cos(f*x + e)^3 - 30*cos(f*x + e)^2 + 35*cos(f*x + e) + 70)*sin(f*x + e) + 35*cos(f*x + e) + 70)/(a^6*f*cos(f*x + e)^5 + 5*a^6*f*cos(f*x + e)^4 - 8*a^6*f*cos(f*x + e)^3 - 20*a^6*f*cos(f*x + e)^2 + 8*a^6*f*cos(f*x + e) + 16*a^6*f + (a^6*f*cos(f*x + e)^4 - 4*a^6*f*cos(f*x + e)^3 - 12*a^6*f*cos(f*x + e)^2 + 8*a^6*f*cos(f*x + e) + 16*a^6*f)*sin(f*x + e))","A",0
322,1,151,0,0.870467," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, \cos\left(d x + c\right)^{6} + 350 \, \cos\left(d x + c\right)^{5} - 500 \, \cos\left(d x + c\right)^{4} - 586 \, \cos\left(d x + c\right)^{3} + 17 \, \cos\left(d x + c\right)^{2} + {\left(315 \, \cos\left(d x + c\right)^{5} - 35 \, \cos\left(d x + c\right)^{4} - 535 \, \cos\left(d x + c\right)^{3} + 51 \, \cos\left(d x + c\right)^{2} + 68 \, \cos\left(d x + c\right) + 136\right)} \sin\left(d x + c\right) - 68 \, \cos\left(d x + c\right) - 136\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3465 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/3465*(315*cos(d*x + c)^6 + 350*cos(d*x + c)^5 - 500*cos(d*x + c)^4 - 586*cos(d*x + c)^3 + 17*cos(d*x + c)^2 + (315*cos(d*x + c)^5 - 35*cos(d*x + c)^4 - 535*cos(d*x + c)^3 + 51*cos(d*x + c)^2 + 68*cos(d*x + c) + 136)*sin(d*x + c) - 68*cos(d*x + c) - 136)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
323,1,130,0,0.880139," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, \cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{4} - 11 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - {\left(7 \, \cos\left(d x + c\right)^{4} + 8 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right) - 8\right)} \sin\left(d x + c\right) - 4 \, \cos\left(d x + c\right) - 8\right)} \sqrt{a \sin\left(d x + c\right) + a}}{63 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/63*(7*cos(d*x + c)^5 - cos(d*x + c)^4 - 11*cos(d*x + c)^3 + cos(d*x + c)^2 - (7*cos(d*x + c)^4 + 8*cos(d*x + c)^3 - 3*cos(d*x + c)^2 - 4*cos(d*x + c) - 8)*sin(d*x + c) - 4*cos(d*x + c) - 8)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
324,1,111,0,0.777639," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} + 18 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)^{2} + {\left(15 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right) - 8\right)} \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right) + 8\right)} \sqrt{a \sin\left(d x + c\right) + a}}{105 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/105*(15*cos(d*x + c)^4 + 18*cos(d*x + c)^3 - cos(d*x + c)^2 + (15*cos(d*x + c)^3 - 3*cos(d*x + c)^2 - 4*cos(d*x + c) - 8)*sin(d*x + c) + 4*cos(d*x + c) + 8)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
325,1,250,0,0.924271," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a} {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right) + 1\right)} \sqrt{a \sin\left(d x + c\right) + a}}{6 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/6*(3*sqrt(a)*(cos(d*x + c) + sin(d*x + c) + 1)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(cos(d*x + c)^2 + (cos(d*x + c) - 1)*sin(d*x + c) + 2*cos(d*x + c) + 1)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c) + d*sin(d*x + c) + d)","B",0
326,1,279,0,0.922675," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(2 \, \cos\left(d x + c\right)^{2} + {\left(2 \, \cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a}}{4 \, {\left(d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/4*((cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(2*cos(d*x + c)^2 + (2*cos(d*x + c) + 3)*sin(d*x + c) - cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^2 - (d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
327,1,319,0,0.796266," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{5 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(3 \, \cos\left(d x + c\right)^{2} + {\left(3 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right) - 1\right)} \sqrt{a \sin\left(d x + c\right) + a}}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/16*(5*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(3*cos(d*x + c)^2 + (3*cos(d*x + c) + 1)*sin(d*x + c) + 2*cos(d*x + c) - 1)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
328,1,361,0,0.895222," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{9 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(9 \, \cos\left(d x + c\right)^{3} + 19 \, \cos\left(d x + c\right)^{2} - {\left(9 \, \cos\left(d x + c\right)^{2} - 10 \, \cos\left(d x + c\right) - 11\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 11\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/96*(9*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(9*cos(d*x + c)^3 + 19*cos(d*x + c)^2 - (9*cos(d*x + c)^2 - 10*cos(d*x + c) - 11)*sin(d*x + c) - cos(d*x + c) - 11)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 - (d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - d)*sin(d*x + c) + d)","B",0
329,1,189,0,0.873049," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3465 \, a \cos\left(d x + c\right)^{7} - 4410 \, a \cos\left(d x + c\right)^{6} - 14140 \, a \cos\left(d x + c\right)^{5} + 7330 \, a \cos\left(d x + c\right)^{4} + 15299 \, a \cos\left(d x + c\right)^{3} - 568 \, a \cos\left(d x + c\right)^{2} + 2272 \, a \cos\left(d x + c\right) - {\left(3465 \, a \cos\left(d x + c\right)^{6} + 7875 \, a \cos\left(d x + c\right)^{5} - 6265 \, a \cos\left(d x + c\right)^{4} - 13595 \, a \cos\left(d x + c\right)^{3} + 1704 \, a \cos\left(d x + c\right)^{2} + 2272 \, a \cos\left(d x + c\right) + 4544 \, a\right)} \sin\left(d x + c\right) + 4544 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{45045 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/45045*(3465*a*cos(d*x + c)^7 - 4410*a*cos(d*x + c)^6 - 14140*a*cos(d*x + c)^5 + 7330*a*cos(d*x + c)^4 + 15299*a*cos(d*x + c)^3 - 568*a*cos(d*x + c)^2 + 2272*a*cos(d*x + c) - (3465*a*cos(d*x + c)^6 + 7875*a*cos(d*x + c)^5 - 6265*a*cos(d*x + c)^4 - 13595*a*cos(d*x + c)^3 + 1704*a*cos(d*x + c)^2 + 2272*a*cos(d*x + c) + 4544*a)*sin(d*x + c) + 4544*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
330,1,166,0,0.975565," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(105 \, a \cos\left(d x + c\right)^{6} + 245 \, a \cos\left(d x + c\right)^{5} - 185 \, a \cos\left(d x + c\right)^{4} - 397 \, a \cos\left(d x + c\right)^{3} + 24 \, a \cos\left(d x + c\right)^{2} - 96 \, a \cos\left(d x + c\right) + {\left(105 \, a \cos\left(d x + c\right)^{5} - 140 \, a \cos\left(d x + c\right)^{4} - 325 \, a \cos\left(d x + c\right)^{3} + 72 \, a \cos\left(d x + c\right)^{2} + 96 \, a \cos\left(d x + c\right) + 192 \, a\right)} \sin\left(d x + c\right) - 192 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{1155 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/1155*(105*a*cos(d*x + c)^6 + 245*a*cos(d*x + c)^5 - 185*a*cos(d*x + c)^4 - 397*a*cos(d*x + c)^3 + 24*a*cos(d*x + c)^2 - 96*a*cos(d*x + c) + (105*a*cos(d*x + c)^5 - 140*a*cos(d*x + c)^4 - 325*a*cos(d*x + c)^3 + 72*a*cos(d*x + c)^2 + 96*a*cos(d*x + c) + 192*a)*sin(d*x + c) - 192*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
331,1,145,0,0.862320," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, a \cos\left(d x + c\right)^{5} - 50 \, a \cos\left(d x + c\right)^{4} - 109 \, a \cos\left(d x + c\right)^{3} + 8 \, a \cos\left(d x + c\right)^{2} - 32 \, a \cos\left(d x + c\right) - {\left(35 \, a \cos\left(d x + c\right)^{4} + 85 \, a \cos\left(d x + c\right)^{3} - 24 \, a \cos\left(d x + c\right)^{2} - 32 \, a \cos\left(d x + c\right) - 64 \, a\right)} \sin\left(d x + c\right) - 64 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{315 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/315*(35*a*cos(d*x + c)^5 - 50*a*cos(d*x + c)^4 - 109*a*cos(d*x + c)^3 + 8*a*cos(d*x + c)^2 - 32*a*cos(d*x + c) - (35*a*cos(d*x + c)^4 + 85*a*cos(d*x + c)^3 - 24*a*cos(d*x + c)^2 - 32*a*cos(d*x + c) - 64*a)*sin(d*x + c) - 64*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
332,1,282,0,0.934759," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{5 \, {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(a \cos\left(d x + c\right)^{3} - 2 \, a \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{2} + 3 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{10 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/10*(5*(a*cos(d*x + c) + a*sin(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(a*cos(d*x + c)^3 - 2*a*cos(d*x + c)^2 - 2*a*cos(d*x + c) - (a*cos(d*x + c)^2 + 3*a*cos(d*x + c) + a)*sin(d*x + c) + a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c) + d*sin(d*x + c) + d)","B",0
333,1,315,0,1.016463," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{9 \, {\left(a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(2 \, a \cos\left(d x + c\right)^{3} - 8 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) - {\left(2 \, a \cos\left(d x + c\right)^{2} + 10 \, a \cos\left(d x + c\right) + 11 \, a\right)} \sin\left(d x + c\right) + 11 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{12 \, {\left(d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/12*(9*(a*cos(d*x + c)^2 - (a*cos(d*x + c) + a)*sin(d*x + c) - a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(2*a*cos(d*x + c)^3 - 8*a*cos(d*x + c)^2 + a*cos(d*x + c) - (2*a*cos(d*x + c)^2 + 10*a*cos(d*x + c) + 11*a)*sin(d*x + c) + 11*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^2 - (d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
334,1,359,0,0.583819," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{{\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(8 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)^{2} - 6 \, a \cos\left(d x + c\right) - {\left(8 \, a \cos\left(d x + c\right)^{2} - 7 \, a \cos\left(d x + c\right) - 13 \, a\right)} \sin\left(d x + c\right) - 13 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{16 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/16*((a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) + (a*cos(d*x + c)^2 - a)*sin(d*x + c) - a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(8*a*cos(d*x + c)^3 + 15*a*cos(d*x + c)^2 - 6*a*cos(d*x + c) - (8*a*cos(d*x + c)^2 - 7*a*cos(d*x + c) - 13*a)*sin(d*x + c) - 13*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
335,1,380,0,0.980391," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{39 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(9 \, a \cos\left(d x + c\right)^{3} - 13 \, a \cos\left(d x + c\right)^{2} - 17 \, a \cos\left(d x + c\right) - {\left(9 \, a \cos\left(d x + c\right)^{2} + 22 \, a \cos\left(d x + c\right) + 5 \, a\right)} \sin\left(d x + c\right) + 5 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/96*(39*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 - (a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - a)*sin(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(9*a*cos(d*x + c)^3 - 13*a*cos(d*x + c)^2 - 17*a*cos(d*x + c) - (9*a*cos(d*x + c)^2 + 22*a*cos(d*x + c) + 5*a)*sin(d*x + c) + 5*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 - (d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - d)*sin(d*x + c) + d)","B",0
336,1,136,0,0.718168," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, \cos\left(d x + c\right)^{5} + 40 \, \cos\left(d x + c\right)^{4} - 64 \, \cos\left(d x + c\right)^{3} - 82 \, \cos\left(d x + c\right)^{2} - {\left(35 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{3} - 69 \, \cos\left(d x + c\right)^{2} + 13 \, \cos\left(d x + c\right) + 26\right)} \sin\left(d x + c\right) + 13 \, \cos\left(d x + c\right) + 26\right)} \sqrt{a \sin\left(d x + c\right) + a}}{315 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"2/315*(35*cos(d*x + c)^5 + 40*cos(d*x + c)^4 - 64*cos(d*x + c)^3 - 82*cos(d*x + c)^2 - (35*cos(d*x + c)^4 - 5*cos(d*x + c)^3 - 69*cos(d*x + c)^2 + 13*cos(d*x + c) + 26)*sin(d*x + c) + 13*cos(d*x + c) + 26)*sqrt(a*sin(d*x + c) + a)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
337,1,115,0,0.912781," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{3} - 29 \, \cos\left(d x + c\right)^{2} + {\left(15 \, \cos\left(d x + c\right)^{3} + 18 \, \cos\left(d x + c\right)^{2} - 11 \, \cos\left(d x + c\right) - 22\right)} \sin\left(d x + c\right) + 11 \, \cos\left(d x + c\right) + 22\right)} \sqrt{a \sin\left(d x + c\right) + a}}{105 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"-2/105*(15*cos(d*x + c)^4 - 3*cos(d*x + c)^3 - 29*cos(d*x + c)^2 + (15*cos(d*x + c)^3 + 18*cos(d*x + c)^2 - 11*cos(d*x + c) - 22)*sin(d*x + c) + 11*cos(d*x + c) + 22)*sqrt(a*sin(d*x + c) + a)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
338,1,96,0,0.900354," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2\right)} \sqrt{a \sin\left(d x + c\right) + a}}{15 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"-2/15*(3*cos(d*x + c)^3 + 4*cos(d*x + c)^2 - (3*cos(d*x + c)^2 - cos(d*x + c) - 2)*sin(d*x + c) - cos(d*x + c) - 2)*sqrt(a*sin(d*x + c) + a)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
339,1,236,0,0.907933," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{2 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"1/2*(sqrt(a)*(cos(d*x + c) + sin(d*x + c) + 1)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1))/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","B",0
340,1,263,0,0.920575," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{4 \, {\left(a d \cos\left(d x + c\right)^{2} - a d - {\left(a d \cos\left(d x + c\right) + a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*((cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1))/(a*d*cos(d*x + c)^2 - a*d - (a*d*cos(d*x + c) + a*d)*sin(d*x + c))","B",0
341,1,320,0,0.890177," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{{\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a}}{16 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} - a d \cos\left(d x + c\right) - a d + {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/16*((cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2 - a*d*cos(d*x + c) - a*d + (a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","B",0
342,1,367,0,0.863905," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(3 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) + 7\right)} \sin\left(d x + c\right) + 5 \, \cos\left(d x + c\right) + 7\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d - {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} - a d \cos\left(d x + c\right) - a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/96*(3*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(3*cos(d*x + c)^3 + cos(d*x + c)^2 - (3*cos(d*x + c)^2 + 2*cos(d*x + c) + 7)*sin(d*x + c) + 5*cos(d*x + c) + 7)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d - (a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2 - a*d*cos(d*x + c) - a*d)*sin(d*x + c))","B",0
343,1,259,0,0.968333," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\frac{105 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - 2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 24 \, \cos\left(d x + c\right)^{3} - 92 \, \cos\left(d x + c\right)^{2} + {\left(15 \, \cos\left(d x + c\right)^{3} + 39 \, \cos\left(d x + c\right)^{2} - 53 \, \cos\left(d x + c\right) - 211\right)} \sin\left(d x + c\right) + 158 \, \cos\left(d x + c\right) + 211\right)} \sqrt{a \sin\left(d x + c\right) + a}}{105 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/105*(105*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - 2*(15*cos(d*x + c)^4 - 24*cos(d*x + c)^3 - 92*cos(d*x + c)^2 + (15*cos(d*x + c)^3 + 39*cos(d*x + c)^2 - 53*cos(d*x + c) - 211)*sin(d*x + c) + 158*cos(d*x + c) + 211)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
344,1,236,0,0.892931," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\frac{5 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - 2 \, {\left(\cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 9\right)} \sin\left(d x + c\right) - 7 \, \cos\left(d x + c\right) - 9\right)} \sqrt{a \sin\left(d x + c\right) + a}}{5 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/5*(5*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - 2*(cos(d*x + c)^3 + 3*cos(d*x + c)^2 - (cos(d*x + c)^2 - 2*cos(d*x + c) - 9)*sin(d*x + c) - 7*cos(d*x + c) - 9)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
345,1,215,0,0.837331," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{\frac{3 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + 2 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 5\right)} \sin\left(d x + c\right) - 4 \, \cos\left(d x + c\right) - 5\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/3*(3*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + 2*(cos(d*x + c)^2 + (cos(d*x + c) + 5)*sin(d*x + c) - 4*cos(d*x + c) - 5)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","B",0
346,1,291,0,1.007959," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} \sqrt{a} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right) + \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right)}{2 \, a^{2} d}"," ",0,"1/2*(2*sqrt(2)*sqrt(a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2)) + sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)))/(a^2*d)","B",0
347,1,421,0,0.691825," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + \frac{4 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d - {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*(3*(cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*sqrt(2)*(a*cos(d*x + c)^2 - (a*cos(d*x + c) + a)*sin(d*x + c) - a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + 4*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1))/(a^2*d*cos(d*x + c)^2 - a^2*d - (a^2*d*cos(d*x + c) + a^2*d)*sin(d*x + c))","B",0
348,1,508,0,1.040863," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{11 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + \frac{16 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - 4 \, {\left(5 \, \cos\left(d x + c\right)^{2} + {\left(5 \, \cos\left(d x + c\right) + 7\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 7\right)} \sqrt{a \sin\left(d x + c\right) + a}}{16 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \cos\left(d x + c\right) - a^{2} d + {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/16*(11*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 16*sqrt(2)*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) + (a*cos(d*x + c)^2 - a)*sin(d*x + c) - a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - 4*(5*cos(d*x + c)^2 + (5*cos(d*x + c) + 7)*sin(d*x + c) - 2*cos(d*x + c) - 7)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2 - a^2*d*cos(d*x + c) - a^2*d + (a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","B",0
349,1,564,0,0.738930," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{69 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + \frac{96 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + 4 \, {\left(27 \, \cos\left(d x + c\right)^{3} + 41 \, \cos\left(d x + c\right)^{2} - {\left(27 \, \cos\left(d x + c\right)^{2} - 14 \, \cos\left(d x + c\right) - 49\right)} \sin\left(d x + c\right) - 35 \, \cos\left(d x + c\right) - 49\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d - {\left(a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/96*(69*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 96*sqrt(2)*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 - (a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - a)*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + 4*(27*cos(d*x + c)^3 + 41*cos(d*x + c)^2 - (27*cos(d*x + c)^2 - 14*cos(d*x + c) - 49)*sin(d*x + c) - 35*cos(d*x + c) - 49)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d - (a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2 - a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))","B",0
350,1,72,0,0.720208," ","integrate(cos(d*x+c)^3*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{70 \, a \cos\left(d x + c\right)^{6} - 105 \, a \cos\left(d x + c\right)^{4} + 12 \, {\left(5 \, a \cos\left(d x + c\right)^{6} - 8 \, a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(70*a*cos(d*x + c)^6 - 105*a*cos(d*x + c)^4 + 12*(5*a*cos(d*x + c)^6 - 8*a*cos(d*x + c)^4 + a*cos(d*x + c)^2 + 2*a)*sin(d*x + c))/d","A",0
351,1,62,0,0.664284," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, a \cos\left(d x + c\right)^{6} - 15 \, a \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2} - 2 \, a\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*a*cos(d*x + c)^6 - 15*a*cos(d*x + c)^4 - 4*(3*a*cos(d*x + c)^4 - a*cos(d*x + c)^2 - 2*a)*sin(d*x + c))/d","A",0
352,1,51,0,0.895124," ","integrate(cos(d*x+c)^3*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, a \cos\left(d x + c\right)^{4} + 4 \, {\left(3 \, a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2} - 2 \, a\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(15*a*cos(d*x + c)^4 + 4*(3*a*cos(d*x + c)^4 - a*cos(d*x + c)^2 - 2*a)*sin(d*x + c))/d","A",0
353,1,39,0,0.852170," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a \cos\left(d x + c\right)^{4} - 4 \, {\left(a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*a*cos(d*x + c)^4 - 4*(a*cos(d*x + c)^2 + 2*a)*sin(d*x + c))/d","A",0
354,1,51,0,0.931597," ","integrate(cos(d*x+c)^3*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right)^{2} + 6 \, a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 2 \, {\left(a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*a*cos(d*x + c)^2 + 6*a*log(1/2*sin(d*x + c)) + 2*(a*cos(d*x + c)^2 + 2*a)*sin(d*x + c))/d","A",0
355,1,68,0,0.961589," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, a \cos\left(d x + c\right)^{2} + 4 \, a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(2 \, a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - 8 \, a}{4 \, d \sin\left(d x + c\right)}"," ",0,"1/4*(4*a*cos(d*x + c)^2 + 4*a*log(1/2*sin(d*x + c))*sin(d*x + c) + (2*a*cos(d*x + c)^2 - a)*sin(d*x + c) - 8*a)/(d*sin(d*x + c))","A",0
356,1,69,0,0.869406," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 2 \, {\left(a \cos\left(d x + c\right)^{2} - 2 \, a\right)} \sin\left(d x + c\right) - a}{2 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/2*(2*(a*cos(d*x + c)^2 - a)*log(1/2*sin(d*x + c)) + 2*(a*cos(d*x + c)^2 - 2*a)*sin(d*x + c) - a)/(d*cos(d*x + c)^2 - d)","A",0
357,1,47,0,1.115786," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, \cos\left(d x + c\right)^{4} - 6 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right)}{12 \, a d}"," ",0,"-1/12*(3*cos(d*x + c)^4 - 6*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 1)*sin(d*x + c))/(a*d)","A",0
358,1,37,0,0.939306," ","integrate(cos(d*x+c)^3*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right)}{6 \, a d}"," ",0,"-1/6*(3*cos(d*x + c)^2 - 2*(cos(d*x + c)^2 - 1)*sin(d*x + c))/(a*d)","A",0
359,1,25,0,1.024056," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"1/2*(cos(d*x + c)^2 + 2*sin(d*x + c))/(a*d)","A",0
360,1,25,0,1.030092," ","integrate(cos(d*x+c)^3*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - \sin\left(d x + c\right)}{a d}"," ",0,"(log(1/2*sin(d*x + c)) - sin(d*x + c))/(a*d)","A",0
361,1,34,0,1.021994," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 1}{a d \sin\left(d x + c\right)}"," ",0,"-(log(1/2*sin(d*x + c))*sin(d*x + c) + 1)/(a*d*sin(d*x + c))","A",0
362,1,30,0,0.554133," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, \sin\left(d x + c\right) - 1}{2 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"-1/2*(2*sin(d*x + c) - 1)/(a*d*cos(d*x + c)^2 - a*d)","A",0
363,1,38,0,0.823605," ","integrate(cos(d*x+c)^3*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, \sin\left(d x + c\right) - 2}{6 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(3*sin(d*x + c) - 2)/((a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
364,1,41,0,0.636009," ","integrate(cos(d*x+c)^3*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \sin\left(d x + c\right) - 3}{12 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"1/12*(4*sin(d*x + c) - 3)/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)","A",0
365,1,95,0,0.908464," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4480 \, a \cos\left(d x + c\right)^{9} - 11520 \, a \cos\left(d x + c\right)^{7} + 8064 \, a \cos\left(d x + c\right)^{5} - 945 \, a d x - 315 \, {\left(16 \, a \cos\left(d x + c\right)^{7} - 24 \, a \cos\left(d x + c\right)^{5} + 2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40320 \, d}"," ",0,"-1/40320*(4480*a*cos(d*x + c)^9 - 11520*a*cos(d*x + c)^7 + 8064*a*cos(d*x + c)^5 - 945*a*d*x - 315*(16*a*cos(d*x + c)^7 - 24*a*cos(d*x + c)^5 + 2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
366,1,84,0,0.922350," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{640 \, a \cos\left(d x + c\right)^{7} - 896 \, a \cos\left(d x + c\right)^{5} + 105 \, a d x + 35 \, {\left(16 \, a \cos\left(d x + c\right)^{7} - 24 \, a \cos\left(d x + c\right)^{5} + 2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4480 \, d}"," ",0,"1/4480*(640*a*cos(d*x + c)^7 - 896*a*cos(d*x + c)^5 + 105*a*d*x + 35*(16*a*cos(d*x + c)^7 - 24*a*cos(d*x + c)^5 + 2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
367,1,73,0,0.950788," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{240 \, a \cos\left(d x + c\right)^{7} - 336 \, a \cos\left(d x + c\right)^{5} + 105 \, a d x - 35 \, {\left(8 \, a \cos\left(d x + c\right)^{5} - 2 \, a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(240*a*cos(d*x + c)^7 - 336*a*cos(d*x + c)^5 + 105*a*d*x - 35*(8*a*cos(d*x + c)^5 - 2*a*cos(d*x + c)^3 - 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
368,1,62,0,0.923529," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{48 \, a \cos\left(d x + c\right)^{5} - 15 \, a d x + 5 \, {\left(8 \, a \cos\left(d x + c\right)^{5} - 2 \, a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(48*a*cos(d*x + c)^5 - 15*a*d*x + 5*(8*a*cos(d*x + c)^5 - 2*a*cos(d*x + c)^3 - 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
369,1,88,0,0.913077," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, a \cos\left(d x + c\right)^{3} + 9 \, a d x + 24 \, a \cos\left(d x + c\right) - 12 \, a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(8*a*cos(d*x + c)^3 + 9*a*d*x + 24*a*cos(d*x + c) - 12*a*log(1/2*cos(d*x + c) + 1/2) + 12*a*log(-1/2*cos(d*x + c) + 1/2) + 3*(2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
370,1,107,0,0.870831," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right)^{3} - 3 \, a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, a \cos\left(d x + c\right) + {\left(2 \, a \cos\left(d x + c\right)^{3} - 9 \, a d x + 6 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d \sin\left(d x + c\right)}"," ",0,"1/6*(3*a*cos(d*x + c)^3 - 3*a*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*a*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*a*cos(d*x + c) + (2*a*cos(d*x + c)^3 - 9*a*d*x + 6*a*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
371,1,139,0,0.881085," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, a d x \cos\left(d x + c\right)^{2} + 4 \, a \cos\left(d x + c\right)^{3} - 6 \, a d x - 6 \, a \cos\left(d x + c\right) - 3 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(6*a*d*x*cos(d*x + c)^2 + 4*a*cos(d*x + c)^3 - 6*a*d*x - 6*a*cos(d*x + c) - 3*(a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + 3*(a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2) + 2*(a*cos(d*x + c)^3 - 3*a*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
372,1,160,0,0.998566," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, a \cos\left(d x + c\right)^{3} + 9 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 12 \, a \cos\left(d x + c\right) + 6 \, {\left(2 \, a d x \cos\left(d x + c\right)^{2} - 2 \, a \cos\left(d x + c\right)^{3} - 2 \, a d x + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(16*a*cos(d*x + c)^3 + 9*(a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*(a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 12*a*cos(d*x + c) + 6*(2*a*d*x*cos(d*x + c)^2 - 2*a*cos(d*x + c)^3 - 2*a*d*x + 3*a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
373,1,180,0,0.979144," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, a d x \cos\left(d x + c\right)^{4} - 96 \, a d x \cos\left(d x + c\right)^{2} - 30 \, a \cos\left(d x + c\right)^{3} + 48 \, a d x + 18 \, a \cos\left(d x + c\right) - 9 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(4 \, a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/48*(48*a*d*x*cos(d*x + c)^4 - 96*a*d*x*cos(d*x + c)^2 - 30*a*cos(d*x + c)^3 + 48*a*d*x + 18*a*cos(d*x + c) - 9*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 9*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2) - 16*(4*a*cos(d*x + c)^3 - 3*a*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
374,1,160,0,1.149175," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a \cos\left(d x + c\right)^{5} + 15 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 10 \, {\left(5 \, a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/80*(16*a*cos(d*x + c)^5 + 15*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 10*(5*a*cos(d*x + c)^3 - 3*a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
375,1,187,0,1.188306," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{96 \, a \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + 30 \, a \cos\left(d x + c\right)^{5} + 80 \, a \cos\left(d x + c\right)^{3} - 30 \, a \cos\left(d x + c\right) - 15 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/480*(96*a*cos(d*x + c)^5*sin(d*x + c) + 30*a*cos(d*x + c)^5 + 80*a*cos(d*x + c)^3 - 30*a*cos(d*x + c) - 15*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + 15*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
376,1,221,0,1.084228," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{192 \, a \cos\left(d x + c\right)^{7} - 672 \, a \cos\left(d x + c\right)^{5} + 105 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 105 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 70 \, {\left(3 \, a \cos\left(d x + c\right)^{5} + 8 \, a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3360 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/3360*(192*a*cos(d*x + c)^7 - 672*a*cos(d*x + c)^5 + 105*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 105*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 70*(3*a*cos(d*x + c)^5 + 8*a*cos(d*x + c)^3 - 3*a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
377,1,239,0,0.737451," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{210 \, a \cos\left(d x + c\right)^{7} - 770 \, a \cos\left(d x + c\right)^{5} - 770 \, a \cos\left(d x + c\right)^{3} + 210 \, a \cos\left(d x + c\right) - 105 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 256 \, {\left(2 \, a \cos\left(d x + c\right)^{7} - 7 \, a \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)}{8960 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/8960*(210*a*cos(d*x + c)^7 - 770*a*cos(d*x + c)^5 - 770*a*cos(d*x + c)^3 + 210*a*cos(d*x + c) - 105*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 105*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2) + 256*(2*a*cos(d*x + c)^7 - 7*a*cos(d*x + c)^5)*sin(d*x + c))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
378,1,124,0,1.041085," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{17920 \, a^{2} \cos\left(d x + c\right)^{9} - 46080 \, a^{2} \cos\left(d x + c\right)^{7} + 32256 \, a^{2} \cos\left(d x + c\right)^{5} - 2835 \, a^{2} d x + 63 \, {\left(128 \, a^{2} \cos\left(d x + c\right)^{9} - 496 \, a^{2} \cos\left(d x + c\right)^{7} + 488 \, a^{2} \cos\left(d x + c\right)^{5} - 30 \, a^{2} \cos\left(d x + c\right)^{3} - 45 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, d}"," ",0,"-1/80640*(17920*a^2*cos(d*x + c)^9 - 46080*a^2*cos(d*x + c)^7 + 32256*a^2*cos(d*x + c)^5 - 2835*a^2*d*x + 63*(128*a^2*cos(d*x + c)^9 - 496*a^2*cos(d*x + c)^7 + 488*a^2*cos(d*x + c)^5 - 30*a^2*cos(d*x + c)^3 - 45*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
379,1,111,0,0.873801," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2240 \, a^{2} \cos\left(d x + c\right)^{9} - 8640 \, a^{2} \cos\left(d x + c\right)^{7} + 8064 \, a^{2} \cos\left(d x + c\right)^{5} - 945 \, a^{2} d x - 315 \, {\left(16 \, a^{2} \cos\left(d x + c\right)^{7} - 24 \, a^{2} \cos\left(d x + c\right)^{5} + 2 \, a^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{20160 \, d}"," ",0,"-1/20160*(2240*a^2*cos(d*x + c)^9 - 8640*a^2*cos(d*x + c)^7 + 8064*a^2*cos(d*x + c)^5 - 945*a^2*d*x - 315*(16*a^2*cos(d*x + c)^7 - 24*a^2*cos(d*x + c)^5 + 2*a^2*cos(d*x + c)^3 + 3*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
380,1,98,0,1.063324," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3840 \, a^{2} \cos\left(d x + c\right)^{7} - 5376 \, a^{2} \cos\left(d x + c\right)^{5} + 1155 \, a^{2} d x + 35 \, {\left(48 \, a^{2} \cos\left(d x + c\right)^{7} - 136 \, a^{2} \cos\left(d x + c\right)^{5} + 22 \, a^{2} \cos\left(d x + c\right)^{3} + 33 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{13440 \, d}"," ",0,"1/13440*(3840*a^2*cos(d*x + c)^7 - 5376*a^2*cos(d*x + c)^5 + 1155*a^2*d*x + 35*(48*a^2*cos(d*x + c)^7 - 136*a^2*cos(d*x + c)^5 + 22*a^2*cos(d*x + c)^3 + 33*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
381,1,85,0,1.598319," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{120 \, a^{2} \cos\left(d x + c\right)^{7} - 336 \, a^{2} \cos\left(d x + c\right)^{5} + 105 \, a^{2} d x - 35 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{5} - 2 \, a^{2} \cos\left(d x + c\right)^{3} - 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(120*a^2*cos(d*x + c)^7 - 336*a^2*cos(d*x + c)^5 + 105*a^2*d*x - 35*(8*a^2*cos(d*x + c)^5 - 2*a^2*cos(d*x + c)^3 - 3*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
382,1,115,0,1.081073," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{12 \, a^{2} \cos\left(d x + c\right)^{5} - 20 \, a^{2} \cos\left(d x + c\right)^{3} - 45 \, a^{2} d x - 60 \, a^{2} \cos\left(d x + c\right) + 30 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 30 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(12*a^2*cos(d*x + c)^5 - 20*a^2*cos(d*x + c)^3 - 45*a^2*d*x - 60*a^2*cos(d*x + c) + 30*a^2*log(1/2*cos(d*x + c) + 1/2) - 30*a^2*log(-1/2*cos(d*x + c) + 1/2) - 15*(2*a^2*cos(d*x + c)^3 + 3*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
383,1,135,0,0.730771," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} \cos\left(d x + c\right)^{5} - 9 \, a^{2} \cos\left(d x + c\right)^{3} + 24 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 24 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 27 \, a^{2} \cos\left(d x + c\right) - {\left(16 \, a^{2} \cos\left(d x + c\right)^{3} - 27 \, a^{2} d x + 48 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d \sin\left(d x + c\right)}"," ",0,"-1/24*(6*a^2*cos(d*x + c)^5 - 9*a^2*cos(d*x + c)^3 + 24*a^2*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 24*a^2*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 27*a^2*cos(d*x + c) - (16*a^2*cos(d*x + c)^3 - 27*a^2*d*x + 48*a^2*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
384,1,172,0,1.148166," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} \cos\left(d x + c\right)^{5} - 36 \, a^{2} d x \cos\left(d x + c\right)^{2} - 4 \, a^{2} \cos\left(d x + c\right)^{3} + 36 \, a^{2} d x + 6 \, a^{2} \cos\left(d x + c\right) + 3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 12 \, {\left(a^{2} \cos\left(d x + c\right)^{3} - 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/12*(4*a^2*cos(d*x + c)^5 - 36*a^2*d*x*cos(d*x + c)^2 - 4*a^2*cos(d*x + c)^3 + 36*a^2*d*x + 6*a^2*cos(d*x + c) + 3*(a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2) - 3*(a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2) - 12*(a^2*cos(d*x + c)^3 - 3*a^2*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
385,1,192,0,0.963843," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} \cos\left(d x + c\right)^{5} - 4 \, a^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} \cos\left(d x + c\right) + 9 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(a^{2} d x \cos\left(d x + c\right)^{2} + 4 \, a^{2} \cos\left(d x + c\right)^{3} - a^{2} d x - 6 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/6*(3*a^2*cos(d*x + c)^5 - 4*a^2*cos(d*x + c)^3 + 3*a^2*cos(d*x + c) + 9*(a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*(a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(a^2*d*x*cos(d*x + c)^2 + 4*a^2*cos(d*x + c)^3 - a^2*d*x - 6*a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
386,1,219,0,1.012498," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{96 \, a^{2} d x \cos\left(d x + c\right)^{4} - 48 \, a^{2} \cos\left(d x + c\right)^{5} - 192 \, a^{2} d x \cos\left(d x + c\right)^{2} + 90 \, a^{2} \cos\left(d x + c\right)^{3} + 96 \, a^{2} d x - 54 \, a^{2} \cos\left(d x + c\right) + 27 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 27 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(4 \, a^{2} \cos\left(d x + c\right)^{3} - 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/48*(96*a^2*d*x*cos(d*x + c)^4 - 48*a^2*cos(d*x + c)^5 - 192*a^2*d*x*cos(d*x + c)^2 + 90*a^2*cos(d*x + c)^3 + 96*a^2*d*x - 54*a^2*cos(d*x + c) + 27*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2) - 27*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2) - 32*(4*a^2*cos(d*x + c)^3 - 3*a^2*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
387,1,239,0,1.184444," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{136 \, a^{2} \cos\left(d x + c\right)^{5} - 280 \, a^{2} \cos\left(d x + c\right)^{3} + 120 \, a^{2} \cos\left(d x + c\right) - 45 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 45 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, {\left(4 \, a^{2} d x \cos\left(d x + c\right)^{4} - 8 \, a^{2} d x \cos\left(d x + c\right)^{2} - 5 \, a^{2} \cos\left(d x + c\right)^{3} + 4 \, a^{2} d x + 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/120*(136*a^2*cos(d*x + c)^5 - 280*a^2*cos(d*x + c)^3 + 120*a^2*cos(d*x + c) - 45*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 45*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*(4*a^2*d*x*cos(d*x + c)^4 - 8*a^2*d*x*cos(d*x + c)^2 - 5*a^2*cos(d*x + c)^3 + 4*a^2*d*x + 3*a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
388,1,211,0,1.203375," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{192 \, a^{2} \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) - 270 \, a^{2} \cos\left(d x + c\right)^{5} + 560 \, a^{2} \cos\left(d x + c\right)^{3} - 210 \, a^{2} \cos\left(d x + c\right) - 105 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/480*(192*a^2*cos(d*x + c)^5*sin(d*x + c) - 270*a^2*cos(d*x + c)^5 + 560*a^2*cos(d*x + c)^3 - 210*a^2*cos(d*x + c) - 105*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2) + 105*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
389,1,271,0,0.906614," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2310 \, a^{2} \cos\left(d x + c\right)^{7} + 490 \, a^{2} \cos\left(d x + c\right)^{5} - 8470 \, a^{2} \cos\left(d x + c\right)^{3} + 2310 \, a^{2} \cos\left(d x + c\right) - 1155 \, {\left(a^{2} \cos\left(d x + c\right)^{8} - 4 \, a^{2} \cos\left(d x + c\right)^{6} + 6 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 1155 \, {\left(a^{2} \cos\left(d x + c\right)^{8} - 4 \, a^{2} \cos\left(d x + c\right)^{6} + 6 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 1536 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{7} - 7 \, a^{2} \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)}{26880 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/26880*(2310*a^2*cos(d*x + c)^7 + 490*a^2*cos(d*x + c)^5 - 8470*a^2*cos(d*x + c)^3 + 2310*a^2*cos(d*x + c) - 1155*(a^2*cos(d*x + c)^8 - 4*a^2*cos(d*x + c)^6 + 6*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2) + 1155*(a^2*cos(d*x + c)^8 - 4*a^2*cos(d*x + c)^6 + 6*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2) + 1536*(2*a^2*cos(d*x + c)^7 - 7*a^2*cos(d*x + c)^5)*sin(d*x + c))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
390,1,304,0,1.203754," ","integrate(cos(d*x+c)^4*csc(d*x+c)^10*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3328 \, a^{2} \cos\left(d x + c\right)^{9} - 14976 \, a^{2} \cos\left(d x + c\right)^{7} + 16128 \, a^{2} \cos\left(d x + c\right)^{5} + 945 \, {\left(a^{2} \cos\left(d x + c\right)^{8} - 4 \, a^{2} \cos\left(d x + c\right)^{6} + 6 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 945 \, {\left(a^{2} \cos\left(d x + c\right)^{8} - 4 \, a^{2} \cos\left(d x + c\right)^{6} + 6 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 630 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{7} - 11 \, a^{2} \cos\left(d x + c\right)^{5} - 11 \, a^{2} \cos\left(d x + c\right)^{3} + 3 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40320 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/40320*(3328*a^2*cos(d*x + c)^9 - 14976*a^2*cos(d*x + c)^7 + 16128*a^2*cos(d*x + c)^5 + 945*(a^2*cos(d*x + c)^8 - 4*a^2*cos(d*x + c)^6 + 6*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 945*(a^2*cos(d*x + c)^8 - 4*a^2*cos(d*x + c)^6 + 6*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 630*(3*a^2*cos(d*x + c)^7 - 11*a^2*cos(d*x + c)^5 - 11*a^2*cos(d*x + c)^3 + 3*a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
391,1,340,0,1.045054," ","integrate(cos(d*x+c)^4*csc(d*x+c)^11*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5670 \, a^{2} \cos\left(d x + c\right)^{9} - 26460 \, a^{2} \cos\left(d x + c\right)^{7} + 16128 \, a^{2} \cos\left(d x + c\right)^{5} + 26460 \, a^{2} \cos\left(d x + c\right)^{3} - 5670 \, a^{2} \cos\left(d x + c\right) - 2835 \, {\left(a^{2} \cos\left(d x + c\right)^{10} - 5 \, a^{2} \cos\left(d x + c\right)^{8} + 10 \, a^{2} \cos\left(d x + c\right)^{6} - 10 \, a^{2} \cos\left(d x + c\right)^{4} + 5 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2835 \, {\left(a^{2} \cos\left(d x + c\right)^{10} - 5 \, a^{2} \cos\left(d x + c\right)^{8} + 10 \, a^{2} \cos\left(d x + c\right)^{6} - 10 \, a^{2} \cos\left(d x + c\right)^{4} + 5 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 1024 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{9} - 36 \, a^{2} \cos\left(d x + c\right)^{7} + 63 \, a^{2} \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)}{161280 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/161280*(5670*a^2*cos(d*x + c)^9 - 26460*a^2*cos(d*x + c)^7 + 16128*a^2*cos(d*x + c)^5 + 26460*a^2*cos(d*x + c)^3 - 5670*a^2*cos(d*x + c) - 2835*(a^2*cos(d*x + c)^10 - 5*a^2*cos(d*x + c)^8 + 10*a^2*cos(d*x + c)^6 - 10*a^2*cos(d*x + c)^4 + 5*a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2) + 2835*(a^2*cos(d*x + c)^10 - 5*a^2*cos(d*x + c)^8 + 10*a^2*cos(d*x + c)^6 - 10*a^2*cos(d*x + c)^4 + 5*a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2) + 1024*(8*a^2*cos(d*x + c)^9 - 36*a^2*cos(d*x + c)^7 + 63*a^2*cos(d*x + c)^5)*sin(d*x + c))/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","A",0
392,1,137,0,1.018661," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{26880 \, a^{3} \cos\left(d x + c\right)^{11} - 197120 \, a^{3} \cos\left(d x + c\right)^{9} + 380160 \, a^{3} \cos\left(d x + c\right)^{7} - 236544 \, a^{3} \cos\left(d x + c\right)^{5} + 17325 \, a^{3} d x - 231 \, {\left(384 \, a^{3} \cos\left(d x + c\right)^{9} - 1168 \, a^{3} \cos\left(d x + c\right)^{7} + 984 \, a^{3} \cos\left(d x + c\right)^{5} - 50 \, a^{3} \cos\left(d x + c\right)^{3} - 75 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{295680 \, d}"," ",0,"1/295680*(26880*a^3*cos(d*x + c)^11 - 197120*a^3*cos(d*x + c)^9 + 380160*a^3*cos(d*x + c)^7 - 236544*a^3*cos(d*x + c)^5 + 17325*a^3*d*x - 231*(384*a^3*cos(d*x + c)^9 - 1168*a^3*cos(d*x + c)^7 + 984*a^3*cos(d*x + c)^5 - 50*a^3*cos(d*x + c)^3 - 75*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
393,1,124,0,0.857528," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{1280 \, a^{3} \cos\left(d x + c\right)^{9} - 3840 \, a^{3} \cos\left(d x + c\right)^{7} + 3072 \, a^{3} \cos\left(d x + c\right)^{5} - 315 \, a^{3} d x + 3 \, {\left(128 \, a^{3} \cos\left(d x + c\right)^{9} - 816 \, a^{3} \cos\left(d x + c\right)^{7} + 968 \, a^{3} \cos\left(d x + c\right)^{5} - 70 \, a^{3} \cos\left(d x + c\right)^{3} - 105 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3840 \, d}"," ",0,"-1/3840*(1280*a^3*cos(d*x + c)^9 - 3840*a^3*cos(d*x + c)^7 + 3072*a^3*cos(d*x + c)^5 - 315*a^3*d*x + 3*(128*a^3*cos(d*x + c)^9 - 816*a^3*cos(d*x + c)^7 + 968*a^3*cos(d*x + c)^5 - 70*a^3*cos(d*x + c)^3 - 105*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
394,1,111,0,0.772413," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4480 \, a^{3} \cos\left(d x + c\right)^{9} - 28800 \, a^{3} \cos\left(d x + c\right)^{7} + 32256 \, a^{3} \cos\left(d x + c\right)^{5} - 5355 \, a^{3} d x - 105 \, {\left(144 \, a^{3} \cos\left(d x + c\right)^{7} - 280 \, a^{3} \cos\left(d x + c\right)^{5} + 34 \, a^{3} \cos\left(d x + c\right)^{3} + 51 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40320 \, d}"," ",0,"-1/40320*(4480*a^3*cos(d*x + c)^9 - 28800*a^3*cos(d*x + c)^7 + 32256*a^3*cos(d*x + c)^5 - 5355*a^3*d*x - 105*(144*a^3*cos(d*x + c)^7 - 280*a^3*cos(d*x + c)^5 + 34*a^3*cos(d*x + c)^3 + 51*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
395,1,98,0,1.093895," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{1920 \, a^{3} \cos\left(d x + c\right)^{7} - 3584 \, a^{3} \cos\left(d x + c\right)^{5} + 945 \, a^{3} d x + 35 \, {\left(16 \, a^{3} \cos\left(d x + c\right)^{7} - 88 \, a^{3} \cos\left(d x + c\right)^{5} + 18 \, a^{3} \cos\left(d x + c\right)^{3} + 27 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4480 \, d}"," ",0,"1/4480*(1920*a^3*cos(d*x + c)^7 - 3584*a^3*cos(d*x + c)^5 + 945*a^3*d*x + 35*(16*a^3*cos(d*x + c)^7 - 88*a^3*cos(d*x + c)^5 + 18*a^3*cos(d*x + c)^3 + 27*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
396,1,128,0,0.960507," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{144 \, a^{3} \cos\left(d x + c\right)^{5} - 80 \, a^{3} \cos\left(d x + c\right)^{3} - 285 \, a^{3} d x - 240 \, a^{3} \cos\left(d x + c\right) + 120 \, a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 120 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5 \, {\left(8 \, a^{3} \cos\left(d x + c\right)^{5} - 38 \, a^{3} \cos\left(d x + c\right)^{3} - 57 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(144*a^3*cos(d*x + c)^5 - 80*a^3*cos(d*x + c)^3 - 285*a^3*d*x - 240*a^3*cos(d*x + c) + 120*a^3*log(1/2*cos(d*x + c) + 1/2) - 120*a^3*log(-1/2*cos(d*x + c) + 1/2) + 5*(8*a^3*cos(d*x + c)^5 - 38*a^3*cos(d*x + c)^3 - 57*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
397,1,147,0,1.168507," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{30 \, a^{3} \cos\left(d x + c\right)^{5} - 5 \, a^{3} \cos\left(d x + c\right)^{3} + 60 \, a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 60 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, a^{3} \cos\left(d x + c\right) + {\left(8 \, a^{3} \cos\left(d x + c\right)^{5} - 40 \, a^{3} \cos\left(d x + c\right)^{3} + 15 \, a^{3} d x - 120 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40 \, d \sin\left(d x + c\right)}"," ",0,"-1/40*(30*a^3*cos(d*x + c)^5 - 5*a^3*cos(d*x + c)^3 + 60*a^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 60*a^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*a^3*cos(d*x + c) + (8*a^3*cos(d*x + c)^5 - 40*a^3*cos(d*x + c)^3 + 15*a^3*d*x - 120*a^3*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
398,1,185,0,0.868548," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, a^{3} \cos\left(d x + c\right)^{5} - 33 \, a^{3} d x \cos\left(d x + c\right)^{2} + 8 \, a^{3} \cos\left(d x + c\right)^{3} + 33 \, a^{3} d x - 12 \, a^{3} \cos\left(d x + c\right) - 6 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 6 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(2 \, a^{3} \cos\left(d x + c\right)^{5} - 11 \, a^{3} \cos\left(d x + c\right)^{3} + 33 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/8*(8*a^3*cos(d*x + c)^5 - 33*a^3*d*x*cos(d*x + c)^2 + 8*a^3*cos(d*x + c)^3 + 33*a^3*d*x - 12*a^3*cos(d*x + c) - 6*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2) + 6*(a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2) + (2*a^3*cos(d*x + c)^5 - 11*a^3*cos(d*x + c)^3 + 33*a^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
399,1,206,0,1.574121," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{18 \, a^{3} \cos\left(d x + c\right)^{5} - 56 \, a^{3} \cos\left(d x + c\right)^{3} + 42 \, a^{3} \cos\left(d x + c\right) + 21 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 21 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(2 \, a^{3} \cos\left(d x + c\right)^{5} - 21 \, a^{3} d x \cos\left(d x + c\right)^{2} - 14 \, a^{3} \cos\left(d x + c\right)^{3} + 21 \, a^{3} d x + 21 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(18*a^3*cos(d*x + c)^5 - 56*a^3*cos(d*x + c)^3 + 42*a^3*cos(d*x + c) + 21*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 21*(a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*(2*a^3*cos(d*x + c)^5 - 21*a^3*d*x*cos(d*x + c)^2 - 14*a^3*cos(d*x + c)^3 + 21*a^3*d*x + 21*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
400,1,231,0,1.001249," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{24 \, a^{3} d x \cos\left(d x + c\right)^{4} - 48 \, a^{3} \cos\left(d x + c\right)^{5} - 48 \, a^{3} d x \cos\left(d x + c\right)^{2} + 110 \, a^{3} \cos\left(d x + c\right)^{3} + 24 \, a^{3} d x - 66 \, a^{3} \cos\left(d x + c\right) + 33 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 33 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 8 \, {\left(a^{3} \cos\left(d x + c\right)^{5} + 4 \, a^{3} \cos\left(d x + c\right)^{3} - 3 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/16*(24*a^3*d*x*cos(d*x + c)^4 - 48*a^3*cos(d*x + c)^5 - 48*a^3*d*x*cos(d*x + c)^2 + 110*a^3*cos(d*x + c)^3 + 24*a^3*d*x - 66*a^3*cos(d*x + c) + 33*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2) - 33*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2) - 8*(a^3*cos(d*x + c)^5 + 4*a^3*cos(d*x + c)^3 - 3*a^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
401,1,252,0,0.961682," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{304 \, a^{3} \cos\left(d x + c\right)^{5} - 560 \, a^{3} \cos\left(d x + c\right)^{3} + 240 \, a^{3} \cos\left(d x + c\right) + 15 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 10 \, {\left(24 \, a^{3} d x \cos\left(d x + c\right)^{4} - 8 \, a^{3} \cos\left(d x + c\right)^{5} - 48 \, a^{3} d x \cos\left(d x + c\right)^{2} + 5 \, a^{3} \cos\left(d x + c\right)^{3} + 24 \, a^{3} d x - 3 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/80*(304*a^3*cos(d*x + c)^5 - 560*a^3*cos(d*x + c)^3 + 240*a^3*cos(d*x + c) + 15*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 10*(24*a^3*d*x*cos(d*x + c)^4 - 8*a^3*cos(d*x + c)^5 - 48*a^3*d*x*cos(d*x + c)^2 + 5*a^3*cos(d*x + c)^3 + 24*a^3*d*x - 3*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
402,1,290,0,0.950603," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{480 \, a^{3} d x \cos\left(d x + c\right)^{6} - 1440 \, a^{3} d x \cos\left(d x + c\right)^{4} - 870 \, a^{3} \cos\left(d x + c\right)^{5} + 1440 \, a^{3} d x \cos\left(d x + c\right)^{2} + 1520 \, a^{3} \cos\left(d x + c\right)^{3} - 480 \, a^{3} d x - 570 \, a^{3} \cos\left(d x + c\right) - 285 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 285 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(11 \, a^{3} \cos\left(d x + c\right)^{5} - 35 \, a^{3} \cos\left(d x + c\right)^{3} + 15 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/480*(480*a^3*d*x*cos(d*x + c)^6 - 1440*a^3*d*x*cos(d*x + c)^4 - 870*a^3*cos(d*x + c)^5 + 1440*a^3*d*x*cos(d*x + c)^2 + 1520*a^3*cos(d*x + c)^3 - 480*a^3*d*x - 570*a^3*cos(d*x + c) - 285*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2) + 285*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2) - 32*(11*a^3*cos(d*x + c)^5 - 35*a^3*cos(d*x + c)^3 + 15*a^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
403,1,247,0,1.049878," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{736 \, a^{3} \cos\left(d x + c\right)^{7} - 896 \, a^{3} \cos\left(d x + c\right)^{5} + 315 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 315 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 70 \, {\left(7 \, a^{3} \cos\left(d x + c\right)^{5} - 24 \, a^{3} \cos\left(d x + c\right)^{3} + 9 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1120 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/1120*(736*a^3*cos(d*x + c)^7 - 896*a^3*cos(d*x + c)^5 + 315*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 315*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 70*(7*a^3*cos(d*x + c)^5 - 24*a^3*cos(d*x + c)^3 + 9*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
404,1,271,0,1.006326," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{1890 \, a^{3} \cos\left(d x + c\right)^{7} + 2030 \, a^{3} \cos\left(d x + c\right)^{5} - 6930 \, a^{3} \cos\left(d x + c\right)^{3} + 1890 \, a^{3} \cos\left(d x + c\right) - 945 \, {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 945 \, {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 256 \, {\left(13 \, a^{3} \cos\left(d x + c\right)^{7} - 28 \, a^{3} \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)}{8960 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/8960*(1890*a^3*cos(d*x + c)^7 + 2030*a^3*cos(d*x + c)^5 - 6930*a^3*cos(d*x + c)^3 + 1890*a^3*cos(d*x + c) - 945*(a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 - 4*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2) + 945*(a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 - 4*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2) + 256*(13*a^3*cos(d*x + c)^7 - 28*a^3*cos(d*x + c)^5)*sin(d*x + c))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
405,1,304,0,0.884732," ","integrate(cos(d*x+c)^4*csc(d*x+c)^10*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15872 \, a^{3} \cos\left(d x + c\right)^{9} - 71424 \, a^{3} \cos\left(d x + c\right)^{7} + 64512 \, a^{3} \cos\left(d x + c\right)^{5} + 5355 \, {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 5355 \, {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 210 \, {\left(51 \, a^{3} \cos\left(d x + c\right)^{7} - 59 \, a^{3} \cos\left(d x + c\right)^{5} - 187 \, a^{3} \cos\left(d x + c\right)^{3} + 51 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/80640*(15872*a^3*cos(d*x + c)^9 - 71424*a^3*cos(d*x + c)^7 + 64512*a^3*cos(d*x + c)^5 + 5355*(a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 - 4*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 5355*(a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 - 4*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 210*(51*a^3*cos(d*x + c)^7 - 59*a^3*cos(d*x + c)^5 - 187*a^3*cos(d*x + c)^3 + 51*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
406,1,340,0,0.902133," ","integrate(cos(d*x+c)^4*csc(d*x+c)^11*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{630 \, a^{3} \cos\left(d x + c\right)^{9} - 2940 \, a^{3} \cos\left(d x + c\right)^{7} + 768 \, a^{3} \cos\left(d x + c\right)^{5} + 2940 \, a^{3} \cos\left(d x + c\right)^{3} - 630 \, a^{3} \cos\left(d x + c\right) - 315 \, {\left(a^{3} \cos\left(d x + c\right)^{10} - 5 \, a^{3} \cos\left(d x + c\right)^{8} + 10 \, a^{3} \cos\left(d x + c\right)^{6} - 10 \, a^{3} \cos\left(d x + c\right)^{4} + 5 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 315 \, {\left(a^{3} \cos\left(d x + c\right)^{10} - 5 \, a^{3} \cos\left(d x + c\right)^{8} + 10 \, a^{3} \cos\left(d x + c\right)^{6} - 10 \, a^{3} \cos\left(d x + c\right)^{4} + 5 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 512 \, {\left(2 \, a^{3} \cos\left(d x + c\right)^{9} - 9 \, a^{3} \cos\left(d x + c\right)^{7} + 12 \, a^{3} \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)}{7680 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/7680*(630*a^3*cos(d*x + c)^9 - 2940*a^3*cos(d*x + c)^7 + 768*a^3*cos(d*x + c)^5 + 2940*a^3*cos(d*x + c)^3 - 630*a^3*cos(d*x + c) - 315*(a^3*cos(d*x + c)^10 - 5*a^3*cos(d*x + c)^8 + 10*a^3*cos(d*x + c)^6 - 10*a^3*cos(d*x + c)^4 + 5*a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2) + 315*(a^3*cos(d*x + c)^10 - 5*a^3*cos(d*x + c)^8 + 10*a^3*cos(d*x + c)^6 - 10*a^3*cos(d*x + c)^4 + 5*a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2) + 512*(2*a^3*cos(d*x + c)^9 - 9*a^3*cos(d*x + c)^7 + 12*a^3*cos(d*x + c)^5)*sin(d*x + c))/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","A",0
407,1,124,0,0.816435," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{35840 \, a^{4} \cos\left(d x + c\right)^{9} - 138240 \, a^{4} \cos\left(d x + c\right)^{7} + 129024 \, a^{4} \cos\left(d x + c\right)^{5} - 17325 \, a^{4} d x + 21 \, {\left(384 \, a^{4} \cos\left(d x + c\right)^{9} - 3888 \, a^{4} \cos\left(d x + c\right)^{7} + 5704 \, a^{4} \cos\left(d x + c\right)^{5} - 550 \, a^{4} \cos\left(d x + c\right)^{3} - 825 \, a^{4} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, d}"," ",0,"-1/80640*(35840*a^4*cos(d*x + c)^9 - 138240*a^4*cos(d*x + c)^7 + 129024*a^4*cos(d*x + c)^5 - 17325*a^4*d*x + 21*(384*a^4*cos(d*x + c)^9 - 3888*a^4*cos(d*x + c)^7 + 5704*a^4*cos(d*x + c)^5 - 550*a^4*cos(d*x + c)^3 - 825*a^4*cos(d*x + c))*sin(d*x + c))/d","A",0
408,1,219,0,0.869999," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{6 \, a^{4} \cos\left(d x + c\right)^{7} - 75 \, a^{4} \cos\left(d x + c\right)^{5} + 244 \, a^{4} \cos\left(d x + c\right)^{3} - 183 \, a^{4} \cos\left(d x + c\right) - 24 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - a^{4}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 24 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - a^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - {\left(32 \, a^{4} \cos\left(d x + c\right)^{5} - 183 \, a^{4} d x \cos\left(d x + c\right)^{2} - 32 \, a^{4} \cos\left(d x + c\right)^{3} + 183 \, a^{4} d x + 48 \, a^{4} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/24*(6*a^4*cos(d*x + c)^7 - 75*a^4*cos(d*x + c)^5 + 244*a^4*cos(d*x + c)^3 - 183*a^4*cos(d*x + c) - 24*(a^4*cos(d*x + c)^2 - a^4)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 24*(a^4*cos(d*x + c)^2 - a^4)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - (32*a^4*cos(d*x + c)^5 - 183*a^4*d*x*cos(d*x + c)^2 - 32*a^4*cos(d*x + c)^3 + 183*a^4*d*x + 48*a^4*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
409,1,80,0,0.862119," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{240 \, \cos\left(d x + c\right)^{7} - 672 \, \cos\left(d x + c\right)^{5} + 560 \, \cos\left(d x + c\right)^{3} + 105 \, d x + 35 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 14 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, a d}"," ",0,"1/1680*(240*cos(d*x + c)^7 - 672*cos(d*x + c)^5 + 560*cos(d*x + c)^3 + 105*d*x + 35*(8*cos(d*x + c)^5 - 14*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
410,1,70,0,0.874897," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, \cos\left(d x + c\right)^{5} - 80 \, \cos\left(d x + c\right)^{3} - 15 \, d x - 5 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 14 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, a d}"," ",0,"1/240*(48*cos(d*x + c)^5 - 80*cos(d*x + c)^3 - 15*d*x - 5*(8*cos(d*x + c)^5 - 14*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
411,1,60,0,0.778101," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{24 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{3} - 15 \, d x + 15 \, {\left(2 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, a d}"," ",0,"-1/120*(24*cos(d*x + c)^5 - 40*cos(d*x + c)^3 - 15*d*x + 15*(2*cos(d*x + c)^3 - cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
412,1,50,0,0.827369," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{3} + 3 \, d x - 3 \, {\left(2 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, a d}"," ",0,"-1/24*(8*cos(d*x + c)^3 + 3*d*x - 3*(2*cos(d*x + c)^3 - cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
413,1,57,0,0.769714," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{d x + \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) + \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, a d}"," ",0,"-1/2*(d*x + cos(d*x + c)*sin(d*x + c) - 2*cos(d*x + c) + log(1/2*cos(d*x + c) + 1/2) - log(-1/2*cos(d*x + c) + 1/2))/(a*d)","A",0
414,1,80,0,0.646361," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(d x + \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right)}{2 \, a d \sin\left(d x + c\right)}"," ",0,"-1/2*(2*(d*x + cos(d*x + c))*sin(d*x + c) - log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*cos(d*x + c))/(a*d*sin(d*x + c))","A",0
415,1,104,0,0.664991," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, d x \cos\left(d x + c\right)^{2} - 4 \, d x + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right)}{4 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"1/4*(4*d*x*cos(d*x + c)^2 - 4*d*x + (cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) - (cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 4*cos(d*x + c)*sin(d*x + c) + 2*cos(d*x + c))/(a*d*cos(d*x + c)^2 - a*d)","A",0
416,1,111,0,0.921233," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \cos\left(d x + c\right)^{3} - 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 6 \, \cos\left(d x + c\right) \sin\left(d x + c\right)}{12 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(4*cos(d*x + c)^3 - 3*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 6*cos(d*x + c)*sin(d*x + c))/((a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","B",0
417,1,132,0,0.880444," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 6 \, \cos\left(d x + c\right)^{3} + 3 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 6 \, \cos\left(d x + c\right)}{48 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"1/48*(16*cos(d*x + c)^3*sin(d*x + c) - 6*cos(d*x + c)^3 + 3*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) - 3*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 6*cos(d*x + c))/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)","A",0
418,1,161,0,0.920640," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{32 \, \cos\left(d x + c\right)^{5} - 80 \, \cos\left(d x + c\right)^{3} - 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)}"," ",0,"1/240*(32*cos(d*x + c)^5 - 80*cos(d*x + c)^3 - 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*(cos(d*x + c)^3 + cos(d*x + c))*sin(d*x + c))/((a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","A",0
419,1,188,0,0.725257," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{30 \, \cos\left(d x + c\right)^{5} - 80 \, \cos\left(d x + c\right)^{3} - 15 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(2 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right) - 30 \, \cos\left(d x + c\right)}{480 \, {\left(a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"-1/480*(30*cos(d*x + c)^5 - 80*cos(d*x + c)^3 - 15*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + 15*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 32*(2*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*sin(d*x + c) - 30*cos(d*x + c))/(a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^2 - a*d)","A",0
420,1,88,0,0.953091," ","integrate(cos(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{120 \, \cos\left(d x + c\right)^{7} - 672 \, \cos\left(d x + c\right)^{5} + 1400 \, \cos\left(d x + c\right)^{3} - 525 \, d x + 35 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 26 \, \cos\left(d x + c\right)^{3} + 33 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 1680 \, \cos\left(d x + c\right)}{840 \, a^{2} d}"," ",0,"1/840*(120*cos(d*x + c)^7 - 672*cos(d*x + c)^5 + 1400*cos(d*x + c)^3 - 525*d*x + 35*(8*cos(d*x + c)^5 - 26*cos(d*x + c)^3 + 33*cos(d*x + c))*sin(d*x + c) - 1680*cos(d*x + c))/(a^2*d)","A",0
421,1,78,0,0.616373," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{96 \, \cos\left(d x + c\right)^{5} - 320 \, \cos\left(d x + c\right)^{3} + 165 \, d x - 5 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 38 \, \cos\left(d x + c\right)^{3} + 63 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 480 \, \cos\left(d x + c\right)}{240 \, a^{2} d}"," ",0,"1/240*(96*cos(d*x + c)^5 - 320*cos(d*x + c)^3 + 165*d*x - 5*(8*cos(d*x + c)^5 - 38*cos(d*x + c)^3 + 63*cos(d*x + c))*sin(d*x + c) + 480*cos(d*x + c))/(a^2*d)","A",0
422,1,68,0,0.754695," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(d x + c\right)^{5} - 20 \, \cos\left(d x + c\right)^{3} + 15 \, d x + 5 \, {\left(2 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 40 \, \cos\left(d x + c\right)}{20 \, a^{2} d}"," ",0,"-1/20*(4*cos(d*x + c)^5 - 20*cos(d*x + c)^3 + 15*d*x + 5*(2*cos(d*x + c)^3 - 5*cos(d*x + c))*sin(d*x + c) + 40*cos(d*x + c))/(a^2*d)","A",0
423,1,58,0,0.900370," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{16 \, \cos\left(d x + c\right)^{3} - 21 \, d x - 3 \, {\left(2 \, \cos\left(d x + c\right)^{3} - 9 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 48 \, \cos\left(d x + c\right)}{24 \, a^{2} d}"," ",0,"-1/24*(16*cos(d*x + c)^3 - 21*d*x - 3*(2*cos(d*x + c)^3 - 9*cos(d*x + c))*sin(d*x + c) - 48*cos(d*x + c))/(a^2*d)","A",0
424,1,43,0,0.866021," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{3} - 3 \, d x + 3 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, \cos\left(d x + c\right)}{3 \, a^{2} d}"," ",0,"1/3*(cos(d*x + c)^3 - 3*d*x + 3*cos(d*x + c)*sin(d*x + c) - 6*cos(d*x + c))/(a^2*d)","A",0
425,1,45,0,0.865203," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, d x + 2 \, \cos\left(d x + c\right) + \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, a^{2} d}"," ",0,"-1/2*(4*d*x + 2*cos(d*x + c) + log(1/2*cos(d*x + c) + 1/2) - log(-1/2*cos(d*x + c) + 1/2))/(a^2*d)","A",0
426,1,70,0,0.928877," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{d x \sin\left(d x + c\right) + \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - \cos\left(d x + c\right)}{a^{2} d \sin\left(d x + c\right)}"," ",0,"(d*x*sin(d*x + c) + log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - cos(d*x + c))/(a^2*d*sin(d*x + c))","A",0
427,1,93,0,0.807584," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 8 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"-1/4*(3*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) - 3*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) + 8*cos(d*x + c)*sin(d*x + c) - 2*cos(d*x + c))/(a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
428,1,123,0,0.828095," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{10 \, \cos\left(d x + c\right)^{3} - 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 12 \, \cos\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(10*cos(d*x + c)^3 - 3*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*cos(d*x + c)*sin(d*x + c) - 12*cos(d*x + c))/((a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","A",0
429,1,149,0,0.709339," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{42 \, \cos\left(d x + c\right)^{3} - 21 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 21 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 54 \, \cos\left(d x + c\right)}{48 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)}}"," ",0,"1/48*(42*cos(d*x + c)^3 - 21*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) + 21*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 32*(2*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c) - 54*cos(d*x + c))/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)","A",0
430,1,179,0,0.633332," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{48 \, \cos\left(d x + c\right)^{5} - 120 \, \cos\left(d x + c\right)^{3} - 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 10 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 80 \, \cos\left(d x + c\right)}{40 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/40*(48*cos(d*x + c)^5 - 120*cos(d*x + c)^3 - 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 10*(3*cos(d*x + c)^3 - 5*cos(d*x + c))*sin(d*x + c) + 80*cos(d*x + c))/((a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)*sin(d*x + c))","A",0
431,1,204,0,0.912058," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{330 \, \cos\left(d x + c\right)^{5} - 880 \, \cos\left(d x + c\right)^{3} - 165 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 165 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 64 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 20 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 630 \, \cos\left(d x + c\right)}{480 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 3 \, a^{2} d \cos\left(d x + c\right)^{4} + 3 \, a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"1/480*(330*cos(d*x + c)^5 - 880*cos(d*x + c)^3 - 165*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + 165*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 64*(8*cos(d*x + c)^5 - 20*cos(d*x + c)^3 + 15*cos(d*x + c))*sin(d*x + c) + 630*cos(d*x + c))/(a^2*d*cos(d*x + c)^6 - 3*a^2*d*cos(d*x + c)^4 + 3*a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
432,1,144,0,0.610770," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{5} + 8 \, \cos\left(d x + c\right)^{4} - 15 \, \cos\left(d x + c\right)^{3} - 51 \, d x - {\left(51 \, d x + 67\right)} \cos\left(d x + c\right) - 56 \, \cos\left(d x + c\right)^{2} - {\left(2 \, \cos\left(d x + c\right)^{4} - 6 \, \cos\left(d x + c\right)^{3} + 51 \, d x - 21 \, \cos\left(d x + c\right)^{2} + 35 \, \cos\left(d x + c\right) - 32\right)} \sin\left(d x + c\right) - 32}{8 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"-1/8*(2*cos(d*x + c)^5 + 8*cos(d*x + c)^4 - 15*cos(d*x + c)^3 - 51*d*x - (51*d*x + 67)*cos(d*x + c) - 56*cos(d*x + c)^2 - (2*cos(d*x + c)^4 - 6*cos(d*x + c)^3 + 51*d*x - 21*cos(d*x + c)^2 + 35*cos(d*x + c) - 32)*sin(d*x + c) - 32)/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","A",0
433,1,123,0,0.975172," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{4} - 7 \, \cos\left(d x + c\right)^{3} - 33 \, d x - 3 \, {\left(11 \, d x + 15\right)} \cos\left(d x + c\right) - 30 \, \cos\left(d x + c\right)^{2} + {\left(2 \, \cos\left(d x + c\right)^{3} - 33 \, d x + 9 \, \cos\left(d x + c\right)^{2} - 21 \, \cos\left(d x + c\right) + 24\right)} \sin\left(d x + c\right) - 24}{6 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/6*(2*cos(d*x + c)^4 - 7*cos(d*x + c)^3 - 33*d*x - 3*(11*d*x + 15)*cos(d*x + c) - 30*cos(d*x + c)^2 + (2*cos(d*x + c)^3 - 33*d*x + 9*cos(d*x + c)^2 - 21*cos(d*x + c) + 24)*sin(d*x + c) - 24)/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","A",0
434,1,100,0,0.886993," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{3} + 9 \, d x + {\left(9 \, d x + 13\right)} \cos\left(d x + c\right) + 6 \, \cos\left(d x + c\right)^{2} + {\left(9 \, d x - \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right) - 8\right)} \sin\left(d x + c\right) + 8}{2 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/2*(cos(d*x + c)^3 + 9*d*x + (9*d*x + 13)*cos(d*x + c) + 6*cos(d*x + c)^2 + (9*d*x - cos(d*x + c)^2 + 5*cos(d*x + c) - 8)*sin(d*x + c) + 8)/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","A",0
435,1,117,0,0.721213," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, d x + 2 \, {\left(d x + 4\right)} \cos\left(d x + c\right) - {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(d x - 4\right)} \sin\left(d x + c\right) + 8}{2 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/2*(2*d*x + 2*(d*x + 4)*cos(d*x + c) - (cos(d*x + c) + sin(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) + (cos(d*x + c) + sin(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) + 2*(d*x - 4)*sin(d*x + c) + 8)/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","B",0
436,1,165,0,0.691342," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, \cos\left(d x + c\right)^{2} + 3 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(5 \, \cos\left(d x + c\right) + 4\right)} \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right) - 8}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d - {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/2*(10*cos(d*x + c)^2 + 3*(cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*log(1/2*cos(d*x + c) + 1/2) - 3*(cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*log(-1/2*cos(d*x + c) + 1/2) + 2*(5*cos(d*x + c) + 4)*sin(d*x + c) + 2*cos(d*x + c) - 8)/(a^3*d*cos(d*x + c)^2 - a^3*d - (a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c))","B",0
437,1,246,0,0.940779," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{28 \, \cos\left(d x + c\right)^{3} + 18 \, \cos\left(d x + c\right)^{2} - 9 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(14 \, \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right) - 8\right)} \sin\left(d x + c\right) - 26 \, \cos\left(d x + c\right) - 16}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*(28*cos(d*x + c)^3 + 18*cos(d*x + c)^2 - 9*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*log(1/2*cos(d*x + c) + 1/2) + 9*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*log(-1/2*cos(d*x + c) + 1/2) - 2*(14*cos(d*x + c)^2 + 5*cos(d*x + c) - 8)*sin(d*x + c) - 26*cos(d*x + c) - 16)/(a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - a^3*d + (a^3*d*cos(d*x + c)^2 - a^3*d)*sin(d*x + c))","B",0
438,1,302,0,0.884813," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{104 \, \cos\left(d x + c\right)^{4} + 38 \, \cos\left(d x + c\right)^{3} - 156 \, \cos\left(d x + c\right)^{2} + 33 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 33 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(52 \, \cos\left(d x + c\right)^{3} + 33 \, \cos\left(d x + c\right)^{2} - 45 \, \cos\left(d x + c\right) - 24\right)} \sin\left(d x + c\right) - 42 \, \cos\left(d x + c\right) + 48}{12 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d - {\left(a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(104*cos(d*x + c)^4 + 38*cos(d*x + c)^3 - 156*cos(d*x + c)^2 + 33*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) - 33*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) + 2*(52*cos(d*x + c)^3 + 33*cos(d*x + c)^2 - 45*cos(d*x + c) - 24)*sin(d*x + c) - 42*cos(d*x + c) + 48)/(a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d - (a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - a^3*d)*sin(d*x + c))","B",0
439,1,381,0,0.880574," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{160 \, \cos\left(d x + c\right)^{5} + 102 \, \cos\left(d x + c\right)^{4} - 298 \, \cos\left(d x + c\right)^{3} - 170 \, \cos\left(d x + c\right)^{2} - 51 \, {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 51 \, {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(80 \, \cos\left(d x + c\right)^{4} + 29 \, \cos\left(d x + c\right)^{3} - 120 \, \cos\left(d x + c\right)^{2} - 35 \, \cos\left(d x + c\right) + 32\right)} \sin\left(d x + c\right) + 134 \, \cos\left(d x + c\right) + 64}{16 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{3} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right) + a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/16*(160*cos(d*x + c)^5 + 102*cos(d*x + c)^4 - 298*cos(d*x + c)^3 - 170*cos(d*x + c)^2 - 51*(cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) + cos(d*x + c) + 1)*log(1/2*cos(d*x + c) + 1/2) + 51*(cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) + cos(d*x + c) + 1)*log(-1/2*cos(d*x + c) + 1/2) - 2*(80*cos(d*x + c)^4 + 29*cos(d*x + c)^3 - 120*cos(d*x + c)^2 - 35*cos(d*x + c) + 32)*sin(d*x + c) + 134*cos(d*x + c) + 64)/(a^3*d*cos(d*x + c)^5 + a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^3 - 2*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c) + a^3*d + (a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d)*sin(d*x + c))","B",0
440,1,195,0,0.777137," ","integrate(cos(f*x+e)^4*sin(f*x+e)/(a+a*sin(f*x+e))^6,x, algorithm=""fricas"")","\frac{6 \, \cos\left(f x + e\right)^{4} - 11 \, \cos\left(f x + e\right)^{3} - 27 \, \cos\left(f x + e\right)^{2} + {\left(6 \, \cos\left(f x + e\right)^{3} + 17 \, \cos\left(f x + e\right)^{2} - 10 \, \cos\left(f x + e\right) - 20\right)} \sin\left(f x + e\right) + 10 \, \cos\left(f x + e\right) + 20}{35 \, {\left(a^{6} f \cos\left(f x + e\right)^{4} - 3 \, a^{6} f \cos\left(f x + e\right)^{3} - 8 \, a^{6} f \cos\left(f x + e\right)^{2} + 4 \, a^{6} f \cos\left(f x + e\right) + 8 \, a^{6} f - {\left(a^{6} f \cos\left(f x + e\right)^{3} + 4 \, a^{6} f \cos\left(f x + e\right)^{2} - 4 \, a^{6} f \cos\left(f x + e\right) - 8 \, a^{6} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/35*(6*cos(f*x + e)^4 - 11*cos(f*x + e)^3 - 27*cos(f*x + e)^2 + (6*cos(f*x + e)^3 + 17*cos(f*x + e)^2 - 10*cos(f*x + e) - 20)*sin(f*x + e) + 10*cos(f*x + e) + 20)/(a^6*f*cos(f*x + e)^4 - 3*a^6*f*cos(f*x + e)^3 - 8*a^6*f*cos(f*x + e)^2 + 4*a^6*f*cos(f*x + e) + 8*a^6*f - (a^6*f*cos(f*x + e)^3 + 4*a^6*f*cos(f*x + e)^2 - 4*a^6*f*cos(f*x + e) - 8*a^6*f)*sin(f*x + e))","B",0
441,1,243,0,0.872770," ","integrate(cos(f*x+e)^4*sin(f*x+e)^2/(a+a*sin(f*x+e))^7,x, algorithm=""fricas"")","-\frac{47 \, \cos\left(f x + e\right)^{5} + 127 \, \cos\left(f x + e\right)^{4} - 115 \, \cos\left(f x + e\right)^{3} - 265 \, \cos\left(f x + e\right)^{2} - {\left(47 \, \cos\left(f x + e\right)^{4} - 80 \, \cos\left(f x + e\right)^{3} - 195 \, \cos\left(f x + e\right)^{2} + 70 \, \cos\left(f x + e\right) + 140\right)} \sin\left(f x + e\right) + 70 \, \cos\left(f x + e\right) + 140}{315 \, {\left(a^{7} f \cos\left(f x + e\right)^{5} + 5 \, a^{7} f \cos\left(f x + e\right)^{4} - 8 \, a^{7} f \cos\left(f x + e\right)^{3} - 20 \, a^{7} f \cos\left(f x + e\right)^{2} + 8 \, a^{7} f \cos\left(f x + e\right) + 16 \, a^{7} f + {\left(a^{7} f \cos\left(f x + e\right)^{4} - 4 \, a^{7} f \cos\left(f x + e\right)^{3} - 12 \, a^{7} f \cos\left(f x + e\right)^{2} + 8 \, a^{7} f \cos\left(f x + e\right) + 16 \, a^{7} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/315*(47*cos(f*x + e)^5 + 127*cos(f*x + e)^4 - 115*cos(f*x + e)^3 - 265*cos(f*x + e)^2 - (47*cos(f*x + e)^4 - 80*cos(f*x + e)^3 - 195*cos(f*x + e)^2 + 70*cos(f*x + e) + 140)*sin(f*x + e) + 70*cos(f*x + e) + 140)/(a^7*f*cos(f*x + e)^5 + 5*a^7*f*cos(f*x + e)^4 - 8*a^7*f*cos(f*x + e)^3 - 20*a^7*f*cos(f*x + e)^2 + 8*a^7*f*cos(f*x + e) + 16*a^7*f + (a^7*f*cos(f*x + e)^4 - 4*a^7*f*cos(f*x + e)^3 - 12*a^7*f*cos(f*x + e)^2 + 8*a^7*f*cos(f*x + e) + 16*a^7*f)*sin(f*x + e))","B",0
442,1,291,0,0.638433," ","integrate(cos(f*x+e)^4*sin(f*x+e)^3/(a+a*sin(f*x+e))^8,x, algorithm=""fricas"")","\frac{152 \, \cos\left(f x + e\right)^{6} - 243 \, \cos\left(f x + e\right)^{5} - 745 \, \cos\left(f x + e\right)^{4} + 455 \, \cos\left(f x + e\right)^{3} + 1015 \, \cos\left(f x + e\right)^{2} + {\left(152 \, \cos\left(f x + e\right)^{5} + 395 \, \cos\left(f x + e\right)^{4} - 350 \, \cos\left(f x + e\right)^{3} - 805 \, \cos\left(f x + e\right)^{2} + 210 \, \cos\left(f x + e\right) + 420\right)} \sin\left(f x + e\right) - 210 \, \cos\left(f x + e\right) - 420}{1155 \, {\left(a^{8} f \cos\left(f x + e\right)^{6} - 5 \, a^{8} f \cos\left(f x + e\right)^{5} - 18 \, a^{8} f \cos\left(f x + e\right)^{4} + 20 \, a^{8} f \cos\left(f x + e\right)^{3} + 48 \, a^{8} f \cos\left(f x + e\right)^{2} - 16 \, a^{8} f \cos\left(f x + e\right) - 32 \, a^{8} f - {\left(a^{8} f \cos\left(f x + e\right)^{5} + 6 \, a^{8} f \cos\left(f x + e\right)^{4} - 12 \, a^{8} f \cos\left(f x + e\right)^{3} - 32 \, a^{8} f \cos\left(f x + e\right)^{2} + 16 \, a^{8} f \cos\left(f x + e\right) + 32 \, a^{8} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/1155*(152*cos(f*x + e)^6 - 243*cos(f*x + e)^5 - 745*cos(f*x + e)^4 + 455*cos(f*x + e)^3 + 1015*cos(f*x + e)^2 + (152*cos(f*x + e)^5 + 395*cos(f*x + e)^4 - 350*cos(f*x + e)^3 - 805*cos(f*x + e)^2 + 210*cos(f*x + e) + 420)*sin(f*x + e) - 210*cos(f*x + e) - 420)/(a^8*f*cos(f*x + e)^6 - 5*a^8*f*cos(f*x + e)^5 - 18*a^8*f*cos(f*x + e)^4 + 20*a^8*f*cos(f*x + e)^3 + 48*a^8*f*cos(f*x + e)^2 - 16*a^8*f*cos(f*x + e) - 32*a^8*f - (a^8*f*cos(f*x + e)^5 + 6*a^8*f*cos(f*x + e)^4 - 12*a^8*f*cos(f*x + e)^3 - 32*a^8*f*cos(f*x + e)^2 + 16*a^8*f*cos(f*x + e) + 32*a^8*f)*sin(f*x + e))","B",0
443,1,172,0,0.792751," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, \cos\left(d x + c\right)^{7} - 315 \, \cos\left(d x + c\right)^{6} - 4585 \, \cos\left(d x + c\right)^{5} + 115 \, \cos\left(d x + c\right)^{4} - 184 \, \cos\left(d x + c\right)^{3} + 368 \, \cos\left(d x + c\right)^{2} - {\left(3465 \, \cos\left(d x + c\right)^{6} + 3780 \, \cos\left(d x + c\right)^{5} - 805 \, \cos\left(d x + c\right)^{4} - 920 \, \cos\left(d x + c\right)^{3} - 1104 \, \cos\left(d x + c\right)^{2} - 1472 \, \cos\left(d x + c\right) - 2944\right)} \sin\left(d x + c\right) - 1472 \, \cos\left(d x + c\right) - 2944\right)} \sqrt{a \sin\left(d x + c\right) + a}}{45045 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/45045*(3465*cos(d*x + c)^7 - 315*cos(d*x + c)^6 - 4585*cos(d*x + c)^5 + 115*cos(d*x + c)^4 - 184*cos(d*x + c)^3 + 368*cos(d*x + c)^2 - (3465*cos(d*x + c)^6 + 3780*cos(d*x + c)^5 - 805*cos(d*x + c)^4 - 920*cos(d*x + c)^3 - 1104*cos(d*x + c)^2 - 1472*cos(d*x + c) - 2944)*sin(d*x + c) - 1472*cos(d*x + c) - 2944)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
444,1,151,0,0.945560," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, \cos\left(d x + c\right)^{6} + 350 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{4} + 8 \, \cos\left(d x + c\right)^{3} - 16 \, \cos\left(d x + c\right)^{2} + {\left(315 \, \cos\left(d x + c\right)^{5} - 35 \, \cos\left(d x + c\right)^{4} - 40 \, \cos\left(d x + c\right)^{3} - 48 \, \cos\left(d x + c\right)^{2} - 64 \, \cos\left(d x + c\right) - 128\right)} \sin\left(d x + c\right) + 64 \, \cos\left(d x + c\right) + 128\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3465 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"-2/3465*(315*cos(d*x + c)^6 + 350*cos(d*x + c)^5 - 5*cos(d*x + c)^4 + 8*cos(d*x + c)^3 - 16*cos(d*x + c)^2 + (315*cos(d*x + c)^5 - 35*cos(d*x + c)^4 - 40*cos(d*x + c)^3 - 48*cos(d*x + c)^2 - 64*cos(d*x + c) - 128)*sin(d*x + c) + 64*cos(d*x + c) + 128)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
445,1,294,0,0.935911," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{a} {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(15 \, \cos\left(d x + c\right)^{4} + 18 \, \cos\left(d x + c\right)^{3} + 34 \, \cos\left(d x + c\right)^{2} + {\left(15 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)^{2} + 31 \, \cos\left(d x + c\right) - 43\right)} \sin\left(d x + c\right) + 74 \, \cos\left(d x + c\right) + 43\right)} \sqrt{a \sin\left(d x + c\right) + a}}{210 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/210*(105*sqrt(a)*(cos(d*x + c) + sin(d*x + c) + 1)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(15*cos(d*x + c)^4 + 18*cos(d*x + c)^3 + 34*cos(d*x + c)^2 + (15*cos(d*x + c)^3 - 3*cos(d*x + c)^2 + 31*cos(d*x + c) - 43)*sin(d*x + c) + 74*cos(d*x + c) + 43)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c) + d*sin(d*x + c) + d)","B",0
446,1,320,0,0.976953," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{15 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(6 \, \cos\left(d x + c\right)^{4} + 8 \, \cos\left(d x + c\right)^{3} + 40 \, \cos\left(d x + c\right)^{2} + {\left(6 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + 38 \, \cos\left(d x + c\right) + 61\right)} \sin\left(d x + c\right) - 23 \, \cos\left(d x + c\right) - 61\right)} \sqrt{a \sin\left(d x + c\right) + a}}{60 \, {\left(d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/60*(15*(cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(6*cos(d*x + c)^4 + 8*cos(d*x + c)^3 + 40*cos(d*x + c)^2 + (6*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + 38*cos(d*x + c) + 61)*sin(d*x + c) - 23*cos(d*x + c) - 61)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^2 - (d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
447,1,359,0,0.956789," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{39 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(8 \, \cos\left(d x + c\right)^{4} + 16 \, \cos\left(d x + c\right)^{3} - 9 \, \cos\left(d x + c\right)^{2} + {\left(8 \, \cos\left(d x + c\right)^{3} - 8 \, \cos\left(d x + c\right)^{2} - 17 \, \cos\left(d x + c\right) + 5\right)} \sin\left(d x + c\right) - 22 \, \cos\left(d x + c\right) - 5\right)} \sqrt{a \sin\left(d x + c\right) + a}}{48 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/48*(39*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(8*cos(d*x + c)^4 + 16*cos(d*x + c)^3 - 9*cos(d*x + c)^2 + (8*cos(d*x + c)^3 - 8*cos(d*x + c)^2 - 17*cos(d*x + c) + 5)*sin(d*x + c) - 22*cos(d*x + c) - 5)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
448,1,380,0,0.810634," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{33 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(48 \, \cos\left(d x + c\right)^{4} - 33 \, \cos\left(d x + c\right)^{3} - 139 \, \cos\left(d x + c\right)^{2} + {\left(48 \, \cos\left(d x + c\right)^{3} + 81 \, \cos\left(d x + c\right)^{2} - 58 \, \cos\left(d x + c\right) - 83\right)} \sin\left(d x + c\right) + 25 \, \cos\left(d x + c\right) + 83\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/96*(33*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(48*cos(d*x + c)^4 - 33*cos(d*x + c)^3 - 139*cos(d*x + c)^2 + (48*cos(d*x + c)^3 + 81*cos(d*x + c)^2 - 58*cos(d*x + c) - 83)*sin(d*x + c) + 25*cos(d*x + c) + 83)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 - (d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - d)*sin(d*x + c) + d)","B",0
449,1,415,0,0.659459," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{201 \, {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(183 \, \cos\left(d x + c\right)^{4} + 122 \, \cos\left(d x + c\right)^{3} - 188 \, \cos\left(d x + c\right)^{2} + {\left(183 \, \cos\left(d x + c\right)^{3} + 61 \, \cos\left(d x + c\right)^{2} - 127 \, \cos\left(d x + c\right) - 53\right)} \sin\left(d x + c\right) - 74 \, \cos\left(d x + c\right) + 53\right)} \sqrt{a \sin\left(d x + c\right) + a}}{768 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} - 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/768*(201*(cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) + cos(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(183*cos(d*x + c)^4 + 122*cos(d*x + c)^3 - 188*cos(d*x + c)^2 + (183*cos(d*x + c)^3 + 61*cos(d*x + c)^2 - 127*cos(d*x + c) - 53)*sin(d*x + c) - 74*cos(d*x + c) + 53)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 - 2*d*cos(d*x + c)^2 + d*cos(d*x + c) + (d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c) + d)","B",0
450,1,461,0,0.837310," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{465 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(465 \, \cos\left(d x + c\right)^{5} + 1435 \, \cos\left(d x + c\right)^{4} - 154 \, \cos\left(d x + c\right)^{3} - 1662 \, \cos\left(d x + c\right)^{2} - {\left(465 \, \cos\left(d x + c\right)^{4} - 970 \, \cos\left(d x + c\right)^{3} - 1124 \, \cos\left(d x + c\right)^{2} + 538 \, \cos\left(d x + c\right) + 611\right)} \sin\left(d x + c\right) + 73 \, \cos\left(d x + c\right) + 611\right)} \sqrt{a \sin\left(d x + c\right) + a}}{7680 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} - 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/7680*(465*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - (cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(465*cos(d*x + c)^5 + 1435*cos(d*x + c)^4 - 154*cos(d*x + c)^3 - 1662*cos(d*x + c)^2 - (465*cos(d*x + c)^4 - 970*cos(d*x + c)^3 - 1124*cos(d*x + c)^2 + 538*cos(d*x + c) + 611)*sin(d*x + c) + 73*cos(d*x + c) + 611)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - (d*cos(d*x + c)^5 + d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 - 2*d*cos(d*x + c)^2 + d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
451,1,525,0,0.986197," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{825 \, {\left(\cos\left(d x + c\right)^{7} + \cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{5} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(825 \, \cos\left(d x + c\right)^{6} + 550 \, \cos\left(d x + c\right)^{5} + 707 \, \cos\left(d x + c\right)^{4} + 1156 \, \cos\left(d x + c\right)^{3} - 225 \, \cos\left(d x + c\right)^{2} + {\left(825 \, \cos\left(d x + c\right)^{5} + 275 \, \cos\left(d x + c\right)^{4} + 982 \, \cos\left(d x + c\right)^{3} - 174 \, \cos\left(d x + c\right)^{2} - 399 \, \cos\left(d x + c\right) + 27\right)} \sin\left(d x + c\right) - 426 \, \cos\left(d x + c\right) - 27\right)} \sqrt{a \sin\left(d x + c\right) + a}}{30720 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{5} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{3} + 3 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/30720*(825*(cos(d*x + c)^7 + cos(d*x + c)^6 - 3*cos(d*x + c)^5 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 + (cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(825*cos(d*x + c)^6 + 550*cos(d*x + c)^5 + 707*cos(d*x + c)^4 + 1156*cos(d*x + c)^3 - 225*cos(d*x + c)^2 + (825*cos(d*x + c)^5 + 275*cos(d*x + c)^4 + 982*cos(d*x + c)^3 - 174*cos(d*x + c)^2 - 399*cos(d*x + c) + 27)*sin(d*x + c) - 426*cos(d*x + c) - 27)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^7 + d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^5 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^3 + 3*d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
452,1,567,0,1.020457," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{6405 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{7} + \cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{5} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(6405 \, \cos\left(d x + c\right)^{7} + 2135 \, \cos\left(d x + c\right)^{6} - 22631 \, \cos\left(d x + c\right)^{5} - 37613 \, \cos\left(d x + c\right)^{4} + 1343 \, \cos\left(d x + c\right)^{3} + 27477 \, \cos\left(d x + c\right)^{2} - {\left(6405 \, \cos\left(d x + c\right)^{6} + 4270 \, \cos\left(d x + c\right)^{5} - 18361 \, \cos\left(d x + c\right)^{4} + 19252 \, \cos\left(d x + c\right)^{3} + 20595 \, \cos\left(d x + c\right)^{2} - 6882 \, \cos\left(d x + c\right) - 7359\right)} \sin\left(d x + c\right) - 477 \, \cos\left(d x + c\right) - 7359\right)} \sqrt{a \sin\left(d x + c\right) + a}}{430080 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{5} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{3} + 3 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/430080*(6405*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 - (cos(d*x + c)^7 + cos(d*x + c)^6 - 3*cos(d*x + c)^5 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^3 + 3*cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(6405*cos(d*x + c)^7 + 2135*cos(d*x + c)^6 - 22631*cos(d*x + c)^5 - 37613*cos(d*x + c)^4 + 1343*cos(d*x + c)^3 + 27477*cos(d*x + c)^2 - (6405*cos(d*x + c)^6 + 4270*cos(d*x + c)^5 - 18361*cos(d*x + c)^4 + 19252*cos(d*x + c)^3 + 20595*cos(d*x + c)^2 - 6882*cos(d*x + c) - 7359)*sin(d*x + c) - 477*cos(d*x + c) - 7359)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 - (d*cos(d*x + c)^7 + d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^5 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^3 + 3*d*cos(d*x + c)^2 - d*cos(d*x + c) - d)*sin(d*x + c) + d)","B",0
453,1,210,0,0.800849," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(429 \, a \cos\left(d x + c\right)^{8} + 957 \, a \cos\left(d x + c\right)^{7} - 633 \, a \cos\left(d x + c\right)^{6} - 1301 \, a \cos\left(d x + c\right)^{5} + 20 \, a \cos\left(d x + c\right)^{4} - 32 \, a \cos\left(d x + c\right)^{3} + 64 \, a \cos\left(d x + c\right)^{2} - 256 \, a \cos\left(d x + c\right) + {\left(429 \, a \cos\left(d x + c\right)^{7} - 528 \, a \cos\left(d x + c\right)^{6} - 1161 \, a \cos\left(d x + c\right)^{5} + 140 \, a \cos\left(d x + c\right)^{4} + 160 \, a \cos\left(d x + c\right)^{3} + 192 \, a \cos\left(d x + c\right)^{2} + 256 \, a \cos\left(d x + c\right) + 512 \, a\right)} \sin\left(d x + c\right) - 512 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{6435 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/6435*(429*a*cos(d*x + c)^8 + 957*a*cos(d*x + c)^7 - 633*a*cos(d*x + c)^6 - 1301*a*cos(d*x + c)^5 + 20*a*cos(d*x + c)^4 - 32*a*cos(d*x + c)^3 + 64*a*cos(d*x + c)^2 - 256*a*cos(d*x + c) + (429*a*cos(d*x + c)^7 - 528*a*cos(d*x + c)^6 - 1161*a*cos(d*x + c)^5 + 140*a*cos(d*x + c)^4 + 160*a*cos(d*x + c)^3 + 192*a*cos(d*x + c)^2 + 256*a*cos(d*x + c) + 512*a)*sin(d*x + c) - 512*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
454,1,189,0,0.901200," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(385 \, a \cos\left(d x + c\right)^{7} - 490 \, a \cos\left(d x + c\right)^{6} - 1015 \, a \cos\left(d x + c\right)^{5} + 20 \, a \cos\left(d x + c\right)^{4} - 32 \, a \cos\left(d x + c\right)^{3} + 64 \, a \cos\left(d x + c\right)^{2} - 256 \, a \cos\left(d x + c\right) - {\left(385 \, a \cos\left(d x + c\right)^{6} + 875 \, a \cos\left(d x + c\right)^{5} - 140 \, a \cos\left(d x + c\right)^{4} - 160 \, a \cos\left(d x + c\right)^{3} - 192 \, a \cos\left(d x + c\right)^{2} - 256 \, a \cos\left(d x + c\right) - 512 \, a\right)} \sin\left(d x + c\right) - 512 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{5005 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/5005*(385*a*cos(d*x + c)^7 - 490*a*cos(d*x + c)^6 - 1015*a*cos(d*x + c)^5 + 20*a*cos(d*x + c)^4 - 32*a*cos(d*x + c)^3 + 64*a*cos(d*x + c)^2 - 256*a*cos(d*x + c) - (385*a*cos(d*x + c)^6 + 875*a*cos(d*x + c)^5 - 140*a*cos(d*x + c)^4 - 160*a*cos(d*x + c)^3 - 192*a*cos(d*x + c)^2 - 256*a*cos(d*x + c) - 512*a)*sin(d*x + c) - 512*a)*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
455,1,332,0,0.954529," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{315 \, {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(35 \, a \cos\left(d x + c\right)^{5} - 50 \, a \cos\left(d x + c\right)^{4} - 46 \, a \cos\left(d x + c\right)^{3} - 118 \, a \cos\left(d x + c\right)^{2} - 158 \, a \cos\left(d x + c\right) - {\left(35 \, a \cos\left(d x + c\right)^{4} + 85 \, a \cos\left(d x + c\right)^{3} + 39 \, a \cos\left(d x + c\right)^{2} + 157 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{630 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/630*(315*(a*cos(d*x + c) + a*sin(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(35*a*cos(d*x + c)^5 - 50*a*cos(d*x + c)^4 - 46*a*cos(d*x + c)^3 - 118*a*cos(d*x + c)^2 - 158*a*cos(d*x + c) - (35*a*cos(d*x + c)^4 + 85*a*cos(d*x + c)^3 + 39*a*cos(d*x + c)^2 + 157*a*cos(d*x + c) - a)*sin(d*x + c) - a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
456,1,360,0,0.906286," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{105 \, {\left(a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(10 \, a \cos\left(d x + c\right)^{5} - 16 \, a \cos\left(d x + c\right)^{4} - 8 \, a \cos\left(d x + c\right)^{3} - 120 \, a \cos\left(d x + c\right)^{2} + 33 \, a \cos\left(d x + c\right) - {\left(10 \, a \cos\left(d x + c\right)^{4} + 26 \, a \cos\left(d x + c\right)^{3} + 18 \, a \cos\left(d x + c\right)^{2} + 138 \, a \cos\left(d x + c\right) + 171 \, a\right)} \sin\left(d x + c\right) + 171 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{140 \, {\left(d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/140*(105*(a*cos(d*x + c)^2 - (a*cos(d*x + c) + a)*sin(d*x + c) - a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(10*a*cos(d*x + c)^5 - 16*a*cos(d*x + c)^4 - 8*a*cos(d*x + c)^3 - 120*a*cos(d*x + c)^2 + 33*a*cos(d*x + c) - (10*a*cos(d*x + c)^4 + 26*a*cos(d*x + c)^3 + 18*a*cos(d*x + c)^2 + 138*a*cos(d*x + c) + 171*a)*sin(d*x + c) + 171*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^2 - (d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
457,1,404,0,0.969537," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{45 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(8 \, a \cos\left(d x + c\right)^{5} - 16 \, a \cos\left(d x + c\right)^{4} + 16 \, a \cos\left(d x + c\right)^{3} + 99 \, a \cos\left(d x + c\right)^{2} - 14 \, a \cos\left(d x + c\right) - {\left(8 \, a \cos\left(d x + c\right)^{4} + 24 \, a \cos\left(d x + c\right)^{3} + 40 \, a \cos\left(d x + c\right)^{2} - 59 \, a \cos\left(d x + c\right) - 73 \, a\right)} \sin\left(d x + c\right) - 73 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{80 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/80*(45*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) + (a*cos(d*x + c)^2 - a)*sin(d*x + c) - a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(8*a*cos(d*x + c)^5 - 16*a*cos(d*x + c)^4 + 16*a*cos(d*x + c)^3 + 99*a*cos(d*x + c)^2 - 14*a*cos(d*x + c) - (8*a*cos(d*x + c)^4 + 24*a*cos(d*x + c)^3 + 40*a*cos(d*x + c)^2 - 59*a*cos(d*x + c) - 73*a)*sin(d*x + c) - 73*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
458,1,424,0,1.002201," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{111 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(16 \, a \cos\left(d x + c\right)^{5} - 64 \, a \cos\left(d x + c\right)^{4} - 17 \, a \cos\left(d x + c\right)^{3} + 165 \, a \cos\left(d x + c\right)^{2} + 9 \, a \cos\left(d x + c\right) - {\left(16 \, a \cos\left(d x + c\right)^{4} + 80 \, a \cos\left(d x + c\right)^{3} + 63 \, a \cos\left(d x + c\right)^{2} - 102 \, a \cos\left(d x + c\right) - 93 \, a\right)} \sin\left(d x + c\right) - 93 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/96*(111*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 - (a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - a)*sin(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(16*a*cos(d*x + c)^5 - 64*a*cos(d*x + c)^4 - 17*a*cos(d*x + c)^3 + 165*a*cos(d*x + c)^2 + 9*a*cos(d*x + c) - (16*a*cos(d*x + c)^4 + 80*a*cos(d*x + c)^3 + 63*a*cos(d*x + c)^2 - 102*a*cos(d*x + c) - 93*a)*sin(d*x + c) - 93*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 - (d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - d)*sin(d*x + c) + d)","B",0
459,1,460,0,0.808258," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{21 \, {\left(a \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} - 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(128 \, a \cos\left(d x + c\right)^{5} + 277 \, a \cos\left(d x + c\right)^{4} - 242 \, a \cos\left(d x + c\right)^{3} - 500 \, a \cos\left(d x + c\right)^{2} + 130 \, a \cos\left(d x + c\right) - {\left(128 \, a \cos\left(d x + c\right)^{4} - 149 \, a \cos\left(d x + c\right)^{3} - 391 \, a \cos\left(d x + c\right)^{2} + 109 \, a \cos\left(d x + c\right) + 239 \, a\right)} \sin\left(d x + c\right) + 239 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{256 \, {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} - 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/256*(21*(a*cos(d*x + c)^5 + a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 - 2*a*cos(d*x + c)^2 + a*cos(d*x + c) + (a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*sin(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(128*a*cos(d*x + c)^5 + 277*a*cos(d*x + c)^4 - 242*a*cos(d*x + c)^3 - 500*a*cos(d*x + c)^2 + 130*a*cos(d*x + c) - (128*a*cos(d*x + c)^4 - 149*a*cos(d*x + c)^3 - 391*a*cos(d*x + c)^2 + 109*a*cos(d*x + c) + 239*a)*sin(d*x + c) + 239*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^5 + d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 - 2*d*cos(d*x + c)^2 + d*cos(d*x + c) + (d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c) + d)","B",0
460,1,488,0,0.970830," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{825 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} - 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(455 \, a \cos\left(d x + c\right)^{5} - 275 \, a \cos\left(d x + c\right)^{4} - 982 \, a \cos\left(d x + c\right)^{3} + 174 \, a \cos\left(d x + c\right)^{2} + 399 \, a \cos\left(d x + c\right) - {\left(455 \, a \cos\left(d x + c\right)^{4} + 730 \, a \cos\left(d x + c\right)^{3} - 252 \, a \cos\left(d x + c\right)^{2} - 426 \, a \cos\left(d x + c\right) - 27 \, a\right)} \sin\left(d x + c\right) - 27 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2560 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{5} + d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} - 2 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/2560*(825*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - (a*cos(d*x + c)^5 + a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 - 2*a*cos(d*x + c)^2 + a*cos(d*x + c) + a)*sin(d*x + c) - a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(455*a*cos(d*x + c)^5 - 275*a*cos(d*x + c)^4 - 982*a*cos(d*x + c)^3 + 174*a*cos(d*x + c)^2 + 399*a*cos(d*x + c) - (455*a*cos(d*x + c)^4 + 730*a*cos(d*x + c)^3 - 252*a*cos(d*x + c)^2 - 426*a*cos(d*x + c) - 27*a)*sin(d*x + c) - 27*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - (d*cos(d*x + c)^5 + d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 - 2*d*cos(d*x + c)^2 + d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
461,1,557,0,1.080246," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2685 \, {\left(a \cos\left(d x + c\right)^{7} + a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{5} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(2685 \, a \cos\left(d x + c\right)^{6} - 3330 \, a \cos\left(d x + c\right)^{5} - 5649 \, a \cos\left(d x + c\right)^{4} + 7188 \, a \cos\left(d x + c\right)^{3} + 6715 \, a \cos\left(d x + c\right)^{2} - 2578 \, a \cos\left(d x + c\right) + {\left(2685 \, a \cos\left(d x + c\right)^{5} + 6015 \, a \cos\left(d x + c\right)^{4} + 366 \, a \cos\left(d x + c\right)^{3} - 6822 \, a \cos\left(d x + c\right)^{2} - 107 \, a \cos\left(d x + c\right) + 2471 \, a\right)} \sin\left(d x + c\right) - 2471 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{30720 \, {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{5} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{3} + 3 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/30720*(2685*(a*cos(d*x + c)^7 + a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^5 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^3 + 3*a*cos(d*x + c)^2 - a*cos(d*x + c) + (a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*sin(d*x + c) - a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(2685*a*cos(d*x + c)^6 - 3330*a*cos(d*x + c)^5 - 5649*a*cos(d*x + c)^4 + 7188*a*cos(d*x + c)^3 + 6715*a*cos(d*x + c)^2 - 2578*a*cos(d*x + c) + (2685*a*cos(d*x + c)^5 + 6015*a*cos(d*x + c)^4 + 366*a*cos(d*x + c)^3 - 6822*a*cos(d*x + c)^2 - 107*a*cos(d*x + c) + 2471*a)*sin(d*x + c) - 2471*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^7 + d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^5 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^3 + 3*d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
462,1,600,0,0.989907," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{5985 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{7} + a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{5} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(5985 \, a \cos\left(d x + c\right)^{7} + 1995 \, a \cos\left(d x + c\right)^{6} - 6811 \, a \cos\left(d x + c\right)^{5} - 14633 \, a \cos\left(d x + c\right)^{4} - 5997 \, a \cos\left(d x + c\right)^{3} + 10097 \, a \cos\left(d x + c\right)^{2} + 1703 \, a \cos\left(d x + c\right) - {\left(5985 \, a \cos\left(d x + c\right)^{6} + 3990 \, a \cos\left(d x + c\right)^{5} - 2821 \, a \cos\left(d x + c\right)^{4} + 11812 \, a \cos\left(d x + c\right)^{3} + 5815 \, a \cos\left(d x + c\right)^{2} - 4282 \, a \cos\left(d x + c\right) - 2579 \, a\right)} \sin\left(d x + c\right) - 2579 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{143360 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{7} + d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{5} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{3} + 3 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/143360*(5985*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 - (a*cos(d*x + c)^7 + a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^5 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^3 + 3*a*cos(d*x + c)^2 - a*cos(d*x + c) - a)*sin(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(5985*a*cos(d*x + c)^7 + 1995*a*cos(d*x + c)^6 - 6811*a*cos(d*x + c)^5 - 14633*a*cos(d*x + c)^4 - 5997*a*cos(d*x + c)^3 + 10097*a*cos(d*x + c)^2 + 1703*a*cos(d*x + c) - (5985*a*cos(d*x + c)^6 + 3990*a*cos(d*x + c)^5 - 2821*a*cos(d*x + c)^4 + 11812*a*cos(d*x + c)^3 + 5815*a*cos(d*x + c)^2 - 4282*a*cos(d*x + c) - 2579*a)*sin(d*x + c) - 2579*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 - (d*cos(d*x + c)^7 + d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^5 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^3 + 3*d*cos(d*x + c)^2 - d*cos(d*x + c) - d)*sin(d*x + c) + d)","B",0
463,1,657,0,1.062330," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{55545 \, {\left(a \cos\left(d x + c\right)^{9} + a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{7} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{5} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{3} - 4 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) + a\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(55545 \, a \cos\left(d x + c\right)^{8} + 37030 \, a \cos\left(d x + c\right)^{7} - 214774 \, a \cos\left(d x + c\right)^{6} + 27358 \, a \cos\left(d x + c\right)^{5} + 199004 \, a \cos\left(d x + c\right)^{4} - 185006 \, a \cos\left(d x + c\right)^{3} - 153786 \, a \cos\left(d x + c\right)^{2} + 48938 \, a \cos\left(d x + c\right) + {\left(55545 \, a \cos\left(d x + c\right)^{7} + 18515 \, a \cos\left(d x + c\right)^{6} - 196259 \, a \cos\left(d x + c\right)^{5} - 223617 \, a \cos\left(d x + c\right)^{4} - 24613 \, a \cos\left(d x + c\right)^{3} + 160393 \, a \cos\left(d x + c\right)^{2} + 6607 \, a \cos\left(d x + c\right) - 42331 \, a\right)} \sin\left(d x + c\right) + 42331 \, a\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2293760 \, {\left(d \cos\left(d x + c\right)^{9} + d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{7} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{5} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{3} - 4 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"1/2293760*(55545*(a*cos(d*x + c)^9 + a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^7 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^5 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^3 - 4*a*cos(d*x + c)^2 + a*cos(d*x + c) + (a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*sin(d*x + c) + a)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(55545*a*cos(d*x + c)^8 + 37030*a*cos(d*x + c)^7 - 214774*a*cos(d*x + c)^6 + 27358*a*cos(d*x + c)^5 + 199004*a*cos(d*x + c)^4 - 185006*a*cos(d*x + c)^3 - 153786*a*cos(d*x + c)^2 + 48938*a*cos(d*x + c) + (55545*a*cos(d*x + c)^7 + 18515*a*cos(d*x + c)^6 - 196259*a*cos(d*x + c)^5 - 223617*a*cos(d*x + c)^4 - 24613*a*cos(d*x + c)^3 + 160393*a*cos(d*x + c)^2 + 6607*a*cos(d*x + c) - 42331*a)*sin(d*x + c) + 42331*a)*sqrt(a*sin(d*x + c) + a))/(d*cos(d*x + c)^9 + d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^7 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^5 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^3 - 4*d*cos(d*x + c)^2 + d*cos(d*x + c) + (d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c) + d)","B",0
464,1,155,0,0.816472," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, \cos\left(d x + c\right)^{6} - 35 \, \cos\left(d x + c\right)^{5} - 445 \, \cos\left(d x + c\right)^{4} + 19 \, \cos\left(d x + c\right)^{3} - 38 \, \cos\left(d x + c\right)^{2} + {\left(315 \, \cos\left(d x + c\right)^{5} + 350 \, \cos\left(d x + c\right)^{4} - 95 \, \cos\left(d x + c\right)^{3} - 114 \, \cos\left(d x + c\right)^{2} - 152 \, \cos\left(d x + c\right) - 304\right)} \sin\left(d x + c\right) + 152 \, \cos\left(d x + c\right) + 304\right)} \sqrt{a \sin\left(d x + c\right) + a}}{3465 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"-2/3465*(315*cos(d*x + c)^6 - 35*cos(d*x + c)^5 - 445*cos(d*x + c)^4 + 19*cos(d*x + c)^3 - 38*cos(d*x + c)^2 + (315*cos(d*x + c)^5 + 350*cos(d*x + c)^4 - 95*cos(d*x + c)^3 - 114*cos(d*x + c)^2 - 152*cos(d*x + c) - 304)*sin(d*x + c) + 152*cos(d*x + c) + 304)*sqrt(a*sin(d*x + c) + a)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
465,1,136,0,0.884502," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, \cos\left(d x + c\right)^{5} + 40 \, \cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{3} + 2 \, \cos\left(d x + c\right)^{2} - {\left(35 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{3} - 6 \, \cos\left(d x + c\right)^{2} - 8 \, \cos\left(d x + c\right) - 16\right)} \sin\left(d x + c\right) - 8 \, \cos\left(d x + c\right) - 16\right)} \sqrt{a \sin\left(d x + c\right) + a}}{315 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"-2/315*(35*cos(d*x + c)^5 + 40*cos(d*x + c)^4 - cos(d*x + c)^3 + 2*cos(d*x + c)^2 - (35*cos(d*x + c)^4 - 5*cos(d*x + c)^3 - 6*cos(d*x + c)^2 - 8*cos(d*x + c) - 16)*sin(d*x + c) - 8*cos(d*x + c) - 16)*sqrt(a*sin(d*x + c) + a)/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","A",0
466,1,279,0,0.987232," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{a} {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(3 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) + 13\right)} \sin\left(d x + c\right) + 14 \, \cos\left(d x + c\right) + 13\right)} \sqrt{a \sin\left(d x + c\right) + a}}{30 \, {\left(a d \cos\left(d x + c\right) + a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"1/30*(15*sqrt(a)*(cos(d*x + c) + sin(d*x + c) + 1)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(3*cos(d*x + c)^3 + 4*cos(d*x + c)^2 - (3*cos(d*x + c)^2 - cos(d*x + c) + 13)*sin(d*x + c) + 14*cos(d*x + c) + 13)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c) + a*d*sin(d*x + c) + a*d)","B",0
467,1,306,0,0.872474," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 4 \, \cos\left(d x + c\right)^{2} - {\left(2 \, \cos\left(d x + c\right)^{2} - 2 \, \cos\left(d x + c\right) - 7\right)} \sin\left(d x + c\right) - 5 \, \cos\left(d x + c\right) - 7\right)} \sqrt{a \sin\left(d x + c\right) + a}}{12 \, {\left(a d \cos\left(d x + c\right)^{2} - a d - {\left(a d \cos\left(d x + c\right) + a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(3*(cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(2*cos(d*x + c)^3 + 4*cos(d*x + c)^2 - (2*cos(d*x + c)^2 - 2*cos(d*x + c) - 7)*sin(d*x + c) - 5*cos(d*x + c) - 7)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^2 - a*d - (a*d*cos(d*x + c) + a*d)*sin(d*x + c))","B",0
468,1,346,0,0.637629," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{9 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(8 \, \cos\left(d x + c\right)^{3} + 9 \, \cos\left(d x + c\right)^{2} - {\left(8 \, \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 11\right)} \sin\left(d x + c\right) - 10 \, \cos\left(d x + c\right) - 11\right)} \sqrt{a \sin\left(d x + c\right) + a}}{16 \, {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} - a d \cos\left(d x + c\right) - a d + {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/16*(9*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(8*cos(d*x + c)^3 + 9*cos(d*x + c)^2 - (8*cos(d*x + c)^2 - cos(d*x + c) - 11)*sin(d*x + c) - 10*cos(d*x + c) - 11)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2 - a*d*cos(d*x + c) - a*d + (a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","B",0
469,1,369,0,0.975762," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{21 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(27 \, \cos\left(d x + c\right)^{3} + 25 \, \cos\left(d x + c\right)^{2} - {\left(27 \, \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right) - 17\right)} \sin\left(d x + c\right) - 19 \, \cos\left(d x + c\right) - 17\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d - {\left(a d \cos\left(d x + c\right)^{3} + a d \cos\left(d x + c\right)^{2} - a d \cos\left(d x + c\right) - a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/96*(21*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(27*cos(d*x + c)^3 + 25*cos(d*x + c)^2 - (27*cos(d*x + c)^2 + 2*cos(d*x + c) - 17)*sin(d*x + c) - 19*cos(d*x + c) - 17)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d - (a*d*cos(d*x + c)^3 + a*d*cos(d*x + c)^2 - a*d*cos(d*x + c) - a*d)*sin(d*x + c))","B",0
470,1,426,0,0.998159," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{33 \, {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(33 \, \cos\left(d x + c\right)^{4} - 106 \, \cos\left(d x + c\right)^{3} - 164 \, \cos\left(d x + c\right)^{2} + {\left(33 \, \cos\left(d x + c\right)^{3} + 139 \, \cos\left(d x + c\right)^{2} - 25 \, \cos\left(d x + c\right) - 83\right)} \sin\left(d x + c\right) + 58 \, \cos\left(d x + c\right) + 83\right)} \sqrt{a \sin\left(d x + c\right) + a}}{768 \, {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{3} - 2 \, a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right) + a d + {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/768*(33*(cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) + cos(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(33*cos(d*x + c)^4 - 106*cos(d*x + c)^3 - 164*cos(d*x + c)^2 + (33*cos(d*x + c)^3 + 139*cos(d*x + c)^2 - 25*cos(d*x + c) - 83)*sin(d*x + c) + 58*cos(d*x + c) + 83)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^3 - 2*a*d*cos(d*x + c)^2 + a*d*cos(d*x + c) + a*d + (a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","B",0
471,1,472,0,1.030250," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\frac{45 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(45 \, \cos\left(d x + c\right)^{5} + 15 \, \cos\left(d x + c\right)^{4} + 142 \, \cos\left(d x + c\right)^{3} + 186 \, \cos\left(d x + c\right)^{2} - {\left(45 \, \cos\left(d x + c\right)^{4} + 30 \, \cos\left(d x + c\right)^{3} + 172 \, \cos\left(d x + c\right)^{2} - 14 \, \cos\left(d x + c\right) - 73\right)} \sin\left(d x + c\right) - 59 \, \cos\left(d x + c\right) - 73\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2560 \, {\left(a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{2} - a d - {\left(a d \cos\left(d x + c\right)^{5} + a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{3} - 2 \, a d \cos\left(d x + c\right)^{2} + a d \cos\left(d x + c\right) + a d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/2560*(45*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - (cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(45*cos(d*x + c)^5 + 15*cos(d*x + c)^4 + 142*cos(d*x + c)^3 + 186*cos(d*x + c)^2 - (45*cos(d*x + c)^4 + 30*cos(d*x + c)^3 + 172*cos(d*x + c)^2 - 14*cos(d*x + c) - 73)*sin(d*x + c) - 59*cos(d*x + c) - 73)*sqrt(a*sin(d*x + c) + a))/(a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^2 - a*d - (a*d*cos(d*x + c)^5 + a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^3 - 2*a*d*cos(d*x + c)^2 + a*d*cos(d*x + c) + a*d)*sin(d*x + c))","B",0
472,1,161,0,0.731191," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(105 \, \cos\left(d x + c\right)^{6} - 140 \, \cos\left(d x + c\right)^{5} - 460 \, \cos\left(d x + c\right)^{4} + 274 \, \cos\left(d x + c\right)^{3} + 607 \, \cos\left(d x + c\right)^{2} + {\left(105 \, \cos\left(d x + c\right)^{5} + 245 \, \cos\left(d x + c\right)^{4} - 215 \, \cos\left(d x + c\right)^{3} - 489 \, \cos\left(d x + c\right)^{2} + 118 \, \cos\left(d x + c\right) + 236\right)} \sin\left(d x + c\right) - 118 \, \cos\left(d x + c\right) - 236\right)} \sqrt{a \sin\left(d x + c\right) + a}}{1155 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-2/1155*(105*cos(d*x + c)^6 - 140*cos(d*x + c)^5 - 460*cos(d*x + c)^4 + 274*cos(d*x + c)^3 + 607*cos(d*x + c)^2 + (105*cos(d*x + c)^5 + 245*cos(d*x + c)^4 - 215*cos(d*x + c)^3 - 489*cos(d*x + c)^2 + 118*cos(d*x + c) + 236)*sin(d*x + c) - 118*cos(d*x + c) - 236)*sqrt(a*sin(d*x + c) + a)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
473,1,142,0,0.730224," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, \cos\left(d x + c\right)^{5} + 85 \, \cos\left(d x + c\right)^{4} - 73 \, \cos\left(d x + c\right)^{3} - 169 \, \cos\left(d x + c\right)^{2} - {\left(35 \, \cos\left(d x + c\right)^{4} - 50 \, \cos\left(d x + c\right)^{3} - 123 \, \cos\left(d x + c\right)^{2} + 46 \, \cos\left(d x + c\right) + 92\right)} \sin\left(d x + c\right) + 46 \, \cos\left(d x + c\right) + 92\right)} \sqrt{a \sin\left(d x + c\right) + a}}{315 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"-2/315*(35*cos(d*x + c)^5 + 85*cos(d*x + c)^4 - 73*cos(d*x + c)^3 - 169*cos(d*x + c)^2 - (35*cos(d*x + c)^4 - 50*cos(d*x + c)^3 - 123*cos(d*x + c)^2 + 46*cos(d*x + c) + 92)*sin(d*x + c) + 46*cos(d*x + c) + 92)*sqrt(a*sin(d*x + c) + a)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","A",0
474,1,121,0,0.822572," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{4} - 8 \, \cos\left(d x + c\right)^{3} - 19 \, \cos\left(d x + c\right)^{2} + {\left(5 \, \cos\left(d x + c\right)^{3} + 13 \, \cos\left(d x + c\right)^{2} - 6 \, \cos\left(d x + c\right) - 12\right)} \sin\left(d x + c\right) + 6 \, \cos\left(d x + c\right) + 12\right)} \sqrt{a \sin\left(d x + c\right) + a}}{35 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"2/35*(5*cos(d*x + c)^4 - 8*cos(d*x + c)^3 - 19*cos(d*x + c)^2 + (5*cos(d*x + c)^3 + 13*cos(d*x + c)^2 - 6*cos(d*x + c) - 12)*sin(d*x + c) + 6*cos(d*x + c) + 12)*sqrt(a*sin(d*x + c) + a)/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","B",0
475,1,260,0,0.900050," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{a} {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 5\right)} \sin\left(d x + c\right) - 4 \, \cos\left(d x + c\right) - 5\right)} \sqrt{a \sin\left(d x + c\right) + a}}{6 \, {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d \sin\left(d x + c\right) + a^{2} d\right)}}"," ",0,"1/6*(3*sqrt(a)*(cos(d*x + c) + sin(d*x + c) + 1)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 5)*sin(d*x + c) - 4*cos(d*x + c) - 5)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c) + a^2*d*sin(d*x + c) + a^2*d)","B",0
476,1,291,0,0.739013," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(2 \, \cos\left(d x + c\right)^{2} + {\left(2 \, \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) - 1\right)} \sqrt{a \sin\left(d x + c\right) + a}}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d - {\left(a^{2} d \cos\left(d x + c\right) + a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*(3*(cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(2*cos(d*x + c)^2 + (2*cos(d*x + c) + 1)*sin(d*x + c) + cos(d*x + c) - 1)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^2 - a^2*d - (a^2*d*cos(d*x + c) + a^2*d)*sin(d*x + c))","B",0
477,1,337,0,0.668742," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) - 4 \, {\left(5 \, \cos\left(d x + c\right)^{2} + {\left(5 \, \cos\left(d x + c\right) + 7\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 7\right)} \sqrt{a \sin\left(d x + c\right) + a}}{16 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \cos\left(d x + c\right) - a^{2} d + {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/16*(3*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) - 4*(5*cos(d*x + c)^2 + (5*cos(d*x + c) + 7)*sin(d*x + c) - 2*cos(d*x + c) - 7)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2 - a^2*d*cos(d*x + c) - a^2*d + (a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","B",0
478,1,383,0,0.900564," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(3 \, \cos\left(d x + c\right)^{3} + 17 \, \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} - 14 \, \cos\left(d x + c\right) - 25\right)} \sin\left(d x + c\right) - 11 \, \cos\left(d x + c\right) - 25\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d - {\left(a^{2} d \cos\left(d x + c\right)^{3} + a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d \cos\left(d x + c\right) - a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/96*(3*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(3*cos(d*x + c)^3 + 17*cos(d*x + c)^2 - (3*cos(d*x + c)^2 - 14*cos(d*x + c) - 25)*sin(d*x + c) - 11*cos(d*x + c) - 25)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d - (a^2*d*cos(d*x + c)^3 + a^2*d*cos(d*x + c)^2 - a^2*d*cos(d*x + c) - a^2*d)*sin(d*x + c))","B",0
479,1,442,0,0.752617," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{3 \, {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(3 \, \cos\left(d x + c\right)^{4} + 2 \, \cos\left(d x + c\right)^{3} + 20 \, \cos\left(d x + c\right)^{2} + {\left(3 \, \cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + 21 \, \cos\left(d x + c\right) + 39\right)} \sin\left(d x + c\right) - 18 \, \cos\left(d x + c\right) - 39\right)} \sqrt{a \sin\left(d x + c\right) + a}}{256 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} + a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right) + a^{2} d + {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/256*(3*(cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) + cos(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(3*cos(d*x + c)^4 + 2*cos(d*x + c)^3 + 20*cos(d*x + c)^2 + (3*cos(d*x + c)^3 + cos(d*x + c)^2 + 21*cos(d*x + c) + 39)*sin(d*x + c) - 18*cos(d*x + c) - 39)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^5 + a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c) + a^2*d + (a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)*sin(d*x + c))","B",0
480,1,492,0,0.677106," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\frac{15 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + \cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + 4 \, {\left(15 \, \cos\left(d x + c\right)^{5} + 5 \, \cos\left(d x + c\right)^{4} - 38 \, \cos\left(d x + c\right)^{3} - 194 \, \cos\left(d x + c\right)^{2} - {\left(15 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{3} - 28 \, \cos\left(d x + c\right)^{2} + 166 \, \cos\left(d x + c\right) + 317\right)} \sin\left(d x + c\right) + 151 \, \cos\left(d x + c\right) + 317\right)} \sqrt{a \sin\left(d x + c\right) + a}}{2560 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 3 \, a^{2} d \cos\left(d x + c\right)^{4} + 3 \, a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d - {\left(a^{2} d \cos\left(d x + c\right)^{5} + a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d \cos\left(d x + c\right) + a^{2} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/2560*(15*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - (cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*(15*cos(d*x + c)^5 + 5*cos(d*x + c)^4 - 38*cos(d*x + c)^3 - 194*cos(d*x + c)^2 - (15*cos(d*x + c)^4 + 10*cos(d*x + c)^3 - 28*cos(d*x + c)^2 + 166*cos(d*x + c) + 317)*sin(d*x + c) + 151*cos(d*x + c) + 317)*sqrt(a*sin(d*x + c) + a))/(a^2*d*cos(d*x + c)^6 - 3*a^2*d*cos(d*x + c)^4 + 3*a^2*d*cos(d*x + c)^2 - a^2*d - (a^2*d*cos(d*x + c)^5 + a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)^2 + a^2*d*cos(d*x + c) + a^2*d)*sin(d*x + c))","B",0
481,1,299,0,0.938506," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\frac{693 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - {\left(63 \, \cos\left(d x + c\right)^{6} - 161 \, \cos\left(d x + c\right)^{5} - 562 \, \cos\left(d x + c\right)^{4} + 622 \, \cos\left(d x + c\right)^{3} + 1759 \, \cos\left(d x + c\right)^{2} + {\left(63 \, \cos\left(d x + c\right)^{5} + 224 \, \cos\left(d x + c\right)^{4} - 338 \, \cos\left(d x + c\right)^{3} - 960 \, \cos\left(d x + c\right)^{2} + 799 \, \cos\left(d x + c\right) + 2984\right)} \sin\left(d x + c\right) - 2185 \, \cos\left(d x + c\right) - 2984\right)} \sqrt{a \sin\left(d x + c\right) + a}\right)}}{693 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"2/693*(693*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - (63*cos(d*x + c)^6 - 161*cos(d*x + c)^5 - 562*cos(d*x + c)^4 + 622*cos(d*x + c)^3 + 1759*cos(d*x + c)^2 + (63*cos(d*x + c)^5 + 224*cos(d*x + c)^4 - 338*cos(d*x + c)^3 - 960*cos(d*x + c)^2 + 799*cos(d*x + c) + 2984)*sin(d*x + c) - 2185*cos(d*x + c) - 2984)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","A",0
482,1,280,0,0.845804," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\frac{315 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - {\left(35 \, \cos\left(d x + c\right)^{5} + 130 \, \cos\left(d x + c\right)^{4} - 208 \, \cos\left(d x + c\right)^{3} - 634 \, \cos\left(d x + c\right)^{2} - {\left(35 \, \cos\left(d x + c\right)^{4} - 95 \, \cos\left(d x + c\right)^{3} - 303 \, \cos\left(d x + c\right)^{2} + 331 \, \cos\left(d x + c\right) + 1292\right)} \sin\left(d x + c\right) + 961 \, \cos\left(d x + c\right) + 1292\right)} \sqrt{a \sin\left(d x + c\right) + a}\right)}}{315 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"2/315*(315*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - (35*cos(d*x + c)^5 + 130*cos(d*x + c)^4 - 208*cos(d*x + c)^3 - 634*cos(d*x + c)^2 - (35*cos(d*x + c)^4 - 95*cos(d*x + c)^3 - 303*cos(d*x + c)^2 + 331*cos(d*x + c) + 1292)*sin(d*x + c) + 961*cos(d*x + c) + 1292)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","A",0
483,1,258,0,0.951638," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\frac{21 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + {\left(3 \, \cos\left(d x + c\right)^{4} - 9 \, \cos\left(d x + c\right)^{3} - 31 \, \cos\left(d x + c\right)^{2} + {\left(3 \, \cos\left(d x + c\right)^{3} + 12 \, \cos\left(d x + c\right)^{2} - 19 \, \cos\left(d x + c\right) - 80\right)} \sin\left(d x + c\right) + 61 \, \cos\left(d x + c\right) + 80\right)} \sqrt{a \sin\left(d x + c\right) + a}\right)}}{21 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"2/21*(21*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + (3*cos(d*x + c)^4 - 9*cos(d*x + c)^3 - 31*cos(d*x + c)^2 + (3*cos(d*x + c)^3 + 12*cos(d*x + c)^2 - 19*cos(d*x + c) - 80)*sin(d*x + c) + 61*cos(d*x + c) + 80)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","A",0
484,1,239,0,0.915111," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\frac{15 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + {\left(3 \, \cos\left(d x + c\right)^{3} + 14 \, \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} - 11 \, \cos\left(d x + c\right) - 52\right)} \sin\left(d x + c\right) - 41 \, \cos\left(d x + c\right) - 52\right)} \sqrt{a \sin\left(d x + c\right) + a}\right)}}{15 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"2/15*(15*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + (3*cos(d*x + c)^3 + 14*cos(d*x + c)^2 - (3*cos(d*x + c)^2 - 11*cos(d*x + c) - 52)*sin(d*x + c) - 41*cos(d*x + c) - 52)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","B",0
485,1,377,0,0.766512," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{a} {\left(\cos\left(d x + c\right) + \sin\left(d x + c\right) + 1\right)} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + \frac{4 \, \sqrt{2} {\left(a \cos\left(d x + c\right) + a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{2 \, {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d \sin\left(d x + c\right) + a^{3} d\right)}}"," ",0,"1/2*(sqrt(a)*(cos(d*x + c) + sin(d*x + c) + 1)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 4*sqrt(2)*(a*cos(d*x + c) + a*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - 4*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1))/(a^3*d*cos(d*x + c) + a^3*d*sin(d*x + c) + a^3*d)","B",0
486,1,421,0,0.989103," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{5 \, {\left(\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 1\right)} \sin\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + \frac{8 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + 4 \, \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d - {\left(a^{3} d \cos\left(d x + c\right) + a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/4*(5*(cos(d*x + c)^2 - (cos(d*x + c) + 1)*sin(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 8*sqrt(2)*(a*cos(d*x + c)^2 - (a*cos(d*x + c) + a)*sin(d*x + c) - a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + 4*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1))/(a^3*d*cos(d*x + c)^2 - a^3*d - (a^3*d*cos(d*x + c) + a^3*d)*sin(d*x + c))","B",0
487,1,508,0,1.049439," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{23 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + \frac{32 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - 4 \, {\left(9 \, \cos\left(d x + c\right)^{2} + {\left(9 \, \cos\left(d x + c\right) + 11\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 11\right)} \sqrt{a \sin\left(d x + c\right) + a}}{16 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/16*(23*(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 32*sqrt(2)*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) + (a*cos(d*x + c)^2 - a)*sin(d*x + c) - a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - 4*(9*cos(d*x + c)^2 + (9*cos(d*x + c) + 11)*sin(d*x + c) - 2*cos(d*x + c) - 11)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - a^3*d + (a^3*d*cos(d*x + c)^2 - a^3*d)*sin(d*x + c))","B",0
488,1,564,0,1.211164," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{135 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} - \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + \frac{192 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} + 4 \, {\left(57 \, \cos\left(d x + c\right)^{3} + 83 \, \cos\left(d x + c\right)^{2} - {\left(57 \, \cos\left(d x + c\right)^{2} - 26 \, \cos\left(d x + c\right) - 91\right)} \sin\left(d x + c\right) - 65 \, \cos\left(d x + c\right) - 91\right)} \sqrt{a \sin\left(d x + c\right) + a}}{96 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d - {\left(a^{3} d \cos\left(d x + c\right)^{3} + a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d \cos\left(d x + c\right) - a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/96*(135*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 - (cos(d*x + c)^3 + cos(d*x + c)^2 - cos(d*x + c) - 1)*sin(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 192*sqrt(2)*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 - (a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - a)*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) - 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) + 4*(57*cos(d*x + c)^3 + 83*cos(d*x + c)^2 - (57*cos(d*x + c)^2 - 26*cos(d*x + c) - 91)*sin(d*x + c) - 65*cos(d*x + c) - 91)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d - (a^3*d*cos(d*x + c)^3 + a^3*d*cos(d*x + c)^2 - a^3*d*cos(d*x + c) - a^3*d)*sin(d*x + c))","B",0
489,1,643,0,1.418287," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\frac{1089 \, {\left(\cos\left(d x + c\right)^{5} + \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + \cos\left(d x + c\right) + 1\right)} \sqrt{a} \log\left(\frac{a \cos\left(d x + c\right)^{3} - 7 \, a \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right) + 3\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right) - 3\right)} \sqrt{a \sin\left(d x + c\right) + a} \sqrt{a} - 9 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + 8 \, a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) - a}{\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 1}\right) + \frac{1536 \, \sqrt{2} {\left(a \cos\left(d x + c\right)^{5} + a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{3} - 2 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) + a\right)} \log\left(-\frac{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) - 2\right)} \sin\left(d x + c\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(d x + c\right) + a} {\left(\cos\left(d x + c\right) - \sin\left(d x + c\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(d x + c\right) + 2}{\cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right) + 2\right)} \sin\left(d x + c\right) - \cos\left(d x + c\right) - 2}\right)}{\sqrt{a}} - 4 \, {\left(447 \, \cos\left(d x + c\right)^{4} - 214 \, \cos\left(d x + c\right)^{3} - 1244 \, \cos\left(d x + c\right)^{2} + {\left(447 \, \cos\left(d x + c\right)^{3} + 661 \, \cos\left(d x + c\right)^{2} - 583 \, \cos\left(d x + c\right) - 845\right)} \sin\left(d x + c\right) + 262 \, \cos\left(d x + c\right) + 845\right)} \sqrt{a \sin\left(d x + c\right) + a}}{768 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{3} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d \cos\left(d x + c\right) + a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/768*(1089*(cos(d*x + c)^5 + cos(d*x + c)^4 - 2*cos(d*x + c)^3 - 2*cos(d*x + c)^2 + (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) + cos(d*x + c) + 1)*sqrt(a)*log((a*cos(d*x + c)^3 - 7*a*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + (cos(d*x + c) + 3)*sin(d*x + c) - 2*cos(d*x + c) - 3)*sqrt(a*sin(d*x + c) + a)*sqrt(a) - 9*a*cos(d*x + c) + (a*cos(d*x + c)^2 + 8*a*cos(d*x + c) - a)*sin(d*x + c) - a)/(cos(d*x + c)^3 + cos(d*x + c)^2 + (cos(d*x + c)^2 - 1)*sin(d*x + c) - cos(d*x + c) - 1)) + 1536*sqrt(2)*(a*cos(d*x + c)^5 + a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^3 - 2*a*cos(d*x + c)^2 + a*cos(d*x + c) + (a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*sin(d*x + c) + a)*log(-(cos(d*x + c)^2 - (cos(d*x + c) - 2)*sin(d*x + c) + 2*sqrt(2)*sqrt(a*sin(d*x + c) + a)*(cos(d*x + c) - sin(d*x + c) + 1)/sqrt(a) + 3*cos(d*x + c) + 2)/(cos(d*x + c)^2 - (cos(d*x + c) + 2)*sin(d*x + c) - cos(d*x + c) - 2))/sqrt(a) - 4*(447*cos(d*x + c)^4 - 214*cos(d*x + c)^3 - 1244*cos(d*x + c)^2 + (447*cos(d*x + c)^3 + 661*cos(d*x + c)^2 - 583*cos(d*x + c) - 845)*sin(d*x + c) + 262*cos(d*x + c) + 845)*sqrt(a*sin(d*x + c) + a))/(a^3*d*cos(d*x + c)^5 + a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^3 - 2*a^3*d*cos(d*x + c)^2 + a^3*d*cos(d*x + c) + a^3*d + (a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d)*sin(d*x + c))","B",0
490,0,0,0,1.096468," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(d x + c\right)^{6} - 2 \, a^{2} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, a^{2} \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^6 - 2*a^2*cos(d*x + c)^4*sin(d*x + c) - 2*a^2*cos(d*x + c)^4)*sin(d*x + c)^n, x)","F",0
491,0,0,0,1.109706," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + a \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral((a*cos(d*x + c)^4*sin(d*x + c) + a*cos(d*x + c)^4)*sin(d*x + c)^n, x)","F",0
492,0,0,0,1.015860," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}}{a \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sin(d*x + c)^n*cos(d*x + c)^4/(a*sin(d*x + c) + a), x)","F",0
493,0,0,0,1.091831," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}}{a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-sin(d*x + c)^n*cos(d*x + c)^4/(a^2*cos(d*x + c)^2 - 2*a^2*sin(d*x + c) - 2*a^2), x)","F",0
494,1,106,0,0.884821," ","integrate(cos(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{1386 \, a \cos\left(d x + c\right)^{10} - 3465 \, a \cos\left(d x + c\right)^{8} + 2310 \, a \cos\left(d x + c\right)^{6} + 20 \, {\left(63 \, a \cos\left(d x + c\right)^{10} - 161 \, a \cos\left(d x + c\right)^{8} + 113 \, a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} - 8 \, a\right)} \sin\left(d x + c\right)}{13860 \, d}"," ",0,"-1/13860*(1386*a*cos(d*x + c)^10 - 3465*a*cos(d*x + c)^8 + 2310*a*cos(d*x + c)^6 + 20*(63*a*cos(d*x + c)^10 - 161*a*cos(d*x + c)^8 + 113*a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 - 8*a)*sin(d*x + c))/d","A",0
495,1,95,0,1.181515," ","integrate(cos(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{126 \, a \cos\left(d x + c\right)^{10} - 315 \, a \cos\left(d x + c\right)^{8} + 210 \, a \cos\left(d x + c\right)^{6} - 4 \, {\left(35 \, a \cos\left(d x + c\right)^{8} - 50 \, a \cos\left(d x + c\right)^{6} + 3 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right)}{1260 \, d}"," ",0,"-1/1260*(126*a*cos(d*x + c)^10 - 315*a*cos(d*x + c)^8 + 210*a*cos(d*x + c)^6 - 4*(35*a*cos(d*x + c)^8 - 50*a*cos(d*x + c)^6 + 3*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c))/d","A",0
496,1,84,0,1.009037," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{315 \, a \cos\left(d x + c\right)^{8} - 420 \, a \cos\left(d x + c\right)^{6} + 8 \, {\left(35 \, a \cos\left(d x + c\right)^{8} - 50 \, a \cos\left(d x + c\right)^{6} + 3 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right)}{2520 \, d}"," ",0,"1/2520*(315*a*cos(d*x + c)^8 - 420*a*cos(d*x + c)^6 + 8*(35*a*cos(d*x + c)^8 - 50*a*cos(d*x + c)^6 + 3*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c))/d","A",0
497,1,73,0,0.878433," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, a \cos\left(d x + c\right)^{8} - 140 \, a \cos\left(d x + c\right)^{6} - 8 \, {\left(15 \, a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} - 8 \, a\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*a*cos(d*x + c)^8 - 140*a*cos(d*x + c)^6 - 8*(15*a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 - 8*a)*sin(d*x + c))/d","A",0
498,1,62,0,0.903534," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{35 \, a \cos\left(d x + c\right)^{6} + 2 \, {\left(15 \, a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} - 8 \, a\right)} \sin\left(d x + c\right)}{210 \, d}"," ",0,"-1/210*(35*a*cos(d*x + c)^6 + 2*(15*a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 - 8*a)*sin(d*x + c))/d","A",0
499,1,74,0,0.697498," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, a \cos\left(d x + c\right)^{4} + 30 \, a \cos\left(d x + c\right)^{2} + 60 \, a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, {\left(3 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(15*a*cos(d*x + c)^4 + 30*a*cos(d*x + c)^2 + 60*a*log(1/2*sin(d*x + c)) + 4*(3*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c))/d","A",0
500,1,91,0,1.050182," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{32 \, a \cos\left(d x + c\right)^{4} + 128 \, a \cos\left(d x + c\right)^{2} + 96 \, a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 3 \, {\left(8 \, a \cos\left(d x + c\right)^{4} + 16 \, a \cos\left(d x + c\right)^{2} - 11 \, a\right)} \sin\left(d x + c\right) - 256 \, a}{96 \, d \sin\left(d x + c\right)}"," ",0,"1/96*(32*a*cos(d*x + c)^4 + 128*a*cos(d*x + c)^2 + 96*a*log(1/2*sin(d*x + c))*sin(d*x + c) + 3*(8*a*cos(d*x + c)^4 + 16*a*cos(d*x + c)^2 - 11*a)*sin(d*x + c) - 256*a)/(d*sin(d*x + c))","A",0
501,1,102,0,0.983386," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, a \cos\left(d x + c\right)^{4} - 9 \, a \cos\left(d x + c\right)^{2} + 24 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, {\left(a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} - 8 \, a\right)} \sin\left(d x + c\right) - 3 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/12*(6*a*cos(d*x + c)^4 - 9*a*cos(d*x + c)^2 + 24*(a*cos(d*x + c)^2 - a)*log(1/2*sin(d*x + c)) + 4*(a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 - 8*a)*sin(d*x + c) - 3*a)/(d*cos(d*x + c)^2 - d)","A",0
502,1,117,0,1.011881," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, a \cos\left(d x + c\right)^{4} - 48 \, a \cos\left(d x + c\right)^{2} + 24 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 3 \, {\left(2 \, a \cos\left(d x + c\right)^{4} - 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) + 32 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(12*a*cos(d*x + c)^4 - 48*a*cos(d*x + c)^2 + 24*(a*cos(d*x + c)^2 - a)*log(1/2*sin(d*x + c))*sin(d*x + c) + 3*(2*a*cos(d*x + c)^4 - 3*a*cos(d*x + c)^2 - a)*sin(d*x + c) + 32*a)/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
503,1,110,0,0.937299," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, a \cos\left(d x + c\right)^{2} - 12 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, {\left(3 \, a \cos\left(d x + c\right)^{4} - 12 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right) - 9 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/12*(12*a*cos(d*x + c)^2 - 12*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*sin(d*x + c)) - 4*(3*a*cos(d*x + c)^4 - 12*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c) - 9*a)/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
504,1,124,0,0.950839," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{60 \, a \cos\left(d x + c\right)^{4} - 80 \, a \cos\left(d x + c\right)^{2} - 60 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 15 \, {\left(4 \, a \cos\left(d x + c\right)^{2} - 3 \, a\right)} \sin\left(d x + c\right) + 32 \, a}{60 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(60*a*cos(d*x + c)^4 - 80*a*cos(d*x + c)^2 - 60*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*sin(d*x + c))*sin(d*x + c) + 15*(4*a*cos(d*x + c)^2 - 3*a)*sin(d*x + c) + 32*a)/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
505,1,100,0,0.771509," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, a \cos\left(d x + c\right)^{4} - 15 \, a \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, a \cos\left(d x + c\right)^{4} - 20 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right) + 5 \, a}{30 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/30*(15*a*cos(d*x + c)^4 - 15*a*cos(d*x + c)^2 + 2*(15*a*cos(d*x + c)^4 - 20*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c) + 5*a)/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
506,1,106,0,1.052394," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{70 \, a \cos\left(d x + c\right)^{4} - 56 \, a \cos\left(d x + c\right)^{2} + 35 \, {\left(3 \, a \cos\left(d x + c\right)^{4} - 3 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) + 16 \, a}{210 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/210*(70*a*cos(d*x + c)^4 - 56*a*cos(d*x + c)^2 + 35*(3*a*cos(d*x + c)^4 - 3*a*cos(d*x + c)^2 + a)*sin(d*x + c) + 16*a)/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
507,1,109,0,0.545582," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{210 \, a \cos\left(d x + c\right)^{4} - 140 \, a \cos\left(d x + c\right)^{2} + 8 \, {\left(35 \, a \cos\left(d x + c\right)^{4} - 28 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right) + 35 \, a}{840 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/840*(210*a*cos(d*x + c)^4 - 140*a*cos(d*x + c)^2 + 8*(35*a*cos(d*x + c)^4 - 28*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c) + 35*a)/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
508,1,115,0,0.822964," ","integrate(cos(d*x+c)^5*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{504 \, a \cos\left(d x + c\right)^{4} - 288 \, a \cos\left(d x + c\right)^{2} + 105 \, {\left(6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) + 64 \, a}{2520 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/2520*(504*a*cos(d*x + c)^4 - 288*a*cos(d*x + c)^2 + 105*(6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*sin(d*x + c) + 64*a)/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
509,1,122,0,0.907532," ","integrate(cos(d*x+c)^5*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{210 \, a \cos\left(d x + c\right)^{4} - 105 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(63 \, a \cos\left(d x + c\right)^{4} - 36 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right) + 21 \, a}{1260 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/1260*(210*a*cos(d*x + c)^4 - 105*a*cos(d*x + c)^2 + 4*(63*a*cos(d*x + c)^4 - 36*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c) + 21*a)/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","A",0
510,1,128,0,0.703527," ","integrate(cos(d*x+c)^5*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{1980 \, a \cos\left(d x + c\right)^{4} - 880 \, a \cos\left(d x + c\right)^{2} + 231 \, {\left(10 \, a \cos\left(d x + c\right)^{4} - 5 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) + 160 \, a}{13860 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/13860*(1980*a*cos(d*x + c)^4 - 880*a*cos(d*x + c)^2 + 231*(10*a*cos(d*x + c)^4 - 5*a*cos(d*x + c)^2 + a)*sin(d*x + c) + 160*a)/((d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
511,1,111,0,0.883402," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{252 \, a^{2} \cos\left(d x + c\right)^{10} - 945 \, a^{2} \cos\left(d x + c\right)^{8} + 840 \, a^{2} \cos\left(d x + c\right)^{6} - 16 \, {\left(35 \, a^{2} \cos\left(d x + c\right)^{8} - 50 \, a^{2} \cos\left(d x + c\right)^{6} + 3 \, a^{2} \cos\left(d x + c\right)^{4} + 4 \, a^{2} \cos\left(d x + c\right)^{2} + 8 \, a^{2}\right)} \sin\left(d x + c\right)}{2520 \, d}"," ",0,"-1/2520*(252*a^2*cos(d*x + c)^10 - 945*a^2*cos(d*x + c)^8 + 840*a^2*cos(d*x + c)^6 - 16*(35*a^2*cos(d*x + c)^8 - 50*a^2*cos(d*x + c)^6 + 3*a^2*cos(d*x + c)^4 + 4*a^2*cos(d*x + c)^2 + 8*a^2)*sin(d*x + c))/d","A",0
512,1,98,0,1.106979," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{315 \, a^{2} \cos\left(d x + c\right)^{8} - 420 \, a^{2} \cos\left(d x + c\right)^{6} + 4 \, {\left(35 \, a^{2} \cos\left(d x + c\right)^{8} - 95 \, a^{2} \cos\left(d x + c\right)^{6} + 12 \, a^{2} \cos\left(d x + c\right)^{4} + 16 \, a^{2} \cos\left(d x + c\right)^{2} + 32 \, a^{2}\right)} \sin\left(d x + c\right)}{1260 \, d}"," ",0,"1/1260*(315*a^2*cos(d*x + c)^8 - 420*a^2*cos(d*x + c)^6 + 4*(35*a^2*cos(d*x + c)^8 - 95*a^2*cos(d*x + c)^6 + 12*a^2*cos(d*x + c)^4 + 16*a^2*cos(d*x + c)^2 + 32*a^2)*sin(d*x + c))/d","A",0
513,1,85,0,1.309351," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{105 \, a^{2} \cos\left(d x + c\right)^{8} - 280 \, a^{2} \cos\left(d x + c\right)^{6} - 16 \, {\left(15 \, a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2}\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*a^2*cos(d*x + c)^8 - 280*a^2*cos(d*x + c)^6 - 16*(15*a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 - 8*a^2)*sin(d*x + c))/d","A",0
514,1,99,0,1.275306," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{10 \, a^{2} \cos\left(d x + c\right)^{6} - 15 \, a^{2} \cos\left(d x + c\right)^{4} - 30 \, a^{2} \cos\left(d x + c\right)^{2} - 60 \, a^{2} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 8 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{4} + 4 \, a^{2} \cos\left(d x + c\right)^{2} + 8 \, a^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(10*a^2*cos(d*x + c)^6 - 15*a^2*cos(d*x + c)^4 - 30*a^2*cos(d*x + c)^2 - 60*a^2*log(1/2*sin(d*x + c)) - 8*(3*a^2*cos(d*x + c)^4 + 4*a^2*cos(d*x + c)^2 + 8*a^2)*sin(d*x + c))/d","A",0
515,1,118,0,1.275746," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{48 \, a^{2} \cos\left(d x + c\right)^{6} - 64 \, a^{2} \cos\left(d x + c\right)^{4} - 256 \, a^{2} \cos\left(d x + c\right)^{2} - 480 \, a^{2} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 512 \, a^{2} - 15 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{4} + 16 \, a^{2} \cos\left(d x + c\right)^{2} - 11 \, a^{2}\right)} \sin\left(d x + c\right)}{240 \, d \sin\left(d x + c\right)}"," ",0,"-1/240*(48*a^2*cos(d*x + c)^6 - 64*a^2*cos(d*x + c)^4 - 256*a^2*cos(d*x + c)^2 - 480*a^2*log(1/2*sin(d*x + c))*sin(d*x + c) + 512*a^2 - 15*(8*a^2*cos(d*x + c)^4 + 16*a^2*cos(d*x + c)^2 - 11*a^2)*sin(d*x + c))/(d*sin(d*x + c))","A",0
516,1,131,0,0.917262," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{24 \, a^{2} \cos\left(d x + c\right)^{6} - 24 \, a^{2} \cos\left(d x + c\right)^{4} - 9 \, a^{2} \cos\left(d x + c\right)^{2} + 57 \, a^{2} - 96 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 64 \, {\left(a^{2} \cos\left(d x + c\right)^{4} + 4 \, a^{2} \cos\left(d x + c\right)^{2} - 8 \, a^{2}\right)} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/96*(24*a^2*cos(d*x + c)^6 - 24*a^2*cos(d*x + c)^4 - 9*a^2*cos(d*x + c)^2 + 57*a^2 - 96*(a^2*cos(d*x + c)^2 - a^2)*log(1/2*sin(d*x + c)) - 64*(a^2*cos(d*x + c)^4 + 4*a^2*cos(d*x + c)^2 - 8*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
517,1,115,0,0.961887," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} \cos\left(d x + c\right)^{6} - 24 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 3 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{4} - 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/6*(2*a^2*cos(d*x + c)^6 - 24*(a^2*cos(d*x + c)^2 - a^2)*log(1/2*sin(d*x + c))*sin(d*x + c) - 3*(2*a^2*cos(d*x + c)^4 - 3*a^2*cos(d*x + c)^2 - a^2)*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
518,1,152,0,0.926324," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} \cos\left(d x + c\right)^{6} - 15 \, a^{2} \cos\left(d x + c\right)^{4} + 18 \, a^{2} \cos\left(d x + c\right)^{2} - 6 \, a^{2} + 12 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 8 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{4} - 12 \, a^{2} \cos\left(d x + c\right)^{2} + 8 \, a^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/12*(6*a^2*cos(d*x + c)^6 - 15*a^2*cos(d*x + c)^4 + 18*a^2*cos(d*x + c)^2 - 6*a^2 + 12*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(1/2*sin(d*x + c)) - 8*(3*a^2*cos(d*x + c)^4 - 12*a^2*cos(d*x + c)^2 + 8*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
519,1,153,0,0.891411," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{30 \, a^{2} \cos\left(d x + c\right)^{6} - 120 \, a^{2} \cos\left(d x + c\right)^{4} + 160 \, a^{2} \cos\left(d x + c\right)^{2} - 60 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 64 \, a^{2} + 15 \, {\left(4 \, a^{2} \cos\left(d x + c\right)^{2} - 3 \, a^{2}\right)} \sin\left(d x + c\right)}{30 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/30*(30*a^2*cos(d*x + c)^6 - 120*a^2*cos(d*x + c)^4 + 160*a^2*cos(d*x + c)^2 - 60*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(1/2*sin(d*x + c))*sin(d*x + c) - 64*a^2 + 15*(4*a^2*cos(d*x + c)^2 - 3*a^2)*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
520,1,167,0,0.914223," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{30 \, a^{2} \cos\left(d x + c\right)^{4} - 75 \, a^{2} \cos\left(d x + c\right)^{2} + 35 \, a^{2} - 60 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 8 \, {\left(15 \, a^{2} \cos\left(d x + c\right)^{4} - 20 \, a^{2} \cos\left(d x + c\right)^{2} + 8 \, a^{2}\right)} \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/60*(30*a^2*cos(d*x + c)^4 - 75*a^2*cos(d*x + c)^2 + 35*a^2 - 60*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(1/2*sin(d*x + c)) - 8*(15*a^2*cos(d*x + c)^4 - 20*a^2*cos(d*x + c)^2 + 8*a^2)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
521,1,111,0,0.971144," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{84 \, a^{3} \cos\left(d x + c\right)^{10} - 525 \, a^{3} \cos\left(d x + c\right)^{8} + 560 \, a^{3} \cos\left(d x + c\right)^{6} - 8 \, {\left(35 \, a^{3} \cos\left(d x + c\right)^{8} - 65 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} + 8 \, a^{3} \cos\left(d x + c\right)^{2} + 16 \, a^{3}\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"-1/840*(84*a^3*cos(d*x + c)^10 - 525*a^3*cos(d*x + c)^8 + 560*a^3*cos(d*x + c)^6 - 8*(35*a^3*cos(d*x + c)^8 - 65*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 + 8*a^3*cos(d*x + c)^2 + 16*a^3)*sin(d*x + c))/d","A",0
522,1,98,0,0.825885," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{189 \, a^{3} \cos\left(d x + c\right)^{8} - 336 \, a^{3} \cos\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{3} \cos\left(d x + c\right)^{8} - 37 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} + 8 \, a^{3} \cos\left(d x + c\right)^{2} + 16 \, a^{3}\right)} \sin\left(d x + c\right)}{504 \, d}"," ",0,"1/504*(189*a^3*cos(d*x + c)^8 - 336*a^3*cos(d*x + c)^6 + 8*(7*a^3*cos(d*x + c)^8 - 37*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 + 8*a^3*cos(d*x + c)^2 + 16*a^3)*sin(d*x + c))/d","A",0
523,1,112,0,1.124617," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{210 \, a^{3} \cos\left(d x + c\right)^{6} - 105 \, a^{3} \cos\left(d x + c\right)^{4} - 210 \, a^{3} \cos\left(d x + c\right)^{2} - 420 \, a^{3} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, {\left(15 \, a^{3} \cos\left(d x + c\right)^{6} - 66 \, a^{3} \cos\left(d x + c\right)^{4} - 88 \, a^{3} \cos\left(d x + c\right)^{2} - 176 \, a^{3}\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"-1/420*(210*a^3*cos(d*x + c)^6 - 105*a^3*cos(d*x + c)^4 - 210*a^3*cos(d*x + c)^2 - 420*a^3*log(1/2*sin(d*x + c)) + 4*(15*a^3*cos(d*x + c)^6 - 66*a^3*cos(d*x + c)^4 - 88*a^3*cos(d*x + c)^2 - 176*a^3)*sin(d*x + c))/d","A",0
524,1,131,0,0.977758," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{144 \, a^{3} \cos\left(d x + c\right)^{6} - 32 \, a^{3} \cos\left(d x + c\right)^{4} - 128 \, a^{3} \cos\left(d x + c\right)^{2} - 720 \, a^{3} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 256 \, a^{3} + 5 \, {\left(8 \, a^{3} \cos\left(d x + c\right)^{6} - 36 \, a^{3} \cos\left(d x + c\right)^{4} - 72 \, a^{3} \cos\left(d x + c\right)^{2} + 47 \, a^{3}\right)} \sin\left(d x + c\right)}{240 \, d \sin\left(d x + c\right)}"," ",0,"-1/240*(144*a^3*cos(d*x + c)^6 - 32*a^3*cos(d*x + c)^4 - 128*a^3*cos(d*x + c)^2 - 720*a^3*log(1/2*sin(d*x + c))*sin(d*x + c) + 256*a^3 + 5*(8*a^3*cos(d*x + c)^6 - 36*a^3*cos(d*x + c)^4 - 72*a^3*cos(d*x + c)^2 + 47*a^3)*sin(d*x + c))/(d*sin(d*x + c))","A",0
525,1,145,0,0.914089," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{360 \, a^{3} \cos\left(d x + c\right)^{6} + 120 \, a^{3} \cos\left(d x + c\right)^{4} - 855 \, a^{3} \cos\left(d x + c\right)^{2} + 615 \, a^{3} + 480 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 32 \, {\left(3 \, a^{3} \cos\left(d x + c\right)^{6} - 14 \, a^{3} \cos\left(d x + c\right)^{4} - 56 \, a^{3} \cos\left(d x + c\right)^{2} + 112 \, a^{3}\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/480*(360*a^3*cos(d*x + c)^6 + 120*a^3*cos(d*x + c)^4 - 855*a^3*cos(d*x + c)^2 + 615*a^3 + 480*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*sin(d*x + c)) + 32*(3*a^3*cos(d*x + c)^6 - 14*a^3*cos(d*x + c)^4 - 56*a^3*cos(d*x + c)^2 + 112*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
526,1,159,0,0.943643," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{96 \, a^{3} \cos\left(d x + c\right)^{6} + 192 \, a^{3} \cos\left(d x + c\right)^{4} - 768 \, a^{3} \cos\left(d x + c\right)^{2} + 512 \, a^{3} - 480 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 3 \, {\left(8 \, a^{3} \cos\left(d x + c\right)^{6} - 40 \, a^{3} \cos\left(d x + c\right)^{4} + 45 \, a^{3} \cos\left(d x + c\right)^{2} + 35 \, a^{3}\right)} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/96*(96*a^3*cos(d*x + c)^6 + 192*a^3*cos(d*x + c)^4 - 768*a^3*cos(d*x + c)^2 + 512*a^3 - 480*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*sin(d*x + c))*sin(d*x + c) + 3*(8*a^3*cos(d*x + c)^6 - 40*a^3*cos(d*x + c)^4 + 45*a^3*cos(d*x + c)^2 + 35*a^3)*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
527,1,159,0,0.989738," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{18 \, a^{3} \cos\left(d x + c\right)^{6} - 45 \, a^{3} \cos\left(d x + c\right)^{4} + 30 \, a^{3} \cos\left(d x + c\right)^{2} + 60 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 6 \, a^{3} \cos\left(d x + c\right)^{4} + 24 \, a^{3} \cos\left(d x + c\right)^{2} - 16 \, a^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/12*(18*a^3*cos(d*x + c)^6 - 45*a^3*cos(d*x + c)^4 + 30*a^3*cos(d*x + c)^2 + 60*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(1/2*sin(d*x + c)) + 4*(a^3*cos(d*x + c)^6 - 6*a^3*cos(d*x + c)^4 + 24*a^3*cos(d*x + c)^2 - 16*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
528,1,179,0,1.247399," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{180 \, a^{3} \cos\left(d x + c\right)^{6} - 840 \, a^{3} \cos\left(d x + c\right)^{4} + 1120 \, a^{3} \cos\left(d x + c\right)^{2} - 448 \, a^{3} - 60 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 15 \, {\left(2 \, a^{3} \cos\left(d x + c\right)^{6} - 5 \, a^{3} \cos\left(d x + c\right)^{4} + 14 \, a^{3} \cos\left(d x + c\right)^{2} - 8 \, a^{3}\right)} \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(180*a^3*cos(d*x + c)^6 - 840*a^3*cos(d*x + c)^4 + 1120*a^3*cos(d*x + c)^2 - 448*a^3 - 60*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(1/2*sin(d*x + c))*sin(d*x + c) + 15*(2*a^3*cos(d*x + c)^6 - 5*a^3*cos(d*x + c)^4 + 14*a^3*cos(d*x + c)^2 - 8*a^3)*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
529,1,180,0,1.070913," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{150 \, a^{3} \cos\left(d x + c\right)^{4} - 285 \, a^{3} \cos\left(d x + c\right)^{2} + 125 \, a^{3} - 180 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, {\left(15 \, a^{3} \cos\left(d x + c\right)^{6} - 30 \, a^{3} \cos\left(d x + c\right)^{4} + 40 \, a^{3} \cos\left(d x + c\right)^{2} - 16 \, a^{3}\right)} \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/60*(150*a^3*cos(d*x + c)^4 - 285*a^3*cos(d*x + c)^2 + 125*a^3 - 180*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(1/2*sin(d*x + c)) - 4*(15*a^3*cos(d*x + c)^6 - 30*a^3*cos(d*x + c)^4 + 40*a^3*cos(d*x + c)^2 - 16*a^3)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
530,1,172,0,1.215169," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{24 \, a^{4} \cos\left(d x + c\right)^{8} - 256 \, a^{4} \cos\left(d x + c\right)^{6} - 576 \, a^{4} \cos\left(d x + c\right)^{4} + 2304 \, a^{4} \cos\left(d x + c\right)^{2} - 1536 \, a^{4} + 480 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - a^{4}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 15 \, {\left(8 \, a^{4} \cos\left(d x + c\right)^{6} - 8 \, a^{4} \cos\left(d x + c\right)^{4} - 3 \, a^{4} \cos\left(d x + c\right)^{2} + 19 \, a^{4}\right)} \sin\left(d x + c\right)}{120 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/120*(24*a^4*cos(d*x + c)^8 - 256*a^4*cos(d*x + c)^6 - 576*a^4*cos(d*x + c)^4 + 2304*a^4*cos(d*x + c)^2 - 1536*a^4 + 480*(a^4*cos(d*x + c)^2 - a^4)*log(1/2*sin(d*x + c))*sin(d*x + c) - 15*(8*a^4*cos(d*x + c)^6 - 8*a^4*cos(d*x + c)^4 - 3*a^4*cos(d*x + c)^2 + 19*a^4)*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
531,1,144,0,1.256644," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{24 \, a^{4} \cos\left(d x + c\right)^{8} - 128 \, a^{4} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - 288 \, a^{4} \cos\left(d x + c\right)^{6} + 615 \, a^{4} \cos\left(d x + c\right)^{4} - 270 \, a^{4} \cos\left(d x + c\right)^{2} - 105 \, a^{4} - 960 \, {\left(a^{4} \cos\left(d x + c\right)^{4} - 2 \, a^{4} \cos\left(d x + c\right)^{2} + a^{4}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/96*(24*a^4*cos(d*x + c)^8 - 128*a^4*cos(d*x + c)^6*sin(d*x + c) - 288*a^4*cos(d*x + c)^6 + 615*a^4*cos(d*x + c)^4 - 270*a^4*cos(d*x + c)^2 - 105*a^4 - 960*(a^4*cos(d*x + c)^4 - 2*a^4*cos(d*x + c)^2 + a^4)*log(1/2*sin(d*x + c)))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
532,1,192,0,1.386092," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{5 \, a^{4} \cos\left(d x + c\right)^{8} - 80 \, a^{4} \cos\left(d x + c\right)^{6} + 360 \, a^{4} \cos\left(d x + c\right)^{4} - 480 \, a^{4} \cos\left(d x + c\right)^{2} + 192 \, a^{4} - 60 \, {\left(a^{4} \cos\left(d x + c\right)^{4} - 2 \, a^{4} \cos\left(d x + c\right)^{2} + a^{4}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 15 \, {\left(2 \, a^{4} \cos\left(d x + c\right)^{6} - 5 \, a^{4} \cos\left(d x + c\right)^{4} + 6 \, a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/15*(5*a^4*cos(d*x + c)^8 - 80*a^4*cos(d*x + c)^6 + 360*a^4*cos(d*x + c)^4 - 480*a^4*cos(d*x + c)^2 + 192*a^4 - 60*(a^4*cos(d*x + c)^4 - 2*a^4*cos(d*x + c)^2 + a^4)*log(1/2*sin(d*x + c))*sin(d*x + c) - 15*(2*a^4*cos(d*x + c)^6 - 5*a^4*cos(d*x + c)^4 + 6*a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
533,1,67,0,0.965624," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{70 \, \cos\left(d x + c\right)^{6} - 105 \, \cos\left(d x + c\right)^{4} - 12 \, {\left(5 \, \cos\left(d x + c\right)^{6} - 8 \, \cos\left(d x + c\right)^{4} + \cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right)}{420 \, a d}"," ",0,"1/420*(70*cos(d*x + c)^6 - 105*cos(d*x + c)^4 - 12*(5*cos(d*x + c)^6 - 8*cos(d*x + c)^4 + cos(d*x + c)^2 + 2)*sin(d*x + c))/(a*d)","A",0
534,1,59,0,1.160601," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{10 \, \cos\left(d x + c\right)^{6} - 15 \, \cos\left(d x + c\right)^{4} + 4 \, {\left(3 \, \cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right)}{60 \, a d}"," ",0,"-1/60*(10*cos(d*x + c)^6 - 15*cos(d*x + c)^4 + 4*(3*cos(d*x + c)^4 - cos(d*x + c)^2 - 2)*sin(d*x + c))/(a*d)","A",0
535,1,49,0,1.006689," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, \cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right)}{60 \, a d}"," ",0,"-1/60*(15*cos(d*x + c)^4 - 4*(3*cos(d*x + c)^4 - cos(d*x + c)^2 - 2)*sin(d*x + c))/(a*d)","A",0
536,1,48,0,1.085972," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right) + 6 \, \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right)}{6 \, a d}"," ",0,"1/6*(3*cos(d*x + c)^2 - 2*(cos(d*x + c)^2 + 2)*sin(d*x + c) + 6*log(1/2*sin(d*x + c)))/(a*d)","A",0
537,1,65,0,0.686314," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \cos\left(d x + c\right)^{2} - {\left(2 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - 4 \, \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 8}{4 \, a d \sin\left(d x + c\right)}"," ",0,"1/4*(4*cos(d*x + c)^2 - (2*cos(d*x + c)^2 - 1)*sin(d*x + c) - 4*log(1/2*sin(d*x + c))*sin(d*x + c) - 8)/(a*d*sin(d*x + c))","A",0
538,1,61,0,1.084542," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 2 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) - 1}{2 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"-1/2*(2*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c)) - 2*(cos(d*x + c)^2 - 2)*sin(d*x + c) - 1)/(a*d*cos(d*x + c)^2 - a*d)","A",0
539,1,75,0,1.108489," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 6 \, \cos\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) - 4}{6 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"1/6*(6*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c))*sin(d*x + c) + 6*cos(d*x + c)^2 - 3*sin(d*x + c) - 4)/((a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
540,1,63,0,0.872755," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) - 3}{12 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"-1/12*(6*cos(d*x + c)^2 - 4*(3*cos(d*x + c)^2 - 2)*sin(d*x + c) - 3)/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)","A",0
541,1,71,0,1.032520," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{20 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(2 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - 8}{60 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(20*cos(d*x + c)^2 - 15*(2*cos(d*x + c)^2 - 1)*sin(d*x + c) - 8)/((a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","A",0
542,1,76,0,0.858623," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) - 5}{60 \, {\left(a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"1/60*(15*cos(d*x + c)^2 - 4*(5*cos(d*x + c)^2 - 2)*sin(d*x + c) - 5)/(a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^2 - a*d)","A",0
543,1,84,0,1.053185," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{84 \, \cos\left(d x + c\right)^{2} - 35 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - 24}{420 \, {\left(a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"1/420*(84*cos(d*x + c)^2 - 35*(3*cos(d*x + c)^2 - 1)*sin(d*x + c) - 24)/((a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
544,1,67,0,1.151961," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{10 \, \cos\left(d x + c\right)^{6} - 45 \, \cos\left(d x + c\right)^{4} + 60 \, \cos\left(d x + c\right)^{2} + 24 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right)}{60 \, a^{2} d}"," ",0,"-1/60*(10*cos(d*x + c)^6 - 45*cos(d*x + c)^4 + 60*cos(d*x + c)^2 + 24*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c))/(a^2*d)","A",0
545,1,59,0,0.937809," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{15 \, \cos\left(d x + c\right)^{4} - 30 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 11 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right)}{30 \, a^{2} d}"," ",0,"-1/30*(15*cos(d*x + c)^4 - 30*cos(d*x + c)^2 - 2*(3*cos(d*x + c)^4 - 11*cos(d*x + c)^2 + 8)*sin(d*x + c))/(a^2*d)","A",0
546,1,47,0,1.039019," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{4} - 12 \, \cos\left(d x + c\right)^{2} + 8 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right)}{12 \, a^{2} d}"," ",0,"1/12*(3*cos(d*x + c)^4 - 12*cos(d*x + c)^2 + 8*(cos(d*x + c)^2 - 1)*sin(d*x + c))/(a^2*d)","A",0
547,1,36,0,0.826449," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} - 2 \, \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, \sin\left(d x + c\right)}{2 \, a^{2} d}"," ",0,"-1/2*(cos(d*x + c)^2 - 2*log(1/2*sin(d*x + c)) + 4*sin(d*x + c))/(a^2*d)","A",0
548,1,42,0,1.006854," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} + 2 \, \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right)}{a^{2} d \sin\left(d x + c\right)}"," ",0,"-(cos(d*x + c)^2 + 2*log(1/2*sin(d*x + c))*sin(d*x + c))/(a^2*d*sin(d*x + c))","A",0
549,1,55,0,1.032166," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, \sin\left(d x + c\right) + 1}{2 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"1/2*(2*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c)) - 4*sin(d*x + c) + 1)/(a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
550,1,52,0,1.106965," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, \cos\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 4}{3 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/3*(3*cos(d*x + c)^2 + 3*sin(d*x + c) - 4)/((a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","A",0
551,1,57,0,0.982030," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, \cos\left(d x + c\right)^{2} + 8 \, \sin\left(d x + c\right) - 9}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)}}"," ",0,"1/12*(6*cos(d*x + c)^2 + 8*sin(d*x + c) - 9)/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)","A",0
552,1,65,0,1.042701," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{10 \, \cos\left(d x + c\right)^{2} + 15 \, \sin\left(d x + c\right) - 16}{30 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"1/30*(10*cos(d*x + c)^2 + 15*sin(d*x + c) - 16)/((a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)*sin(d*x + c))","A",0
553,1,72,0,1.063615," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{15 \, \cos\left(d x + c\right)^{2} + 24 \, \sin\left(d x + c\right) - 25}{60 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 3 \, a^{2} d \cos\left(d x + c\right)^{4} + 3 \, a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"-1/60*(15*cos(d*x + c)^2 + 24*sin(d*x + c) - 25)/(a^2*d*cos(d*x + c)^6 - 3*a^2*d*cos(d*x + c)^4 + 3*a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
554,1,70,0,1.129344," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{45 \, \cos\left(d x + c\right)^{4} - 210 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 26 \, \cos\left(d x + c\right)^{2} + 83\right)} \sin\left(d x + c\right) + 240 \, \log\left(\sin\left(d x + c\right) + 1\right)}{60 \, a^{3} d}"," ",0,"-1/60*(45*cos(d*x + c)^4 - 210*cos(d*x + c)^2 - 4*(3*cos(d*x + c)^4 - 26*cos(d*x + c)^2 + 83)*sin(d*x + c) + 240*log(sin(d*x + c) + 1))/(a^3*d)","A",0
555,1,56,0,0.814747," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(\cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) + 16 \, \log\left(\sin\left(d x + c\right) + 1\right)}{4 \, a^{3} d}"," ",0,"1/4*(cos(d*x + c)^4 - 10*cos(d*x + c)^2 + 4*(cos(d*x + c)^2 - 5)*sin(d*x + c) + 16*log(sin(d*x + c) + 1))/(a^3*d)","A",0
556,1,48,0,1.064003," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{9 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right)^{2} - 13\right)} \sin\left(d x + c\right) - 24 \, \log\left(\sin\left(d x + c\right) + 1\right)}{6 \, a^{3} d}"," ",0,"1/6*(9*cos(d*x + c)^2 - 2*(cos(d*x + c)^2 - 13)*sin(d*x + c) - 24*log(sin(d*x + c) + 1))/(a^3*d)","A",0
557,1,34,0,1.292039," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{\log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, \log\left(\sin\left(d x + c\right) + 1\right) + \sin\left(d x + c\right)}{a^{3} d}"," ",0,"(log(1/2*sin(d*x + c)) - 4*log(sin(d*x + c) + 1) + sin(d*x + c))/(a^3*d)","A",0
558,1,52,0,1.180729," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 4 \, \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 1}{a^{3} d \sin\left(d x + c\right)}"," ",0,"-(3*log(1/2*sin(d*x + c))*sin(d*x + c) - 4*log(sin(d*x + c) + 1)*sin(d*x + c) + 1)/(a^3*d*sin(d*x + c))","A",0
559,1,76,0,1.417739," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 8 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6 \, \sin\left(d x + c\right) + 1}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}"," ",0,"1/2*(8*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c)) - 8*(cos(d*x + c)^2 - 1)*log(sin(d*x + c) + 1) - 6*sin(d*x + c) + 1)/(a^3*d*cos(d*x + c)^2 - a^3*d)","A",0
560,1,106,0,1.118788," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{24 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 24 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 24 \, \cos\left(d x + c\right)^{2} + 9 \, \sin\left(d x + c\right) - 26}{6 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(24*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c))*sin(d*x + c) - 24*(cos(d*x + c)^2 - 1)*log(sin(d*x + c) + 1)*sin(d*x + c) + 24*cos(d*x + c)^2 + 9*sin(d*x + c) - 26)/((a^3*d*cos(d*x + c)^2 - a^3*d)*sin(d*x + c))","A",0
561,1,131,0,1.023117," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{2} + 16 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 16 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 4 \, {\left(4 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) - 9}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)}}"," ",0,"1/4*(8*cos(d*x + c)^2 + 16*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*sin(d*x + c)) - 16*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(sin(d*x + c) + 1) - 4*(4*cos(d*x + c)^2 - 5)*sin(d*x + c) - 9)/(a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d)","A",0
562,1,161,0,1.311132," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{240 \, \cos\left(d x + c\right)^{4} + 240 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 240 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 560 \, \cos\left(d x + c\right)^{2} + 15 \, {\left(8 \, \cos\left(d x + c\right)^{2} - 11\right)} \sin\left(d x + c\right) + 332}{60 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(240*cos(d*x + c)^4 + 240*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*sin(d*x + c))*sin(d*x + c) - 240*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(sin(d*x + c) + 1)*sin(d*x + c) - 560*cos(d*x + c)^2 + 15*(8*cos(d*x + c)^2 - 11)*sin(d*x + c) + 332)/((a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d)*sin(d*x + c))","A",0
563,1,235,0,1.390106," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{192 \, \cos\left(d x + c\right)^{4} - 352 \, \cos\left(d x + c\right)^{2} + 192 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 192 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(96 \, \cos\left(d x + c\right)^{2} - 109\right)} \sin\left(d x + c\right) + 157}{12 \, {\left(a^{4} d \cos\left(d x + c\right)^{4} - 2 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d + {\left(a^{4} d \cos\left(d x + c\right)^{4} - 2 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(192*cos(d*x + c)^4 - 352*cos(d*x + c)^2 + 192*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) + 1)*log(1/2*sin(d*x + c)) - 192*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) + 1)*log(sin(d*x + c) + 1) - (96*cos(d*x + c)^2 - 109)*sin(d*x + c) + 157)/(a^4*d*cos(d*x + c)^4 - 2*a^4*d*cos(d*x + c)^2 + a^4*d + (a^4*d*cos(d*x + c)^4 - 2*a^4*d*cos(d*x + c)^2 + a^4*d)*sin(d*x + c))","B",0
564,1,283,0,1.036440," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{150 \, \cos\left(d x + c\right)^{4} - 325 \, \cos\left(d x + c\right)^{2} - 300 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 300 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) - 1\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2 \, {\left(150 \, \cos\left(d x + c\right)^{4} - 275 \, \cos\left(d x + c\right)^{2} + 119\right)} \sin\left(d x + c\right) + 178}{15 \, {\left(a^{4} d \cos\left(d x + c\right)^{6} - 3 \, a^{4} d \cos\left(d x + c\right)^{4} + 3 \, a^{4} d \cos\left(d x + c\right)^{2} - a^{4} d - {\left(a^{4} d \cos\left(d x + c\right)^{4} - 2 \, a^{4} d \cos\left(d x + c\right)^{2} + a^{4} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/15*(150*cos(d*x + c)^4 - 325*cos(d*x + c)^2 - 300*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) - 1)*log(1/2*sin(d*x + c)) + 300*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - (cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*sin(d*x + c) - 1)*log(sin(d*x + c) + 1) + 2*(150*cos(d*x + c)^4 - 275*cos(d*x + c)^2 + 119)*sin(d*x + c) + 178)/(a^4*d*cos(d*x + c)^6 - 3*a^4*d*cos(d*x + c)^4 + 3*a^4*d*cos(d*x + c)^2 - a^4*d - (a^4*d*cos(d*x + c)^4 - 2*a^4*d*cos(d*x + c)^2 + a^4*d)*sin(d*x + c))","B",0
565,1,616,0,1.062569," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(a^{3} n^{7} + 28 \, a^{3} n^{6} + 322 \, a^{3} n^{5} + 1960 \, a^{3} n^{4} + 6769 \, a^{3} n^{3} + 13132 \, a^{3} n^{2} + 13068 \, a^{3} n + 5040 \, a^{3}\right)} \cos\left(d x + c\right)^{8} + 32 \, a^{3} n^{5} + 720 \, a^{3} n^{4} - {\left(5 \, a^{3} n^{7} + 142 \, a^{3} n^{6} + 1654 \, a^{3} n^{5} + 10180 \, a^{3} n^{4} + 35485 \, a^{3} n^{3} + 69358 \, a^{3} n^{2} + 69416 \, a^{3} n + 26880 \, a^{3}\right)} \cos\left(d x + c\right)^{6} + 6080 \, a^{3} n^{3} + 23520 \, a^{3} n^{2} + 2 \, {\left(2 \, a^{3} n^{7} + 49 \, a^{3} n^{6} + 470 \, a^{3} n^{5} + 2230 \, a^{3} n^{4} + 5438 \, a^{3} n^{3} + 6361 \, a^{3} n^{2} + 2730 \, a^{3} n\right)} \cos\left(d x + c\right)^{4} + 39968 \, a^{3} n + 21840 \, a^{3} + 8 \, {\left(2 \, a^{3} n^{6} + 45 \, a^{3} n^{5} + 380 \, a^{3} n^{4} + 1470 \, a^{3} n^{3} + 2498 \, a^{3} n^{2} + 1365 \, a^{3} n\right)} \cos\left(d x + c\right)^{2} + {\left(32 \, a^{3} n^{5} + 720 \, a^{3} n^{4} - 3 \, {\left(a^{3} n^{7} + 29 \, a^{3} n^{6} + 343 \, a^{3} n^{5} + 2135 \, a^{3} n^{4} + 7504 \, a^{3} n^{3} + 14756 \, a^{3} n^{2} + 14832 \, a^{3} n + 5760 \, a^{3}\right)} \cos\left(d x + c\right)^{6} + 6080 \, a^{3} n^{3} + 24000 \, a^{3} n^{2} + 2 \, {\left(2 \, a^{3} n^{7} + 53 \, a^{3} n^{6} + 566 \, a^{3} n^{5} + 3155 \, a^{3} n^{4} + 9908 \, a^{3} n^{3} + 17492 \, a^{3} n^{2} + 15984 \, a^{3} n + 5760 \, a^{3}\right)} \cos\left(d x + c\right)^{4} + 44288 \, a^{3} n + 30720 \, a^{3} + 8 \, {\left(2 \, a^{3} n^{6} + 47 \, a^{3} n^{5} + 425 \, a^{3} n^{4} + 1880 \, a^{3} n^{3} + 4268 \, a^{3} n^{2} + 4688 \, a^{3} n + 1920 \, a^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{d n^{8} + 36 \, d n^{7} + 546 \, d n^{6} + 4536 \, d n^{5} + 22449 \, d n^{4} + 67284 \, d n^{3} + 118124 \, d n^{2} + 109584 \, d n + 40320 \, d}"," ",0,"((a^3*n^7 + 28*a^3*n^6 + 322*a^3*n^5 + 1960*a^3*n^4 + 6769*a^3*n^3 + 13132*a^3*n^2 + 13068*a^3*n + 5040*a^3)*cos(d*x + c)^8 + 32*a^3*n^5 + 720*a^3*n^4 - (5*a^3*n^7 + 142*a^3*n^6 + 1654*a^3*n^5 + 10180*a^3*n^4 + 35485*a^3*n^3 + 69358*a^3*n^2 + 69416*a^3*n + 26880*a^3)*cos(d*x + c)^6 + 6080*a^3*n^3 + 23520*a^3*n^2 + 2*(2*a^3*n^7 + 49*a^3*n^6 + 470*a^3*n^5 + 2230*a^3*n^4 + 5438*a^3*n^3 + 6361*a^3*n^2 + 2730*a^3*n)*cos(d*x + c)^4 + 39968*a^3*n + 21840*a^3 + 8*(2*a^3*n^6 + 45*a^3*n^5 + 380*a^3*n^4 + 1470*a^3*n^3 + 2498*a^3*n^2 + 1365*a^3*n)*cos(d*x + c)^2 + (32*a^3*n^5 + 720*a^3*n^4 - 3*(a^3*n^7 + 29*a^3*n^6 + 343*a^3*n^5 + 2135*a^3*n^4 + 7504*a^3*n^3 + 14756*a^3*n^2 + 14832*a^3*n + 5760*a^3)*cos(d*x + c)^6 + 6080*a^3*n^3 + 24000*a^3*n^2 + 2*(2*a^3*n^7 + 53*a^3*n^6 + 566*a^3*n^5 + 3155*a^3*n^4 + 9908*a^3*n^3 + 17492*a^3*n^2 + 15984*a^3*n + 5760*a^3)*cos(d*x + c)^4 + 44288*a^3*n + 30720*a^3 + 8*(2*a^3*n^6 + 47*a^3*n^5 + 425*a^3*n^4 + 1880*a^3*n^3 + 4268*a^3*n^2 + 4688*a^3*n + 1920*a^3)*cos(d*x + c)^2)*sin(d*x + c))*sin(d*x + c)^n/(d*n^8 + 36*d*n^7 + 546*d*n^6 + 4536*d*n^5 + 22449*d*n^4 + 67284*d*n^3 + 118124*d*n^2 + 109584*d*n + 40320*d)","B",0
566,1,473,0,1.132350," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(a^{2} n^{6} + 22 \, a^{2} n^{5} + 190 \, a^{2} n^{4} + 820 \, a^{2} n^{3} + 1849 \, a^{2} n^{2} + 2038 \, a^{2} n + 840 \, a^{2}\right)} \cos\left(d x + c\right)^{6} - 16 \, a^{2} n^{4} - 256 \, a^{2} n^{3} - 2 \, {\left(a^{2} n^{6} + 18 \, a^{2} n^{5} + 118 \, a^{2} n^{4} + 348 \, a^{2} n^{3} + 457 \, a^{2} n^{2} + 210 \, a^{2} n\right)} \cos\left(d x + c\right)^{4} - 1376 \, a^{2} n^{2} - 2816 \, a^{2} n - 8 \, {\left(a^{2} n^{5} + 16 \, a^{2} n^{4} + 86 \, a^{2} n^{3} + 176 \, a^{2} n^{2} + 105 \, a^{2} n\right)} \cos\left(d x + c\right)^{2} - 1680 \, a^{2} + {\left({\left(a^{2} n^{6} + 21 \, a^{2} n^{5} + 175 \, a^{2} n^{4} + 735 \, a^{2} n^{3} + 1624 \, a^{2} n^{2} + 1764 \, a^{2} n + 720 \, a^{2}\right)} \cos\left(d x + c\right)^{6} - 16 \, a^{2} n^{4} - 256 \, a^{2} n^{3} - 2 \, {\left(a^{2} n^{6} + 20 \, a^{2} n^{5} + 159 \, a^{2} n^{4} + 640 \, a^{2} n^{3} + 1364 \, a^{2} n^{2} + 1440 \, a^{2} n + 576 \, a^{2}\right)} \cos\left(d x + c\right)^{4} - 1472 \, a^{2} n^{2} - 3584 \, a^{2} n - 8 \, {\left(a^{2} n^{5} + 17 \, a^{2} n^{4} + 108 \, a^{2} n^{3} + 316 \, a^{2} n^{2} + 416 \, a^{2} n + 192 \, a^{2}\right)} \cos\left(d x + c\right)^{2} - 3072 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{d n^{7} + 28 \, d n^{6} + 322 \, d n^{5} + 1960 \, d n^{4} + 6769 \, d n^{3} + 13132 \, d n^{2} + 13068 \, d n + 5040 \, d}"," ",0,"-(2*(a^2*n^6 + 22*a^2*n^5 + 190*a^2*n^4 + 820*a^2*n^3 + 1849*a^2*n^2 + 2038*a^2*n + 840*a^2)*cos(d*x + c)^6 - 16*a^2*n^4 - 256*a^2*n^3 - 2*(a^2*n^6 + 18*a^2*n^5 + 118*a^2*n^4 + 348*a^2*n^3 + 457*a^2*n^2 + 210*a^2*n)*cos(d*x + c)^4 - 1376*a^2*n^2 - 2816*a^2*n - 8*(a^2*n^5 + 16*a^2*n^4 + 86*a^2*n^3 + 176*a^2*n^2 + 105*a^2*n)*cos(d*x + c)^2 - 1680*a^2 + ((a^2*n^6 + 21*a^2*n^5 + 175*a^2*n^4 + 735*a^2*n^3 + 1624*a^2*n^2 + 1764*a^2*n + 720*a^2)*cos(d*x + c)^6 - 16*a^2*n^4 - 256*a^2*n^3 - 2*(a^2*n^6 + 20*a^2*n^5 + 159*a^2*n^4 + 640*a^2*n^3 + 1364*a^2*n^2 + 1440*a^2*n + 576*a^2)*cos(d*x + c)^4 - 1472*a^2*n^2 - 3584*a^2*n - 8*(a^2*n^5 + 17*a^2*n^4 + 108*a^2*n^3 + 316*a^2*n^2 + 416*a^2*n + 192*a^2)*cos(d*x + c)^2 - 3072*a^2)*sin(d*x + c))*sin(d*x + c)^n/(d*n^7 + 28*d*n^6 + 322*d*n^5 + 1960*d*n^4 + 6769*d*n^3 + 13132*d*n^2 + 13068*d*n + 5040*d)","B",0
567,1,282,0,1.258487," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left({\left(a n^{5} + 15 \, a n^{4} + 85 \, a n^{3} + 225 \, a n^{2} + 274 \, a n + 120 \, a\right)} \cos\left(d x + c\right)^{6} - {\left(a n^{5} + 11 \, a n^{4} + 41 \, a n^{3} + 61 \, a n^{2} + 30 \, a n\right)} \cos\left(d x + c\right)^{4} - 8 \, a n^{3} - 72 \, a n^{2} - 4 \, {\left(a n^{4} + 9 \, a n^{3} + 23 \, a n^{2} + 15 \, a n\right)} \cos\left(d x + c\right)^{2} - 184 \, a n - {\left({\left(a n^{5} + 16 \, a n^{4} + 95 \, a n^{3} + 260 \, a n^{2} + 324 \, a n + 144 \, a\right)} \cos\left(d x + c\right)^{4} + 8 \, a n^{3} + 96 \, a n^{2} + 4 \, {\left(a n^{4} + 13 \, a n^{3} + 56 \, a n^{2} + 92 \, a n + 48 \, a\right)} \cos\left(d x + c\right)^{2} + 352 \, a n + 384 \, a\right)} \sin\left(d x + c\right) - 120 \, a\right)} \sin\left(d x + c\right)^{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}"," ",0,"-((a*n^5 + 15*a*n^4 + 85*a*n^3 + 225*a*n^2 + 274*a*n + 120*a)*cos(d*x + c)^6 - (a*n^5 + 11*a*n^4 + 41*a*n^3 + 61*a*n^2 + 30*a*n)*cos(d*x + c)^4 - 8*a*n^3 - 72*a*n^2 - 4*(a*n^4 + 9*a*n^3 + 23*a*n^2 + 15*a*n)*cos(d*x + c)^2 - 184*a*n - ((a*n^5 + 16*a*n^4 + 95*a*n^3 + 260*a*n^2 + 324*a*n + 144*a)*cos(d*x + c)^4 + 8*a*n^3 + 96*a*n^2 + 4*(a*n^4 + 13*a*n^3 + 56*a*n^2 + 92*a*n + 48*a)*cos(d*x + c)^2 + 352*a*n + 384*a)*sin(d*x + c) - 120*a)*sin(d*x + c)^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)","B",0
568,1,134,0,0.867918," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} \cos\left(d x + c\right)^{4} - {\left(n^{3} + 4 \, n^{2} + 3 \, n\right)} \cos\left(d x + c\right)^{2} - 2 \, n^{2} + {\left({\left(n^{3} + 7 \, n^{2} + 14 \, n + 8\right)} \cos\left(d x + c\right)^{2} + 2 \, n^{2} + 12 \, n + 16\right)} \sin\left(d x + c\right) - 8 \, n - 6\right)} \sin\left(d x + c\right)^{n}}{a d n^{4} + 10 \, a d n^{3} + 35 \, a d n^{2} + 50 \, a d n + 24 \, a d}"," ",0,"((n^3 + 6*n^2 + 11*n + 6)*cos(d*x + c)^4 - (n^3 + 4*n^2 + 3*n)*cos(d*x + c)^2 - 2*n^2 + ((n^3 + 7*n^2 + 14*n + 8)*cos(d*x + c)^2 + 2*n^2 + 12*n + 16)*sin(d*x + c) - 8*n - 6)*sin(d*x + c)^n/(a*d*n^4 + 10*a*d*n^3 + 35*a*d*n^2 + 50*a*d*n + 24*a*d)","A",0
569,1,105,0,0.919585," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(n^{2} + 4 \, n + 3\right)} \cos\left(d x + c\right)^{2} - 2 \, n^{2} - {\left({\left(n^{2} + 3 \, n + 2\right)} \cos\left(d x + c\right)^{2} - 2 \, n^{2} - 8 \, n - 8\right)} \sin\left(d x + c\right) - 8 \, n - 6\right)} \sin\left(d x + c\right)^{n}}{a^{2} d n^{3} + 6 \, a^{2} d n^{2} + 11 \, a^{2} d n + 6 \, a^{2} d}"," ",0,"(2*(n^2 + 4*n + 3)*cos(d*x + c)^2 - 2*n^2 - ((n^2 + 3*n + 2)*cos(d*x + c)^2 - 2*n^2 - 8*n - 8)*sin(d*x + c) - 8*n - 6)*sin(d*x + c)^n/(a^2*d*n^3 + 6*a^2*d*n^2 + 11*a^2*d*n + 6*a^2*d)","A",0
570,0,0,0,0.981334," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sin(d*x + c)^n*cos(d*x + c)^5/(3*a^3*cos(d*x + c)^2 - 4*a^3 + (a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c)), x)","F",0
571,0,0,0,0.727983," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sin(d*x + c)^n*cos(d*x + c)^5/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
572,1,106,0,1.104373," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{80640 \, a \cos\left(d x + c\right)^{11} - 197120 \, a \cos\left(d x + c\right)^{9} + 126720 \, a \cos\left(d x + c\right)^{7} - 10395 \, a d x - 693 \, {\left(128 \, a \cos\left(d x + c\right)^{9} - 176 \, a \cos\left(d x + c\right)^{7} + 8 \, a \cos\left(d x + c\right)^{5} + 10 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{887040 \, d}"," ",0,"-1/887040*(80640*a*cos(d*x + c)^11 - 197120*a*cos(d*x + c)^9 + 126720*a*cos(d*x + c)^7 - 10395*a*d*x - 693*(128*a*cos(d*x + c)^9 - 176*a*cos(d*x + c)^7 + 8*a*cos(d*x + c)^5 + 10*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/d","A",0
573,1,95,0,1.098324," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8960 \, a \cos\left(d x + c\right)^{9} - 11520 \, a \cos\left(d x + c\right)^{7} + 945 \, a d x + 63 \, {\left(128 \, a \cos\left(d x + c\right)^{9} - 176 \, a \cos\left(d x + c\right)^{7} + 8 \, a \cos\left(d x + c\right)^{5} + 10 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(8960*a*cos(d*x + c)^9 - 11520*a*cos(d*x + c)^7 + 945*a*d*x + 63*(128*a*cos(d*x + c)^9 - 176*a*cos(d*x + c)^7 + 8*a*cos(d*x + c)^5 + 10*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/d","A",0
574,1,84,0,0.793980," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{896 \, a \cos\left(d x + c\right)^{9} - 1152 \, a \cos\left(d x + c\right)^{7} + 315 \, a d x - 21 \, {\left(48 \, a \cos\left(d x + c\right)^{7} - 8 \, a \cos\left(d x + c\right)^{5} - 10 \, a \cos\left(d x + c\right)^{3} - 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8064 \, d}"," ",0,"1/8064*(896*a*cos(d*x + c)^9 - 1152*a*cos(d*x + c)^7 + 315*a*d*x - 21*(48*a*cos(d*x + c)^7 - 8*a*cos(d*x + c)^5 - 10*a*cos(d*x + c)^3 - 15*a*cos(d*x + c))*sin(d*x + c))/d","A",0
575,1,73,0,1.189968," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{384 \, a \cos\left(d x + c\right)^{7} - 105 \, a d x + 7 \, {\left(48 \, a \cos\left(d x + c\right)^{7} - 8 \, a \cos\left(d x + c\right)^{5} - 10 \, a \cos\left(d x + c\right)^{3} - 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2688 \, d}"," ",0,"-1/2688*(384*a*cos(d*x + c)^7 - 105*a*d*x + 7*(48*a*cos(d*x + c)^7 - 8*a*cos(d*x + c)^5 - 10*a*cos(d*x + c)^3 - 15*a*cos(d*x + c))*sin(d*x + c))/d","A",0
576,1,110,0,1.514212," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, a \cos\left(d x + c\right)^{5} + 80 \, a \cos\left(d x + c\right)^{3} + 75 \, a d x + 240 \, a \cos\left(d x + c\right) - 120 \, a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 120 \, a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5 \, {\left(8 \, a \cos\left(d x + c\right)^{5} + 10 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(48*a*cos(d*x + c)^5 + 80*a*cos(d*x + c)^3 + 75*a*d*x + 240*a*cos(d*x + c) - 120*a*log(1/2*cos(d*x + c) + 1/2) + 120*a*log(-1/2*cos(d*x + c) + 1/2) + 5*(8*a*cos(d*x + c)^5 + 10*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/d","A",0
577,1,129,0,0.849609," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, a \cos\left(d x + c\right)^{5} + 75 \, a \cos\left(d x + c\right)^{3} - 60 \, a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 60 \, a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 225 \, a \cos\left(d x + c\right) + {\left(24 \, a \cos\left(d x + c\right)^{5} + 40 \, a \cos\left(d x + c\right)^{3} - 225 \, a d x + 120 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d \sin\left(d x + c\right)}"," ",0,"1/120*(30*a*cos(d*x + c)^5 + 75*a*cos(d*x + c)^3 - 60*a*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 60*a*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 225*a*cos(d*x + c) + (24*a*cos(d*x + c)^5 + 40*a*cos(d*x + c)^3 - 225*a*d*x + 120*a*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
578,1,162,0,1.075758," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, a \cos\left(d x + c\right)^{5} + 45 \, a d x \cos\left(d x + c\right)^{2} + 40 \, a \cos\left(d x + c\right)^{3} - 45 \, a d x - 60 \, a \cos\left(d x + c\right) - 30 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 30 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(2 \, a \cos\left(d x + c\right)^{5} + 5 \, a \cos\left(d x + c\right)^{3} - 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/24*(8*a*cos(d*x + c)^5 + 45*a*d*x*cos(d*x + c)^2 + 40*a*cos(d*x + c)^3 - 45*a*d*x - 60*a*cos(d*x + c) - 30*(a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + 30*(a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2) + 3*(2*a*cos(d*x + c)^5 + 5*a*cos(d*x + c)^3 - 15*a*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
579,1,182,0,1.033429," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, a \cos\left(d x + c\right)^{5} - 40 \, a \cos\left(d x + c\right)^{3} - 15 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, a \cos\left(d x + c\right) + 2 \, {\left(2 \, a \cos\left(d x + c\right)^{5} - 15 \, a d x \cos\left(d x + c\right)^{2} + 10 \, a \cos\left(d x + c\right)^{3} + 15 \, a d x - 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(6*a*cos(d*x + c)^5 - 40*a*cos(d*x + c)^3 - 15*(a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*a*cos(d*x + c) + 2*(2*a*cos(d*x + c)^5 - 15*a*d*x*cos(d*x + c)^2 + 10*a*cos(d*x + c)^3 + 15*a*d*x - 15*a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
580,1,202,0,1.261329," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{120 \, a d x \cos\left(d x + c\right)^{4} + 48 \, a \cos\left(d x + c\right)^{5} - 240 \, a d x \cos\left(d x + c\right)^{2} - 150 \, a \cos\left(d x + c\right)^{3} + 120 \, a d x + 90 \, a \cos\left(d x + c\right) - 45 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 45 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 8 \, {\left(3 \, a \cos\left(d x + c\right)^{5} - 20 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/48*(120*a*d*x*cos(d*x + c)^4 + 48*a*cos(d*x + c)^5 - 240*a*d*x*cos(d*x + c)^2 - 150*a*cos(d*x + c)^3 + 120*a*d*x + 90*a*cos(d*x + c) - 45*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 45*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2) + 8*(3*a*cos(d*x + c)^5 - 20*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
581,1,222,0,0.884145," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{368 \, a \cos\left(d x + c\right)^{5} - 560 \, a \cos\left(d x + c\right)^{3} + 225 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 225 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 240 \, a \cos\left(d x + c\right) + 30 \, {\left(8 \, a d x \cos\left(d x + c\right)^{4} - 8 \, a \cos\left(d x + c\right)^{5} - 16 \, a d x \cos\left(d x + c\right)^{2} + 25 \, a \cos\left(d x + c\right)^{3} + 8 \, a d x - 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/240*(368*a*cos(d*x + c)^5 - 560*a*cos(d*x + c)^3 + 225*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 225*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 240*a*cos(d*x + c) + 30*(8*a*d*x*cos(d*x + c)^4 - 8*a*cos(d*x + c)^5 - 16*a*d*x*cos(d*x + c)^2 + 25*a*cos(d*x + c)^3 + 8*a*d*x - 15*a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
582,1,254,0,1.080857," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{480 \, a d x \cos\left(d x + c\right)^{6} - 1440 \, a d x \cos\left(d x + c\right)^{4} - 330 \, a \cos\left(d x + c\right)^{5} + 1440 \, a d x \cos\left(d x + c\right)^{2} + 400 \, a \cos\left(d x + c\right)^{3} - 480 \, a d x - 150 \, a \cos\left(d x + c\right) - 75 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 75 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(23 \, a \cos\left(d x + c\right)^{5} - 35 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/480*(480*a*d*x*cos(d*x + c)^6 - 1440*a*d*x*cos(d*x + c)^4 - 330*a*cos(d*x + c)^5 + 1440*a*d*x*cos(d*x + c)^2 + 400*a*cos(d*x + c)^3 - 480*a*d*x - 150*a*cos(d*x + c) - 75*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + 75*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2) - 32*(23*a*cos(d*x + c)^5 - 35*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
583,1,210,0,1.052668," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{96 \, a \cos\left(d x + c\right)^{7} + 105 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 105 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 14 \, {\left(33 \, a \cos\left(d x + c\right)^{5} - 40 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{672 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/672*(96*a*cos(d*x + c)^7 + 105*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 105*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 14*(33*a*cos(d*x + c)^5 - 40*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
584,1,225,0,1.273195," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{768 \, a \cos\left(d x + c\right)^{7} \sin\left(d x + c\right) + 210 \, a \cos\left(d x + c\right)^{7} + 1022 \, a \cos\left(d x + c\right)^{5} - 770 \, a \cos\left(d x + c\right)^{3} + 210 \, a \cos\left(d x + c\right) - 105 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{5376 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/5376*(768*a*cos(d*x + c)^7*sin(d*x + c) + 210*a*cos(d*x + c)^7 + 1022*a*cos(d*x + c)^5 - 770*a*cos(d*x + c)^3 + 210*a*cos(d*x + c) - 105*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 105*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","B",0
585,1,259,0,1.137028," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{512 \, a \cos\left(d x + c\right)^{9} - 2304 \, a \cos\left(d x + c\right)^{7} + 315 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 315 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 42 \, {\left(15 \, a \cos\left(d x + c\right)^{7} + 73 \, a \cos\left(d x + c\right)^{5} - 55 \, a \cos\left(d x + c\right)^{3} + 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16128 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/16128*(512*a*cos(d*x + c)^9 - 2304*a*cos(d*x + c)^7 + 315*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 315*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 42*(15*a*cos(d*x + c)^7 + 73*a*cos(d*x + c)^5 - 55*a*cos(d*x + c)^3 + 15*a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
586,1,289,0,1.240318," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{1890 \, a \cos\left(d x + c\right)^{9} - 8820 \, a \cos\left(d x + c\right)^{7} - 16128 \, a \cos\left(d x + c\right)^{5} + 8820 \, a \cos\left(d x + c\right)^{3} - 1890 \, a \cos\left(d x + c\right) - 945 \, {\left(a \cos\left(d x + c\right)^{10} - 5 \, a \cos\left(d x + c\right)^{8} + 10 \, a \cos\left(d x + c\right)^{6} - 10 \, a \cos\left(d x + c\right)^{4} + 5 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 945 \, {\left(a \cos\left(d x + c\right)^{10} - 5 \, a \cos\left(d x + c\right)^{8} + 10 \, a \cos\left(d x + c\right)^{6} - 10 \, a \cos\left(d x + c\right)^{4} + 5 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2560 \, {\left(2 \, a \cos\left(d x + c\right)^{9} - 9 \, a \cos\left(d x + c\right)^{7}\right)} \sin\left(d x + c\right)}{161280 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/161280*(1890*a*cos(d*x + c)^9 - 8820*a*cos(d*x + c)^7 - 16128*a*cos(d*x + c)^5 + 8820*a*cos(d*x + c)^3 - 1890*a*cos(d*x + c) - 945*(a*cos(d*x + c)^10 - 5*a*cos(d*x + c)^8 + 10*a*cos(d*x + c)^6 - 10*a*cos(d*x + c)^4 + 5*a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + 945*(a*cos(d*x + c)^10 - 5*a*cos(d*x + c)^8 + 10*a*cos(d*x + c)^6 - 10*a*cos(d*x + c)^4 + 5*a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2) + 2560*(2*a*cos(d*x + c)^9 - 9*a*cos(d*x + c)^7)*sin(d*x + c))/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","B",0
587,1,320,0,1.039256," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{20480 \, a \cos\left(d x + c\right)^{11} - 112640 \, a \cos\left(d x + c\right)^{9} + 253440 \, a \cos\left(d x + c\right)^{7} + 10395 \, {\left(a \cos\left(d x + c\right)^{10} - 5 \, a \cos\left(d x + c\right)^{8} + 10 \, a \cos\left(d x + c\right)^{6} - 10 \, a \cos\left(d x + c\right)^{4} + 5 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 10395 \, {\left(a \cos\left(d x + c\right)^{10} - 5 \, a \cos\left(d x + c\right)^{8} + 10 \, a \cos\left(d x + c\right)^{6} - 10 \, a \cos\left(d x + c\right)^{4} + 5 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 1386 \, {\left(15 \, a \cos\left(d x + c\right)^{9} - 70 \, a \cos\left(d x + c\right)^{7} - 128 \, a \cos\left(d x + c\right)^{5} + 70 \, a \cos\left(d x + c\right)^{3} - 15 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1774080 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/1774080*(20480*a*cos(d*x + c)^11 - 112640*a*cos(d*x + c)^9 + 253440*a*cos(d*x + c)^7 + 10395*(a*cos(d*x + c)^10 - 5*a*cos(d*x + c)^8 + 10*a*cos(d*x + c)^6 - 10*a*cos(d*x + c)^4 + 5*a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 10395*(a*cos(d*x + c)^10 - 5*a*cos(d*x + c)^8 + 10*a*cos(d*x + c)^6 - 10*a*cos(d*x + c)^4 + 5*a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 1386*(15*a*cos(d*x + c)^9 - 70*a*cos(d*x + c)^7 - 128*a*cos(d*x + c)^5 + 70*a*cos(d*x + c)^3 - 15*a*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
588,1,137,0,1.216542," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{645120 \, a^{2} \cos\left(d x + c\right)^{11} - 1576960 \, a^{2} \cos\left(d x + c\right)^{9} + 1013760 \, a^{2} \cos\left(d x + c\right)^{7} - 58905 \, a^{2} d x + 231 \, {\left(1280 \, a^{2} \cos\left(d x + c\right)^{11} - 4736 \, a^{2} \cos\left(d x + c\right)^{9} + 4272 \, a^{2} \cos\left(d x + c\right)^{7} - 136 \, a^{2} \cos\left(d x + c\right)^{5} - 170 \, a^{2} \cos\left(d x + c\right)^{3} - 255 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3548160 \, d}"," ",0,"-1/3548160*(645120*a^2*cos(d*x + c)^11 - 1576960*a^2*cos(d*x + c)^9 + 1013760*a^2*cos(d*x + c)^7 - 58905*a^2*d*x + 231*(1280*a^2*cos(d*x + c)^11 - 4736*a^2*cos(d*x + c)^9 + 4272*a^2*cos(d*x + c)^7 - 136*a^2*cos(d*x + c)^5 - 170*a^2*cos(d*x + c)^3 - 255*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
589,1,124,0,1.290658," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{13440 \, a^{2} \cos\left(d x + c\right)^{11} - 49280 \, a^{2} \cos\left(d x + c\right)^{9} + 42240 \, a^{2} \cos\left(d x + c\right)^{7} - 3465 \, a^{2} d x - 231 \, {\left(128 \, a^{2} \cos\left(d x + c\right)^{9} - 176 \, a^{2} \cos\left(d x + c\right)^{7} + 8 \, a^{2} \cos\left(d x + c\right)^{5} + 10 \, a^{2} \cos\left(d x + c\right)^{3} + 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{147840 \, d}"," ",0,"-1/147840*(13440*a^2*cos(d*x + c)^11 - 49280*a^2*cos(d*x + c)^9 + 42240*a^2*cos(d*x + c)^7 - 3465*a^2*d*x - 231*(128*a^2*cos(d*x + c)^9 - 176*a^2*cos(d*x + c)^7 + 8*a^2*cos(d*x + c)^5 + 10*a^2*cos(d*x + c)^3 + 15*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
590,1,111,0,1.259833," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{17920 \, a^{2} \cos\left(d x + c\right)^{9} - 23040 \, a^{2} \cos\left(d x + c\right)^{7} + 4095 \, a^{2} d x + 21 \, {\left(384 \, a^{2} \cos\left(d x + c\right)^{9} - 1008 \, a^{2} \cos\left(d x + c\right)^{7} + 104 \, a^{2} \cos\left(d x + c\right)^{5} + 130 \, a^{2} \cos\left(d x + c\right)^{3} + 195 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(17920*a^2*cos(d*x + c)^9 - 23040*a^2*cos(d*x + c)^7 + 4095*a^2*d*x + 21*(384*a^2*cos(d*x + c)^9 - 1008*a^2*cos(d*x + c)^7 + 104*a^2*cos(d*x + c)^5 + 130*a^2*cos(d*x + c)^3 + 195*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
591,1,98,0,1.052564," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{448 \, a^{2} \cos\left(d x + c\right)^{9} - 1152 \, a^{2} \cos\left(d x + c\right)^{7} + 315 \, a^{2} d x - 21 \, {\left(48 \, a^{2} \cos\left(d x + c\right)^{7} - 8 \, a^{2} \cos\left(d x + c\right)^{5} - 10 \, a^{2} \cos\left(d x + c\right)^{3} - 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4032 \, d}"," ",0,"1/4032*(448*a^2*cos(d*x + c)^9 - 1152*a^2*cos(d*x + c)^7 + 315*a^2*d*x - 21*(48*a^2*cos(d*x + c)^7 - 8*a^2*cos(d*x + c)^5 - 10*a^2*cos(d*x + c)^3 - 15*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
592,1,141,0,1.264663," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{120 \, a^{2} \cos\left(d x + c\right)^{7} - 168 \, a^{2} \cos\left(d x + c\right)^{5} - 280 \, a^{2} \cos\left(d x + c\right)^{3} - 525 \, a^{2} d x - 840 \, a^{2} \cos\left(d x + c\right) + 420 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 420 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 35 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{5} + 10 \, a^{2} \cos\left(d x + c\right)^{3} + 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"-1/840*(120*a^2*cos(d*x + c)^7 - 168*a^2*cos(d*x + c)^5 - 280*a^2*cos(d*x + c)^3 - 525*a^2*d*x - 840*a^2*cos(d*x + c) + 420*a^2*log(1/2*cos(d*x + c) + 1/2) - 420*a^2*log(-1/2*cos(d*x + c) + 1/2) - 35*(8*a^2*cos(d*x + c)^5 + 10*a^2*cos(d*x + c)^3 + 15*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
593,1,161,0,1.009151," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{40 \, a^{2} \cos\left(d x + c\right)^{7} - 50 \, a^{2} \cos\left(d x + c\right)^{5} - 125 \, a^{2} \cos\left(d x + c\right)^{3} + 240 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 240 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 375 \, a^{2} \cos\left(d x + c\right) - {\left(96 \, a^{2} \cos\left(d x + c\right)^{5} + 160 \, a^{2} \cos\left(d x + c\right)^{3} - 375 \, a^{2} d x + 480 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d \sin\left(d x + c\right)}"," ",0,"-1/240*(40*a^2*cos(d*x + c)^7 - 50*a^2*cos(d*x + c)^5 - 125*a^2*cos(d*x + c)^3 + 240*a^2*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 240*a^2*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 375*a^2*cos(d*x + c) - (96*a^2*cos(d*x + c)^5 + 160*a^2*cos(d*x + c)^3 - 375*a^2*d*x + 480*a^2*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
594,1,199,0,1.074318," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} \cos\left(d x + c\right)^{7} - 4 \, a^{2} \cos\left(d x + c\right)^{5} - 75 \, a^{2} d x \cos\left(d x + c\right)^{2} - 20 \, a^{2} \cos\left(d x + c\right)^{3} + 75 \, a^{2} d x + 30 \, a^{2} \cos\left(d x + c\right) + 15 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 5 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{5} + 5 \, a^{2} \cos\left(d x + c\right)^{3} - 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{20 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/20*(4*a^2*cos(d*x + c)^7 - 4*a^2*cos(d*x + c)^5 - 75*a^2*d*x*cos(d*x + c)^2 - 20*a^2*cos(d*x + c)^3 + 75*a^2*d*x + 30*a^2*cos(d*x + c) + 15*(a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2) - 15*(a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2) - 5*(2*a^2*cos(d*x + c)^5 + 5*a^2*cos(d*x + c)^3 - 15*a^2*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
595,1,219,0,0.875540," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, a^{2} \cos\left(d x + c\right)^{7} - 3 \, a^{2} \cos\left(d x + c\right)^{5} + 20 \, a^{2} \cos\left(d x + c\right)^{3} - 15 \, a^{2} \cos\left(d x + c\right) + 60 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 60 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - {\left(16 \, a^{2} \cos\left(d x + c\right)^{5} - 15 \, a^{2} d x \cos\left(d x + c\right)^{2} + 80 \, a^{2} \cos\left(d x + c\right)^{3} + 15 \, a^{2} d x - 120 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/24*(6*a^2*cos(d*x + c)^7 - 3*a^2*cos(d*x + c)^5 + 20*a^2*cos(d*x + c)^3 - 15*a^2*cos(d*x + c) + 60*(a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 60*(a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - (16*a^2*cos(d*x + c)^5 - 15*a^2*d*x*cos(d*x + c)^2 + 80*a^2*cos(d*x + c)^3 + 15*a^2*d*x - 120*a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
596,1,245,0,1.063357," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{16 \, a^{2} \cos\left(d x + c\right)^{7} - 240 \, a^{2} d x \cos\left(d x + c\right)^{4} + 16 \, a^{2} \cos\left(d x + c\right)^{5} + 480 \, a^{2} d x \cos\left(d x + c\right)^{2} - 50 \, a^{2} \cos\left(d x + c\right)^{3} - 240 \, a^{2} d x + 30 \, a^{2} \cos\left(d x + c\right) - 15 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(3 \, a^{2} \cos\left(d x + c\right)^{5} - 20 \, a^{2} \cos\left(d x + c\right)^{3} + 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/48*(16*a^2*cos(d*x + c)^7 - 240*a^2*d*x*cos(d*x + c)^4 + 16*a^2*cos(d*x + c)^5 + 480*a^2*d*x*cos(d*x + c)^2 - 50*a^2*cos(d*x + c)^3 - 240*a^2*d*x + 30*a^2*cos(d*x + c) - 15*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2) + 15*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2) - 16*(3*a^2*cos(d*x + c)^5 - 20*a^2*cos(d*x + c)^3 + 15*a^2*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
597,1,265,0,1.209317," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{20 \, a^{2} \cos\left(d x + c\right)^{7} - 92 \, a^{2} \cos\left(d x + c\right)^{5} + 140 \, a^{2} \cos\left(d x + c\right)^{3} - 60 \, a^{2} \cos\left(d x + c\right) + 75 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 75 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 10 \, {\left(6 \, a^{2} d x \cos\left(d x + c\right)^{4} + 8 \, a^{2} \cos\left(d x + c\right)^{5} - 12 \, a^{2} d x \cos\left(d x + c\right)^{2} - 25 \, a^{2} \cos\left(d x + c\right)^{3} + 6 \, a^{2} d x + 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/40*(20*a^2*cos(d*x + c)^7 - 92*a^2*cos(d*x + c)^5 + 140*a^2*cos(d*x + c)^3 - 60*a^2*cos(d*x + c) + 75*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 75*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 10*(6*a^2*d*x*cos(d*x + c)^4 + 8*a^2*cos(d*x + c)^5 - 12*a^2*d*x*cos(d*x + c)^2 - 25*a^2*cos(d*x + c)^3 + 6*a^2*d*x + 15*a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
598,1,303,0,1.166507," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{960 \, a^{2} d x \cos\left(d x + c\right)^{6} - 480 \, a^{2} \cos\left(d x + c\right)^{7} - 2880 \, a^{2} d x \cos\left(d x + c\right)^{4} + 1650 \, a^{2} \cos\left(d x + c\right)^{5} + 2880 \, a^{2} d x \cos\left(d x + c\right)^{2} - 2000 \, a^{2} \cos\left(d x + c\right)^{3} - 960 \, a^{2} d x + 750 \, a^{2} \cos\left(d x + c\right) + 375 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 375 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 64 \, {\left(23 \, a^{2} \cos\left(d x + c\right)^{5} - 35 \, a^{2} \cos\left(d x + c\right)^{3} + 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/480*(960*a^2*d*x*cos(d*x + c)^6 - 480*a^2*cos(d*x + c)^7 - 2880*a^2*d*x*cos(d*x + c)^4 + 1650*a^2*cos(d*x + c)^5 + 2880*a^2*d*x*cos(d*x + c)^2 - 2000*a^2*cos(d*x + c)^3 - 960*a^2*d*x + 750*a^2*cos(d*x + c) + 375*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2) - 375*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2) - 64*(23*a^2*cos(d*x + c)^5 - 35*a^2*cos(d*x + c)^3 + 15*a^2*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
599,1,323,0,1.352065," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2336 \, a^{2} \cos\left(d x + c\right)^{7} - 6496 \, a^{2} \cos\left(d x + c\right)^{5} + 5600 \, a^{2} \cos\left(d x + c\right)^{3} - 1680 \, a^{2} \cos\left(d x + c\right) - 525 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 525 \, {\left(a^{2} \cos\left(d x + c\right)^{6} - 3 \, a^{2} \cos\left(d x + c\right)^{4} + 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 70 \, {\left(24 \, a^{2} d x \cos\left(d x + c\right)^{6} - 72 \, a^{2} d x \cos\left(d x + c\right)^{4} - 33 \, a^{2} \cos\left(d x + c\right)^{5} + 72 \, a^{2} d x \cos\left(d x + c\right)^{2} + 40 \, a^{2} \cos\left(d x + c\right)^{3} - 24 \, a^{2} d x - 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/1680*(2336*a^2*cos(d*x + c)^7 - 6496*a^2*cos(d*x + c)^5 + 5600*a^2*cos(d*x + c)^3 - 1680*a^2*cos(d*x + c) - 525*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 525*(a^2*cos(d*x + c)^6 - 3*a^2*cos(d*x + c)^4 + 3*a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 70*(24*a^2*d*x*cos(d*x + c)^6 - 72*a^2*d*x*cos(d*x + c)^4 - 33*a^2*cos(d*x + c)^5 + 72*a^2*d*x*cos(d*x + c)^2 + 40*a^2*cos(d*x + c)^3 - 24*a^2*d*x - 15*a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
600,1,255,0,1.117876," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{512 \, a^{2} \cos\left(d x + c\right)^{7} \sin\left(d x + c\right) - 1162 \, a^{2} \cos\left(d x + c\right)^{7} + 3066 \, a^{2} \cos\left(d x + c\right)^{5} - 2310 \, a^{2} \cos\left(d x + c\right)^{3} + 630 \, a^{2} \cos\left(d x + c\right) - 315 \, {\left(a^{2} \cos\left(d x + c\right)^{8} - 4 \, a^{2} \cos\left(d x + c\right)^{6} + 6 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 315 \, {\left(a^{2} \cos\left(d x + c\right)^{8} - 4 \, a^{2} \cos\left(d x + c\right)^{6} + 6 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{1792 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/1792*(512*a^2*cos(d*x + c)^7*sin(d*x + c) - 1162*a^2*cos(d*x + c)^7 + 3066*a^2*cos(d*x + c)^5 - 2310*a^2*cos(d*x + c)^3 + 630*a^2*cos(d*x + c) - 315*(a^2*cos(d*x + c)^8 - 4*a^2*cos(d*x + c)^6 + 6*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2) + 315*(a^2*cos(d*x + c)^8 - 4*a^2*cos(d*x + c)^6 + 6*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
601,1,291,0,1.094184," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{1408 \, a^{2} \cos\left(d x + c\right)^{9} - 2304 \, a^{2} \cos\left(d x + c\right)^{7} + 315 \, {\left(a^{2} \cos\left(d x + c\right)^{8} - 4 \, a^{2} \cos\left(d x + c\right)^{6} + 6 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 315 \, {\left(a^{2} \cos\left(d x + c\right)^{8} - 4 \, a^{2} \cos\left(d x + c\right)^{6} + 6 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 42 \, {\left(15 \, a^{2} \cos\left(d x + c\right)^{7} + 73 \, a^{2} \cos\left(d x + c\right)^{5} - 55 \, a^{2} \cos\left(d x + c\right)^{3} + 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8064 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/8064*(1408*a^2*cos(d*x + c)^9 - 2304*a^2*cos(d*x + c)^7 + 315*(a^2*cos(d*x + c)^8 - 4*a^2*cos(d*x + c)^6 + 6*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 315*(a^2*cos(d*x + c)^8 - 4*a^2*cos(d*x + c)^6 + 6*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 42*(15*a^2*cos(d*x + c)^7 + 73*a^2*cos(d*x + c)^5 - 55*a^2*cos(d*x + c)^3 + 15*a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
602,1,327,0,0.631172," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8190 \, a^{2} \cos\left(d x + c\right)^{9} + 15540 \, a^{2} \cos\left(d x + c\right)^{7} - 69888 \, a^{2} \cos\left(d x + c\right)^{5} + 38220 \, a^{2} \cos\left(d x + c\right)^{3} - 8190 \, a^{2} \cos\left(d x + c\right) - 4095 \, {\left(a^{2} \cos\left(d x + c\right)^{10} - 5 \, a^{2} \cos\left(d x + c\right)^{8} + 10 \, a^{2} \cos\left(d x + c\right)^{6} - 10 \, a^{2} \cos\left(d x + c\right)^{4} + 5 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4095 \, {\left(a^{2} \cos\left(d x + c\right)^{10} - 5 \, a^{2} \cos\left(d x + c\right)^{8} + 10 \, a^{2} \cos\left(d x + c\right)^{6} - 10 \, a^{2} \cos\left(d x + c\right)^{4} + 5 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5120 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{9} - 9 \, a^{2} \cos\left(d x + c\right)^{7}\right)} \sin\left(d x + c\right)}{161280 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/161280*(8190*a^2*cos(d*x + c)^9 + 15540*a^2*cos(d*x + c)^7 - 69888*a^2*cos(d*x + c)^5 + 38220*a^2*cos(d*x + c)^3 - 8190*a^2*cos(d*x + c) - 4095*(a^2*cos(d*x + c)^10 - 5*a^2*cos(d*x + c)^8 + 10*a^2*cos(d*x + c)^6 - 10*a^2*cos(d*x + c)^4 + 5*a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2) + 4095*(a^2*cos(d*x + c)^10 - 5*a^2*cos(d*x + c)^8 + 10*a^2*cos(d*x + c)^6 - 10*a^2*cos(d*x + c)^4 + 5*a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2) + 5120*(2*a^2*cos(d*x + c)^9 - 9*a^2*cos(d*x + c)^7)*sin(d*x + c))/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","A",0
603,1,360,0,1.860329," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{12800 \, a^{2} \cos\left(d x + c\right)^{11} - 70400 \, a^{2} \cos\left(d x + c\right)^{9} + 84480 \, a^{2} \cos\left(d x + c\right)^{7} + 3465 \, {\left(a^{2} \cos\left(d x + c\right)^{10} - 5 \, a^{2} \cos\left(d x + c\right)^{8} + 10 \, a^{2} \cos\left(d x + c\right)^{6} - 10 \, a^{2} \cos\left(d x + c\right)^{4} + 5 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3465 \, {\left(a^{2} \cos\left(d x + c\right)^{10} - 5 \, a^{2} \cos\left(d x + c\right)^{8} + 10 \, a^{2} \cos\left(d x + c\right)^{6} - 10 \, a^{2} \cos\left(d x + c\right)^{4} + 5 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 462 \, {\left(15 \, a^{2} \cos\left(d x + c\right)^{9} - 70 \, a^{2} \cos\left(d x + c\right)^{7} - 128 \, a^{2} \cos\left(d x + c\right)^{5} + 70 \, a^{2} \cos\left(d x + c\right)^{3} - 15 \, a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{295680 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/295680*(12800*a^2*cos(d*x + c)^11 - 70400*a^2*cos(d*x + c)^9 + 84480*a^2*cos(d*x + c)^7 + 3465*(a^2*cos(d*x + c)^10 - 5*a^2*cos(d*x + c)^8 + 10*a^2*cos(d*x + c)^6 - 10*a^2*cos(d*x + c)^4 + 5*a^2*cos(d*x + c)^2 - a^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3465*(a^2*cos(d*x + c)^10 - 5*a^2*cos(d*x + c)^8 + 10*a^2*cos(d*x + c)^6 - 10*a^2*cos(d*x + c)^4 + 5*a^2*cos(d*x + c)^2 - a^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 462*(15*a^2*cos(d*x + c)^9 - 70*a^2*cos(d*x + c)^7 - 128*a^2*cos(d*x + c)^5 + 70*a^2*cos(d*x + c)^3 - 15*a^2*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
604,1,384,0,0.929451," ","integrate(cos(d*x+c)^6*csc(d*x+c)^13*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{117810 \, a^{2} \cos\left(d x + c\right)^{11} - 667590 \, a^{2} \cos\left(d x + c\right)^{9} + 135828 \, a^{2} \cos\left(d x + c\right)^{7} + 1555092 \, a^{2} \cos\left(d x + c\right)^{5} - 667590 \, a^{2} \cos\left(d x + c\right)^{3} + 117810 \, a^{2} \cos\left(d x + c\right) - 58905 \, {\left(a^{2} \cos\left(d x + c\right)^{12} - 6 \, a^{2} \cos\left(d x + c\right)^{10} + 15 \, a^{2} \cos\left(d x + c\right)^{8} - 20 \, a^{2} \cos\left(d x + c\right)^{6} + 15 \, a^{2} \cos\left(d x + c\right)^{4} - 6 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 58905 \, {\left(a^{2} \cos\left(d x + c\right)^{12} - 6 \, a^{2} \cos\left(d x + c\right)^{10} + 15 \, a^{2} \cos\left(d x + c\right)^{8} - 20 \, a^{2} \cos\left(d x + c\right)^{6} + 15 \, a^{2} \cos\left(d x + c\right)^{4} - 6 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 20480 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{11} - 44 \, a^{2} \cos\left(d x + c\right)^{9} + 99 \, a^{2} \cos\left(d x + c\right)^{7}\right)} \sin\left(d x + c\right)}{7096320 \, {\left(d \cos\left(d x + c\right)^{12} - 6 \, d \cos\left(d x + c\right)^{10} + 15 \, d \cos\left(d x + c\right)^{8} - 20 \, d \cos\left(d x + c\right)^{6} + 15 \, d \cos\left(d x + c\right)^{4} - 6 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/7096320*(117810*a^2*cos(d*x + c)^11 - 667590*a^2*cos(d*x + c)^9 + 135828*a^2*cos(d*x + c)^7 + 1555092*a^2*cos(d*x + c)^5 - 667590*a^2*cos(d*x + c)^3 + 117810*a^2*cos(d*x + c) - 58905*(a^2*cos(d*x + c)^12 - 6*a^2*cos(d*x + c)^10 + 15*a^2*cos(d*x + c)^8 - 20*a^2*cos(d*x + c)^6 + 15*a^2*cos(d*x + c)^4 - 6*a^2*cos(d*x + c)^2 + a^2)*log(1/2*cos(d*x + c) + 1/2) + 58905*(a^2*cos(d*x + c)^12 - 6*a^2*cos(d*x + c)^10 + 15*a^2*cos(d*x + c)^8 - 20*a^2*cos(d*x + c)^6 + 15*a^2*cos(d*x + c)^4 - 6*a^2*cos(d*x + c)^2 + a^2)*log(-1/2*cos(d*x + c) + 1/2) + 20480*(8*a^2*cos(d*x + c)^11 - 44*a^2*cos(d*x + c)^9 + 99*a^2*cos(d*x + c)^7)*sin(d*x + c))/(d*cos(d*x + c)^12 - 6*d*cos(d*x + c)^10 + 15*d*cos(d*x + c)^8 - 20*d*cos(d*x + c)^6 + 15*d*cos(d*x + c)^4 - 6*d*cos(d*x + c)^2 + d)","A",0
605,1,150,0,0.869114," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{394240 \, a^{3} \cos\left(d x + c\right)^{13} - 2795520 \, a^{3} \cos\left(d x + c\right)^{11} + 5125120 \, a^{3} \cos\left(d x + c\right)^{9} - 2928640 \, a^{3} \cos\left(d x + c\right)^{7} + 135135 \, a^{3} d x - 1001 \, {\left(1280 \, a^{3} \cos\left(d x + c\right)^{11} - 3712 \, a^{3} \cos\left(d x + c\right)^{9} + 2864 \, a^{3} \cos\left(d x + c\right)^{7} - 72 \, a^{3} \cos\left(d x + c\right)^{5} - 90 \, a^{3} \cos\left(d x + c\right)^{3} - 135 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{5125120 \, d}"," ",0,"1/5125120*(394240*a^3*cos(d*x + c)^13 - 2795520*a^3*cos(d*x + c)^11 + 5125120*a^3*cos(d*x + c)^9 - 2928640*a^3*cos(d*x + c)^7 + 135135*a^3*d*x - 1001*(1280*a^3*cos(d*x + c)^11 - 3712*a^3*cos(d*x + c)^9 + 2864*a^3*cos(d*x + c)^7 - 72*a^3*cos(d*x + c)^5 - 90*a^3*cos(d*x + c)^3 - 135*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
606,1,137,0,1.681453," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{967680 \, a^{3} \cos\left(d x + c\right)^{11} - 2759680 \, a^{3} \cos\left(d x + c\right)^{9} + 2027520 \, a^{3} \cos\left(d x + c\right)^{7} - 142065 \, a^{3} d x + 231 \, {\left(1280 \, a^{3} \cos\left(d x + c\right)^{11} - 7808 \, a^{3} \cos\left(d x + c\right)^{9} + 8496 \, a^{3} \cos\left(d x + c\right)^{7} - 328 \, a^{3} \cos\left(d x + c\right)^{5} - 410 \, a^{3} \cos\left(d x + c\right)^{3} - 615 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3548160 \, d}"," ",0,"-1/3548160*(967680*a^3*cos(d*x + c)^11 - 2759680*a^3*cos(d*x + c)^9 + 2027520*a^3*cos(d*x + c)^7 - 142065*a^3*d*x + 231*(1280*a^3*cos(d*x + c)^11 - 7808*a^3*cos(d*x + c)^9 + 8496*a^3*cos(d*x + c)^7 - 328*a^3*cos(d*x + c)^5 - 410*a^3*cos(d*x + c)^3 - 615*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
607,1,124,0,0.925792," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{80640 \, a^{3} \cos\left(d x + c\right)^{11} - 492800 \, a^{3} \cos\left(d x + c\right)^{9} + 506880 \, a^{3} \cos\left(d x + c\right)^{7} - 65835 \, a^{3} d x - 231 \, {\left(1152 \, a^{3} \cos\left(d x + c\right)^{9} - 2064 \, a^{3} \cos\left(d x + c\right)^{7} + 152 \, a^{3} \cos\left(d x + c\right)^{5} + 190 \, a^{3} \cos\left(d x + c\right)^{3} + 285 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{887040 \, d}"," ",0,"-1/887040*(80640*a^3*cos(d*x + c)^11 - 492800*a^3*cos(d*x + c)^9 + 506880*a^3*cos(d*x + c)^7 - 65835*a^3*d*x - 231*(1152*a^3*cos(d*x + c)^9 - 2064*a^3*cos(d*x + c)^7 + 152*a^3*cos(d*x + c)^5 + 190*a^3*cos(d*x + c)^3 + 285*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
608,1,111,0,0.799315," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8960 \, a^{3} \cos\left(d x + c\right)^{9} - 15360 \, a^{3} \cos\left(d x + c\right)^{7} + 3465 \, a^{3} d x + 21 \, {\left(128 \, a^{3} \cos\left(d x + c\right)^{9} - 656 \, a^{3} \cos\left(d x + c\right)^{7} + 88 \, a^{3} \cos\left(d x + c\right)^{5} + 110 \, a^{3} \cos\left(d x + c\right)^{3} + 165 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{26880 \, d}"," ",0,"1/26880*(8960*a^3*cos(d*x + c)^9 - 15360*a^3*cos(d*x + c)^7 + 3465*a^3*d*x + 21*(128*a^3*cos(d*x + c)^9 - 656*a^3*cos(d*x + c)^7 + 88*a^3*cos(d*x + c)^5 + 110*a^3*cos(d*x + c)^3 + 165*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
609,1,154,0,1.122312," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{5760 \, a^{3} \cos\left(d x + c\right)^{7} - 2688 \, a^{3} \cos\left(d x + c\right)^{5} - 4480 \, a^{3} \cos\left(d x + c\right)^{3} - 13125 \, a^{3} d x - 13440 \, a^{3} \cos\left(d x + c\right) + 6720 \, a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 6720 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 35 \, {\left(48 \, a^{3} \cos\left(d x + c\right)^{7} - 200 \, a^{3} \cos\left(d x + c\right)^{5} - 250 \, a^{3} \cos\left(d x + c\right)^{3} - 375 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{13440 \, d}"," ",0,"-1/13440*(5760*a^3*cos(d*x + c)^7 - 2688*a^3*cos(d*x + c)^5 - 4480*a^3*cos(d*x + c)^3 - 13125*a^3*d*x - 13440*a^3*cos(d*x + c) + 6720*a^3*log(1/2*cos(d*x + c) + 1/2) - 6720*a^3*log(-1/2*cos(d*x + c) + 1/2) + 35*(48*a^3*cos(d*x + c)^7 - 200*a^3*cos(d*x + c)^5 - 250*a^3*cos(d*x + c)^3 - 375*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
610,1,173,0,1.157245," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{280 \, a^{3} \cos\left(d x + c\right)^{7} - 70 \, a^{3} \cos\left(d x + c\right)^{5} - 175 \, a^{3} \cos\left(d x + c\right)^{3} + 840 \, a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 840 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 525 \, a^{3} \cos\left(d x + c\right) + {\left(80 \, a^{3} \cos\left(d x + c\right)^{7} - 336 \, a^{3} \cos\left(d x + c\right)^{5} - 560 \, a^{3} \cos\left(d x + c\right)^{3} + 525 \, a^{3} d x - 1680 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{560 \, d \sin\left(d x + c\right)}"," ",0,"-1/560*(280*a^3*cos(d*x + c)^7 - 70*a^3*cos(d*x + c)^5 - 175*a^3*cos(d*x + c)^3 + 840*a^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 840*a^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 525*a^3*cos(d*x + c) + (80*a^3*cos(d*x + c)^7 - 336*a^3*cos(d*x + c)^5 - 560*a^3*cos(d*x + c)^3 + 525*a^3*d*x - 1680*a^3*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
611,1,212,0,0.997585," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{144 \, a^{3} \cos\left(d x + c\right)^{7} + 16 \, a^{3} \cos\left(d x + c\right)^{5} - 1275 \, a^{3} d x \cos\left(d x + c\right)^{2} + 80 \, a^{3} \cos\left(d x + c\right)^{3} + 1275 \, a^{3} d x - 120 \, a^{3} \cos\left(d x + c\right) - 60 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 60 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5 \, {\left(8 \, a^{3} \cos\left(d x + c\right)^{7} - 34 \, a^{3} \cos\left(d x + c\right)^{5} - 85 \, a^{3} \cos\left(d x + c\right)^{3} + 255 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/240*(144*a^3*cos(d*x + c)^7 + 16*a^3*cos(d*x + c)^5 - 1275*a^3*d*x*cos(d*x + c)^2 + 80*a^3*cos(d*x + c)^3 + 1275*a^3*d*x - 120*a^3*cos(d*x + c) - 60*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2) + 60*(a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2) + 5*(8*a^3*cos(d*x + c)^7 - 34*a^3*cos(d*x + c)^5 - 85*a^3*cos(d*x + c)^3 + 255*a^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
612,1,231,0,1.033389," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{90 \, a^{3} \cos\left(d x + c\right)^{7} + 75 \, a^{3} \cos\left(d x + c\right)^{5} - 500 \, a^{3} \cos\left(d x + c\right)^{3} + 375 \, a^{3} \cos\left(d x + c\right) + 390 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 390 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(24 \, a^{3} \cos\left(d x + c\right)^{7} - 104 \, a^{3} \cos\left(d x + c\right)^{5} - 375 \, a^{3} d x \cos\left(d x + c\right)^{2} - 520 \, a^{3} \cos\left(d x + c\right)^{3} + 375 \, a^{3} d x + 780 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/120*(90*a^3*cos(d*x + c)^7 + 75*a^3*cos(d*x + c)^5 - 500*a^3*cos(d*x + c)^3 + 375*a^3*cos(d*x + c) + 390*(a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 390*(a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + (24*a^3*cos(d*x + c)^7 - 104*a^3*cos(d*x + c)^5 - 375*a^3*d*x*cos(d*x + c)^2 - 520*a^3*cos(d*x + c)^3 + 375*a^3*d*x + 780*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
613,1,258,0,0.979204," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{16 \, a^{3} \cos\left(d x + c\right)^{7} - 90 \, a^{3} d x \cos\left(d x + c\right)^{4} + 48 \, a^{3} \cos\left(d x + c\right)^{5} + 180 \, a^{3} d x \cos\left(d x + c\right)^{2} - 150 \, a^{3} \cos\left(d x + c\right)^{3} - 90 \, a^{3} d x + 90 \, a^{3} \cos\left(d x + c\right) - 45 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 45 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(2 \, a^{3} \cos\left(d x + c\right)^{7} - 9 \, a^{3} \cos\left(d x + c\right)^{5} + 60 \, a^{3} \cos\left(d x + c\right)^{3} - 45 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/16*(16*a^3*cos(d*x + c)^7 - 90*a^3*d*x*cos(d*x + c)^4 + 48*a^3*cos(d*x + c)^5 + 180*a^3*d*x*cos(d*x + c)^2 - 150*a^3*cos(d*x + c)^3 - 90*a^3*d*x + 90*a^3*cos(d*x + c) - 45*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2) + 45*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2) + 2*(2*a^3*cos(d*x + c)^7 - 9*a^3*cos(d*x + c)^5 + 60*a^3*cos(d*x + c)^3 - 45*a^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
614,1,278,0,1.223167," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{360 \, a^{3} \cos\left(d x + c\right)^{7} - 2392 \, a^{3} \cos\left(d x + c\right)^{5} + 3640 \, a^{3} \cos\left(d x + c\right)^{3} - 1560 \, a^{3} \cos\left(d x + c\right) + 375 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 375 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 10 \, {\left(8 \, a^{3} \cos\left(d x + c\right)^{7} - 156 \, a^{3} d x \cos\left(d x + c\right)^{4} - 40 \, a^{3} \cos\left(d x + c\right)^{5} + 312 \, a^{3} d x \cos\left(d x + c\right)^{2} + 125 \, a^{3} \cos\left(d x + c\right)^{3} - 156 \, a^{3} d x - 75 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/240*(360*a^3*cos(d*x + c)^7 - 2392*a^3*cos(d*x + c)^5 + 3640*a^3*cos(d*x + c)^3 - 1560*a^3*cos(d*x + c) + 375*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 375*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 10*(8*a^3*cos(d*x + c)^7 - 156*a^3*d*x*cos(d*x + c)^4 - 40*a^3*cos(d*x + c)^5 + 312*a^3*d*x*cos(d*x + c)^2 + 125*a^3*cos(d*x + c)^3 - 156*a^3*d*x - 75*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
615,1,316,0,1.057425," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{240 \, a^{3} d x \cos\left(d x + c\right)^{6} - 1440 \, a^{3} \cos\left(d x + c\right)^{7} - 720 \, a^{3} d x \cos\left(d x + c\right)^{4} + 5610 \, a^{3} \cos\left(d x + c\right)^{5} + 720 \, a^{3} d x \cos\left(d x + c\right)^{2} - 6800 \, a^{3} \cos\left(d x + c\right)^{3} - 240 \, a^{3} d x + 2550 \, a^{3} \cos\left(d x + c\right) + 1275 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 1275 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(15 \, a^{3} \cos\left(d x + c\right)^{7} + 23 \, a^{3} \cos\left(d x + c\right)^{5} - 35 \, a^{3} \cos\left(d x + c\right)^{3} + 15 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/480*(240*a^3*d*x*cos(d*x + c)^6 - 1440*a^3*cos(d*x + c)^7 - 720*a^3*d*x*cos(d*x + c)^4 + 5610*a^3*cos(d*x + c)^5 + 720*a^3*d*x*cos(d*x + c)^2 - 6800*a^3*cos(d*x + c)^3 - 240*a^3*d*x + 2550*a^3*cos(d*x + c) + 1275*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2) - 1275*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2) - 16*(15*a^3*cos(d*x + c)^7 + 23*a^3*cos(d*x + c)^5 - 35*a^3*cos(d*x + c)^3 + 15*a^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
616,1,336,0,1.156850," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4992 \, a^{3} \cos\left(d x + c\right)^{7} - 12992 \, a^{3} \cos\left(d x + c\right)^{5} + 11200 \, a^{3} \cos\left(d x + c\right)^{3} - 3360 \, a^{3} \cos\left(d x + c\right) + 525 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 525 \, {\left(a^{3} \cos\left(d x + c\right)^{6} - 3 \, a^{3} \cos\left(d x + c\right)^{4} + 3 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 70 \, {\left(48 \, a^{3} d x \cos\left(d x + c\right)^{6} - 16 \, a^{3} \cos\left(d x + c\right)^{7} - 144 \, a^{3} d x \cos\left(d x + c\right)^{4} + 33 \, a^{3} \cos\left(d x + c\right)^{5} + 144 \, a^{3} d x \cos\left(d x + c\right)^{2} - 40 \, a^{3} \cos\left(d x + c\right)^{3} - 48 \, a^{3} d x + 15 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1120 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/1120*(4992*a^3*cos(d*x + c)^7 - 12992*a^3*cos(d*x + c)^5 + 11200*a^3*cos(d*x + c)^3 - 3360*a^3*cos(d*x + c) + 525*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 525*(a^3*cos(d*x + c)^6 - 3*a^3*cos(d*x + c)^4 + 3*a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 70*(48*a^3*d*x*cos(d*x + c)^6 - 16*a^3*cos(d*x + c)^7 - 144*a^3*d*x*cos(d*x + c)^4 + 33*a^3*cos(d*x + c)^5 + 144*a^3*d*x*cos(d*x + c)^2 - 40*a^3*cos(d*x + c)^3 - 48*a^3*d*x + 15*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
617,1,362,0,1.031189," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{26880 \, a^{3} d x \cos\left(d x + c\right)^{8} - 107520 \, a^{3} d x \cos\left(d x + c\right)^{6} - 54390 \, a^{3} \cos\left(d x + c\right)^{7} + 161280 \, a^{3} d x \cos\left(d x + c\right)^{4} + 127750 \, a^{3} \cos\left(d x + c\right)^{5} - 107520 \, a^{3} d x \cos\left(d x + c\right)^{2} - 96250 \, a^{3} \cos\left(d x + c\right)^{3} + 26880 \, a^{3} d x + 26250 \, a^{3} \cos\left(d x + c\right) - 13125 \, {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 13125 \, {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 256 \, {\left(116 \, a^{3} \cos\left(d x + c\right)^{7} - 406 \, a^{3} \cos\left(d x + c\right)^{5} + 350 \, a^{3} \cos\left(d x + c\right)^{3} - 105 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{26880 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/26880*(26880*a^3*d*x*cos(d*x + c)^8 - 107520*a^3*d*x*cos(d*x + c)^6 - 54390*a^3*cos(d*x + c)^7 + 161280*a^3*d*x*cos(d*x + c)^4 + 127750*a^3*cos(d*x + c)^5 - 107520*a^3*d*x*cos(d*x + c)^2 - 96250*a^3*cos(d*x + c)^3 + 26880*a^3*d*x + 26250*a^3*cos(d*x + c) - 13125*(a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 - 4*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2) + 13125*(a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 - 4*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2) - 256*(116*a^3*cos(d*x + c)^7 - 406*a^3*cos(d*x + c)^5 + 350*a^3*cos(d*x + c)^3 - 105*a^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
618,1,291,0,1.205730," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{7424 \, a^{3} \cos\left(d x + c\right)^{9} - 9216 \, a^{3} \cos\left(d x + c\right)^{7} + 3465 \, {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3465 \, {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + 6 \, a^{3} \cos\left(d x + c\right)^{4} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 42 \, {\left(219 \, a^{3} \cos\left(d x + c\right)^{7} - 803 \, a^{3} \cos\left(d x + c\right)^{5} + 605 \, a^{3} \cos\left(d x + c\right)^{3} - 165 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16128 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/16128*(7424*a^3*cos(d*x + c)^9 - 9216*a^3*cos(d*x + c)^7 + 3465*(a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 - 4*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3465*(a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + 6*a^3*cos(d*x + c)^4 - 4*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 42*(219*a^3*cos(d*x + c)^7 - 803*a^3*cos(d*x + c)^5 + 605*a^3*cos(d*x + c)^3 - 165*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
619,1,327,0,1.086121," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6930 \, a^{3} \cos\left(d x + c\right)^{9} + 21420 \, a^{3} \cos\left(d x + c\right)^{7} - 59136 \, a^{3} \cos\left(d x + c\right)^{5} + 32340 \, a^{3} \cos\left(d x + c\right)^{3} - 6930 \, a^{3} \cos\left(d x + c\right) - 3465 \, {\left(a^{3} \cos\left(d x + c\right)^{10} - 5 \, a^{3} \cos\left(d x + c\right)^{8} + 10 \, a^{3} \cos\left(d x + c\right)^{6} - 10 \, a^{3} \cos\left(d x + c\right)^{4} + 5 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3465 \, {\left(a^{3} \cos\left(d x + c\right)^{10} - 5 \, a^{3} \cos\left(d x + c\right)^{8} + 10 \, a^{3} \cos\left(d x + c\right)^{6} - 10 \, a^{3} \cos\left(d x + c\right)^{4} + 5 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2560 \, {\left(5 \, a^{3} \cos\left(d x + c\right)^{9} - 12 \, a^{3} \cos\left(d x + c\right)^{7}\right)} \sin\left(d x + c\right)}{53760 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/53760*(6930*a^3*cos(d*x + c)^9 + 21420*a^3*cos(d*x + c)^7 - 59136*a^3*cos(d*x + c)^5 + 32340*a^3*cos(d*x + c)^3 - 6930*a^3*cos(d*x + c) - 3465*(a^3*cos(d*x + c)^10 - 5*a^3*cos(d*x + c)^8 + 10*a^3*cos(d*x + c)^6 - 10*a^3*cos(d*x + c)^4 + 5*a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2) + 3465*(a^3*cos(d*x + c)^10 - 5*a^3*cos(d*x + c)^8 + 10*a^3*cos(d*x + c)^6 - 10*a^3*cos(d*x + c)^4 + 5*a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2) + 2560*(5*a^3*cos(d*x + c)^9 - 12*a^3*cos(d*x + c)^7)*sin(d*x + c))/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","A",0
620,1,360,0,1.218742," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{189440 \, a^{3} \cos\left(d x + c\right)^{11} - 1041920 \, a^{3} \cos\left(d x + c\right)^{9} + 1013760 \, a^{3} \cos\left(d x + c\right)^{7} + 65835 \, {\left(a^{3} \cos\left(d x + c\right)^{10} - 5 \, a^{3} \cos\left(d x + c\right)^{8} + 10 \, a^{3} \cos\left(d x + c\right)^{6} - 10 \, a^{3} \cos\left(d x + c\right)^{4} + 5 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 65835 \, {\left(a^{3} \cos\left(d x + c\right)^{10} - 5 \, a^{3} \cos\left(d x + c\right)^{8} + 10 \, a^{3} \cos\left(d x + c\right)^{6} - 10 \, a^{3} \cos\left(d x + c\right)^{4} + 5 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 462 \, {\left(285 \, a^{3} \cos\left(d x + c\right)^{9} - 50 \, a^{3} \cos\left(d x + c\right)^{7} - 2432 \, a^{3} \cos\left(d x + c\right)^{5} + 1330 \, a^{3} \cos\left(d x + c\right)^{3} - 285 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1774080 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/1774080*(189440*a^3*cos(d*x + c)^11 - 1041920*a^3*cos(d*x + c)^9 + 1013760*a^3*cos(d*x + c)^7 + 65835*(a^3*cos(d*x + c)^10 - 5*a^3*cos(d*x + c)^8 + 10*a^3*cos(d*x + c)^6 - 10*a^3*cos(d*x + c)^4 + 5*a^3*cos(d*x + c)^2 - a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 65835*(a^3*cos(d*x + c)^10 - 5*a^3*cos(d*x + c)^8 + 10*a^3*cos(d*x + c)^6 - 10*a^3*cos(d*x + c)^4 + 5*a^3*cos(d*x + c)^2 - a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 462*(285*a^3*cos(d*x + c)^9 - 50*a^3*cos(d*x + c)^7 - 2432*a^3*cos(d*x + c)^5 + 1330*a^3*cos(d*x + c)^3 - 285*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
621,1,384,0,1.180973," ","integrate(cos(d*x+c)^6*csc(d*x+c)^13*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{284130 \, a^{3} \cos\left(d x + c\right)^{11} - 1610070 \, a^{3} \cos\left(d x + c\right)^{9} - 507276 \, a^{3} \cos\left(d x + c\right)^{7} + 3750516 \, a^{3} \cos\left(d x + c\right)^{5} - 1610070 \, a^{3} \cos\left(d x + c\right)^{3} + 284130 \, a^{3} \cos\left(d x + c\right) - 142065 \, {\left(a^{3} \cos\left(d x + c\right)^{12} - 6 \, a^{3} \cos\left(d x + c\right)^{10} + 15 \, a^{3} \cos\left(d x + c\right)^{8} - 20 \, a^{3} \cos\left(d x + c\right)^{6} + 15 \, a^{3} \cos\left(d x + c\right)^{4} - 6 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 142065 \, {\left(a^{3} \cos\left(d x + c\right)^{12} - 6 \, a^{3} \cos\left(d x + c\right)^{10} + 15 \, a^{3} \cos\left(d x + c\right)^{8} - 20 \, a^{3} \cos\left(d x + c\right)^{6} + 15 \, a^{3} \cos\left(d x + c\right)^{4} - 6 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 10240 \, {\left(46 \, a^{3} \cos\left(d x + c\right)^{11} - 253 \, a^{3} \cos\left(d x + c\right)^{9} + 396 \, a^{3} \cos\left(d x + c\right)^{7}\right)} \sin\left(d x + c\right)}{7096320 \, {\left(d \cos\left(d x + c\right)^{12} - 6 \, d \cos\left(d x + c\right)^{10} + 15 \, d \cos\left(d x + c\right)^{8} - 20 \, d \cos\left(d x + c\right)^{6} + 15 \, d \cos\left(d x + c\right)^{4} - 6 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/7096320*(284130*a^3*cos(d*x + c)^11 - 1610070*a^3*cos(d*x + c)^9 - 507276*a^3*cos(d*x + c)^7 + 3750516*a^3*cos(d*x + c)^5 - 1610070*a^3*cos(d*x + c)^3 + 284130*a^3*cos(d*x + c) - 142065*(a^3*cos(d*x + c)^12 - 6*a^3*cos(d*x + c)^10 + 15*a^3*cos(d*x + c)^8 - 20*a^3*cos(d*x + c)^6 + 15*a^3*cos(d*x + c)^4 - 6*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2) + 142065*(a^3*cos(d*x + c)^12 - 6*a^3*cos(d*x + c)^10 + 15*a^3*cos(d*x + c)^8 - 20*a^3*cos(d*x + c)^6 + 15*a^3*cos(d*x + c)^4 - 6*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2) + 10240*(46*a^3*cos(d*x + c)^11 - 253*a^3*cos(d*x + c)^9 + 396*a^3*cos(d*x + c)^7)*sin(d*x + c))/(d*cos(d*x + c)^12 - 6*d*cos(d*x + c)^10 + 15*d*cos(d*x + c)^8 - 20*d*cos(d*x + c)^6 + 15*d*cos(d*x + c)^4 - 6*d*cos(d*x + c)^2 + d)","A",0
622,1,417,0,1.365556," ","integrate(cos(d*x+c)^6*csc(d*x+c)^14*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{409600 \, a^{3} \cos\left(d x + c\right)^{13} - 2662400 \, a^{3} \cos\left(d x + c\right)^{11} + 7321600 \, a^{3} \cos\left(d x + c\right)^{9} - 5857280 \, a^{3} \cos\left(d x + c\right)^{7} + 135135 \, {\left(a^{3} \cos\left(d x + c\right)^{12} - 6 \, a^{3} \cos\left(d x + c\right)^{10} + 15 \, a^{3} \cos\left(d x + c\right)^{8} - 20 \, a^{3} \cos\left(d x + c\right)^{6} + 15 \, a^{3} \cos\left(d x + c\right)^{4} - 6 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 135135 \, {\left(a^{3} \cos\left(d x + c\right)^{12} - 6 \, a^{3} \cos\left(d x + c\right)^{10} + 15 \, a^{3} \cos\left(d x + c\right)^{8} - 20 \, a^{3} \cos\left(d x + c\right)^{6} + 15 \, a^{3} \cos\left(d x + c\right)^{4} - 6 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2002 \, {\left(135 \, a^{3} \cos\left(d x + c\right)^{11} - 765 \, a^{3} \cos\left(d x + c\right)^{9} + 758 \, a^{3} \cos\left(d x + c\right)^{7} + 1782 \, a^{3} \cos\left(d x + c\right)^{5} - 765 \, a^{3} \cos\left(d x + c\right)^{3} + 135 \, a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{10250240 \, {\left(d \cos\left(d x + c\right)^{12} - 6 \, d \cos\left(d x + c\right)^{10} + 15 \, d \cos\left(d x + c\right)^{8} - 20 \, d \cos\left(d x + c\right)^{6} + 15 \, d \cos\left(d x + c\right)^{4} - 6 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/10250240*(409600*a^3*cos(d*x + c)^13 - 2662400*a^3*cos(d*x + c)^11 + 7321600*a^3*cos(d*x + c)^9 - 5857280*a^3*cos(d*x + c)^7 + 135135*(a^3*cos(d*x + c)^12 - 6*a^3*cos(d*x + c)^10 + 15*a^3*cos(d*x + c)^8 - 20*a^3*cos(d*x + c)^6 + 15*a^3*cos(d*x + c)^4 - 6*a^3*cos(d*x + c)^2 + a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 135135*(a^3*cos(d*x + c)^12 - 6*a^3*cos(d*x + c)^10 + 15*a^3*cos(d*x + c)^8 - 20*a^3*cos(d*x + c)^6 + 15*a^3*cos(d*x + c)^4 - 6*a^3*cos(d*x + c)^2 + a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2002*(135*a^3*cos(d*x + c)^11 - 765*a^3*cos(d*x + c)^9 + 758*a^3*cos(d*x + c)^7 + 1782*a^3*cos(d*x + c)^5 - 765*a^3*cos(d*x + c)^3 + 135*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^12 - 6*d*cos(d*x + c)^10 + 15*d*cos(d*x + c)^8 - 20*d*cos(d*x + c)^6 + 15*d*cos(d*x + c)^4 - 6*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
623,1,245,0,1.133207," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{40 \, a^{4} \cos\left(d x + c\right)^{9} - 390 \, a^{4} \cos\left(d x + c\right)^{7} - 405 \, a^{4} \cos\left(d x + c\right)^{5} + 2700 \, a^{4} \cos\left(d x + c\right)^{3} - 2025 \, a^{4} \cos\left(d x + c\right) - 720 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - a^{4}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 720 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - a^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(64 \, a^{4} \cos\left(d x + c\right)^{7} - 64 \, a^{4} \cos\left(d x + c\right)^{5} - 675 \, a^{4} d x \cos\left(d x + c\right)^{2} - 320 \, a^{4} \cos\left(d x + c\right)^{3} + 675 \, a^{4} d x + 480 \, a^{4} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/240*(40*a^4*cos(d*x + c)^9 - 390*a^4*cos(d*x + c)^7 - 405*a^4*cos(d*x + c)^5 + 2700*a^4*cos(d*x + c)^3 - 2025*a^4*cos(d*x + c) - 720*(a^4*cos(d*x + c)^2 - a^4)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 720*(a^4*cos(d*x + c)^2 - a^4)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(64*a^4*cos(d*x + c)^7 - 64*a^4*cos(d*x + c)^5 - 675*a^4*d*x*cos(d*x + c)^2 - 320*a^4*cos(d*x + c)^3 + 675*a^4*d*x + 480*a^4*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
624,1,90,0,1.106299," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4480 \, \cos\left(d x + c\right)^{9} - 11520 \, \cos\left(d x + c\right)^{7} + 8064 \, \cos\left(d x + c\right)^{5} + 945 \, d x + 315 \, {\left(16 \, \cos\left(d x + c\right)^{7} - 24 \, \cos\left(d x + c\right)^{5} + 2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40320 \, a d}"," ",0,"1/40320*(4480*cos(d*x + c)^9 - 11520*cos(d*x + c)^7 + 8064*cos(d*x + c)^5 + 945*d*x + 315*(16*cos(d*x + c)^7 - 24*cos(d*x + c)^5 + 2*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
625,1,80,0,1.007429," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{640 \, \cos\left(d x + c\right)^{7} - 896 \, \cos\left(d x + c\right)^{5} - 105 \, d x - 35 \, {\left(16 \, \cos\left(d x + c\right)^{7} - 24 \, \cos\left(d x + c\right)^{5} + 2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4480 \, a d}"," ",0,"1/4480*(640*cos(d*x + c)^7 - 896*cos(d*x + c)^5 - 105*d*x - 35*(16*cos(d*x + c)^7 - 24*cos(d*x + c)^5 + 2*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
626,1,70,0,1.029769," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{240 \, \cos\left(d x + c\right)^{7} - 336 \, \cos\left(d x + c\right)^{5} - 105 \, d x + 35 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, a d}"," ",0,"-1/1680*(240*cos(d*x + c)^7 - 336*cos(d*x + c)^5 - 105*d*x + 35*(8*cos(d*x + c)^5 - 2*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
627,1,60,0,2.136133," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{48 \, \cos\left(d x + c\right)^{5} + 15 \, d x - 5 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, a d}"," ",0,"-1/240*(48*cos(d*x + c)^5 + 15*d*x - 5*(8*cos(d*x + c)^5 - 2*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
628,1,84,0,1.230303," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{3} - 9 \, d x - 3 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 24 \, \cos\left(d x + c\right) - 12 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{24 \, a d}"," ",0,"1/24*(8*cos(d*x + c)^3 - 9*d*x - 3*(2*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c) + 24*cos(d*x + c) - 12*log(1/2*cos(d*x + c) + 1/2) + 12*log(-1/2*cos(d*x + c) + 1/2))/(a*d)","A",0
629,1,104,0,0.976611," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{3} - {\left(2 \, \cos\left(d x + c\right)^{3} + 9 \, d x + 6 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 3 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, \cos\left(d x + c\right)}{6 \, a d \sin\left(d x + c\right)}"," ",0,"1/6*(3*cos(d*x + c)^3 - (2*cos(d*x + c)^3 + 9*d*x + 6*cos(d*x + c))*sin(d*x + c) + 3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*cos(d*x + c))/(a*d*sin(d*x + c))","A",0
630,1,126,0,1.443440," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, d x \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right)^{3} - 6 \, d x + 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 6 \, \cos\left(d x + c\right)}{4 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"1/4*(6*d*x*cos(d*x + c)^2 - 4*cos(d*x + c)^3 - 6*d*x + 3*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) - 3*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) + 2*(cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c) + 6*cos(d*x + c))/(a*d*cos(d*x + c)^2 - a*d)","A",0
631,1,148,0,0.850387," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, \cos\left(d x + c\right)^{3} - 9 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 9 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, {\left(2 \, d x \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)^{3} - 2 \, d x - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 12 \, \cos\left(d x + c\right)}{12 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(16*cos(d*x + c)^3 - 9*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 9*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*(2*d*x*cos(d*x + c)^2 + 2*cos(d*x + c)^3 - 2*d*x - 3*cos(d*x + c))*sin(d*x + c) - 12*cos(d*x + c))/((a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
632,1,171,0,0.841145," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{48 \, d x \cos\left(d x + c\right)^{4} - 96 \, d x \cos\left(d x + c\right)^{2} + 30 \, \cos\left(d x + c\right)^{3} + 48 \, d x + 9 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 9 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(4 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 18 \, \cos\left(d x + c\right)}{48 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"-1/48*(48*d*x*cos(d*x + c)^4 - 96*d*x*cos(d*x + c)^2 + 30*cos(d*x + c)^3 + 48*d*x + 9*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) - 9*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 16*(4*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c) - 18*cos(d*x + c))/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)","A",0
633,1,155,0,0.717441," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, \cos\left(d x + c\right)^{5} - 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 10 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/80*(16*cos(d*x + c)^5 - 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 10*(5*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c))/((a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","B",0
634,1,80,0,0.973873," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{120 \, \cos\left(d x + c\right)^{7} - 504 \, \cos\left(d x + c\right)^{5} + 560 \, \cos\left(d x + c\right)^{3} + 105 \, d x + 35 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 14 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, a^{2} d}"," ",0,"-1/840*(120*cos(d*x + c)^7 - 504*cos(d*x + c)^5 + 560*cos(d*x + c)^3 + 105*d*x + 35*(8*cos(d*x + c)^5 - 14*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
635,1,70,0,1.207571," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{96 \, \cos\left(d x + c\right)^{5} - 160 \, \cos\left(d x + c\right)^{3} - 45 \, d x - 5 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 26 \, \cos\left(d x + c\right)^{3} + 9 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, a^{2} d}"," ",0,"-1/240*(96*cos(d*x + c)^5 - 160*cos(d*x + c)^3 - 45*d*x - 5*(8*cos(d*x + c)^5 - 26*cos(d*x + c)^3 + 9*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
636,1,60,0,1.108367," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{12 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{3} - 15 \, d x + 15 \, {\left(2 \, \cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, a^{2} d}"," ",0,"1/60*(12*cos(d*x + c)^5 - 40*cos(d*x + c)^3 - 15*d*x + 15*(2*cos(d*x + c)^3 - cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
637,1,71,0,1.330170," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{3} + 6 \, d x + 6 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, \cos\left(d x + c\right) + 3 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{6 \, a^{2} d}"," ",0,"-1/6*(2*cos(d*x + c)^3 + 6*d*x + 6*cos(d*x + c)*sin(d*x + c) - 6*cos(d*x + c) + 3*log(1/2*cos(d*x + c) + 1/2) - 3*log(-1/2*cos(d*x + c) + 1/2))/(a^2*d)","A",0
638,1,88,0,1.362593," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{3} + {\left(d x + 4 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 2 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + \cos\left(d x + c\right)}{2 \, a^{2} d \sin\left(d x + c\right)}"," ",0,"-1/2*(cos(d*x + c)^3 + (d*x + 4*cos(d*x + c))*sin(d*x + c) - 2*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + cos(d*x + c))/(a^2*d*sin(d*x + c))","A",0
639,1,118,0,1.366217," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{8 \, d x \cos\left(d x + c\right)^{2} + 4 \, \cos\left(d x + c\right)^{3} - 8 \, d x - {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 8 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)}{4 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"1/4*(8*d*x*cos(d*x + c)^2 + 4*cos(d*x + c)^3 - 8*d*x - (cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + (cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 8*cos(d*x + c)*sin(d*x + c) - 2*cos(d*x + c))/(a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
640,1,139,0,1.079084," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(d x + c\right)^{3} + 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, {\left(d x \cos\left(d x + c\right)^{2} - d x + \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 6 \, \cos\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(4*cos(d*x + c)^3 + 3*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*(d*x*cos(d*x + c)^2 - d*x + cos(d*x + c))*sin(d*x + c) - 6*cos(d*x + c))/((a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","A",0
641,1,138,0,0.911336," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{32 \, \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + 18 \, \cos\left(d x + c\right)^{3} + 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 30 \, \cos\left(d x + c\right)}{48 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)}}"," ",0,"1/48*(32*cos(d*x + c)^3*sin(d*x + c) + 18*cos(d*x + c)^3 + 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) - 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 30*cos(d*x + c))/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)","A",0
642,1,167,0,0.752600," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{56 \, \cos\left(d x + c\right)^{5} - 80 \, \cos\left(d x + c\right)^{3} - 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"1/120*(56*cos(d*x + c)^5 - 80*cos(d*x + c)^3 - 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*(cos(d*x + c)^3 + cos(d*x + c))*sin(d*x + c))/((a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)*sin(d*x + c))","A",0
643,1,196,0,1.124587," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{90 \, \cos\left(d x + c\right)^{5} - 80 \, \cos\left(d x + c\right)^{3} - 45 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 45 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 64 \, {\left(2 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right) - 90 \, \cos\left(d x + c\right)}{480 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 3 \, a^{2} d \cos\left(d x + c\right)^{4} + 3 \, a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"-1/480*(90*cos(d*x + c)^5 - 80*cos(d*x + c)^3 - 45*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + 45*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 64*(2*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*sin(d*x + c) - 90*cos(d*x + c))/(a^2*d*cos(d*x + c)^6 - 3*a^2*d*cos(d*x + c)^4 + 3*a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
644,1,78,0,0.933060," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{144 \, \cos\left(d x + c\right)^{5} - 560 \, \cos\left(d x + c\right)^{3} + 345 \, d x - 5 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 62 \, \cos\left(d x + c\right)^{3} + 123 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 960 \, \cos\left(d x + c\right)}{240 \, a^{3} d}"," ",0,"-1/240*(144*cos(d*x + c)^5 - 560*cos(d*x + c)^3 + 345*d*x - 5*(8*cos(d*x + c)^5 - 62*cos(d*x + c)^3 + 123*cos(d*x + c))*sin(d*x + c) + 960*cos(d*x + c))/(a^3*d)","A",0
645,1,68,0,0.807436," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{24 \, \cos\left(d x + c\right)^{5} - 200 \, \cos\left(d x + c\right)^{3} + 195 \, d x + 15 \, {\left(6 \, \cos\left(d x + c\right)^{3} - 19 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 480 \, \cos\left(d x + c\right)}{120 \, a^{3} d}"," ",0,"1/120*(24*cos(d*x + c)^5 - 200*cos(d*x + c)^3 + 195*d*x + 15*(6*cos(d*x + c)^3 - 19*cos(d*x + c))*sin(d*x + c) + 480*cos(d*x + c))/(a^3*d)","A",0
646,1,58,0,1.232402," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{3} - 15 \, d x - {\left(2 \, \cos\left(d x + c\right)^{3} - 17 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 32 \, \cos\left(d x + c\right)}{8 \, a^{3} d}"," ",0,"1/8*(8*cos(d*x + c)^3 - 15*d*x - (2*cos(d*x + c)^3 - 17*cos(d*x + c))*sin(d*x + c) - 32*cos(d*x + c))/(a^3*d)","A",0
647,1,59,0,0.869647," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{7 \, d x - \cos\left(d x + c\right) \sin\left(d x + c\right) + 6 \, \cos\left(d x + c\right) + \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, a^{3} d}"," ",0,"-1/2*(7*d*x - cos(d*x + c)*sin(d*x + c) + 6*cos(d*x + c) + log(1/2*cos(d*x + c) + 1/2) - log(-1/2*cos(d*x + c) + 1/2))/(a^3*d)","A",0
648,1,82,0,0.645690," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, d x + \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 3 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)}{2 \, a^{3} d \sin\left(d x + c\right)}"," ",0,"1/2*(2*(3*d*x + cos(d*x + c))*sin(d*x + c) + 3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*cos(d*x + c))/(a^3*d*sin(d*x + c))","A",0
649,1,109,0,0.972832," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4 \, d x \cos\left(d x + c\right)^{2} - 4 \, d x + 7 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 7 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}"," ",0,"-1/4*(4*d*x*cos(d*x + c)^2 - 4*d*x + 7*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) - 7*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) + 12*cos(d*x + c)*sin(d*x + c) - 2*cos(d*x + c))/(a^3*d*cos(d*x + c)^2 - a^3*d)","A",0
650,1,123,0,1.412122," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{44 \, \cos\left(d x + c\right)^{3} - 15 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 18 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 48 \, \cos\left(d x + c\right)}{12 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(44*cos(d*x + c)^3 - 15*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 18*cos(d*x + c)*sin(d*x + c) - 48*cos(d*x + c))/((a^3*d*cos(d*x + c)^2 - a^3*d)*sin(d*x + c))","A",0
651,1,149,0,0.948144," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{3} - 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(3 \, \cos\left(d x + c\right)^{3} - 4 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 34 \, \cos\left(d x + c\right)}{16 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)}}"," ",0,"1/16*(30*cos(d*x + c)^3 - 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) + 15*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 16*(3*cos(d*x + c)^3 - 4*cos(d*x + c))*sin(d*x + c) - 34*cos(d*x + c))/(a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d)","A",0
652,1,179,0,0.959251," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{608 \, \cos\left(d x + c\right)^{5} - 1520 \, \cos\left(d x + c\right)^{3} - 195 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 195 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, {\left(13 \, \cos\left(d x + c\right)^{3} - 19 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 960 \, \cos\left(d x + c\right)}{240 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/240*(608*cos(d*x + c)^5 - 1520*cos(d*x + c)^3 - 195*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 195*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*(13*cos(d*x + c)^3 - 19*cos(d*x + c))*sin(d*x + c) + 960*cos(d*x + c))/((a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d)*sin(d*x + c))","A",0
653,0,0,0,0.987051," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6} + {\left(a^{3} \cos\left(d x + c\right)^{8} - 4 \, a^{3} \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-(3*a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6 + (a^3*cos(d*x + c)^8 - 4*a^3*cos(d*x + c)^6)*sin(d*x + c))*sin(d*x + c)^n, x)","F",0
654,0,0,0,0.949102," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(d x + c\right)^{8} - 2 \, a^{2} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - 2 \, a^{2} \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-(a^2*cos(d*x + c)^8 - 2*a^2*cos(d*x + c)^6*sin(d*x + c) - 2*a^2*cos(d*x + c)^6)*sin(d*x + c)^n, x)","F",0
655,0,0,0,0.648157," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral((a*cos(d*x + c)^6*sin(d*x + c) + a*cos(d*x + c)^6)*sin(d*x + c)^n, x)","F",0
656,1,128,0,1.017771," ","integrate(cos(d*x+c)^7*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8580 \, a \cos\left(d x + c\right)^{14} - 30030 \, a \cos\left(d x + c\right)^{12} + 36036 \, a \cos\left(d x + c\right)^{10} - 15015 \, a \cos\left(d x + c\right)^{8} - 40 \, {\left(231 \, a \cos\left(d x + c\right)^{12} - 567 \, a \cos\left(d x + c\right)^{10} + 371 \, a \cos\left(d x + c\right)^{8} - 5 \, a \cos\left(d x + c\right)^{6} - 6 \, a \cos\left(d x + c\right)^{4} - 8 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right)}{120120 \, d}"," ",0,"1/120120*(8580*a*cos(d*x + c)^14 - 30030*a*cos(d*x + c)^12 + 36036*a*cos(d*x + c)^10 - 15015*a*cos(d*x + c)^8 - 40*(231*a*cos(d*x + c)^12 - 567*a*cos(d*x + c)^10 + 371*a*cos(d*x + c)^8 - 5*a*cos(d*x + c)^6 - 6*a*cos(d*x + c)^4 - 8*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c))/d","A",0
657,1,117,0,1.234154," ","integrate(cos(d*x+c)^7*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{10010 \, a \cos\left(d x + c\right)^{12} - 24024 \, a \cos\left(d x + c\right)^{10} + 15015 \, a \cos\left(d x + c\right)^{8} + 40 \, {\left(231 \, a \cos\left(d x + c\right)^{12} - 567 \, a \cos\left(d x + c\right)^{10} + 371 \, a \cos\left(d x + c\right)^{8} - 5 \, a \cos\left(d x + c\right)^{6} - 6 \, a \cos\left(d x + c\right)^{4} - 8 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right)}{120120 \, d}"," ",0,"-1/120120*(10010*a*cos(d*x + c)^12 - 24024*a*cos(d*x + c)^10 + 15015*a*cos(d*x + c)^8 + 40*(231*a*cos(d*x + c)^12 - 567*a*cos(d*x + c)^10 + 371*a*cos(d*x + c)^8 - 5*a*cos(d*x + c)^6 - 6*a*cos(d*x + c)^4 - 8*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c))/d","A",0
658,1,106,0,1.245711," ","integrate(cos(d*x+c)^7*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{770 \, a \cos\left(d x + c\right)^{12} - 1848 \, a \cos\left(d x + c\right)^{10} + 1155 \, a \cos\left(d x + c\right)^{8} - 8 \, {\left(105 \, a \cos\left(d x + c\right)^{10} - 140 \, a \cos\left(d x + c\right)^{8} + 5 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} + 8 \, a \cos\left(d x + c\right)^{2} + 16 \, a\right)} \sin\left(d x + c\right)}{9240 \, d}"," ",0,"-1/9240*(770*a*cos(d*x + c)^12 - 1848*a*cos(d*x + c)^10 + 1155*a*cos(d*x + c)^8 - 8*(105*a*cos(d*x + c)^10 - 140*a*cos(d*x + c)^8 + 5*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 + 8*a*cos(d*x + c)^2 + 16*a)*sin(d*x + c))/d","A",0
659,1,95,0,0.814067," ","integrate(cos(d*x+c)^7*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{924 \, a \cos\left(d x + c\right)^{10} - 1155 \, a \cos\left(d x + c\right)^{8} + 8 \, {\left(105 \, a \cos\left(d x + c\right)^{10} - 140 \, a \cos\left(d x + c\right)^{8} + 5 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} + 8 \, a \cos\left(d x + c\right)^{2} + 16 \, a\right)} \sin\left(d x + c\right)}{9240 \, d}"," ",0,"1/9240*(924*a*cos(d*x + c)^10 - 1155*a*cos(d*x + c)^8 + 8*(105*a*cos(d*x + c)^10 - 140*a*cos(d*x + c)^8 + 5*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 + 8*a*cos(d*x + c)^2 + 16*a)*sin(d*x + c))/d","A",0
660,1,84,0,1.104857," ","integrate(cos(d*x+c)^7*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{252 \, a \cos\left(d x + c\right)^{10} - 315 \, a \cos\left(d x + c\right)^{8} - 8 \, {\left(35 \, a \cos\left(d x + c\right)^{8} - 5 \, a \cos\left(d x + c\right)^{6} - 6 \, a \cos\left(d x + c\right)^{4} - 8 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right)}{2520 \, d}"," ",0,"1/2520*(252*a*cos(d*x + c)^10 - 315*a*cos(d*x + c)^8 - 8*(35*a*cos(d*x + c)^8 - 5*a*cos(d*x + c)^6 - 6*a*cos(d*x + c)^4 - 8*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c))/d","A",0
661,1,73,0,0.931836," ","integrate(cos(d*x+c)^7*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{315 \, a \cos\left(d x + c\right)^{8} + 8 \, {\left(35 \, a \cos\left(d x + c\right)^{8} - 5 \, a \cos\left(d x + c\right)^{6} - 6 \, a \cos\left(d x + c\right)^{4} - 8 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right)}{2520 \, d}"," ",0,"-1/2520*(315*a*cos(d*x + c)^8 + 8*(35*a*cos(d*x + c)^8 - 5*a*cos(d*x + c)^6 - 6*a*cos(d*x + c)^4 - 8*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c))/d","A",0
662,1,96,0,0.905959," ","integrate(cos(d*x+c)^7*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{70 \, a \cos\left(d x + c\right)^{6} + 105 \, a \cos\left(d x + c\right)^{4} + 210 \, a \cos\left(d x + c\right)^{2} + 420 \, a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 12 \, {\left(5 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} + 8 \, a \cos\left(d x + c\right)^{2} + 16 \, a\right)} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(70*a*cos(d*x + c)^6 + 105*a*cos(d*x + c)^4 + 210*a*cos(d*x + c)^2 + 420*a*log(1/2*sin(d*x + c)) + 12*(5*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 + 8*a*cos(d*x + c)^2 + 16*a)*sin(d*x + c))/d","A",0
663,1,113,0,0.687503," ","integrate(cos(d*x+c)^7*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, a \cos\left(d x + c\right)^{6} + 96 \, a \cos\left(d x + c\right)^{4} + 384 \, a \cos\left(d x + c\right)^{2} + 240 \, a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 5 \, {\left(8 \, a \cos\left(d x + c\right)^{6} + 12 \, a \cos\left(d x + c\right)^{4} + 24 \, a \cos\left(d x + c\right)^{2} - 19 \, a\right)} \sin\left(d x + c\right) - 768 \, a}{240 \, d \sin\left(d x + c\right)}"," ",0,"1/240*(48*a*cos(d*x + c)^6 + 96*a*cos(d*x + c)^4 + 384*a*cos(d*x + c)^2 + 240*a*log(1/2*sin(d*x + c))*sin(d*x + c) + 5*(8*a*cos(d*x + c)^6 + 12*a*cos(d*x + c)^4 + 24*a*cos(d*x + c)^2 - 19*a)*sin(d*x + c) - 768*a)/(d*sin(d*x + c))","A",0
664,1,124,0,0.720744," ","integrate(cos(d*x+c)^7*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{40 \, a \cos\left(d x + c\right)^{6} + 120 \, a \cos\left(d x + c\right)^{4} - 255 \, a \cos\left(d x + c\right)^{2} + 480 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 32 \, {\left(a \cos\left(d x + c\right)^{6} + 2 \, a \cos\left(d x + c\right)^{4} + 8 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right) + 15 \, a}{160 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/160*(40*a*cos(d*x + c)^6 + 120*a*cos(d*x + c)^4 - 255*a*cos(d*x + c)^2 + 480*(a*cos(d*x + c)^2 - a)*log(1/2*sin(d*x + c)) + 32*(a*cos(d*x + c)^6 + 2*a*cos(d*x + c)^4 + 8*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c) + 15*a)/(d*cos(d*x + c)^2 - d)","A",0
665,1,139,0,1.036441," ","integrate(cos(d*x+c)^7*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{32 \, a \cos\left(d x + c\right)^{6} + 192 \, a \cos\left(d x + c\right)^{4} - 768 \, a \cos\left(d x + c\right)^{2} + 288 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 3 \, {\left(8 \, a \cos\left(d x + c\right)^{6} + 24 \, a \cos\left(d x + c\right)^{4} - 51 \, a \cos\left(d x + c\right)^{2} + 3 \, a\right)} \sin\left(d x + c\right) + 512 \, a}{96 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/96*(32*a*cos(d*x + c)^6 + 192*a*cos(d*x + c)^4 - 768*a*cos(d*x + c)^2 + 288*(a*cos(d*x + c)^2 - a)*log(1/2*sin(d*x + c))*sin(d*x + c) + 3*(8*a*cos(d*x + c)^6 + 24*a*cos(d*x + c)^4 - 51*a*cos(d*x + c)^2 + 3*a)*sin(d*x + c) + 512*a)/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
666,1,142,0,1.035577," ","integrate(cos(d*x+c)^7*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, a \cos\left(d x + c\right)^{6} - 15 \, a \cos\left(d x + c\right)^{4} - 6 \, a \cos\left(d x + c\right)^{2} + 36 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, {\left(a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 24 \, a \cos\left(d x + c\right)^{2} + 16 \, a\right)} \sin\left(d x + c\right) + 12 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/12*(6*a*cos(d*x + c)^6 - 15*a*cos(d*x + c)^4 - 6*a*cos(d*x + c)^2 + 36*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*sin(d*x + c)) + 4*(a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 24*a*cos(d*x + c)^2 + 16*a)*sin(d*x + c) + 12*a)/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
667,1,157,0,1.327373," ","integrate(cos(d*x+c)^7*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{20 \, a \cos\left(d x + c\right)^{6} - 120 \, a \cos\left(d x + c\right)^{4} + 160 \, a \cos\left(d x + c\right)^{2} + 60 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 5 \, {\left(2 \, a \cos\left(d x + c\right)^{6} - 5 \, a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + 4 \, a\right)} \sin\left(d x + c\right) - 64 \, a}{20 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/20*(20*a*cos(d*x + c)^6 - 120*a*cos(d*x + c)^4 + 160*a*cos(d*x + c)^2 + 60*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*sin(d*x + c))*sin(d*x + c) + 5*(2*a*cos(d*x + c)^6 - 5*a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + 4*a)*sin(d*x + c) - 64*a)/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
668,1,158,0,1.199597," ","integrate(cos(d*x+c)^7*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{90 \, a \cos\left(d x + c\right)^{4} - 135 \, a \cos\left(d x + c\right)^{2} - 60 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 12 \, {\left(5 \, a \cos\left(d x + c\right)^{6} - 30 \, a \cos\left(d x + c\right)^{4} + 40 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right) + 55 \, a}{60 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/60*(90*a*cos(d*x + c)^4 - 135*a*cos(d*x + c)^2 - 60*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(1/2*sin(d*x + c)) - 12*(5*a*cos(d*x + c)^6 - 30*a*cos(d*x + c)^4 + 40*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c) + 55*a)/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
669,1,172,0,2.001109," ","integrate(cos(d*x+c)^7*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{420 \, a \cos\left(d x + c\right)^{6} - 840 \, a \cos\left(d x + c\right)^{4} + 672 \, a \cos\left(d x + c\right)^{2} - 420 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 35 \, {\left(18 \, a \cos\left(d x + c\right)^{4} - 27 \, a \cos\left(d x + c\right)^{2} + 11 \, a\right)} \sin\left(d x + c\right) - 192 \, a}{420 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/420*(420*a*cos(d*x + c)^6 - 840*a*cos(d*x + c)^4 + 672*a*cos(d*x + c)^2 - 420*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(1/2*sin(d*x + c))*sin(d*x + c) + 35*(18*a*cos(d*x + c)^4 - 27*a*cos(d*x + c)^2 + 11*a)*sin(d*x + c) - 192*a)/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
670,1,131,0,0.828636," ","integrate(cos(d*x+c)^7*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{140 \, a \cos\left(d x + c\right)^{6} - 210 \, a \cos\left(d x + c\right)^{4} + 140 \, a \cos\left(d x + c\right)^{2} + 8 \, {\left(35 \, a \cos\left(d x + c\right)^{6} - 70 \, a \cos\left(d x + c\right)^{4} + 56 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right) - 35 \, a}{280 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/280*(140*a*cos(d*x + c)^6 - 210*a*cos(d*x + c)^4 + 140*a*cos(d*x + c)^2 + 8*(35*a*cos(d*x + c)^6 - 70*a*cos(d*x + c)^4 + 56*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c) - 35*a)/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
671,1,139,0,0.785044," ","integrate(cos(d*x+c)^7*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{840 \, a \cos\left(d x + c\right)^{6} - 1008 \, a \cos\left(d x + c\right)^{4} + 576 \, a \cos\left(d x + c\right)^{2} + 315 \, {\left(4 \, a \cos\left(d x + c\right)^{6} - 6 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - 128 \, a}{2520 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/2520*(840*a*cos(d*x + c)^6 - 1008*a*cos(d*x + c)^4 + 576*a*cos(d*x + c)^2 + 315*(4*a*cos(d*x + c)^6 - 6*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 - a)*sin(d*x + c) - 128*a)/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
672,1,144,0,0.879346," ","integrate(cos(d*x+c)^7*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{630 \, a \cos\left(d x + c\right)^{6} - 630 \, a \cos\left(d x + c\right)^{4} + 315 \, a \cos\left(d x + c\right)^{2} + 8 \, {\left(105 \, a \cos\left(d x + c\right)^{6} - 126 \, a \cos\left(d x + c\right)^{4} + 72 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right) - 63 \, a}{2520 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/2520*(630*a*cos(d*x + c)^6 - 630*a*cos(d*x + c)^4 + 315*a*cos(d*x + c)^2 + 8*(105*a*cos(d*x + c)^6 - 126*a*cos(d*x + c)^4 + 72*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c) - 63*a)/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","A",0
673,1,152,0,0.998958," ","integrate(cos(d*x+c)^7*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{1848 \, a \cos\left(d x + c\right)^{6} - 1584 \, a \cos\left(d x + c\right)^{4} + 704 \, a \cos\left(d x + c\right)^{2} + 231 \, {\left(10 \, a \cos\left(d x + c\right)^{6} - 10 \, a \cos\left(d x + c\right)^{4} + 5 \, a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - 128 \, a}{9240 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/9240*(1848*a*cos(d*x + c)^6 - 1584*a*cos(d*x + c)^4 + 704*a*cos(d*x + c)^2 + 231*(10*a*cos(d*x + c)^6 - 10*a*cos(d*x + c)^4 + 5*a*cos(d*x + c)^2 - a)*sin(d*x + c) - 128*a)/((d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
674,1,153,0,0.897176," ","integrate(cos(d*x+c)^7*csc(d*x+c)^13*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{1540 \, a \cos\left(d x + c\right)^{6} - 1155 \, a \cos\left(d x + c\right)^{4} + 462 \, a \cos\left(d x + c\right)^{2} + 8 \, {\left(231 \, a \cos\left(d x + c\right)^{6} - 198 \, a \cos\left(d x + c\right)^{4} + 88 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right) - 77 \, a}{9240 \, {\left(d \cos\left(d x + c\right)^{12} - 6 \, d \cos\left(d x + c\right)^{10} + 15 \, d \cos\left(d x + c\right)^{8} - 20 \, d \cos\left(d x + c\right)^{6} + 15 \, d \cos\left(d x + c\right)^{4} - 6 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/9240*(1540*a*cos(d*x + c)^6 - 1155*a*cos(d*x + c)^4 + 462*a*cos(d*x + c)^2 + 8*(231*a*cos(d*x + c)^6 - 198*a*cos(d*x + c)^4 + 88*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c) - 77*a)/(d*cos(d*x + c)^12 - 6*d*cos(d*x + c)^10 + 15*d*cos(d*x + c)^8 - 20*d*cos(d*x + c)^6 + 15*d*cos(d*x + c)^4 - 6*d*cos(d*x + c)^2 + d)","A",0
675,1,161,0,1.017694," ","integrate(cos(d*x+c)^7*csc(d*x+c)^14*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{17160 \, a \cos\left(d x + c\right)^{6} - 11440 \, a \cos\left(d x + c\right)^{4} + 4160 \, a \cos\left(d x + c\right)^{2} + 1001 \, {\left(20 \, a \cos\left(d x + c\right)^{6} - 15 \, a \cos\left(d x + c\right)^{4} + 6 \, a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - 640 \, a}{120120 \, {\left(d \cos\left(d x + c\right)^{12} - 6 \, d \cos\left(d x + c\right)^{10} + 15 \, d \cos\left(d x + c\right)^{8} - 20 \, d \cos\left(d x + c\right)^{6} + 15 \, d \cos\left(d x + c\right)^{4} - 6 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/120120*(17160*a*cos(d*x + c)^6 - 11440*a*cos(d*x + c)^4 + 4160*a*cos(d*x + c)^2 + 1001*(20*a*cos(d*x + c)^6 - 15*a*cos(d*x + c)^4 + 6*a*cos(d*x + c)^2 - a)*sin(d*x + c) - 640*a)/((d*cos(d*x + c)^12 - 6*d*cos(d*x + c)^10 + 15*d*cos(d*x + c)^8 - 20*d*cos(d*x + c)^6 + 15*d*cos(d*x + c)^4 - 6*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
676,1,166,0,0.713656," ","integrate(cos(d*x+c)^7*csc(d*x+c)^15*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15015 \, a \cos\left(d x + c\right)^{6} - 9009 \, a \cos\left(d x + c\right)^{4} + 3003 \, a \cos\left(d x + c\right)^{2} + 40 \, {\left(429 \, a \cos\left(d x + c\right)^{6} - 286 \, a \cos\left(d x + c\right)^{4} + 104 \, a \cos\left(d x + c\right)^{2} - 16 \, a\right)} \sin\left(d x + c\right) - 429 \, a}{120120 \, {\left(d \cos\left(d x + c\right)^{14} - 7 \, d \cos\left(d x + c\right)^{12} + 21 \, d \cos\left(d x + c\right)^{10} - 35 \, d \cos\left(d x + c\right)^{8} + 35 \, d \cos\left(d x + c\right)^{6} - 21 \, d \cos\left(d x + c\right)^{4} + 7 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/120120*(15015*a*cos(d*x + c)^6 - 9009*a*cos(d*x + c)^4 + 3003*a*cos(d*x + c)^2 + 40*(429*a*cos(d*x + c)^6 - 286*a*cos(d*x + c)^4 + 104*a*cos(d*x + c)^2 - 16*a)*sin(d*x + c) - 429*a)/(d*cos(d*x + c)^14 - 7*d*cos(d*x + c)^12 + 21*d*cos(d*x + c)^10 - 35*d*cos(d*x + c)^8 + 35*d*cos(d*x + c)^6 - 21*d*cos(d*x + c)^4 + 7*d*cos(d*x + c)^2 - d)","A",0
677,1,109,0,1.013207," ","integrate(cos(d*x+c)^7*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2310 \, \cos\left(d x + c\right)^{12} - 8316 \, \cos\left(d x + c\right)^{10} + 10395 \, \cos\left(d x + c\right)^{8} - 4620 \, \cos\left(d x + c\right)^{6} + 40 \, {\left(63 \, \cos\left(d x + c\right)^{10} - 161 \, \cos\left(d x + c\right)^{8} + 113 \, \cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} - 8\right)} \sin\left(d x + c\right)}{27720 \, a d}"," ",0,"-1/27720*(2310*cos(d*x + c)^12 - 8316*cos(d*x + c)^10 + 10395*cos(d*x + c)^8 - 4620*cos(d*x + c)^6 + 40*(63*cos(d*x + c)^10 - 161*cos(d*x + c)^8 + 113*cos(d*x + c)^6 - 3*cos(d*x + c)^4 - 4*cos(d*x + c)^2 - 8)*sin(d*x + c))/(a*d)","A",0
678,1,99,0,0.780947," ","integrate(cos(d*x+c)^7*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{1386 \, \cos\left(d x + c\right)^{10} - 3465 \, \cos\left(d x + c\right)^{8} + 2310 \, \cos\left(d x + c\right)^{6} - 20 \, {\left(63 \, \cos\left(d x + c\right)^{10} - 161 \, \cos\left(d x + c\right)^{8} + 113 \, \cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} - 8\right)} \sin\left(d x + c\right)}{13860 \, a d}"," ",0,"-1/13860*(1386*cos(d*x + c)^10 - 3465*cos(d*x + c)^8 + 2310*cos(d*x + c)^6 - 20*(63*cos(d*x + c)^10 - 161*cos(d*x + c)^8 + 113*cos(d*x + c)^6 - 3*cos(d*x + c)^4 - 4*cos(d*x + c)^2 - 8)*sin(d*x + c))/(a*d)","A",0
679,1,89,0,0.861023," ","integrate(cos(d*x+c)^7*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{126 \, \cos\left(d x + c\right)^{10} - 315 \, \cos\left(d x + c\right)^{8} + 210 \, \cos\left(d x + c\right)^{6} + 4 \, {\left(35 \, \cos\left(d x + c\right)^{8} - 50 \, \cos\left(d x + c\right)^{6} + 3 \, \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right)}{1260 \, a d}"," ",0,"1/1260*(126*cos(d*x + c)^10 - 315*cos(d*x + c)^8 + 210*cos(d*x + c)^6 + 4*(35*cos(d*x + c)^8 - 50*cos(d*x + c)^6 + 3*cos(d*x + c)^4 + 4*cos(d*x + c)^2 + 8)*sin(d*x + c))/(a*d)","A",0
680,1,79,0,0.912754," ","integrate(cos(d*x+c)^7*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{315 \, \cos\left(d x + c\right)^{8} - 420 \, \cos\left(d x + c\right)^{6} - 8 \, {\left(35 \, \cos\left(d x + c\right)^{8} - 50 \, \cos\left(d x + c\right)^{6} + 3 \, \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right)}{2520 \, a d}"," ",0,"1/2520*(315*cos(d*x + c)^8 - 420*cos(d*x + c)^6 - 8*(35*cos(d*x + c)^8 - 50*cos(d*x + c)^6 + 3*cos(d*x + c)^4 + 4*cos(d*x + c)^2 + 8)*sin(d*x + c))/(a*d)","A",0
681,1,69,0,0.879524," ","integrate(cos(d*x+c)^7*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{105 \, \cos\left(d x + c\right)^{8} - 140 \, \cos\left(d x + c\right)^{6} + 8 \, {\left(15 \, \cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} - 8\right)} \sin\left(d x + c\right)}{840 \, a d}"," ",0,"-1/840*(105*cos(d*x + c)^8 - 140*cos(d*x + c)^6 + 8*(15*cos(d*x + c)^6 - 3*cos(d*x + c)^4 - 4*cos(d*x + c)^2 - 8)*sin(d*x + c))/(a*d)","A",0
682,1,59,0,0.901409," ","integrate(cos(d*x+c)^7*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{35 \, \cos\left(d x + c\right)^{6} - 2 \, {\left(15 \, \cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} - 8\right)} \sin\left(d x + c\right)}{210 \, a d}"," ",0,"-1/210*(35*cos(d*x + c)^6 - 2*(15*cos(d*x + c)^6 - 3*cos(d*x + c)^4 - 4*cos(d*x + c)^2 - 8)*sin(d*x + c))/(a*d)","A",0
683,1,49,0,0.889605," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{5 \, \cos\left(d x + c\right)^{6} + 2 \, {\left(3 \, \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right)}{30 \, a d}"," ",0,"1/30*(5*cos(d*x + c)^6 + 2*(3*cos(d*x + c)^4 + 4*cos(d*x + c)^2 + 8)*sin(d*x + c))/(a*d)","A",0
684,1,70,0,1.658346," ","integrate(cos(d*x+c)^7*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, \cos\left(d x + c\right)^{4} + 30 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(3 \, \cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 60 \, \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right)}{60 \, a d}"," ",0,"1/60*(15*cos(d*x + c)^4 + 30*cos(d*x + c)^2 - 4*(3*cos(d*x + c)^4 + 4*cos(d*x + c)^2 + 8)*sin(d*x + c) + 60*log(1/2*sin(d*x + c)))/(a*d)","A",0
685,1,85,0,1.090643," ","integrate(cos(d*x+c)^7*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{32 \, \cos\left(d x + c\right)^{4} + 128 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(8 \, \cos\left(d x + c\right)^{4} + 16 \, \cos\left(d x + c\right)^{2} - 11\right)} \sin\left(d x + c\right) - 96 \, \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 256}{96 \, a d \sin\left(d x + c\right)}"," ",0,"1/96*(32*cos(d*x + c)^4 + 128*cos(d*x + c)^2 - 3*(8*cos(d*x + c)^4 + 16*cos(d*x + c)^2 - 11)*sin(d*x + c) - 96*log(1/2*sin(d*x + c))*sin(d*x + c) - 256)/(a*d*sin(d*x + c))","A",0
686,1,91,0,1.039261," ","integrate(cos(d*x+c)^7*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{4} - 9 \, \cos\left(d x + c\right)^{2} + 24 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, {\left(\cos\left(d x + c\right)^{4} + 4 \, \cos\left(d x + c\right)^{2} - 8\right)} \sin\left(d x + c\right) - 3}{12 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"-1/12*(6*cos(d*x + c)^4 - 9*cos(d*x + c)^2 + 24*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c)) - 4*(cos(d*x + c)^4 + 4*cos(d*x + c)^2 - 8)*sin(d*x + c) - 3)/(a*d*cos(d*x + c)^2 - a*d)","A",0
687,1,107,0,0.897366," ","integrate(cos(d*x+c)^7*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, \cos\left(d x + c\right)^{4} - 24 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 48 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(2 \, \cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) + 32}{12 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(12*cos(d*x + c)^4 - 24*(cos(d*x + c)^2 - 1)*log(1/2*sin(d*x + c))*sin(d*x + c) - 48*cos(d*x + c)^2 - 3*(2*cos(d*x + c)^4 - 3*cos(d*x + c)^2 - 1)*sin(d*x + c) + 32)/((a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
688,1,104,0,1.415905," ","integrate(cos(d*x+c)^7*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, \cos\left(d x + c\right)^{2} - 12 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 12 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) - 9}{12 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"-1/12*(12*cos(d*x + c)^2 - 12*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*sin(d*x + c)) + 4*(3*cos(d*x + c)^4 - 12*cos(d*x + c)^2 + 8)*sin(d*x + c) - 9)/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)","A",0
689,1,118,0,0.869780," ","integrate(cos(d*x+c)^7*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{60 \, \cos\left(d x + c\right)^{4} + 60 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 80 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(4 \, \cos\left(d x + c\right)^{2} - 3\right)} \sin\left(d x + c\right) + 32}{60 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(60*cos(d*x + c)^4 + 60*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*sin(d*x + c))*sin(d*x + c) - 80*cos(d*x + c)^2 - 15*(4*cos(d*x + c)^2 - 3)*sin(d*x + c) + 32)/((a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","A",0
690,1,96,0,0.901077," ","integrate(cos(d*x+c)^7*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, \cos\left(d x + c\right)^{4} - 15 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 5}{30 \, {\left(a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"1/30*(15*cos(d*x + c)^4 - 15*cos(d*x + c)^2 - 2*(15*cos(d*x + c)^4 - 20*cos(d*x + c)^2 + 8)*sin(d*x + c) + 5)/(a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^2 - a*d)","A",0
691,1,104,0,0.714276," ","integrate(cos(d*x+c)^7*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{70 \, \cos\left(d x + c\right)^{4} - 56 \, \cos\left(d x + c\right)^{2} - 35 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 16}{210 \, {\left(a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"1/210*(70*cos(d*x + c)^4 - 56*cos(d*x + c)^2 - 35*(3*cos(d*x + c)^4 - 3*cos(d*x + c)^2 + 1)*sin(d*x + c) + 16)/((a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
692,1,107,0,0.876740," ","integrate(cos(d*x+c)^7*csc(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{210 \, \cos\left(d x + c\right)^{4} - 140 \, \cos\left(d x + c\right)^{2} - 8 \, {\left(35 \, \cos\left(d x + c\right)^{4} - 28 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 35}{840 \, {\left(a d \cos\left(d x + c\right)^{8} - 4 \, a d \cos\left(d x + c\right)^{6} + 6 \, a d \cos\left(d x + c\right)^{4} - 4 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"-1/840*(210*cos(d*x + c)^4 - 140*cos(d*x + c)^2 - 8*(35*cos(d*x + c)^4 - 28*cos(d*x + c)^2 + 8)*sin(d*x + c) + 35)/(a*d*cos(d*x + c)^8 - 4*a*d*cos(d*x + c)^6 + 6*a*d*cos(d*x + c)^4 - 4*a*d*cos(d*x + c)^2 + a*d)","A",0
693,1,115,0,0.846159," ","integrate(cos(d*x+c)^7*csc(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{504 \, \cos\left(d x + c\right)^{4} - 288 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 64}{2520 \, {\left(a d \cos\left(d x + c\right)^{8} - 4 \, a d \cos\left(d x + c\right)^{6} + 6 \, a d \cos\left(d x + c\right)^{4} - 4 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/2520*(504*cos(d*x + c)^4 - 288*cos(d*x + c)^2 - 105*(6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*sin(d*x + c) + 64)/((a*d*cos(d*x + c)^8 - 4*a*d*cos(d*x + c)^6 + 6*a*d*cos(d*x + c)^4 - 4*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","A",0
694,1,120,0,0.836737," ","integrate(cos(d*x+c)^7*csc(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{210 \, \cos\left(d x + c\right)^{4} - 105 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(63 \, \cos\left(d x + c\right)^{4} - 36 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 21}{1260 \, {\left(a d \cos\left(d x + c\right)^{10} - 5 \, a d \cos\left(d x + c\right)^{8} + 10 \, a d \cos\left(d x + c\right)^{6} - 10 \, a d \cos\left(d x + c\right)^{4} + 5 \, a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"1/1260*(210*cos(d*x + c)^4 - 105*cos(d*x + c)^2 - 4*(63*cos(d*x + c)^4 - 36*cos(d*x + c)^2 + 8)*sin(d*x + c) + 21)/(a*d*cos(d*x + c)^10 - 5*a*d*cos(d*x + c)^8 + 10*a*d*cos(d*x + c)^6 - 10*a*d*cos(d*x + c)^4 + 5*a*d*cos(d*x + c)^2 - a*d)","A",0
695,1,128,0,0.599850," ","integrate(cos(d*x+c)^7*csc(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{1980 \, \cos\left(d x + c\right)^{4} - 880 \, \cos\left(d x + c\right)^{2} - 231 \, {\left(10 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 160}{13860 \, {\left(a d \cos\left(d x + c\right)^{10} - 5 \, a d \cos\left(d x + c\right)^{8} + 10 \, a d \cos\left(d x + c\right)^{6} - 10 \, a d \cos\left(d x + c\right)^{4} + 5 \, a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"1/13860*(1980*cos(d*x + c)^4 - 880*cos(d*x + c)^2 - 231*(10*cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 1)*sin(d*x + c) + 160)/((a*d*cos(d*x + c)^10 - 5*a*d*cos(d*x + c)^8 + 10*a*d*cos(d*x + c)^6 - 10*a*d*cos(d*x + c)^4 + 5*a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
696,1,131,0,0.905921," ","integrate(cos(d*x+c)^7*csc(d*x+c)^13/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3465 \, \cos\left(d x + c\right)^{4} - 1386 \, \cos\left(d x + c\right)^{2} - 40 \, {\left(99 \, \cos\left(d x + c\right)^{4} - 44 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 231}{27720 \, {\left(a d \cos\left(d x + c\right)^{12} - 6 \, a d \cos\left(d x + c\right)^{10} + 15 \, a d \cos\left(d x + c\right)^{8} - 20 \, a d \cos\left(d x + c\right)^{6} + 15 \, a d \cos\left(d x + c\right)^{4} - 6 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"-1/27720*(3465*cos(d*x + c)^4 - 1386*cos(d*x + c)^2 - 40*(99*cos(d*x + c)^4 - 44*cos(d*x + c)^2 + 8)*sin(d*x + c) + 231)/(a*d*cos(d*x + c)^12 - 6*a*d*cos(d*x + c)^10 + 15*a*d*cos(d*x + c)^8 - 20*a*d*cos(d*x + c)^6 + 15*a*d*cos(d*x + c)^4 - 6*a*d*cos(d*x + c)^2 + a*d)","A",0
697,1,697,0,1.069511," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{{\left({\left(a^{3} n^{7} + 34 \, a^{3} n^{6} + 472 \, a^{3} n^{5} + 3442 \, a^{3} n^{4} + 14083 \, a^{3} n^{3} + 31804 \, a^{3} n^{2} + 35844 \, a^{3} n + 15120 \, a^{3}\right)} \cos\left(d x + c\right)^{10} - 5 \, {\left(a^{3} n^{7} + 34 \, a^{3} n^{6} + 472 \, a^{3} n^{5} + 3442 \, a^{3} n^{4} + 14083 \, a^{3} n^{3} + 31804 \, a^{3} n^{2} + 35844 \, a^{3} n + 15120 \, a^{3}\right)} \cos\left(d x + c\right)^{8} + 192 \, a^{3} n^{4} + 4 \, {\left(a^{3} n^{7} + 28 \, a^{3} n^{6} + 304 \, a^{3} n^{5} + 1618 \, a^{3} n^{4} + 4375 \, a^{3} n^{3} + 5554 \, a^{3} n^{2} + 2520 \, a^{3} n\right)} \cos\left(d x + c\right)^{6} + 4224 \, a^{3} n^{3} + 31488 \, a^{3} n^{2} + 24 \, {\left(a^{3} n^{6} + 24 \, a^{3} n^{5} + 208 \, a^{3} n^{4} + 786 \, a^{3} n^{3} + 1231 \, a^{3} n^{2} + 630 \, a^{3} n\right)} \cos\left(d x + c\right)^{4} + 87936 \, a^{3} n + 60480 \, a^{3} + 96 \, {\left(a^{3} n^{5} + 22 \, a^{3} n^{4} + 164 \, a^{3} n^{3} + 458 \, a^{3} n^{2} + 315 \, a^{3} n\right)} \cos\left(d x + c\right)^{2} - {\left(3 \, {\left(a^{3} n^{7} + 35 \, a^{3} n^{6} + 497 \, a^{3} n^{5} + 3689 \, a^{3} n^{4} + 15302 \, a^{3} n^{3} + 34916 \, a^{3} n^{2} + 39640 \, a^{3} n + 16800 \, a^{3}\right)} \cos\left(d x + c\right)^{8} - 192 \, a^{3} n^{4} - 4 \, {\left(a^{3} n^{7} + 31 \, a^{3} n^{6} + 385 \, a^{3} n^{5} + 2485 \, a^{3} n^{4} + 8974 \, a^{3} n^{3} + 18004 \, a^{3} n^{2} + 18360 \, a^{3} n + 7200 \, a^{3}\right)} \cos\left(d x + c\right)^{6} - 4224 \, a^{3} n^{3} - 31488 \, a^{3} n^{2} - 24 \, {\left(a^{3} n^{6} + 26 \, a^{3} n^{5} + 255 \, a^{3} n^{4} + 1210 \, a^{3} n^{3} + 2924 \, a^{3} n^{2} + 3384 \, a^{3} n + 1440 \, a^{3}\right)} \cos\left(d x + c\right)^{4} - 93696 \, a^{3} n - 92160 \, a^{3} - 96 \, {\left(a^{3} n^{5} + 23 \, a^{3} n^{4} + 186 \, a^{3} n^{3} + 652 \, a^{3} n^{2} + 968 \, a^{3} n + 480 \, a^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{d n^{8} + 44 \, d n^{7} + 812 \, d n^{6} + 8162 \, d n^{5} + 48503 \, d n^{4} + 172634 \, d n^{3} + 353884 \, d n^{2} + 373560 \, d n + 151200 \, d}"," ",0,"((a^3*n^7 + 34*a^3*n^6 + 472*a^3*n^5 + 3442*a^3*n^4 + 14083*a^3*n^3 + 31804*a^3*n^2 + 35844*a^3*n + 15120*a^3)*cos(d*x + c)^10 - 5*(a^3*n^7 + 34*a^3*n^6 + 472*a^3*n^5 + 3442*a^3*n^4 + 14083*a^3*n^3 + 31804*a^3*n^2 + 35844*a^3*n + 15120*a^3)*cos(d*x + c)^8 + 192*a^3*n^4 + 4*(a^3*n^7 + 28*a^3*n^6 + 304*a^3*n^5 + 1618*a^3*n^4 + 4375*a^3*n^3 + 5554*a^3*n^2 + 2520*a^3*n)*cos(d*x + c)^6 + 4224*a^3*n^3 + 31488*a^3*n^2 + 24*(a^3*n^6 + 24*a^3*n^5 + 208*a^3*n^4 + 786*a^3*n^3 + 1231*a^3*n^2 + 630*a^3*n)*cos(d*x + c)^4 + 87936*a^3*n + 60480*a^3 + 96*(a^3*n^5 + 22*a^3*n^4 + 164*a^3*n^3 + 458*a^3*n^2 + 315*a^3*n)*cos(d*x + c)^2 - (3*(a^3*n^7 + 35*a^3*n^6 + 497*a^3*n^5 + 3689*a^3*n^4 + 15302*a^3*n^3 + 34916*a^3*n^2 + 39640*a^3*n + 16800*a^3)*cos(d*x + c)^8 - 192*a^3*n^4 - 4*(a^3*n^7 + 31*a^3*n^6 + 385*a^3*n^5 + 2485*a^3*n^4 + 8974*a^3*n^3 + 18004*a^3*n^2 + 18360*a^3*n + 7200*a^3)*cos(d*x + c)^6 - 4224*a^3*n^3 - 31488*a^3*n^2 - 24*(a^3*n^6 + 26*a^3*n^5 + 255*a^3*n^4 + 1210*a^3*n^3 + 2924*a^3*n^2 + 3384*a^3*n + 1440*a^3)*cos(d*x + c)^4 - 93696*a^3*n - 92160*a^3 - 96*(a^3*n^5 + 23*a^3*n^4 + 186*a^3*n^3 + 652*a^3*n^2 + 968*a^3*n + 480*a^3)*cos(d*x + c)^2)*sin(d*x + c))*sin(d*x + c)^n/(d*n^8 + 44*d*n^7 + 812*d*n^6 + 8162*d*n^5 + 48503*d*n^4 + 172634*d*n^3 + 353884*d*n^2 + 373560*d*n + 151200*d)","B",0
698,1,628,0,1.086353," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(a^{2} n^{7} + 32 \, a^{2} n^{6} + 414 \, a^{2} n^{5} + 2788 \, a^{2} n^{4} + 10469 \, a^{2} n^{3} + 21708 \, a^{2} n^{2} + 22716 \, a^{2} n + 9072 \, a^{2}\right)} \cos\left(d x + c\right)^{8} - 2 \, {\left(a^{2} n^{7} + 26 \, a^{2} n^{6} + 258 \, a^{2} n^{5} + 1240 \, a^{2} n^{4} + 3029 \, a^{2} n^{3} + 3534 \, a^{2} n^{2} + 1512 \, a^{2} n\right)} \cos\left(d x + c\right)^{6} - 96 \, a^{2} n^{4} - 1920 \, a^{2} n^{3} - 12 \, {\left(a^{2} n^{6} + 22 \, a^{2} n^{5} + 170 \, a^{2} n^{4} + 560 \, a^{2} n^{3} + 789 \, a^{2} n^{2} + 378 \, a^{2} n\right)} \cos\left(d x + c\right)^{4} - 12480 \, a^{2} n^{2} - 28800 \, a^{2} n - 48 \, {\left(a^{2} n^{5} + 20 \, a^{2} n^{4} + 130 \, a^{2} n^{3} + 300 \, a^{2} n^{2} + 189 \, a^{2} n\right)} \cos\left(d x + c\right)^{2} - 18144 \, a^{2} + {\left({\left(a^{2} n^{7} + 31 \, a^{2} n^{6} + 391 \, a^{2} n^{5} + 2581 \, a^{2} n^{4} + 9544 \, a^{2} n^{3} + 19564 \, a^{2} n^{2} + 20304 \, a^{2} n + 8064 \, a^{2}\right)} \cos\left(d x + c\right)^{8} - 2 \, {\left(a^{2} n^{7} + 29 \, a^{2} n^{6} + 343 \, a^{2} n^{5} + 2135 \, a^{2} n^{4} + 7504 \, a^{2} n^{3} + 14756 \, a^{2} n^{2} + 14832 \, a^{2} n + 5760 \, a^{2}\right)} \cos\left(d x + c\right)^{6} - 96 \, a^{2} n^{4} - 1920 \, a^{2} n^{3} - 12 \, {\left(a^{2} n^{6} + 24 \, a^{2} n^{5} + 223 \, a^{2} n^{4} + 1020 \, a^{2} n^{3} + 2404 \, a^{2} n^{2} + 2736 \, a^{2} n + 1152 \, a^{2}\right)} \cos\left(d x + c\right)^{4} - 13440 \, a^{2} n^{2} - 38400 \, a^{2} n - 48 \, {\left(a^{2} n^{5} + 21 \, a^{2} n^{4} + 160 \, a^{2} n^{3} + 540 \, a^{2} n^{2} + 784 \, a^{2} n + 384 \, a^{2}\right)} \cos\left(d x + c\right)^{2} - 36864 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{d n^{8} + 40 \, d n^{7} + 670 \, d n^{6} + 6100 \, d n^{5} + 32773 \, d n^{4} + 105460 \, d n^{3} + 196380 \, d n^{2} + 190800 \, d n + 72576 \, d}"," ",0,"-(2*(a^2*n^7 + 32*a^2*n^6 + 414*a^2*n^5 + 2788*a^2*n^4 + 10469*a^2*n^3 + 21708*a^2*n^2 + 22716*a^2*n + 9072*a^2)*cos(d*x + c)^8 - 2*(a^2*n^7 + 26*a^2*n^6 + 258*a^2*n^5 + 1240*a^2*n^4 + 3029*a^2*n^3 + 3534*a^2*n^2 + 1512*a^2*n)*cos(d*x + c)^6 - 96*a^2*n^4 - 1920*a^2*n^3 - 12*(a^2*n^6 + 22*a^2*n^5 + 170*a^2*n^4 + 560*a^2*n^3 + 789*a^2*n^2 + 378*a^2*n)*cos(d*x + c)^4 - 12480*a^2*n^2 - 28800*a^2*n - 48*(a^2*n^5 + 20*a^2*n^4 + 130*a^2*n^3 + 300*a^2*n^2 + 189*a^2*n)*cos(d*x + c)^2 - 18144*a^2 + ((a^2*n^7 + 31*a^2*n^6 + 391*a^2*n^5 + 2581*a^2*n^4 + 9544*a^2*n^3 + 19564*a^2*n^2 + 20304*a^2*n + 8064*a^2)*cos(d*x + c)^8 - 2*(a^2*n^7 + 29*a^2*n^6 + 343*a^2*n^5 + 2135*a^2*n^4 + 7504*a^2*n^3 + 14756*a^2*n^2 + 14832*a^2*n + 5760*a^2)*cos(d*x + c)^6 - 96*a^2*n^4 - 1920*a^2*n^3 - 12*(a^2*n^6 + 24*a^2*n^5 + 223*a^2*n^4 + 1020*a^2*n^3 + 2404*a^2*n^2 + 2736*a^2*n + 1152*a^2)*cos(d*x + c)^4 - 13440*a^2*n^2 - 38400*a^2*n - 48*(a^2*n^5 + 21*a^2*n^4 + 160*a^2*n^3 + 540*a^2*n^2 + 784*a^2*n + 384*a^2)*cos(d*x + c)^2 - 36864*a^2)*sin(d*x + c))*sin(d*x + c)^n/(d*n^8 + 40*d*n^7 + 670*d*n^6 + 6100*d*n^5 + 32773*d*n^4 + 105460*d*n^3 + 196380*d*n^2 + 190800*d*n + 72576*d)","B",0
699,1,445,0,0.923416," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left({\left(a n^{7} + 28 \, a n^{6} + 322 \, a n^{5} + 1960 \, a n^{4} + 6769 \, a n^{3} + 13132 \, a n^{2} + 13068 \, a n + 5040 \, a\right)} \cos\left(d x + c\right)^{8} - {\left(a n^{7} + 22 \, a n^{6} + 190 \, a n^{5} + 820 \, a n^{4} + 1849 \, a n^{3} + 2038 \, a n^{2} + 840 \, a n\right)} \cos\left(d x + c\right)^{6} - 48 \, a n^{4} - 6 \, {\left(a n^{6} + 18 \, a n^{5} + 118 \, a n^{4} + 348 \, a n^{3} + 457 \, a n^{2} + 210 \, a n\right)} \cos\left(d x + c\right)^{4} - 768 \, a n^{3} - 4128 \, a n^{2} - 24 \, {\left(a n^{5} + 16 \, a n^{4} + 86 \, a n^{3} + 176 \, a n^{2} + 105 \, a n\right)} \cos\left(d x + c\right)^{2} - 8448 \, a n - {\left({\left(a n^{7} + 29 \, a n^{6} + 343 \, a n^{5} + 2135 \, a n^{4} + 7504 \, a n^{3} + 14756 \, a n^{2} + 14832 \, a n + 5760 \, a\right)} \cos\left(d x + c\right)^{6} + 48 \, a n^{4} + 6 \, {\left(a n^{6} + 24 \, a n^{5} + 223 \, a n^{4} + 1020 \, a n^{3} + 2404 \, a n^{2} + 2736 \, a n + 1152 \, a\right)} \cos\left(d x + c\right)^{4} + 960 \, a n^{3} + 6720 \, a n^{2} + 24 \, {\left(a n^{5} + 21 \, a n^{4} + 160 \, a n^{3} + 540 \, a n^{2} + 784 \, a n + 384 \, a\right)} \cos\left(d x + c\right)^{2} + 19200 \, a n + 18432 \, a\right)} \sin\left(d x + c\right) - 5040 \, a\right)} \sin\left(d x + c\right)^{n}}{d n^{8} + 36 \, d n^{7} + 546 \, d n^{6} + 4536 \, d n^{5} + 22449 \, d n^{4} + 67284 \, d n^{3} + 118124 \, d n^{2} + 109584 \, d n + 40320 \, d}"," ",0,"-((a*n^7 + 28*a*n^6 + 322*a*n^5 + 1960*a*n^4 + 6769*a*n^3 + 13132*a*n^2 + 13068*a*n + 5040*a)*cos(d*x + c)^8 - (a*n^7 + 22*a*n^6 + 190*a*n^5 + 820*a*n^4 + 1849*a*n^3 + 2038*a*n^2 + 840*a*n)*cos(d*x + c)^6 - 48*a*n^4 - 6*(a*n^6 + 18*a*n^5 + 118*a*n^4 + 348*a*n^3 + 457*a*n^2 + 210*a*n)*cos(d*x + c)^4 - 768*a*n^3 - 4128*a*n^2 - 24*(a*n^5 + 16*a*n^4 + 86*a*n^3 + 176*a*n^2 + 105*a*n)*cos(d*x + c)^2 - 8448*a*n - ((a*n^7 + 29*a*n^6 + 343*a*n^5 + 2135*a*n^4 + 7504*a*n^3 + 14756*a*n^2 + 14832*a*n + 5760*a)*cos(d*x + c)^6 + 48*a*n^4 + 6*(a*n^6 + 24*a*n^5 + 223*a*n^4 + 1020*a*n^3 + 2404*a*n^2 + 2736*a*n + 1152*a)*cos(d*x + c)^4 + 960*a*n^3 + 6720*a*n^2 + 24*(a*n^5 + 21*a*n^4 + 160*a*n^3 + 540*a*n^2 + 784*a*n + 384*a)*cos(d*x + c)^2 + 19200*a*n + 18432*a)*sin(d*x + c) - 5040*a)*sin(d*x + c)^n/(d*n^8 + 36*d*n^7 + 546*d*n^6 + 4536*d*n^5 + 22449*d*n^4 + 67284*d*n^3 + 118124*d*n^2 + 109584*d*n + 40320*d)","B",0
700,1,243,0,0.917747," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(n^{5} + 15 \, n^{4} + 85 \, n^{3} + 225 \, n^{2} + 274 \, n + 120\right)} \cos\left(d x + c\right)^{6} - {\left(n^{5} + 11 \, n^{4} + 41 \, n^{3} + 61 \, n^{2} + 30 \, n\right)} \cos\left(d x + c\right)^{4} - 8 \, n^{3} - 4 \, {\left(n^{4} + 9 \, n^{3} + 23 \, n^{2} + 15 \, n\right)} \cos\left(d x + c\right)^{2} - 72 \, n^{2} + {\left({\left(n^{5} + 16 \, n^{4} + 95 \, n^{3} + 260 \, n^{2} + 324 \, n + 144\right)} \cos\left(d x + c\right)^{4} + 8 \, n^{3} + 4 \, {\left(n^{4} + 13 \, n^{3} + 56 \, n^{2} + 92 \, n + 48\right)} \cos\left(d x + c\right)^{2} + 96 \, n^{2} + 352 \, n + 384\right)} \sin\left(d x + c\right) - 184 \, n - 120\right)} \sin\left(d x + c\right)^{n}}{a d n^{6} + 21 \, a d n^{5} + 175 \, a d n^{4} + 735 \, a d n^{3} + 1624 \, a d n^{2} + 1764 \, a d n + 720 \, a d}"," ",0,"((n^5 + 15*n^4 + 85*n^3 + 225*n^2 + 274*n + 120)*cos(d*x + c)^6 - (n^5 + 11*n^4 + 41*n^3 + 61*n^2 + 30*n)*cos(d*x + c)^4 - 8*n^3 - 4*(n^4 + 9*n^3 + 23*n^2 + 15*n)*cos(d*x + c)^2 - 72*n^2 + ((n^5 + 16*n^4 + 95*n^3 + 260*n^2 + 324*n + 144)*cos(d*x + c)^4 + 8*n^3 + 4*(n^4 + 13*n^3 + 56*n^2 + 92*n + 48)*cos(d*x + c)^2 + 96*n^2 + 352*n + 384)*sin(d*x + c) - 184*n - 120)*sin(d*x + c)^n/(a*d*n^6 + 21*a*d*n^5 + 175*a*d*n^4 + 735*a*d*n^3 + 1624*a*d*n^2 + 1764*a*d*n + 720*a*d)","A",0
701,1,169,0,0.850635," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(n^{3} + 8 \, n^{2} + 17 \, n + 10\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(n^{3} + 6 \, n^{2} + 5 \, n\right)} \cos\left(d x + c\right)^{2} - 4 \, n^{2} - {\left({\left(n^{3} + 7 \, n^{2} + 14 \, n + 8\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(n^{3} + 7 \, n^{2} + 14 \, n + 8\right)} \cos\left(d x + c\right)^{2} - 4 \, n^{2} - 24 \, n - 32\right)} \sin\left(d x + c\right) - 24 \, n - 20\right)} \sin\left(d x + c\right)^{n}}{a^{2} d n^{4} + 12 \, a^{2} d n^{3} + 49 \, a^{2} d n^{2} + 78 \, a^{2} d n + 40 \, a^{2} d}"," ",0,"(2*(n^3 + 8*n^2 + 17*n + 10)*cos(d*x + c)^4 - 2*(n^3 + 6*n^2 + 5*n)*cos(d*x + c)^2 - 4*n^2 - ((n^3 + 7*n^2 + 14*n + 8)*cos(d*x + c)^4 - 2*(n^3 + 7*n^2 + 14*n + 8)*cos(d*x + c)^2 - 4*n^2 - 24*n - 32)*sin(d*x + c) - 24*n - 20)*sin(d*x + c)^n/(a^2*d*n^4 + 12*a^2*d*n^3 + 49*a^2*d*n^2 + 78*a^2*d*n + 40*a^2*d)","A",0
702,1,160,0,0.978986," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left({\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} \cos\left(d x + c\right)^{4} + 4 \, n^{3} - {\left(5 \, n^{3} + 36 \, n^{2} + 79 \, n + 48\right)} \cos\left(d x + c\right)^{2} + 30 \, n^{2} - {\left(4 \, n^{3} - 3 \, {\left(n^{3} + 7 \, n^{2} + 14 \, n + 8\right)} \cos\left(d x + c\right)^{2} + 30 \, n^{2} + 68 \, n + 48\right)} \sin\left(d x + c\right) + 68 \, n + 42\right)} \sin\left(d x + c\right)^{n}}{a^{3} d n^{4} + 10 \, a^{3} d n^{3} + 35 \, a^{3} d n^{2} + 50 \, a^{3} d n + 24 \, a^{3} d}"," ",0,"-((n^3 + 6*n^2 + 11*n + 6)*cos(d*x + c)^4 + 4*n^3 - (5*n^3 + 36*n^2 + 79*n + 48)*cos(d*x + c)^2 + 30*n^2 - (4*n^3 - 3*(n^3 + 7*n^2 + 14*n + 8)*cos(d*x + c)^2 + 30*n^2 + 68*n + 48)*sin(d*x + c) + 68*n + 42)*sin(d*x + c)^n/(a^3*d*n^4 + 10*a^3*d*n^3 + 35*a^3*d*n^2 + 50*a^3*d*n + 24*a^3*d)","A",0
703,0,0,0,1.214641," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{a^{4} \cos\left(d x + c\right)^{4} - 8 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(d x + c\right)^{2} - 2 \, a^{4}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sin(d*x + c)^n*cos(d*x + c)^7/(a^4*cos(d*x + c)^4 - 8*a^4*cos(d*x + c)^2 + 8*a^4 - 4*(a^4*cos(d*x + c)^2 - 2*a^4)*sin(d*x + c)), x)","F",0
704,0,0,0,0.899042," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{5 \, a^{5} \cos\left(d x + c\right)^{4} - 20 \, a^{5} \cos\left(d x + c\right)^{2} + 16 \, a^{5} + {\left(a^{5} \cos\left(d x + c\right)^{4} - 12 \, a^{5} \cos\left(d x + c\right)^{2} + 16 \, a^{5}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(sin(d*x + c)^n*cos(d*x + c)^7/(5*a^5*cos(d*x + c)^4 - 20*a^5*cos(d*x + c)^2 + 16*a^5 + (a^5*cos(d*x + c)^4 - 12*a^5*cos(d*x + c)^2 + 16*a^5)*sin(d*x + c)), x)","F",0
705,1,110,0,1.150657," ","integrate(cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{64512 \, \cos\left(d x + c\right)^{11} - 157696 \, \cos\left(d x + c\right)^{9} + 101376 \, \cos\left(d x + c\right)^{7} + 3465 \, d x - 231 \, {\left(256 \, \cos\left(d x + c\right)^{11} - 640 \, \cos\left(d x + c\right)^{9} + 432 \, \cos\left(d x + c\right)^{7} - 8 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} - 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{709632 \, a d}"," ",0,"-1/709632*(64512*cos(d*x + c)^11 - 157696*cos(d*x + c)^9 + 101376*cos(d*x + c)^7 + 3465*d*x - 231*(256*cos(d*x + c)^11 - 640*cos(d*x + c)^9 + 432*cos(d*x + c)^7 - 8*cos(d*x + c)^5 - 10*cos(d*x + c)^3 - 15*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
706,1,100,0,0.974423," ","integrate(cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{80640 \, \cos\left(d x + c\right)^{11} - 197120 \, \cos\left(d x + c\right)^{9} + 126720 \, \cos\left(d x + c\right)^{7} + 10395 \, d x + 693 \, {\left(128 \, \cos\left(d x + c\right)^{9} - 176 \, \cos\left(d x + c\right)^{7} + 8 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{887040 \, a d}"," ",0,"1/887040*(80640*cos(d*x + c)^11 - 197120*cos(d*x + c)^9 + 126720*cos(d*x + c)^7 + 10395*d*x + 693*(128*cos(d*x + c)^9 - 176*cos(d*x + c)^7 + 8*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 15*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
707,1,90,0,1.030625," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8960 \, \cos\left(d x + c\right)^{9} - 11520 \, \cos\left(d x + c\right)^{7} - 945 \, d x - 63 \, {\left(128 \, \cos\left(d x + c\right)^{9} - 176 \, \cos\left(d x + c\right)^{7} + 8 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, a d}"," ",0,"1/80640*(8960*cos(d*x + c)^9 - 11520*cos(d*x + c)^7 - 945*d*x - 63*(128*cos(d*x + c)^9 - 176*cos(d*x + c)^7 + 8*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 15*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
708,1,80,0,1.130942," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{896 \, \cos\left(d x + c\right)^{9} - 1152 \, \cos\left(d x + c\right)^{7} - 315 \, d x + 21 \, {\left(48 \, \cos\left(d x + c\right)^{7} - 8 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} - 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8064 \, a d}"," ",0,"-1/8064*(896*cos(d*x + c)^9 - 1152*cos(d*x + c)^7 - 315*d*x + 21*(48*cos(d*x + c)^7 - 8*cos(d*x + c)^5 - 10*cos(d*x + c)^3 - 15*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
709,1,70,0,0.956213," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{384 \, \cos\left(d x + c\right)^{7} + 105 \, d x - 7 \, {\left(48 \, \cos\left(d x + c\right)^{7} - 8 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} - 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2688 \, a d}"," ",0,"-1/2688*(384*cos(d*x + c)^7 + 105*d*x - 7*(48*cos(d*x + c)^7 - 8*cos(d*x + c)^5 - 10*cos(d*x + c)^3 - 15*cos(d*x + c))*sin(d*x + c))/(a*d)","A",0
710,1,104,0,0.978075," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, \cos\left(d x + c\right)^{5} + 80 \, \cos\left(d x + c\right)^{3} - 75 \, d x - 5 \, {\left(8 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 240 \, \cos\left(d x + c\right) - 120 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 120 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{240 \, a d}"," ",0,"1/240*(48*cos(d*x + c)^5 + 80*cos(d*x + c)^3 - 75*d*x - 5*(8*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 15*cos(d*x + c))*sin(d*x + c) + 240*cos(d*x + c) - 120*log(1/2*cos(d*x + c) + 1/2) + 120*log(-1/2*cos(d*x + c) + 1/2))/(a*d)","A",0
711,1,124,0,0.941541," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{5} + 75 \, \cos\left(d x + c\right)^{3} - {\left(24 \, \cos\left(d x + c\right)^{5} + 40 \, \cos\left(d x + c\right)^{3} + 225 \, d x + 120 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 60 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 60 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 225 \, \cos\left(d x + c\right)}{120 \, a d \sin\left(d x + c\right)}"," ",0,"1/120*(30*cos(d*x + c)^5 + 75*cos(d*x + c)^3 - (24*cos(d*x + c)^5 + 40*cos(d*x + c)^3 + 225*d*x + 120*cos(d*x + c))*sin(d*x + c) + 60*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 60*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 225*cos(d*x + c))/(a*d*sin(d*x + c))","A",0
712,1,148,0,0.779947," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{5} - 45 \, d x \cos\left(d x + c\right)^{2} + 40 \, \cos\left(d x + c\right)^{3} + 45 \, d x - 30 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 30 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(2 \, \cos\left(d x + c\right)^{5} + 5 \, \cos\left(d x + c\right)^{3} - 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 60 \, \cos\left(d x + c\right)}{24 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"-1/24*(8*cos(d*x + c)^5 - 45*d*x*cos(d*x + c)^2 + 40*cos(d*x + c)^3 + 45*d*x - 30*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + 30*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 3*(2*cos(d*x + c)^5 + 5*cos(d*x + c)^3 - 15*cos(d*x + c))*sin(d*x + c) - 60*cos(d*x + c))/(a*d*cos(d*x + c)^2 - a*d)","A",0
713,1,168,0,0.938802," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{3} + 15 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, {\left(2 \, \cos\left(d x + c\right)^{5} + 15 \, d x \cos\left(d x + c\right)^{2} + 10 \, \cos\left(d x + c\right)^{3} - 15 \, d x - 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 30 \, \cos\left(d x + c\right)}{12 \, {\left(a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(6*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*(2*cos(d*x + c)^5 + 15*d*x*cos(d*x + c)^2 + 10*cos(d*x + c)^3 - 15*d*x - 15*cos(d*x + c))*sin(d*x + c) + 30*cos(d*x + c))/((a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
714,1,191,0,0.978427," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{120 \, d x \cos\left(d x + c\right)^{4} - 48 \, \cos\left(d x + c\right)^{5} - 240 \, d x \cos\left(d x + c\right)^{2} + 150 \, \cos\left(d x + c\right)^{3} + 120 \, d x + 45 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 45 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 8 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 20 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 90 \, \cos\left(d x + c\right)}{48 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"-1/48*(120*d*x*cos(d*x + c)^4 - 48*cos(d*x + c)^5 - 240*d*x*cos(d*x + c)^2 + 150*cos(d*x + c)^3 + 120*d*x + 45*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) - 45*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) + 8*(3*cos(d*x + c)^5 - 20*cos(d*x + c)^3 + 15*cos(d*x + c))*sin(d*x + c) - 90*cos(d*x + c))/(a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)","A",0
715,1,211,0,1.071927," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{368 \, \cos\left(d x + c\right)^{5} - 560 \, \cos\left(d x + c\right)^{3} - 225 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 225 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, {\left(8 \, d x \cos\left(d x + c\right)^{4} + 8 \, \cos\left(d x + c\right)^{5} - 16 \, d x \cos\left(d x + c\right)^{2} - 25 \, \cos\left(d x + c\right)^{3} + 8 \, d x + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 240 \, \cos\left(d x + c\right)}{240 \, {\left(a d \cos\left(d x + c\right)^{4} - 2 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)}"," ",0,"-1/240*(368*cos(d*x + c)^5 - 560*cos(d*x + c)^3 - 225*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 225*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*(8*d*x*cos(d*x + c)^4 + 8*cos(d*x + c)^5 - 16*d*x*cos(d*x + c)^2 - 25*cos(d*x + c)^3 + 8*d*x + 15*cos(d*x + c))*sin(d*x + c) + 240*cos(d*x + c))/((a*d*cos(d*x + c)^4 - 2*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","A",0
716,1,236,0,0.574487," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{480 \, d x \cos\left(d x + c\right)^{6} - 1440 \, d x \cos\left(d x + c\right)^{4} + 330 \, \cos\left(d x + c\right)^{5} + 1440 \, d x \cos\left(d x + c\right)^{2} - 400 \, \cos\left(d x + c\right)^{3} - 480 \, d x + 75 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 75 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(23 \, \cos\left(d x + c\right)^{5} - 35 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 150 \, \cos\left(d x + c\right)}{480 \, {\left(a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"1/480*(480*d*x*cos(d*x + c)^6 - 1440*d*x*cos(d*x + c)^4 + 330*cos(d*x + c)^5 + 1440*d*x*cos(d*x + c)^2 - 400*cos(d*x + c)^3 - 480*d*x + 75*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) - 75*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 32*(23*cos(d*x + c)^5 - 35*cos(d*x + c)^3 + 15*cos(d*x + c))*sin(d*x + c) + 150*cos(d*x + c))/(a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^2 - a*d)","A",0
717,1,198,0,1.289196," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{96 \, \cos\left(d x + c\right)^{7} - 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 14 \, {\left(33 \, \cos\left(d x + c\right)^{5} - 40 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{672 \, {\left(a d \cos\left(d x + c\right)^{6} - 3 \, a d \cos\left(d x + c\right)^{4} + 3 \, a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"1/672*(96*cos(d*x + c)^7 - 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 14*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))*sin(d*x + c))/((a*d*cos(d*x + c)^6 - 3*a*d*cos(d*x + c)^4 + 3*a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","B",0
718,1,216,0,1.173498," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{768 \, \cos\left(d x + c\right)^{7} \sin\left(d x + c\right) - 210 \, \cos\left(d x + c\right)^{7} - 1022 \, \cos\left(d x + c\right)^{5} + 770 \, \cos\left(d x + c\right)^{3} + 105 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 105 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 210 \, \cos\left(d x + c\right)}{5376 \, {\left(a d \cos\left(d x + c\right)^{8} - 4 \, a d \cos\left(d x + c\right)^{6} + 6 \, a d \cos\left(d x + c\right)^{4} - 4 \, a d \cos\left(d x + c\right)^{2} + a d\right)}}"," ",0,"1/5376*(768*cos(d*x + c)^7*sin(d*x + c) - 210*cos(d*x + c)^7 - 1022*cos(d*x + c)^5 + 770*cos(d*x + c)^3 + 105*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) - 105*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 210*cos(d*x + c))/(a*d*cos(d*x + c)^8 - 4*a*d*cos(d*x + c)^6 + 6*a*d*cos(d*x + c)^4 - 4*a*d*cos(d*x + c)^2 + a*d)","A",0
719,1,249,0,1.125167," ","integrate(cos(d*x+c)^8*csc(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{512 \, \cos\left(d x + c\right)^{9} - 2304 \, \cos\left(d x + c\right)^{7} - 315 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 315 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 42 \, {\left(15 \, \cos\left(d x + c\right)^{7} + 73 \, \cos\left(d x + c\right)^{5} - 55 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16128 \, {\left(a d \cos\left(d x + c\right)^{8} - 4 \, a d \cos\left(d x + c\right)^{6} + 6 \, a d \cos\left(d x + c\right)^{4} - 4 \, a d \cos\left(d x + c\right)^{2} + a d\right)} \sin\left(d x + c\right)}"," ",0,"1/16128*(512*cos(d*x + c)^9 - 2304*cos(d*x + c)^7 - 315*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 315*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 42*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))*sin(d*x + c))/((a*d*cos(d*x + c)^8 - 4*a*d*cos(d*x + c)^6 + 6*a*d*cos(d*x + c)^4 - 4*a*d*cos(d*x + c)^2 + a*d)*sin(d*x + c))","A",0
720,1,272,0,0.687337," ","integrate(cos(d*x+c)^8*csc(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{1890 \, \cos\left(d x + c\right)^{9} - 8820 \, \cos\left(d x + c\right)^{7} - 16128 \, \cos\left(d x + c\right)^{5} + 8820 \, \cos\left(d x + c\right)^{3} - 945 \, {\left(\cos\left(d x + c\right)^{10} - 5 \, \cos\left(d x + c\right)^{8} + 10 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 945 \, {\left(\cos\left(d x + c\right)^{10} - 5 \, \cos\left(d x + c\right)^{8} + 10 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2560 \, {\left(2 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} \sin\left(d x + c\right) - 1890 \, \cos\left(d x + c\right)}{161280 \, {\left(a d \cos\left(d x + c\right)^{10} - 5 \, a d \cos\left(d x + c\right)^{8} + 10 \, a d \cos\left(d x + c\right)^{6} - 10 \, a d \cos\left(d x + c\right)^{4} + 5 \, a d \cos\left(d x + c\right)^{2} - a d\right)}}"," ",0,"-1/161280*(1890*cos(d*x + c)^9 - 8820*cos(d*x + c)^7 - 16128*cos(d*x + c)^5 + 8820*cos(d*x + c)^3 - 945*(cos(d*x + c)^10 - 5*cos(d*x + c)^8 + 10*cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 5*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + 945*(cos(d*x + c)^10 - 5*cos(d*x + c)^8 + 10*cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 5*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 2560*(2*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*sin(d*x + c) - 1890*cos(d*x + c))/(a*d*cos(d*x + c)^10 - 5*a*d*cos(d*x + c)^8 + 10*a*d*cos(d*x + c)^6 - 10*a*d*cos(d*x + c)^4 + 5*a*d*cos(d*x + c)^2 - a*d)","A",0
721,1,302,0,1.053250," ","integrate(cos(d*x+c)^8*csc(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{20480 \, \cos\left(d x + c\right)^{11} - 112640 \, \cos\left(d x + c\right)^{9} + 253440 \, \cos\left(d x + c\right)^{7} - 10395 \, {\left(\cos\left(d x + c\right)^{10} - 5 \, \cos\left(d x + c\right)^{8} + 10 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 10395 \, {\left(\cos\left(d x + c\right)^{10} - 5 \, \cos\left(d x + c\right)^{8} + 10 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 1386 \, {\left(15 \, \cos\left(d x + c\right)^{9} - 70 \, \cos\left(d x + c\right)^{7} - 128 \, \cos\left(d x + c\right)^{5} + 70 \, \cos\left(d x + c\right)^{3} - 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1774080 \, {\left(a d \cos\left(d x + c\right)^{10} - 5 \, a d \cos\left(d x + c\right)^{8} + 10 \, a d \cos\left(d x + c\right)^{6} - 10 \, a d \cos\left(d x + c\right)^{4} + 5 \, a d \cos\left(d x + c\right)^{2} - a d\right)} \sin\left(d x + c\right)}"," ",0,"1/1774080*(20480*cos(d*x + c)^11 - 112640*cos(d*x + c)^9 + 253440*cos(d*x + c)^7 - 10395*(cos(d*x + c)^10 - 5*cos(d*x + c)^8 + 10*cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 5*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 10395*(cos(d*x + c)^10 - 5*cos(d*x + c)^8 + 10*cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 5*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 1386*(15*cos(d*x + c)^9 - 70*cos(d*x + c)^7 - 128*cos(d*x + c)^5 + 70*cos(d*x + c)^3 - 15*cos(d*x + c))*sin(d*x + c))/((a*d*cos(d*x + c)^10 - 5*a*d*cos(d*x + c)^8 + 10*a*d*cos(d*x + c)^6 - 10*a*d*cos(d*x + c)^4 + 5*a*d*cos(d*x + c)^2 - a*d)*sin(d*x + c))","A",0
722,1,110,0,0.989247," ","integrate(cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{40320 \, \cos\left(d x + c\right)^{11} - 197120 \, \cos\left(d x + c\right)^{9} + 316800 \, \cos\left(d x + c\right)^{7} - 177408 \, \cos\left(d x + c\right)^{5} - 10395 \, d x + 693 \, {\left(128 \, \cos\left(d x + c\right)^{9} - 336 \, \cos\left(d x + c\right)^{7} + 248 \, \cos\left(d x + c\right)^{5} - 10 \, \cos\left(d x + c\right)^{3} - 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{443520 \, a^{2} d}"," ",0,"1/443520*(40320*cos(d*x + c)^11 - 197120*cos(d*x + c)^9 + 316800*cos(d*x + c)^7 - 177408*cos(d*x + c)^5 - 10395*d*x + 693*(128*cos(d*x + c)^9 - 336*cos(d*x + c)^7 + 248*cos(d*x + c)^5 - 10*cos(d*x + c)^3 - 15*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
723,1,100,0,0.836019," ","integrate(cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{17920 \, \cos\left(d x + c\right)^{9} - 46080 \, \cos\left(d x + c\right)^{7} + 32256 \, \cos\left(d x + c\right)^{5} + 2835 \, d x - 63 \, {\left(128 \, \cos\left(d x + c\right)^{9} - 496 \, \cos\left(d x + c\right)^{7} + 488 \, \cos\left(d x + c\right)^{5} - 30 \, \cos\left(d x + c\right)^{3} - 45 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, a^{2} d}"," ",0,"1/80640*(17920*cos(d*x + c)^9 - 46080*cos(d*x + c)^7 + 32256*cos(d*x + c)^5 + 2835*d*x - 63*(128*cos(d*x + c)^9 - 496*cos(d*x + c)^7 + 488*cos(d*x + c)^5 - 30*cos(d*x + c)^3 - 45*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
724,1,90,0,1.293960," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2240 \, \cos\left(d x + c\right)^{9} - 8640 \, \cos\left(d x + c\right)^{7} + 8064 \, \cos\left(d x + c\right)^{5} + 945 \, d x + 315 \, {\left(16 \, \cos\left(d x + c\right)^{7} - 24 \, \cos\left(d x + c\right)^{5} + 2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{20160 \, a^{2} d}"," ",0,"-1/20160*(2240*cos(d*x + c)^9 - 8640*cos(d*x + c)^7 + 8064*cos(d*x + c)^5 + 945*d*x + 315*(16*cos(d*x + c)^7 - 24*cos(d*x + c)^5 + 2*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
725,1,80,0,0.902155," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3840 \, \cos\left(d x + c\right)^{7} - 5376 \, \cos\left(d x + c\right)^{5} - 1155 \, d x - 35 \, {\left(48 \, \cos\left(d x + c\right)^{7} - 136 \, \cos\left(d x + c\right)^{5} + 22 \, \cos\left(d x + c\right)^{3} + 33 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{13440 \, a^{2} d}"," ",0,"-1/13440*(3840*cos(d*x + c)^7 - 5376*cos(d*x + c)^5 - 1155*d*x - 35*(48*cos(d*x + c)^7 - 136*cos(d*x + c)^5 + 22*cos(d*x + c)^3 + 33*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
726,1,70,0,0.912055," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{120 \, \cos\left(d x + c\right)^{7} - 336 \, \cos\left(d x + c\right)^{5} - 105 \, d x + 35 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, a^{2} d}"," ",0,"1/840*(120*cos(d*x + c)^7 - 336*cos(d*x + c)^5 - 105*d*x + 35*(8*cos(d*x + c)^5 - 2*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c))/(a^2*d)","A",0
727,1,94,0,0.891540," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{12 \, \cos\left(d x + c\right)^{5} - 20 \, \cos\left(d x + c\right)^{3} + 45 \, d x + 15 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 60 \, \cos\left(d x + c\right) + 30 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 30 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{60 \, a^{2} d}"," ",0,"-1/60*(12*cos(d*x + c)^5 - 20*cos(d*x + c)^3 + 45*d*x + 15*(2*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c) - 60*cos(d*x + c) + 30*log(1/2*cos(d*x + c) + 1/2) - 30*log(-1/2*cos(d*x + c) + 1/2))/(a^2*d)","A",0
728,1,113,0,0.813428," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{5} - 9 \, \cos\left(d x + c\right)^{3} + {\left(16 \, \cos\left(d x + c\right)^{3} + 27 \, d x + 48 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 24 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 24 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 27 \, \cos\left(d x + c\right)}{24 \, a^{2} d \sin\left(d x + c\right)}"," ",0,"-1/24*(6*cos(d*x + c)^5 - 9*cos(d*x + c)^3 + (16*cos(d*x + c)^3 + 27*d*x + 48*cos(d*x + c))*sin(d*x + c) - 24*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 24*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 27*cos(d*x + c))/(a^2*d*sin(d*x + c))","A",0
729,1,140,0,0.821904," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, \cos\left(d x + c\right)^{5} + 36 \, d x \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right)^{3} - 36 \, d x + 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, {\left(\cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 6 \, \cos\left(d x + c\right)}{12 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"1/12*(4*cos(d*x + c)^5 + 36*d*x*cos(d*x + c)^2 - 4*cos(d*x + c)^3 - 36*d*x + 3*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) - 3*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) + 12*(cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c) + 6*cos(d*x + c))/(a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
730,1,161,0,0.678080," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3} - 9 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 9 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(d x \cos\left(d x + c\right)^{2} - 4 \, \cos\left(d x + c\right)^{3} - d x + 6 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 3 \, \cos\left(d x + c\right)}{6 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"1/6*(3*cos(d*x + c)^5 - 4*cos(d*x + c)^3 - 9*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 9*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(d*x*cos(d*x + c)^2 - 4*cos(d*x + c)^3 - d*x + 6*cos(d*x + c))*sin(d*x + c) + 3*cos(d*x + c))/((a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","A",0
731,1,187,0,0.937377," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{96 \, d x \cos\left(d x + c\right)^{4} + 48 \, \cos\left(d x + c\right)^{5} - 192 \, d x \cos\left(d x + c\right)^{2} - 90 \, \cos\left(d x + c\right)^{3} + 96 \, d x - 27 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 27 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(4 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 54 \, \cos\left(d x + c\right)}{48 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)}}"," ",0,"-1/48*(96*d*x*cos(d*x + c)^4 + 48*cos(d*x + c)^5 - 192*d*x*cos(d*x + c)^2 - 90*cos(d*x + c)^3 + 96*d*x - 27*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) + 27*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 32*(4*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c) + 54*cos(d*x + c))/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)","A",0
732,1,207,0,1.488765," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{136 \, \cos\left(d x + c\right)^{5} - 280 \, \cos\left(d x + c\right)^{3} + 45 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 45 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 30 \, {\left(4 \, d x \cos\left(d x + c\right)^{4} - 8 \, d x \cos\left(d x + c\right)^{2} + 5 \, \cos\left(d x + c\right)^{3} + 4 \, d x - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 120 \, \cos\left(d x + c\right)}{120 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"1/120*(136*cos(d*x + c)^5 - 280*cos(d*x + c)^3 + 45*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 45*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 30*(4*d*x*cos(d*x + c)^4 - 8*d*x*cos(d*x + c)^2 + 5*cos(d*x + c)^3 + 4*d*x - 3*cos(d*x + c))*sin(d*x + c) + 120*cos(d*x + c))/((a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2 + a^2*d)*sin(d*x + c))","A",0
733,1,183,0,0.725979," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{192 \, \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + 270 \, \cos\left(d x + c\right)^{5} - 560 \, \cos\left(d x + c\right)^{3} + 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 210 \, \cos\left(d x + c\right)}{480 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 3 \, a^{2} d \cos\left(d x + c\right)^{4} + 3 \, a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"-1/480*(192*cos(d*x + c)^5*sin(d*x + c) + 270*cos(d*x + c)^5 - 560*cos(d*x + c)^3 + 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) - 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) + 210*cos(d*x + c))/(a^2*d*cos(d*x + c)^6 - 3*a^2*d*cos(d*x + c)^4 + 3*a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
734,1,216,0,0.913187," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{432 \, \cos\left(d x + c\right)^{7} - 672 \, \cos\left(d x + c\right)^{5} - 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 70 \, {\left(3 \, \cos\left(d x + c\right)^{5} + 8 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 3 \, a^{2} d \cos\left(d x + c\right)^{4} + 3 \, a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/1680*(432*cos(d*x + c)^7 - 672*cos(d*x + c)^5 - 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 70*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))*sin(d*x + c))/((a^2*d*cos(d*x + c)^6 - 3*a^2*d*cos(d*x + c)^4 + 3*a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","A",0
735,1,239,0,0.997149," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2310 \, \cos\left(d x + c\right)^{7} + 490 \, \cos\left(d x + c\right)^{5} - 8470 \, \cos\left(d x + c\right)^{3} - 1155 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 1155 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 1536 \, {\left(2 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right) + 2310 \, \cos\left(d x + c\right)}{26880 \, {\left(a^{2} d \cos\left(d x + c\right)^{8} - 4 \, a^{2} d \cos\left(d x + c\right)^{6} + 6 \, a^{2} d \cos\left(d x + c\right)^{4} - 4 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)}}"," ",0,"1/26880*(2310*cos(d*x + c)^7 + 490*cos(d*x + c)^5 - 8470*cos(d*x + c)^3 - 1155*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) + 1155*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 1536*(2*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*sin(d*x + c) + 2310*cos(d*x + c))/(a^2*d*cos(d*x + c)^8 - 4*a^2*d*cos(d*x + c)^6 + 6*a^2*d*cos(d*x + c)^4 - 4*a^2*d*cos(d*x + c)^2 + a^2*d)","A",0
736,1,269,0,0.841151," ","integrate(cos(d*x+c)^8*csc(d*x+c)^10/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3328 \, \cos\left(d x + c\right)^{9} - 14976 \, \cos\left(d x + c\right)^{7} + 16128 \, \cos\left(d x + c\right)^{5} - 945 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 945 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 630 \, {\left(3 \, \cos\left(d x + c\right)^{7} - 11 \, \cos\left(d x + c\right)^{5} - 11 \, \cos\left(d x + c\right)^{3} + 3 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40320 \, {\left(a^{2} d \cos\left(d x + c\right)^{8} - 4 \, a^{2} d \cos\left(d x + c\right)^{6} + 6 \, a^{2} d \cos\left(d x + c\right)^{4} - 4 \, a^{2} d \cos\left(d x + c\right)^{2} + a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/40320*(3328*cos(d*x + c)^9 - 14976*cos(d*x + c)^7 + 16128*cos(d*x + c)^5 - 945*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 945*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 630*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))*sin(d*x + c))/((a^2*d*cos(d*x + c)^8 - 4*a^2*d*cos(d*x + c)^6 + 6*a^2*d*cos(d*x + c)^4 - 4*a^2*d*cos(d*x + c)^2 + a^2*d)*sin(d*x + c))","A",0
737,1,294,0,0.904756," ","integrate(cos(d*x+c)^8*csc(d*x+c)^11/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5670 \, \cos\left(d x + c\right)^{9} - 26460 \, \cos\left(d x + c\right)^{7} + 16128 \, \cos\left(d x + c\right)^{5} + 26460 \, \cos\left(d x + c\right)^{3} - 2835 \, {\left(\cos\left(d x + c\right)^{10} - 5 \, \cos\left(d x + c\right)^{8} + 10 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2835 \, {\left(\cos\left(d x + c\right)^{10} - 5 \, \cos\left(d x + c\right)^{8} + 10 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 1024 \, {\left(8 \, \cos\left(d x + c\right)^{9} - 36 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right) - 5670 \, \cos\left(d x + c\right)}{161280 \, {\left(a^{2} d \cos\left(d x + c\right)^{10} - 5 \, a^{2} d \cos\left(d x + c\right)^{8} + 10 \, a^{2} d \cos\left(d x + c\right)^{6} - 10 \, a^{2} d \cos\left(d x + c\right)^{4} + 5 \, a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)}}"," ",0,"1/161280*(5670*cos(d*x + c)^9 - 26460*cos(d*x + c)^7 + 16128*cos(d*x + c)^5 + 26460*cos(d*x + c)^3 - 2835*(cos(d*x + c)^10 - 5*cos(d*x + c)^8 + 10*cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 5*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + 2835*(cos(d*x + c)^10 - 5*cos(d*x + c)^8 + 10*cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 5*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 1024*(8*cos(d*x + c)^9 - 36*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*sin(d*x + c) - 5670*cos(d*x + c))/(a^2*d*cos(d*x + c)^10 - 5*a^2*d*cos(d*x + c)^8 + 10*a^2*d*cos(d*x + c)^6 - 10*a^2*d*cos(d*x + c)^4 + 5*a^2*d*cos(d*x + c)^2 - a^2*d)","A",0
738,1,324,0,1.013150," ","integrate(cos(d*x+c)^8*csc(d*x+c)^12/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{34816 \, \cos\left(d x + c\right)^{11} - 191488 \, \cos\left(d x + c\right)^{9} + 430848 \, \cos\left(d x + c\right)^{7} - 354816 \, \cos\left(d x + c\right)^{5} - 10395 \, {\left(\cos\left(d x + c\right)^{10} - 5 \, \cos\left(d x + c\right)^{8} + 10 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 10395 \, {\left(\cos\left(d x + c\right)^{10} - 5 \, \cos\left(d x + c\right)^{8} + 10 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} + 5 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 1386 \, {\left(15 \, \cos\left(d x + c\right)^{9} - 70 \, \cos\left(d x + c\right)^{7} + 128 \, \cos\left(d x + c\right)^{5} + 70 \, \cos\left(d x + c\right)^{3} - 15 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{887040 \, {\left(a^{2} d \cos\left(d x + c\right)^{10} - 5 \, a^{2} d \cos\left(d x + c\right)^{8} + 10 \, a^{2} d \cos\left(d x + c\right)^{6} - 10 \, a^{2} d \cos\left(d x + c\right)^{4} + 5 \, a^{2} d \cos\left(d x + c\right)^{2} - a^{2} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/887040*(34816*cos(d*x + c)^11 - 191488*cos(d*x + c)^9 + 430848*cos(d*x + c)^7 - 354816*cos(d*x + c)^5 - 10395*(cos(d*x + c)^10 - 5*cos(d*x + c)^8 + 10*cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 5*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 10395*(cos(d*x + c)^10 - 5*cos(d*x + c)^8 + 10*cos(d*x + c)^6 - 10*cos(d*x + c)^4 + 5*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 1386*(15*cos(d*x + c)^9 - 70*cos(d*x + c)^7 + 128*cos(d*x + c)^5 + 70*cos(d*x + c)^3 - 15*cos(d*x + c))*sin(d*x + c))/((a^2*d*cos(d*x + c)^10 - 5*a^2*d*cos(d*x + c)^8 + 10*a^2*d*cos(d*x + c)^6 - 10*a^2*d*cos(d*x + c)^4 + 5*a^2*d*cos(d*x + c)^2 - a^2*d)*sin(d*x + c))","A",0
739,1,90,0,0.885275," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{5760 \, \cos\left(d x + c\right)^{7} - 18816 \, \cos\left(d x + c\right)^{5} + 17920 \, \cos\left(d x + c\right)^{3} + 3045 \, d x - 35 \, {\left(48 \, \cos\left(d x + c\right)^{7} - 328 \, \cos\left(d x + c\right)^{5} + 454 \, \cos\left(d x + c\right)^{3} - 87 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{13440 \, a^{3} d}"," ",0,"-1/13440*(5760*cos(d*x + c)^7 - 18816*cos(d*x + c)^5 + 17920*cos(d*x + c)^3 + 3045*d*x - 35*(48*cos(d*x + c)^7 - 328*cos(d*x + c)^5 + 454*cos(d*x + c)^3 - 87*cos(d*x + c))*sin(d*x + c))/(a^3*d)","A",0
740,1,80,0,0.652251," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{48 \, \cos\left(d x + c\right)^{7} - 336 \, \cos\left(d x + c\right)^{5} + 448 \, \cos\left(d x + c\right)^{3} + 105 \, d x + 21 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 18 \, \cos\left(d x + c\right)^{3} + 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{336 \, a^{3} d}"," ",0,"1/336*(48*cos(d*x + c)^7 - 336*cos(d*x + c)^5 + 448*cos(d*x + c)^3 + 105*d*x + 21*(8*cos(d*x + c)^5 - 18*cos(d*x + c)^3 + 5*cos(d*x + c))*sin(d*x + c))/(a^3*d)","A",0
741,1,70,0,0.843104," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{144 \, \cos\left(d x + c\right)^{5} - 320 \, \cos\left(d x + c\right)^{3} - 105 \, d x - 5 \, {\left(8 \, \cos\left(d x + c\right)^{5} - 50 \, \cos\left(d x + c\right)^{3} + 21 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, a^{3} d}"," ",0,"1/240*(144*cos(d*x + c)^5 - 320*cos(d*x + c)^3 - 105*d*x - 5*(8*cos(d*x + c)^5 - 50*cos(d*x + c)^3 + 21*cos(d*x + c))*sin(d*x + c))/(a^3*d)","A",0
742,1,84,0,0.944596," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{3} + 13 \, d x - {\left(2 \, \cos\left(d x + c\right)^{3} - 13 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 8 \, \cos\left(d x + c\right) + 4 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{8 \, a^{3} d}"," ",0,"-1/8*(8*cos(d*x + c)^3 + 13*d*x - (2*cos(d*x + c)^3 - 13*cos(d*x + c))*sin(d*x + c) - 8*cos(d*x + c) + 4*log(1/2*cos(d*x + c) + 1/2) - 4*log(-1/2*cos(d*x + c) + 1/2))/(a^3*d)","A",0
743,1,104,0,0.924361," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{9 \, \cos\left(d x + c\right)^{3} - {\left(2 \, \cos\left(d x + c\right)^{3} + 3 \, d x - 18 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 9 \, \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 9 \, \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, \cos\left(d x + c\right)}{6 \, a^{3} d \sin\left(d x + c\right)}"," ",0,"-1/6*(9*cos(d*x + c)^3 - (2*cos(d*x + c)^3 + 3*d*x - 18*cos(d*x + c))*sin(d*x + c) - 9*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 9*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*cos(d*x + c))/(a^3*d*sin(d*x + c))","A",0
744,1,130,0,0.926031," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, d x \cos\left(d x + c\right)^{2} + 12 \, \cos\left(d x + c\right)^{3} - 10 \, d x - 5 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(\cos\left(d x + c\right)^{3} + 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 10 \, \cos\left(d x + c\right)}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}"," ",0,"1/4*(10*d*x*cos(d*x + c)^2 + 12*cos(d*x + c)^3 - 10*d*x - 5*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + 5*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 2*(cos(d*x + c)^3 + 5*cos(d*x + c))*sin(d*x + c) - 10*cos(d*x + c))/(a^3*d*cos(d*x + c)^2 - a^3*d)","A",0
745,1,150,0,0.976091," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{32 \, \cos\left(d x + c\right)^{3} + 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(\cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, {\left(6 \, d x \cos\left(d x + c\right)^{2} + 2 \, \cos\left(d x + c\right)^{3} - 6 \, d x + \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 36 \, \cos\left(d x + c\right)}{12 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(32*cos(d*x + c)^3 + 3*(cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*(6*d*x*cos(d*x + c)^2 + 2*cos(d*x + c)^3 - 6*d*x + cos(d*x + c))*sin(d*x + c) - 36*cos(d*x + c))/((a^3*d*cos(d*x + c)^2 - a^3*d)*sin(d*x + c))","A",0
746,1,164,0,0.762562," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{16 \, d x \cos\left(d x + c\right)^{4} - 32 \, d x \cos\left(d x + c\right)^{2} + 22 \, \cos\left(d x + c\right)^{3} + 16 \, d x + 13 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 13 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 16 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 26 \, \cos\left(d x + c\right)}{16 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)}}"," ",0,"1/16*(16*d*x*cos(d*x + c)^4 - 32*d*x*cos(d*x + c)^2 + 22*cos(d*x + c)^3 + 16*d*x + 13*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) - 13*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) + 16*cos(d*x + c)*sin(d*x + c) - 26*cos(d*x + c))/(a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d)","A",0
747,1,169,0,0.922469," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{272 \, \cos\left(d x + c\right)^{5} - 320 \, \cos\left(d x + c\right)^{3} - 105 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 105 \, {\left(\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left(\cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"1/240*(272*cos(d*x + c)^5 - 320*cos(d*x + c)^3 - 105*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 105*(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*(cos(d*x + c)^3 - 7*cos(d*x + c))*sin(d*x + c))/((a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^2 + a^3*d)*sin(d*x + c))","A",0
748,1,196,0,0.881767," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{210 \, \cos\left(d x + c\right)^{5} - 80 \, \cos\left(d x + c\right)^{3} - 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(11 \, \cos\left(d x + c\right)^{5} - 20 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right) - 210 \, \cos\left(d x + c\right)}{480 \, {\left(a^{3} d \cos\left(d x + c\right)^{6} - 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}"," ",0,"-1/480*(210*cos(d*x + c)^5 - 80*cos(d*x + c)^3 - 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2) + 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2) - 32*(11*cos(d*x + c)^5 - 20*cos(d*x + c)^3)*sin(d*x + c) - 210*cos(d*x + c))/(a^3*d*cos(d*x + c)^6 - 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^2 - a^3*d)","A",0
749,1,226,0,0.884921," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{320 \, \cos\left(d x + c\right)^{7} - 1120 \, \cos\left(d x + c\right)^{5} + 896 \, \cos\left(d x + c\right)^{3} - 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 105 \, {\left(\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 42 \, {\left(5 \, \cos\left(d x + c\right)^{5} - 8 \, \cos\left(d x + c\right)^{3} - 5 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{672 \, {\left(a^{3} d \cos\left(d x + c\right)^{6} - 3 \, a^{3} d \cos\left(d x + c\right)^{4} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)} \sin\left(d x + c\right)}"," ",0,"1/672*(320*cos(d*x + c)^7 - 1120*cos(d*x + c)^5 + 896*cos(d*x + c)^3 - 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 105*(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 42*(5*cos(d*x + c)^5 - 8*cos(d*x + c)^3 - 5*cos(d*x + c))*sin(d*x + c))/((a^3*d*cos(d*x + c)^6 - 3*a^3*d*cos(d*x + c)^4 + 3*a^3*d*cos(d*x + c)^2 - a^3*d)*sin(d*x + c))","A",0
750,1,249,0,0.986986," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6090 \, \cos\left(d x + c\right)^{7} - 22330 \, \cos\left(d x + c\right)^{5} + 13510 \, \cos\left(d x + c\right)^{3} - 3045 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3045 \, {\left(\cos\left(d x + c\right)^{8} - 4 \, \cos\left(d x + c\right)^{6} + 6 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} + 1\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 256 \, {\left(38 \, \cos\left(d x + c\right)^{7} - 133 \, \cos\left(d x + c\right)^{5} + 140 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right) + 6090 \, \cos\left(d x + c\right)}{26880 \, {\left(a^{3} d \cos\left(d x + c\right)^{8} - 4 \, a^{3} d \cos\left(d x + c\right)^{6} + 6 \, a^{3} d \cos\left(d x + c\right)^{4} - 4 \, a^{3} d \cos\left(d x + c\right)^{2} + a^{3} d\right)}}"," ",0,"-1/26880*(6090*cos(d*x + c)^7 - 22330*cos(d*x + c)^5 + 13510*cos(d*x + c)^3 - 3045*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(1/2*cos(d*x + c) + 1/2) + 3045*(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1)*log(-1/2*cos(d*x + c) + 1/2) - 256*(38*cos(d*x + c)^7 - 133*cos(d*x + c)^5 + 140*cos(d*x + c)^3)*sin(d*x + c) + 6090*cos(d*x + c))/(a^3*d*cos(d*x + c)^8 - 4*a^3*d*cos(d*x + c)^6 + 6*a^3*d*cos(d*x + c)^4 - 4*a^3*d*cos(d*x + c)^2 + a^3*d)","A",0
751,1,130,0,0.745055," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{3} + 9 \, a d x - 12 \, a \cos\left(d x + c\right)^{2} + 3 \, {\left(3 \, a d x - 5 \, a\right)} \cos\left(d x + c\right) - {\left(2 \, a \cos\left(d x + c\right)^{3} + 9 \, a d x + 3 \, a \cos\left(d x + c\right)^{2} - 9 \, a \cos\left(d x + c\right) + 6 \, a\right)} \sin\left(d x + c\right) - 6 \, a}{6 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"-1/6*(2*a*cos(d*x + c)^4 - a*cos(d*x + c)^3 + 9*a*d*x - 12*a*cos(d*x + c)^2 + 3*(3*a*d*x - 5*a)*cos(d*x + c) - (2*a*cos(d*x + c)^3 + 9*a*d*x + 3*a*cos(d*x + c)^2 - 9*a*cos(d*x + c) + 6*a)*sin(d*x + c) - 6*a)/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
752,1,104,0,0.866479," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right)^{3} - 3 \, a d x + 2 \, a \cos\left(d x + c\right)^{2} - 3 \, {\left(a d x - a\right)} \cos\left(d x + c\right) + {\left(3 \, a d x + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) + 2 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{2 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/2*(a*cos(d*x + c)^3 - 3*a*d*x + 2*a*cos(d*x + c)^2 - 3*(a*d*x - a)*cos(d*x + c) + (3*a*d*x + a*cos(d*x + c)^2 - a*cos(d*x + c) + 2*a)*sin(d*x + c) + 2*a)/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
753,1,80,0,0.844702," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a d x - a \cos\left(d x + c\right)^{2} + {\left(a d x - 2 \, a\right)} \cos\left(d x + c\right) - {\left(a d x - a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - a}{d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d}"," ",0,"-(a*d*x - a*cos(d*x + c)^2 + (a*d*x - 2*a)*cos(d*x + c) - (a*d*x - a*cos(d*x + c) + a)*sin(d*x + c) - a)/(d*cos(d*x + c) - d*sin(d*x + c) + d)","B",0
754,1,60,0,0.949525," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a d x + {\left(a d x - a\right)} \cos\left(d x + c\right) - {\left(a d x + a\right)} \sin\left(d x + c\right) - a}{d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d}"," ",0,"-(a*d*x + (a*d*x - a)*cos(d*x + c) - (a*d*x + a)*sin(d*x + c) - a)/(d*cos(d*x + c) - d*sin(d*x + c) + d)","B",0
755,1,108,0,0.923644," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a \cos\left(d x + c\right) - a \sin\left(d x + c\right) + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, a \sin\left(d x + c\right) + 2 \, a}{2 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/2*(2*a*cos(d*x + c) - (a*cos(d*x + c) - a*sin(d*x + c) + a)*log(1/2*cos(d*x + c) + 1/2) + (a*cos(d*x + c) - a*sin(d*x + c) + a)*log(-1/2*cos(d*x + c) + 1/2) + 2*a*sin(d*x + c) + 2*a)/(d*cos(d*x + c) - d*sin(d*x + c) + d)","B",0
756,1,165,0,0.827333," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a \cos\left(d x + c\right)^{2} + 2 \, a \cos\left(d x + c\right) + {\left(a \cos\left(d x + c\right)^{2} + {\left(a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a \cos\left(d x + c\right)^{2} + {\left(a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, a \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) - 2 \, a}{2 \, {\left(d \cos\left(d x + c\right)^{2} + {\left(d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"-1/2*(4*a*cos(d*x + c)^2 + 2*a*cos(d*x + c) + (a*cos(d*x + c)^2 + (a*cos(d*x + c) + a)*sin(d*x + c) - a)*log(1/2*cos(d*x + c) + 1/2) - (a*cos(d*x + c)^2 + (a*cos(d*x + c) + a)*sin(d*x + c) - a)*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*a*cos(d*x + c) + a)*sin(d*x + c) - 2*a)/(d*cos(d*x + c)^2 + (d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
757,1,261,0,0.783819," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, a \cos\left(d x + c\right)^{3} + 6 \, a \cos\left(d x + c\right)^{2} - 6 \, a \cos\left(d x + c\right) - 3 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(4 \, a \cos\left(d x + c\right)^{2} + a \cos\left(d x + c\right) - 2 \, a\right)} \sin\left(d x + c\right) - 4 \, a}{4 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/4*(8*a*cos(d*x + c)^3 + 6*a*cos(d*x + c)^2 - 6*a*cos(d*x + c) - 3*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - (a*cos(d*x + c)^2 - a)*sin(d*x + c) - a)*log(1/2*cos(d*x + c) + 1/2) + 3*(a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - (a*cos(d*x + c)^2 - a)*sin(d*x + c) - a)*log(-1/2*cos(d*x + c) + 1/2) + 2*(4*a*cos(d*x + c)^2 + a*cos(d*x + c) - 2*a)*sin(d*x + c) - 4*a)/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - (d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
758,1,308,0,0.715411," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{32 \, a \cos\left(d x + c\right)^{4} + 14 \, a \cos\left(d x + c\right)^{3} - 48 \, a \cos\left(d x + c\right)^{2} - 18 \, a \cos\left(d x + c\right) + 9 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 9 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right)^{2} - a \cos\left(d x + c\right) - a\right)} \sin\left(d x + c\right) + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(16 \, a \cos\left(d x + c\right)^{3} + 9 \, a \cos\left(d x + c\right)^{2} - 15 \, a \cos\left(d x + c\right) - 6 \, a\right)} \sin\left(d x + c\right) + 12 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"-1/12*(32*a*cos(d*x + c)^4 + 14*a*cos(d*x + c)^3 - 48*a*cos(d*x + c)^2 - 18*a*cos(d*x + c) + 9*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + (a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - a)*sin(d*x + c) + a)*log(1/2*cos(d*x + c) + 1/2) - 9*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + (a*cos(d*x + c)^3 + a*cos(d*x + c)^2 - a*cos(d*x + c) - a)*sin(d*x + c) + a)*log(-1/2*cos(d*x + c) + 1/2) - 2*(16*a*cos(d*x + c)^3 + 9*a*cos(d*x + c)^2 - 15*a*cos(d*x + c) - 6*a)*sin(d*x + c) + 12*a)/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + (d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - d)*sin(d*x + c) + d)","B",0
759,1,152,0,0.921232," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{2} \cos\left(d x + c\right)^{3} + 9 \, a^{2} d x - 9 \, a^{2} \cos\left(d x + c\right)^{2} - 6 \, a^{2} + 3 \, {\left(3 \, a^{2} d x - 4 \, a^{2}\right)} \cos\left(d x + c\right) - {\left(a^{2} \cos\left(d x + c\right)^{3} + 9 \, a^{2} d x + 3 \, a^{2} \cos\left(d x + c\right)^{2} - 6 \, a^{2} \cos\left(d x + c\right) + 6 \, a^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"-1/3*(a^2*cos(d*x + c)^4 - 2*a^2*cos(d*x + c)^3 + 9*a^2*d*x - 9*a^2*cos(d*x + c)^2 - 6*a^2 + 3*(3*a^2*d*x - 4*a^2)*cos(d*x + c) - (a^2*cos(d*x + c)^3 + 9*a^2*d*x + 3*a^2*cos(d*x + c)^2 - 6*a^2*cos(d*x + c) + 6*a^2)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
760,1,125,0,0.857349," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{a^{2} \cos\left(d x + c\right)^{3} - 5 \, a^{2} d x + 4 \, a^{2} \cos\left(d x + c\right)^{2} + 4 \, a^{2} - {\left(5 \, a^{2} d x - 7 \, a^{2}\right)} \cos\left(d x + c\right) + {\left(5 \, a^{2} d x + a^{2} \cos\left(d x + c\right)^{2} - 3 \, a^{2} \cos\left(d x + c\right) + 4 \, a^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/2*(a^2*cos(d*x + c)^3 - 5*a^2*d*x + 4*a^2*cos(d*x + c)^2 + 4*a^2 - (5*a^2*d*x - 7*a^2)*cos(d*x + c) + (5*a^2*d*x + a^2*cos(d*x + c)^2 - 3*a^2*cos(d*x + c) + 4*a^2)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
761,1,101,0,0.607100," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} d x - a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} + {\left(2 \, a^{2} d x - 3 \, a^{2}\right)} \cos\left(d x + c\right) - {\left(2 \, a^{2} d x - a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d}"," ",0,"-(2*a^2*d*x - a^2*cos(d*x + c)^2 - 2*a^2 + (2*a^2*d*x - 3*a^2)*cos(d*x + c) - (2*a^2*d*x - a^2*cos(d*x + c) + 2*a^2)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","B",0
762,1,126,0,0.854456," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} \cos\left(d x + c\right) + 4 \, a^{2} \sin\left(d x + c\right) + 4 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right) - a^{2} \sin\left(d x + c\right) + a^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{2} \cos\left(d x + c\right) - a^{2} \sin\left(d x + c\right) + a^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/2*(4*a^2*cos(d*x + c) + 4*a^2*sin(d*x + c) + 4*a^2 - (a^2*cos(d*x + c) - a^2*sin(d*x + c) + a^2)*log(1/2*cos(d*x + c) + 1/2) + (a^2*cos(d*x + c) - a^2*sin(d*x + c) + a^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","B",0
763,1,192,0,0.710148," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right) - 2 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} + {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} + {\left(a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(3 \, a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right)^{2} + {\left(d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d}"," ",0,"-(3*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c) - 2*a^2 + (a^2*cos(d*x + c)^2 - a^2 + (a^2*cos(d*x + c) + a^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - (a^2*cos(d*x + c)^2 - a^2 + (a^2*cos(d*x + c) + a^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - (3*a^2*cos(d*x + c) + 2*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2 + (d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
764,1,300,0,0.798351," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, a^{2} \cos\left(d x + c\right)^{3} + 10 \, a^{2} \cos\left(d x + c\right)^{2} - 14 \, a^{2} \cos\left(d x + c\right) - 8 \, a^{2} - 5 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(8 \, a^{2} \cos\left(d x + c\right)^{2} + 3 \, a^{2} \cos\left(d x + c\right) - 4 \, a^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/4*(16*a^2*cos(d*x + c)^3 + 10*a^2*cos(d*x + c)^2 - 14*a^2*cos(d*x + c) - 8*a^2 - 5*(a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - a^2 - (a^2*cos(d*x + c)^2 - a^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 5*(a^2*cos(d*x + c)^3 + a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - a^2 - (a^2*cos(d*x + c)^2 - a^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(8*a^2*cos(d*x + c)^2 + 3*a^2*cos(d*x + c) - 4*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - (d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
765,1,178,0,0.863974," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} \cos\left(d x + c\right)^{5} + 8 \, a^{3} \cos\left(d x + c\right)^{4} - 15 \, a^{3} \cos\left(d x + c\right)^{3} + 51 \, a^{3} d x - 56 \, a^{3} \cos\left(d x + c\right)^{2} - 32 \, a^{3} + {\left(51 \, a^{3} d x - 67 \, a^{3}\right)} \cos\left(d x + c\right) + {\left(2 \, a^{3} \cos\left(d x + c\right)^{4} - 6 \, a^{3} \cos\left(d x + c\right)^{3} - 51 \, a^{3} d x - 21 \, a^{3} \cos\left(d x + c\right)^{2} + 35 \, a^{3} \cos\left(d x + c\right) - 32 \, a^{3}\right)} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"-1/8*(2*a^3*cos(d*x + c)^5 + 8*a^3*cos(d*x + c)^4 - 15*a^3*cos(d*x + c)^3 + 51*a^3*d*x - 56*a^3*cos(d*x + c)^2 - 32*a^3 + (51*a^3*d*x - 67*a^3)*cos(d*x + c) + (2*a^3*cos(d*x + c)^4 - 6*a^3*cos(d*x + c)^3 - 51*a^3*d*x - 21*a^3*cos(d*x + c)^2 + 35*a^3*cos(d*x + c) - 32*a^3)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
766,1,154,0,0.828935," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} \cos\left(d x + c\right)^{4} - 7 \, a^{3} \cos\left(d x + c\right)^{3} + 33 \, a^{3} d x - 30 \, a^{3} \cos\left(d x + c\right)^{2} - 24 \, a^{3} + 3 \, {\left(11 \, a^{3} d x - 15 \, a^{3}\right)} \cos\left(d x + c\right) - {\left(2 \, a^{3} \cos\left(d x + c\right)^{3} + 33 \, a^{3} d x + 9 \, a^{3} \cos\left(d x + c\right)^{2} - 21 \, a^{3} \cos\left(d x + c\right) + 24 \, a^{3}\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"-1/6*(2*a^3*cos(d*x + c)^4 - 7*a^3*cos(d*x + c)^3 + 33*a^3*d*x - 30*a^3*cos(d*x + c)^2 - 24*a^3 + 3*(11*a^3*d*x - 15*a^3)*cos(d*x + c) - (2*a^3*cos(d*x + c)^3 + 33*a^3*d*x + 9*a^3*cos(d*x + c)^2 - 21*a^3*cos(d*x + c) + 24*a^3)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
767,1,125,0,0.697666," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{a^{3} \cos\left(d x + c\right)^{3} - 9 \, a^{3} d x + 6 \, a^{3} \cos\left(d x + c\right)^{2} + 8 \, a^{3} - {\left(9 \, a^{3} d x - 13 \, a^{3}\right)} \cos\left(d x + c\right) + {\left(9 \, a^{3} d x + a^{3} \cos\left(d x + c\right)^{2} - 5 \, a^{3} \cos\left(d x + c\right) + 8 \, a^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/2*(a^3*cos(d*x + c)^3 - 9*a^3*d*x + 6*a^3*cos(d*x + c)^2 + 8*a^3 - (9*a^3*d*x - 13*a^3)*cos(d*x + c) + (9*a^3*d*x + a^3*cos(d*x + c)^2 - 5*a^3*cos(d*x + c) + 8*a^3)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
768,1,151,0,0.918810," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} d x - 8 \, a^{3} + 2 \, {\left(a^{3} d x - 4 \, a^{3}\right)} \cos\left(d x + c\right) + {\left(a^{3} \cos\left(d x + c\right) - a^{3} \sin\left(d x + c\right) + a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{3} \cos\left(d x + c\right) - a^{3} \sin\left(d x + c\right) + a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{3} d x + 4 \, a^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"-1/2*(2*a^3*d*x - 8*a^3 + 2*(a^3*d*x - 4*a^3)*cos(d*x + c) + (a^3*cos(d*x + c) - a^3*sin(d*x + c) + a^3)*log(1/2*cos(d*x + c) + 1/2) - (a^3*cos(d*x + c) - a^3*sin(d*x + c) + a^3)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^3*d*x + 4*a^3)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","B",0
769,1,194,0,0.935593," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{10 \, a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \cos\left(d x + c\right) - 8 \, a^{3} + 3 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3} + {\left(a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3} + {\left(a^{3} \cos\left(d x + c\right) + a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(5 \, a^{3} \cos\left(d x + c\right) + 4 \, a^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + {\left(d \cos\left(d x + c\right) + d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"-1/2*(10*a^3*cos(d*x + c)^2 + 2*a^3*cos(d*x + c) - 8*a^3 + 3*(a^3*cos(d*x + c)^2 - a^3 + (a^3*cos(d*x + c) + a^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^3*cos(d*x + c)^2 - a^3 + (a^3*cos(d*x + c) + a^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(5*a^3*cos(d*x + c) + 4*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2 + (d*cos(d*x + c) + d)*sin(d*x + c) - d)","B",0
770,1,300,0,0.686808," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{28 \, a^{3} \cos\left(d x + c\right)^{3} + 18 \, a^{3} \cos\left(d x + c\right)^{2} - 26 \, a^{3} \cos\left(d x + c\right) - 16 \, a^{3} - 9 \, {\left(a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left(a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(14 \, a^{3} \cos\left(d x + c\right)^{2} + 5 \, a^{3} \cos\left(d x + c\right) - 8 \, a^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) - d\right)}}"," ",0,"1/4*(28*a^3*cos(d*x + c)^3 + 18*a^3*cos(d*x + c)^2 - 26*a^3*cos(d*x + c) - 16*a^3 - 9*(a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - a^3 - (a^3*cos(d*x + c)^2 - a^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 9*(a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - a^3 - (a^3*cos(d*x + c)^2 - a^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(14*a^3*cos(d*x + c)^2 + 5*a^3*cos(d*x + c) - 8*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - (d*cos(d*x + c)^2 - d)*sin(d*x + c) - d)","B",0
771,1,354,0,0.869437," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{104 \, a^{3} \cos\left(d x + c\right)^{4} + 38 \, a^{3} \cos\left(d x + c\right)^{3} - 156 \, a^{3} \cos\left(d x + c\right)^{2} - 42 \, a^{3} \cos\left(d x + c\right) + 48 \, a^{3} + 33 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 33 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{3} + a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(52 \, a^{3} \cos\left(d x + c\right)^{3} + 33 \, a^{3} \cos\left(d x + c\right)^{2} - 45 \, a^{3} \cos\left(d x + c\right) - 24 \, a^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - d\right)} \sin\left(d x + c\right) + d\right)}}"," ",0,"-1/12*(104*a^3*cos(d*x + c)^4 + 38*a^3*cos(d*x + c)^3 - 156*a^3*cos(d*x + c)^2 - 42*a^3*cos(d*x + c) + 48*a^3 + 33*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3 + (a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - a^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 33*(a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^2 + a^3 + (a^3*cos(d*x + c)^3 + a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - a^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(52*a^3*cos(d*x + c)^3 + 33*a^3*cos(d*x + c)^2 - 45*a^3*cos(d*x + c) - 24*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + (d*cos(d*x + c)^3 + d*cos(d*x + c)^2 - d*cos(d*x + c) - d)*sin(d*x + c) + d)","B",0
772,1,80,0,0.848516," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, d x \cos\left(d x + c\right) + 7 \, \cos\left(d x + c\right)^{2} + {\left(3 \, d x \cos\left(d x + c\right) + 3 \, \cos\left(d x + c\right)^{2} + 2\right)} \sin\left(d x + c\right) + 1}{3 \, {\left(a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)}}"," ",0,"1/3*(3*d*x*cos(d*x + c) + 7*cos(d*x + c)^2 + (3*d*x*cos(d*x + c) + 3*cos(d*x + c)^2 + 2)*sin(d*x + c) + 1)/(a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))","A",0
773,1,70,0,0.850719," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, d x \cos\left(d x + c\right) + 4 \, \cos\left(d x + c\right)^{2} + {\left(3 \, d x \cos\left(d x + c\right) - 1\right)} \sin\left(d x + c\right) - 2}{3 \, {\left(a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*d*x*cos(d*x + c) + 4*cos(d*x + c)^2 + (3*d*x*cos(d*x + c) - 1)*sin(d*x + c) - 2)/(a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))","A",0
774,1,47,0,0.892065," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{2} + 2 \, \sin\left(d x + c\right) + 1}{3 \, {\left(a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)}}"," ",0,"1/3*(cos(d*x + c)^2 + 2*sin(d*x + c) + 1)/(a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))","A",0
775,1,47,0,0.917388," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\cos\left(d x + c\right)^{2} - \sin\left(d x + c\right) - 2}{3 \, {\left(a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(cos(d*x + c)^2 - sin(d*x + c) - 2)/(a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))","A",0
776,1,115,0,0.729368," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(\cos\left(d x + c\right) \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(\cos\left(d x + c\right) \sin\left(d x + c\right) + \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, \sin\left(d x + c\right) + 4}{6 \, {\left(a d \cos\left(d x + c\right) \sin\left(d x + c\right) + a d \cos\left(d x + c\right)\right)}}"," ",0,"1/6*(4*cos(d*x + c)^2 - 3*(cos(d*x + c)*sin(d*x + c) + cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(cos(d*x + c)*sin(d*x + c) + cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*sin(d*x + c) + 4)/(a*d*cos(d*x + c)*sin(d*x + c) + a*d*cos(d*x + c))","A",0
777,1,162,0,1.223247," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, \cos\left(d x + c\right)^{2} + 3 \, {\left(\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right) \sin\left(d x + c\right) - \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right) \sin\left(d x + c\right) - \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(8 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - 4}{6 \, {\left(a d \cos\left(d x + c\right)^{3} - a d \cos\left(d x + c\right) \sin\left(d x + c\right) - a d \cos\left(d x + c\right)\right)}}"," ",0,"1/6*(10*cos(d*x + c)^2 + 3*(cos(d*x + c)^3 - cos(d*x + c)*sin(d*x + c) - cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(cos(d*x + c)^3 - cos(d*x + c)*sin(d*x + c) - cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(8*cos(d*x + c)^2 - 1)*sin(d*x + c) - 4)/(a*d*cos(d*x + c)^3 - a*d*cos(d*x + c)*sin(d*x + c) - a*d*cos(d*x + c))","A",0
778,1,132,0,0.846420," ","integrate(sec(d*x+c)^2*sin(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{45 \, d x \cos\left(d x + c\right)^{3} + 10 \, \cos\left(d x + c\right)^{4} - 90 \, d x \cos\left(d x + c\right) - 78 \, \cos\left(d x + c\right)^{2} - {\left(5 \, \cos\left(d x + c\right)^{4} + 90 \, d x \cos\left(d x + c\right) + 84 \, \cos\left(d x + c\right)^{2} - 6\right)} \sin\left(d x + c\right) + 4}{10 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/10*(45*d*x*cos(d*x + c)^3 + 10*cos(d*x + c)^4 - 90*d*x*cos(d*x + c) - 78*cos(d*x + c)^2 - (5*cos(d*x + c)^4 + 90*d*x*cos(d*x + c) + 84*cos(d*x + c)^2 - 6)*sin(d*x + c) + 4)/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","A",0
779,1,122,0,0.905685," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{30 \, d x \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)^{4} - 60 \, d x \cos\left(d x + c\right) - 62 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(30 \, d x \cos\left(d x + c\right) + 38 \, \cos\left(d x + c\right)^{2} + 3\right)} \sin\left(d x + c\right) - 9}{15 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"1/15*(30*d*x*cos(d*x + c)^3 + 15*cos(d*x + c)^4 - 60*d*x*cos(d*x + c) - 62*cos(d*x + c)^2 - 2*(30*d*x*cos(d*x + c) + 38*cos(d*x + c)^2 + 3)*sin(d*x + c) - 9)/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","A",0
780,1,112,0,0.794763," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{15 \, d x \cos\left(d x + c\right)^{3} - 30 \, d x \cos\left(d x + c\right) - 22 \, \cos\left(d x + c\right)^{2} - {\left(30 \, d x \cos\left(d x + c\right) + 26 \, \cos\left(d x + c\right)^{2} - 9\right)} \sin\left(d x + c\right) + 6}{15 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/15*(15*d*x*cos(d*x + c)^3 - 30*d*x*cos(d*x + c) - 22*cos(d*x + c)^2 - (30*d*x*cos(d*x + c) + 26*cos(d*x + c)^2 - 9)*sin(d*x + c) + 6)/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","A",0
781,1,76,0,0.705739," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) - 3}{5 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"1/5*(cos(d*x + c)^2 - 2*(cos(d*x + c)^2 + 1)*sin(d*x + c) - 3)/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","A",0
782,1,77,0,0.853709," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{2} + {\left(\cos\left(d x + c\right)^{2} - 9\right)} \sin\left(d x + c\right) - 6}{15 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"1/15*(2*cos(d*x + c)^2 + (cos(d*x + c)^2 - 9)*sin(d*x + c) - 6)/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","A",0
783,1,80,0,0.630967," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{8 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, \cos\left(d x + c\right)^{2} - 3\right)} \sin\left(d x + c\right) - 9}{15 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"1/15*(8*cos(d*x + c)^2 + 2*(2*cos(d*x + c)^2 - 3)*sin(d*x + c) - 9)/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","A",0
784,1,168,0,0.786621," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{34 \, \cos\left(d x + c\right)^{2} + 15 \, {\left(\cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(\cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(8 \, \cos\left(d x + c\right)^{2} + 3\right)} \sin\left(d x + c\right) + 18}{30 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)\right)}}"," ",0,"-1/30*(34*cos(d*x + c)^2 + 15*(cos(d*x + c)^3 - 2*cos(d*x + c)*sin(d*x + c) - 2*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 15*(cos(d*x + c)^3 - 2*cos(d*x + c)*sin(d*x + c) - 2*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(8*cos(d*x + c)^2 + 3)*sin(d*x + c) + 18)/(a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c)*sin(d*x + c) - 2*a^2*d*cos(d*x + c))","A",0
785,1,218,0,0.936001," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{56 \, \cos\left(d x + c\right)^{4} - 80 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(2 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(2 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{3} - 2 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(41 \, \cos\left(d x + c\right)^{2} - 3\right)} \sin\left(d x + c\right) + 9}{15 \, {\left(2 \, a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right) + {\left(a^{2} d \cos\left(d x + c\right)^{3} - 2 \, a^{2} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/15*(56*cos(d*x + c)^4 - 80*cos(d*x + c)^2 - 15*(2*cos(d*x + c)^3 + (cos(d*x + c)^3 - 2*cos(d*x + c))*sin(d*x + c) - 2*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 15*(2*cos(d*x + c)^3 + (cos(d*x + c)^3 - 2*cos(d*x + c))*sin(d*x + c) - 2*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(41*cos(d*x + c)^2 - 3)*sin(d*x + c) + 9)/(2*a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c) + (a^2*d*cos(d*x + c)^3 - 2*a^2*d*cos(d*x + c))*sin(d*x + c))","A",0
786,1,260,0,0.938744," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{166 \, \cos\left(d x + c\right)^{4} - 144 \, \cos\left(d x + c\right)^{2} + 45 \, {\left(\cos\left(d x + c\right)^{5} - 3 \, \cos\left(d x + c\right)^{3} - 2 \, {\left(\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 45 \, {\left(\cos\left(d x + c\right)^{5} - 3 \, \cos\left(d x + c\right)^{3} - 2 \, {\left(\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 2 \, \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(32 \, \cos\left(d x + c\right)^{4} - 35 \, \cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) - 12}{20 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 3 \, a^{2} d \cos\left(d x + c\right)^{3} + 2 \, a^{2} d \cos\left(d x + c\right) - 2 \, {\left(a^{2} d \cos\left(d x + c\right)^{3} - a^{2} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/20*(166*cos(d*x + c)^4 - 144*cos(d*x + c)^2 + 45*(cos(d*x + c)^5 - 3*cos(d*x + c)^3 - 2*(cos(d*x + c)^3 - cos(d*x + c))*sin(d*x + c) + 2*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 45*(cos(d*x + c)^5 - 3*cos(d*x + c)^3 - 2*(cos(d*x + c)^3 - cos(d*x + c))*sin(d*x + c) + 2*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(32*cos(d*x + c)^4 - 35*cos(d*x + c)^2 - 2)*sin(d*x + c) - 12)/(a^2*d*cos(d*x + c)^5 - 3*a^2*d*cos(d*x + c)^3 + 2*a^2*d*cos(d*x + c) - 2*(a^2*d*cos(d*x + c)^3 - a^2*d*cos(d*x + c))*sin(d*x + c))","A",0
787,1,159,0,1.111086," ","integrate(sec(d*x+c)^2*sin(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{315 \, d x \cos\left(d x + c\right)^{3} + 286 \, \cos\left(d x + c\right)^{4} - 420 \, d x \cos\left(d x + c\right) - 447 \, \cos\left(d x + c\right)^{2} + {\left(105 \, d x \cos\left(d x + c\right)^{3} + 35 \, \cos\left(d x + c\right)^{4} - 420 \, d x \cos\left(d x + c\right) - 438 \, \cos\left(d x + c\right)^{2} - 20\right)} \sin\left(d x + c\right) - 15}{35 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/35*(315*d*x*cos(d*x + c)^3 + 286*cos(d*x + c)^4 - 420*d*x*cos(d*x + c) - 447*cos(d*x + c)^2 + (105*d*x*cos(d*x + c)^3 + 35*cos(d*x + c)^4 - 420*d*x*cos(d*x + c) - 438*cos(d*x + c)^2 - 20)*sin(d*x + c) - 15)/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
788,1,150,0,0.986386," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{315 \, d x \cos\left(d x + c\right)^{3} + 221 \, \cos\left(d x + c\right)^{4} - 420 \, d x \cos\left(d x + c\right) - 417 \, \cos\left(d x + c\right)^{2} + 3 \, {\left(35 \, d x \cos\left(d x + c\right)^{3} - 140 \, d x \cos\left(d x + c\right) - 116 \, \cos\left(d x + c\right)^{2} + 15\right)} \sin\left(d x + c\right) + 60}{105 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/105*(315*d*x*cos(d*x + c)^3 + 221*cos(d*x + c)^4 - 420*d*x*cos(d*x + c) - 417*cos(d*x + c)^2 + 3*(35*d*x*cos(d*x + c)^3 - 140*d*x*cos(d*x + c) - 116*cos(d*x + c)^2 + 15)*sin(d*x + c) + 60)/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
789,1,104,0,0.955277," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{13 \, \cos\left(d x + c\right)^{4} - 6 \, \cos\left(d x + c\right)^{2} - 4 \, {\left(\cos\left(d x + c\right)^{2} + 5\right)} \sin\left(d x + c\right) - 15}{35 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/35*(13*cos(d*x + c)^4 - 6*cos(d*x + c)^2 - 4*(cos(d*x + c)^2 + 5)*sin(d*x + c) - 15)/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
790,1,102,0,0.862476," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{4} + 13 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(\cos\left(d x + c\right)^{2} + 5\right)} \sin\left(d x + c\right) - 20}{35 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/35*(cos(d*x + c)^4 + 13*cos(d*x + c)^2 - 3*(cos(d*x + c)^2 + 5)*sin(d*x + c) - 20)/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
791,1,104,0,1.185290," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{4} - 9 \, \cos\left(d x + c\right)^{2} - 6 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 9}{21 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/21*(2*cos(d*x + c)^4 - 9*cos(d*x + c)^2 - 6*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 9)/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
792,1,106,0,1.113214," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, \cos\left(d x + c\right)^{4} - 27 \, \cos\left(d x + c\right)^{2} - 3 \, {\left(6 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) + 20}{35 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/35*(6*cos(d*x + c)^4 - 27*cos(d*x + c)^2 - 3*(6*cos(d*x + c)^2 - 5)*sin(d*x + c) + 20)/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
793,1,218,0,1.115408," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{272 \, \cos\left(d x + c\right)^{4} - 594 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(3 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{3} - 4 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 4 \, \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(3 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{3} - 4 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) - 4 \, \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 6 \, {\left(101 \, \cos\left(d x + c\right)^{2} + 15\right)} \sin\left(d x + c\right) - 120}{210 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right) + {\left(a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/210*(272*cos(d*x + c)^4 - 594*cos(d*x + c)^2 - 105*(3*cos(d*x + c)^3 + (cos(d*x + c)^3 - 4*cos(d*x + c))*sin(d*x + c) - 4*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 105*(3*cos(d*x + c)^3 + (cos(d*x + c)^3 - 4*cos(d*x + c))*sin(d*x + c) - 4*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 6*(101*cos(d*x + c)^2 + 15)*sin(d*x + c) - 120)/(3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c) + (a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
794,1,265,0,1.270034," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{846 \, \cos\left(d x + c\right)^{4} - 956 \, \cos\left(d x + c\right)^{2} + 105 \, {\left(\cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3} - {\left(3 \, \cos\left(d x + c\right)^{3} - 4 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 105 \, {\left(\cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3} - {\left(3 \, \cos\left(d x + c\right)^{3} - 4 \, \cos\left(d x + c\right)\right)} \sin\left(d x + c\right) + 4 \, \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(176 \, \cos\left(d x + c\right)^{4} - 477 \, \cos\left(d x + c\right)^{2} + 15\right)} \sin\left(d x + c\right) + 40}{70 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} - 5 \, a^{3} d \cos\left(d x + c\right)^{3} + 4 \, a^{3} d \cos\left(d x + c\right) - {\left(3 \, a^{3} d \cos\left(d x + c\right)^{3} - 4 \, a^{3} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/70*(846*cos(d*x + c)^4 - 956*cos(d*x + c)^2 + 105*(cos(d*x + c)^5 - 5*cos(d*x + c)^3 - (3*cos(d*x + c)^3 - 4*cos(d*x + c))*sin(d*x + c) + 4*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 105*(cos(d*x + c)^5 - 5*cos(d*x + c)^3 - (3*cos(d*x + c)^3 - 4*cos(d*x + c))*sin(d*x + c) + 4*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(176*cos(d*x + c)^4 - 477*cos(d*x + c)^2 + 15)*sin(d*x + c) + 40)/(a^3*d*cos(d*x + c)^5 - 5*a^3*d*cos(d*x + c)^3 + 4*a^3*d*cos(d*x + c) - (3*a^3*d*cos(d*x + c)^3 - 4*a^3*d*cos(d*x + c))*sin(d*x + c))","A",0
795,1,108,0,1.128933," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right)^{4} - 15 \, a d x \cos\left(d x + c\right) + 29 \, a \cos\left(d x + c\right)^{2} + {\left(2 \, a \cos\left(d x + c\right)^{4} + 15 \, a d x \cos\left(d x + c\right) - 15 \, a \cos\left(d x + c\right)^{2} - 4 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{6 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"1/6*(a*cos(d*x + c)^4 - 15*a*d*x*cos(d*x + c) + 29*a*cos(d*x + c)^2 + (2*a*cos(d*x + c)^4 + 15*a*d*x*cos(d*x + c) - 15*a*cos(d*x + c)^2 - 4*a)*sin(d*x + c) + 2*a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
796,1,98,0,1.201295," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right)^{4} - 15 \, a d x \cos\left(d x + c\right) + 17 \, a \cos\left(d x + c\right)^{2} + {\left(15 \, a d x \cos\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right) - 4 \, a}{6 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"1/6*(3*a*cos(d*x + c)^4 - 15*a*d*x*cos(d*x + c) + 17*a*cos(d*x + c)^2 + (15*a*d*x*cos(d*x + c) - 3*a*cos(d*x + c)^2 + 2*a)*sin(d*x + c) - 4*a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
797,1,88,0,1.086972," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a d x \cos\left(d x + c\right) - 7 \, a \cos\left(d x + c\right)^{2} - {\left(3 \, a d x \cos\left(d x + c\right) - 3 \, a \cos\left(d x + c\right)^{2} - 2 \, a\right)} \sin\left(d x + c\right) - a}{3 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*a*d*x*cos(d*x + c) - 7*a*cos(d*x + c)^2 - (3*a*d*x*cos(d*x + c) - 3*a*cos(d*x + c)^2 - 2*a)*sin(d*x + c) - a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
798,1,75,0,1.155836," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a d x \cos\left(d x + c\right) - 4 \, a \cos\left(d x + c\right)^{2} - {\left(3 \, a d x \cos\left(d x + c\right) + a\right)} \sin\left(d x + c\right) + 2 \, a}{3 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*(3*a*d*x*cos(d*x + c) - 4*a*cos(d*x + c)^2 - (3*a*d*x*cos(d*x + c) + a)*sin(d*x + c) + 2*a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
799,1,49,0,1.133740," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right) + a}{3 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"1/3*(a*cos(d*x + c)^2 - 2*a*sin(d*x + c) + a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
800,1,50,0,1.284708," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a \cos\left(d x + c\right)^{2} + a \sin\left(d x + c\right) - 2 \, a}{3 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"1/3*(a*cos(d*x + c)^2 + a*sin(d*x + c) - 2*a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
801,1,126,0,1.375355," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a \cos\left(d x + c\right)^{2} + 3 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) - a \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) - a \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, a \sin\left(d x + c\right) + 4 \, a}{6 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"-1/6*(4*a*cos(d*x + c)^2 + 3*(a*cos(d*x + c)*sin(d*x + c) - a*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a*cos(d*x + c)*sin(d*x + c) - a*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*a*sin(d*x + c) + 4*a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
802,1,170,0,0.893585," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{10 \, a \cos\left(d x + c\right)^{2} + 3 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right) \sin\left(d x + c\right) - a \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a \cos\left(d x + c\right)^{3} + a \cos\left(d x + c\right) \sin\left(d x + c\right) - a \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(8 \, a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - 4 \, a}{6 \, {\left(d \cos\left(d x + c\right)^{3} + d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"-1/6*(10*a*cos(d*x + c)^2 + 3*(a*cos(d*x + c)^3 + a*cos(d*x + c)*sin(d*x + c) - a*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a*cos(d*x + c)^3 + a*cos(d*x + c)*sin(d*x + c) - a*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(8*a*cos(d*x + c)^2 - a)*sin(d*x + c) - 4*a)/(d*cos(d*x + c)^3 + d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","B",0
803,1,222,0,0.817535," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{32 \, a \cos\left(d x + c\right)^{4} - 18 \, a \cos\left(d x + c\right)^{2} - 15 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right) - 8 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(32*a*cos(d*x + c)^4 - 18*a*cos(d*x + c)^2 - 15*(a*cos(d*x + c)^3 - a*cos(d*x + c) - (a*cos(d*x + c)^3 - a*cos(d*x + c))*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 15*(a*cos(d*x + c)^3 - a*cos(d*x + c) - (a*cos(d*x + c)^3 - a*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(a*cos(d*x + c)^2 + 2*a)*sin(d*x + c) - 8*a)/(d*cos(d*x + c)^3 - d*cos(d*x + c) - (d*cos(d*x + c)^3 - d*cos(d*x + c))*sin(d*x + c))","B",0
804,1,196,0,1.042428," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, a^{2} \cos\left(d x + c\right)^{4} - 6 \, a^{2} \cos\left(d x + c\right)^{3} - 42 \, a^{2} d x + {\left(21 \, a^{2} d x + 31 \, a^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - {\left(21 \, a^{2} d x - 38 \, a^{2}\right)} \cos\left(d x + c\right) - {\left(3 \, a^{2} \cos\left(d x + c\right)^{3} - 42 \, a^{2} d x + 9 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} - {\left(21 \, a^{2} d x - 40 \, a^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/6*(3*a^2*cos(d*x + c)^4 - 6*a^2*cos(d*x + c)^3 - 42*a^2*d*x + (21*a^2*d*x + 31*a^2)*cos(d*x + c)^2 - 2*a^2 - (21*a^2*d*x - 38*a^2)*cos(d*x + c) - (3*a^2*cos(d*x + c)^3 - 42*a^2*d*x + 9*a^2*cos(d*x + c)^2 + 2*a^2 - (21*a^2*d*x - 40*a^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
805,1,168,0,0.687555," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, a^{2} \cos\left(d x + c\right)^{3} + 12 \, a^{2} d x - {\left(6 \, a^{2} d x + 11 \, a^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} + {\left(6 \, a^{2} d x - 13 \, a^{2}\right)} \cos\left(d x + c\right) - {\left(12 \, a^{2} d x - 3 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} + 2 \, {\left(3 \, a^{2} d x - 7 \, a^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/3*(3*a^2*cos(d*x + c)^3 + 12*a^2*d*x - (6*a^2*d*x + 11*a^2)*cos(d*x + c)^2 + a^2 + (6*a^2*d*x - 13*a^2)*cos(d*x + c) - (12*a^2*d*x - 3*a^2*cos(d*x + c)^2 - a^2 + 2*(3*a^2*d*x - 7*a^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
806,1,141,0,1.041809," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} d x - {\left(3 \, a^{2} d x + 5 \, a^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} + {\left(3 \, a^{2} d x - 4 \, a^{2}\right)} \cos\left(d x + c\right) - {\left(6 \, a^{2} d x - a^{2} + {\left(3 \, a^{2} d x - 5 \, a^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/3*(6*a^2*d*x - (3*a^2*d*x + 5*a^2)*cos(d*x + c)^2 + a^2 + (3*a^2*d*x - 4*a^2)*cos(d*x + c) - (6*a^2*d*x - a^2 + (3*a^2*d*x - 5*a^2)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
807,1,98,0,0.885253," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right) - a^{2} - {\left(2 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/3*(2*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c) - a^2 - (2*a^2*cos(d*x + c) + a^2)*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","A",0
808,1,231,0,0.725112," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, a^{2} \cos\left(d x + c\right)^{2} + 10 \, a^{2} \cos\left(d x + c\right) + 2 \, a^{2} + 3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - 2 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - 2 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(4 \, a^{2} \cos\left(d x + c\right) - a^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/6*(8*a^2*cos(d*x + c)^2 + 10*a^2*cos(d*x + c) + 2*a^2 + 3*(a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - 2*a^2 + (a^2*cos(d*x + c) + 2*a^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - 2*a^2 + (a^2*cos(d*x + c) + 2*a^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(4*a^2*cos(d*x + c) - a^2)*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
809,1,329,0,1.474017," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{10 \, a^{2} \cos\left(d x + c\right)^{3} - 4 \, a^{2} \cos\left(d x + c\right)^{2} - 13 \, a^{2} \cos\left(d x + c\right) + a^{2} - 3 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - 2 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a^{2} \cos\left(d x + c\right)^{3} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - 2 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(10 \, a^{2} \cos\left(d x + c\right)^{2} + 14 \, a^{2} \cos\left(d x + c\right) + a^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/3*(10*a^2*cos(d*x + c)^3 - 4*a^2*cos(d*x + c)^2 - 13*a^2*cos(d*x + c) + a^2 - 3*(a^2*cos(d*x + c)^3 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - 2*a^2 - (a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - 2*a^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(a^2*cos(d*x + c)^3 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - 2*a^2 - (a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - 2*a^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + (10*a^2*cos(d*x + c)^2 + 14*a^2*cos(d*x + c) + a^2)*sin(d*x + c))/(d*cos(d*x + c)^3 + 2*d*cos(d*x + c)^2 - d*cos(d*x + c) - (d*cos(d*x + c)^2 - d*cos(d*x + c) - 2*d)*sin(d*x + c) - 2*d)","B",0
810,1,428,0,0.819597," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{64 \, a^{2} \cos\left(d x + c\right)^{4} + 86 \, a^{2} \cos\left(d x + c\right)^{3} - 54 \, a^{2} \cos\left(d x + c\right)^{2} - 80 \, a^{2} \cos\left(d x + c\right) - 4 \, a^{2} + 21 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - a^{2} \cos\left(d x + c\right)^{3} - 3 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right) + 2 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right)^{3} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 21 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - a^{2} \cos\left(d x + c\right)^{3} - 3 \, a^{2} \cos\left(d x + c\right)^{2} + a^{2} \cos\left(d x + c\right) + 2 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right)^{3} + 2 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2} \cos\left(d x + c\right) - 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(32 \, a^{2} \cos\left(d x + c\right)^{3} - 11 \, a^{2} \cos\left(d x + c\right)^{2} - 38 \, a^{2} \cos\left(d x + c\right) + 2 \, a^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{3} - 3 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - 2 \, d\right)} \sin\left(d x + c\right) + 2 \, d\right)}}"," ",0,"-1/12*(64*a^2*cos(d*x + c)^4 + 86*a^2*cos(d*x + c)^3 - 54*a^2*cos(d*x + c)^2 - 80*a^2*cos(d*x + c) - 4*a^2 + 21*(a^2*cos(d*x + c)^4 - a^2*cos(d*x + c)^3 - 3*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c) + 2*a^2 + (a^2*cos(d*x + c)^3 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - 2*a^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 21*(a^2*cos(d*x + c)^4 - a^2*cos(d*x + c)^3 - 3*a^2*cos(d*x + c)^2 + a^2*cos(d*x + c) + 2*a^2 + (a^2*cos(d*x + c)^3 + 2*a^2*cos(d*x + c)^2 - a^2*cos(d*x + c) - 2*a^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(32*a^2*cos(d*x + c)^3 - 11*a^2*cos(d*x + c)^2 - 38*a^2*cos(d*x + c) + 2*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4 - d*cos(d*x + c)^3 - 3*d*cos(d*x + c)^2 + d*cos(d*x + c) + (d*cos(d*x + c)^3 + 2*d*cos(d*x + c)^2 - d*cos(d*x + c) - 2*d)*sin(d*x + c) + 2*d)","B",0
811,1,220,0,1.343078," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} \cos\left(d x + c\right)^{5} + 7 \, a^{3} \cos\left(d x + c\right)^{4} - 22 \, a^{3} \cos\left(d x + c\right)^{3} - 102 \, a^{3} d x - 4 \, a^{3} + {\left(51 \, a^{3} d x + 77 \, a^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(51 \, a^{3} d x - 100 \, a^{3}\right)} \cos\left(d x + c\right) + {\left(2 \, a^{3} \cos\left(d x + c\right)^{4} - 5 \, a^{3} \cos\left(d x + c\right)^{3} + 102 \, a^{3} d x - 27 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3} + {\left(51 \, a^{3} d x - 104 \, a^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/6*(2*a^3*cos(d*x + c)^5 + 7*a^3*cos(d*x + c)^4 - 22*a^3*cos(d*x + c)^3 - 102*a^3*d*x - 4*a^3 + (51*a^3*d*x + 77*a^3)*cos(d*x + c)^2 - (51*a^3*d*x - 100*a^3)*cos(d*x + c) + (2*a^3*cos(d*x + c)^4 - 5*a^3*cos(d*x + c)^3 + 102*a^3*d*x - 27*a^3*cos(d*x + c)^2 - 4*a^3 + (51*a^3*d*x - 104*a^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
812,1,196,0,0.970135," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, a^{3} \cos\left(d x + c\right)^{4} - 12 \, a^{3} \cos\left(d x + c\right)^{3} - 66 \, a^{3} d x - 4 \, a^{3} + {\left(33 \, a^{3} d x + 53 \, a^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(33 \, a^{3} d x - 64 \, a^{3}\right)} \cos\left(d x + c\right) - {\left(3 \, a^{3} \cos\left(d x + c\right)^{3} - 66 \, a^{3} d x + 15 \, a^{3} \cos\left(d x + c\right)^{2} + 4 \, a^{3} - {\left(33 \, a^{3} d x - 68 \, a^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/6*(3*a^3*cos(d*x + c)^4 - 12*a^3*cos(d*x + c)^3 - 66*a^3*d*x - 4*a^3 + (33*a^3*d*x + 53*a^3)*cos(d*x + c)^2 - (33*a^3*d*x - 64*a^3)*cos(d*x + c) - (3*a^3*cos(d*x + c)^3 - 66*a^3*d*x + 15*a^3*cos(d*x + c)^2 + 4*a^3 - (33*a^3*d*x - 68*a^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
813,1,169,0,0.832939," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, a^{3} \cos\left(d x + c\right)^{3} + 18 \, a^{3} d x + 2 \, a^{3} - {\left(9 \, a^{3} d x + 16 \, a^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{3} d x - 17 \, a^{3}\right)} \cos\left(d x + c\right) - {\left(18 \, a^{3} d x - 3 \, a^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{3} + {\left(9 \, a^{3} d x - 19 \, a^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/3*(3*a^3*cos(d*x + c)^3 + 18*a^3*d*x + 2*a^3 - (9*a^3*d*x + 16*a^3)*cos(d*x + c)^2 + (9*a^3*d*x - 17*a^3)*cos(d*x + c) - (18*a^3*d*x - 3*a^3*cos(d*x + c)^2 - 2*a^3 + (9*a^3*d*x - 19*a^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
814,1,143,0,0.934042," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{6 \, a^{3} d x + 2 \, a^{3} - {\left(3 \, a^{3} d x + 7 \, a^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} d x - 5 \, a^{3}\right)} \cos\left(d x + c\right) - {\left(6 \, a^{3} d x - 2 \, a^{3} + {\left(3 \, a^{3} d x - 7 \, a^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/3*(6*a^3*d*x + 2*a^3 - (3*a^3*d*x + 7*a^3)*cos(d*x + c)^2 + (3*a^3*d*x - 5*a^3)*cos(d*x + c) - (6*a^3*d*x - 2*a^3 + (3*a^3*d*x - 7*a^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
815,1,231,0,0.922598," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{10 \, a^{3} \cos\left(d x + c\right)^{2} + 14 \, a^{3} \cos\left(d x + c\right) + 4 \, a^{3} + 3 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right) + 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right) + 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(5 \, a^{3} \cos\left(d x + c\right) - 2 \, a^{3}\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/6*(10*a^3*cos(d*x + c)^2 + 14*a^3*cos(d*x + c) + 4*a^3 + 3*(a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3 + (a^3*cos(d*x + c) + 2*a^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3 + (a^3*cos(d*x + c) + 2*a^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(5*a^3*cos(d*x + c) - 2*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
816,1,334,0,1.201609," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{28 \, a^{3} \cos\left(d x + c\right)^{3} - 10 \, a^{3} \cos\left(d x + c\right)^{2} - 34 \, a^{3} \cos\left(d x + c\right) + 4 \, a^{3} - 9 \, {\left(a^{3} \cos\left(d x + c\right)^{3} + 2 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left(a^{3} \cos\left(d x + c\right)^{3} + 2 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(14 \, a^{3} \cos\left(d x + c\right)^{2} + 19 \, a^{3} \cos\left(d x + c\right) + 2 \, a^{3}\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/6*(28*a^3*cos(d*x + c)^3 - 10*a^3*cos(d*x + c)^2 - 34*a^3*cos(d*x + c) + 4*a^3 - 9*(a^3*cos(d*x + c)^3 + 2*a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3 - (a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 9*(a^3*cos(d*x + c)^3 + 2*a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3 - (a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(14*a^3*cos(d*x + c)^2 + 19*a^3*cos(d*x + c) + 2*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3 + 2*d*cos(d*x + c)^2 - d*cos(d*x + c) - (d*cos(d*x + c)^2 - d*cos(d*x + c) - 2*d)*sin(d*x + c) - 2*d)","B",0
817,1,428,0,1.123337," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{104 \, a^{3} \cos\left(d x + c\right)^{4} + 142 \, a^{3} \cos\left(d x + c\right)^{3} - 90 \, a^{3} \cos\left(d x + c\right)^{2} - 136 \, a^{3} \cos\left(d x + c\right) - 8 \, a^{3} + 33 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - a^{3} \cos\left(d x + c\right)^{3} - 3 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right) + 2 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{3} + 2 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 33 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - a^{3} \cos\left(d x + c\right)^{3} - 3 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right) + 2 \, a^{3} + {\left(a^{3} \cos\left(d x + c\right)^{3} + 2 \, a^{3} \cos\left(d x + c\right)^{2} - a^{3} \cos\left(d x + c\right) - 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(52 \, a^{3} \cos\left(d x + c\right)^{3} - 19 \, a^{3} \cos\left(d x + c\right)^{2} - 64 \, a^{3} \cos\left(d x + c\right) + 4 \, a^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{3} - 3 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) - 2 \, d\right)} \sin\left(d x + c\right) + 2 \, d\right)}}"," ",0,"-1/12*(104*a^3*cos(d*x + c)^4 + 142*a^3*cos(d*x + c)^3 - 90*a^3*cos(d*x + c)^2 - 136*a^3*cos(d*x + c) - 8*a^3 + 33*(a^3*cos(d*x + c)^4 - a^3*cos(d*x + c)^3 - 3*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c) + 2*a^3 + (a^3*cos(d*x + c)^3 + 2*a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 33*(a^3*cos(d*x + c)^4 - a^3*cos(d*x + c)^3 - 3*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c) + 2*a^3 + (a^3*cos(d*x + c)^3 + 2*a^3*cos(d*x + c)^2 - a^3*cos(d*x + c) - 2*a^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(52*a^3*cos(d*x + c)^3 - 19*a^3*cos(d*x + c)^2 - 64*a^3*cos(d*x + c) + 4*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4 - d*cos(d*x + c)^3 - 3*d*cos(d*x + c)^2 + d*cos(d*x + c) + (d*cos(d*x + c)^3 + 2*d*cos(d*x + c)^2 - d*cos(d*x + c) - 2*d)*sin(d*x + c) + 2*d)","B",0
818,1,528,0,1.130306," ","integrate(csc(d*x+c)^4*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{160 \, a^{3} \cos\left(d x + c\right)^{5} - 58 \, a^{3} \cos\left(d x + c\right)^{4} - 356 \, a^{3} \cos\left(d x + c\right)^{3} + 70 \, a^{3} \cos\left(d x + c\right)^{2} + 200 \, a^{3} \cos\left(d x + c\right) - 8 \, a^{3} - 51 \, {\left(a^{3} \cos\left(d x + c\right)^{5} + 2 \, a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{3} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right) + 2 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{4} - a^{3} \cos\left(d x + c\right)^{3} - 3 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right) + 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 51 \, {\left(a^{3} \cos\left(d x + c\right)^{5} + 2 \, a^{3} \cos\left(d x + c\right)^{4} - 2 \, a^{3} \cos\left(d x + c\right)^{3} - 4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right) + 2 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{4} - a^{3} \cos\left(d x + c\right)^{3} - 3 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} \cos\left(d x + c\right) + 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(80 \, a^{3} \cos\left(d x + c\right)^{4} + 109 \, a^{3} \cos\left(d x + c\right)^{3} - 69 \, a^{3} \cos\left(d x + c\right)^{2} - 104 \, a^{3} \cos\left(d x + c\right) - 4 \, a^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{5} + 2 \, d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{3} - 4 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{3} - 3 \, d \cos\left(d x + c\right)^{2} + d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) + 2 \, d\right)}}"," ",0,"1/12*(160*a^3*cos(d*x + c)^5 - 58*a^3*cos(d*x + c)^4 - 356*a^3*cos(d*x + c)^3 + 70*a^3*cos(d*x + c)^2 + 200*a^3*cos(d*x + c) - 8*a^3 - 51*(a^3*cos(d*x + c)^5 + 2*a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^3 - 4*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c) + 2*a^3 - (a^3*cos(d*x + c)^4 - a^3*cos(d*x + c)^3 - 3*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c) + 2*a^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 51*(a^3*cos(d*x + c)^5 + 2*a^3*cos(d*x + c)^4 - 2*a^3*cos(d*x + c)^3 - 4*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c) + 2*a^3 - (a^3*cos(d*x + c)^4 - a^3*cos(d*x + c)^3 - 3*a^3*cos(d*x + c)^2 + a^3*cos(d*x + c) + 2*a^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(80*a^3*cos(d*x + c)^4 + 109*a^3*cos(d*x + c)^3 - 69*a^3*cos(d*x + c)^2 - 104*a^3*cos(d*x + c) - 4*a^3)*sin(d*x + c))/(d*cos(d*x + c)^5 + 2*d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^3 - 4*d*cos(d*x + c)^2 + d*cos(d*x + c) - (d*cos(d*x + c)^4 - d*cos(d*x + c)^3 - 3*d*cos(d*x + c)^2 + d*cos(d*x + c) + 2*d)*sin(d*x + c) + 2*d)","B",0
819,1,247,0,1.205358," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{6 \, a^{4} \cos\left(d x + c\right)^{6} - 20 \, a^{4} \cos\left(d x + c\right)^{5} - 85 \, a^{4} \cos\left(d x + c\right)^{4} + 214 \, a^{4} \cos\left(d x + c\right)^{3} + 978 \, a^{4} d x + 32 \, a^{4} - {\left(489 \, a^{4} d x + 721 \, a^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(489 \, a^{4} d x - 962 \, a^{4}\right)} \cos\left(d x + c\right) - {\left(6 \, a^{4} \cos\left(d x + c\right)^{5} + 26 \, a^{4} \cos\left(d x + c\right)^{4} - 59 \, a^{4} \cos\left(d x + c\right)^{3} + 978 \, a^{4} d x - 273 \, a^{4} \cos\left(d x + c\right)^{2} - 32 \, a^{4} + {\left(489 \, a^{4} d x - 994 \, a^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/24*(6*a^4*cos(d*x + c)^6 - 20*a^4*cos(d*x + c)^5 - 85*a^4*cos(d*x + c)^4 + 214*a^4*cos(d*x + c)^3 + 978*a^4*d*x + 32*a^4 - (489*a^4*d*x + 721*a^4)*cos(d*x + c)^2 + (489*a^4*d*x - 962*a^4)*cos(d*x + c) - (6*a^4*cos(d*x + c)^5 + 26*a^4*cos(d*x + c)^4 - 59*a^4*cos(d*x + c)^3 + 978*a^4*d*x - 273*a^4*cos(d*x + c)^2 - 32*a^4 + (489*a^4*d*x - 994*a^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","A",0
820,1,197,0,1.005405," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{3 \, a^{4} \cos\left(d x + c\right)^{4} - 18 \, a^{4} \cos\left(d x + c\right)^{3} - 102 \, a^{4} d x - 8 \, a^{4} + 17 \, {\left(3 \, a^{4} d x + 5 \, a^{4}\right)} \cos\left(d x + c\right)^{2} - {\left(51 \, a^{4} d x - 98 \, a^{4}\right)} \cos\left(d x + c\right) - {\left(3 \, a^{4} \cos\left(d x + c\right)^{3} - 102 \, a^{4} d x + 21 \, a^{4} \cos\left(d x + c\right)^{2} + 8 \, a^{4} - {\left(51 \, a^{4} d x - 106 \, a^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/6*(3*a^4*cos(d*x + c)^4 - 18*a^4*cos(d*x + c)^3 - 102*a^4*d*x - 8*a^4 + 17*(3*a^4*d*x + 5*a^4)*cos(d*x + c)^2 - (51*a^4*d*x - 98*a^4)*cos(d*x + c) - (3*a^4*cos(d*x + c)^3 - 102*a^4*d*x + 21*a^4*cos(d*x + c)^2 + 8*a^4 - (51*a^4*d*x - 106*a^4)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
821,1,108,0,1.158667," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, d x \cos\left(d x + c\right)^{3} + 38 \, \cos\left(d x + c\right)^{4} + 11 \, \cos\left(d x + c\right)^{2} + {\left(15 \, d x \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)^{4} + 22 \, \cos\left(d x + c\right)^{2} - 4\right)} \sin\left(d x + c\right) - 1}{15 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/15*(15*d*x*cos(d*x + c)^3 + 38*cos(d*x + c)^4 + 11*cos(d*x + c)^2 + (15*d*x*cos(d*x + c)^3 + 15*cos(d*x + c)^4 + 22*cos(d*x + c)^2 - 4)*sin(d*x + c) - 1)/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
822,1,98,0,1.589714," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, d x \cos\left(d x + c\right)^{3} + 23 \, \cos\left(d x + c\right)^{4} - 19 \, \cos\left(d x + c\right)^{2} + {\left(15 \, d x \cos\left(d x + c\right)^{3} - 8 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 4}{15 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/15*(15*d*x*cos(d*x + c)^3 + 23*cos(d*x + c)^4 - 19*cos(d*x + c)^2 + (15*d*x*cos(d*x + c)^3 - 8*cos(d*x + c)^2 + 1)*sin(d*x + c) + 4)/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
823,1,75,0,1.101590," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - 1}{15 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/15*(3*cos(d*x + c)^4 + 6*cos(d*x + c)^2 + 4*(3*cos(d*x + c)^2 - 1)*sin(d*x + c) - 1)/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
824,1,75,0,1.019396," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, \cos\left(d x + c\right)^{4} - 9 \, \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) + 4}{15 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/15*(3*cos(d*x + c)^4 - 9*cos(d*x + c)^2 - (3*cos(d*x + c)^2 - 1)*sin(d*x + c) + 4)/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
825,1,73,0,0.785929," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{2} - 2 \, {\left(\cos\left(d x + c\right)^{2} - 2\right)} \sin\left(d x + c\right) + 1}{15 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/15*(2*cos(d*x + c)^4 - cos(d*x + c)^2 - 2*(cos(d*x + c)^2 - 2)*sin(d*x + c) + 1)/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
826,1,75,0,0.878143," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, \cos\left(d x + c\right)^{4} - \cos\left(d x + c\right)^{2} - {\left(2 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) - 4}{15 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/15*(2*cos(d*x + c)^4 - cos(d*x + c)^2 - (2*cos(d*x + c)^2 + 1)*sin(d*x + c) - 4)/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
827,1,149,0,0.960389," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, \cos\left(d x + c\right)^{4} + 22 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(\cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(7 \, \cos\left(d x + c\right)^{2} + 1\right)} \sin\left(d x + c\right) + 8}{30 \, {\left(a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/30*(16*cos(d*x + c)^4 + 22*cos(d*x + c)^2 - 15*(cos(d*x + c)^3*sin(d*x + c) + cos(d*x + c)^3)*log(1/2*cos(d*x + c) + 1/2) + 15*(cos(d*x + c)^3*sin(d*x + c) + cos(d*x + c)^3)*log(-1/2*cos(d*x + c) + 1/2) + 2*(7*cos(d*x + c)^2 + 1)*sin(d*x + c) + 8)/(a*d*cos(d*x + c)^3*sin(d*x + c) + a*d*cos(d*x + c)^3)","A",0
828,1,194,0,1.161744," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{66 \, \cos\left(d x + c\right)^{4} - 28 \, \cos\left(d x + c\right)^{2} + 15 \, {\left(\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(48 \, \cos\left(d x + c\right)^{4} - 9 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) - 8}{30 \, {\left(a d \cos\left(d x + c\right)^{5} - a d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - a d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/30*(66*cos(d*x + c)^4 - 28*cos(d*x + c)^2 + 15*(cos(d*x + c)^5 - cos(d*x + c)^3*sin(d*x + c) - cos(d*x + c)^3)*log(1/2*cos(d*x + c) + 1/2) - 15*(cos(d*x + c)^5 - cos(d*x + c)^3*sin(d*x + c) - cos(d*x + c)^3)*log(-1/2*cos(d*x + c) + 1/2) + 2*(48*cos(d*x + c)^4 - 9*cos(d*x + c)^2 - 1)*sin(d*x + c) - 8)/(a*d*cos(d*x + c)^5 - a*d*cos(d*x + c)^3*sin(d*x + c) - a*d*cos(d*x + c)^3)","A",0
829,1,150,0,1.077389," ","integrate(sec(d*x+c)^4*sin(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{210 \, d x \cos\left(d x + c\right)^{5} + 105 \, \cos\left(d x + c\right)^{6} - 420 \, d x \cos\left(d x + c\right)^{3} - 389 \, \cos\left(d x + c\right)^{4} - 173 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(210 \, d x \cos\left(d x + c\right)^{3} + 281 \, \cos\left(d x + c\right)^{4} + 51 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) + 25}{105 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/105*(210*d*x*cos(d*x + c)^5 + 105*cos(d*x + c)^6 - 420*d*x*cos(d*x + c)^3 - 389*cos(d*x + c)^4 - 173*cos(d*x + c)^2 - 2*(210*d*x*cos(d*x + c)^3 + 281*cos(d*x + c)^4 + 51*cos(d*x + c)^2 - 5)*sin(d*x + c) + 25)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
830,1,140,0,0.906545," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{105 \, d x \cos\left(d x + c\right)^{5} - 210 \, d x \cos\left(d x + c\right)^{3} - 172 \, \cos\left(d x + c\right)^{4} + 86 \, \cos\left(d x + c\right)^{2} - {\left(210 \, d x \cos\left(d x + c\right)^{3} + 191 \, \cos\left(d x + c\right)^{4} - 129 \, \cos\left(d x + c\right)^{2} + 25\right)} \sin\left(d x + c\right) - 10}{105 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/105*(105*d*x*cos(d*x + c)^5 - 210*d*x*cos(d*x + c)^3 - 172*cos(d*x + c)^4 + 86*cos(d*x + c)^2 - (210*d*x*cos(d*x + c)^3 + 191*cos(d*x + c)^4 - 129*cos(d*x + c)^2 + 25)*sin(d*x + c) - 10)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
831,1,104,0,0.765586," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{9 \, \cos\left(d x + c\right)^{4} - 22 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(3 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{2} - 1\right)} \sin\left(d x + c\right) + 5}{21 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/21*(9*cos(d*x + c)^4 - 22*cos(d*x + c)^2 - 2*(3*cos(d*x + c)^4 + 6*cos(d*x + c)^2 - 1)*sin(d*x + c) + 5)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
832,1,103,0,1.646036," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{18 \, \cos\left(d x + c\right)^{4} - 44 \, \cos\left(d x + c\right)^{2} + {\left(9 \, \cos\left(d x + c\right)^{4} - 66 \, \cos\left(d x + c\right)^{2} + 25\right)} \sin\left(d x + c\right) + 10}{105 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/105*(18*cos(d*x + c)^4 - 44*cos(d*x + c)^2 + (9*cos(d*x + c)^4 - 66*cos(d*x + c)^2 + 25)*sin(d*x + c) + 10)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
833,1,104,0,1.699593," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{24 \, \cos\left(d x + c\right)^{4} - 47 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, \cos\left(d x + c\right)^{4} - 9 \, \cos\left(d x + c\right)^{2} + 5\right)} \sin\left(d x + c\right) + 25}{105 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/105*(24*cos(d*x + c)^4 - 47*cos(d*x + c)^2 + 2*(6*cos(d*x + c)^4 - 9*cos(d*x + c)^2 + 5)*sin(d*x + c) + 25)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
834,1,103,0,1.011699," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, \cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + {\left(2 \, \cos\left(d x + c\right)^{4} - 3 \, \cos\left(d x + c\right)^{2} + 25\right)} \sin\left(d x + c\right) + 10}{105 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/105*(4*cos(d*x + c)^4 - 2*cos(d*x + c)^2 + (2*cos(d*x + c)^4 - 3*cos(d*x + c)^2 + 25)*sin(d*x + c) + 10)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
835,1,104,0,0.813818," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{32 \, \cos\left(d x + c\right)^{4} - 16 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, \cos\left(d x + c\right)^{4} - 12 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) - 25}{105 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"1/105*(32*cos(d*x + c)^4 - 16*cos(d*x + c)^2 + 2*(8*cos(d*x + c)^4 - 12*cos(d*x + c)^2 - 5)*sin(d*x + c) - 25)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
836,1,200,0,1.222895," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{174 \, \cos\left(d x + c\right)^{4} + 158 \, \cos\left(d x + c\right)^{2} + 105 \, {\left(\cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 105 \, {\left(\cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(48 \, \cos\left(d x + c\right)^{4} + 33 \, \cos\left(d x + c\right)^{2} + 5\right)} \sin\left(d x + c\right) + 50}{210 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/210*(174*cos(d*x + c)^4 + 158*cos(d*x + c)^2 + 105*(cos(d*x + c)^5 - 2*cos(d*x + c)^3*sin(d*x + c) - 2*cos(d*x + c)^3)*log(1/2*cos(d*x + c) + 1/2) - 105*(cos(d*x + c)^5 - 2*cos(d*x + c)^3*sin(d*x + c) - 2*cos(d*x + c)^3)*log(-1/2*cos(d*x + c) + 1/2) + 4*(48*cos(d*x + c)^4 + 33*cos(d*x + c)^2 + 5)*sin(d*x + c) + 50)/(a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^3)","A",0
837,1,250,0,1.136418," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{432 \, \cos\left(d x + c\right)^{6} - 660 \, \cos\left(d x + c\right)^{4} + 98 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(2 \, \cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(2 \, \cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{5} - 2 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(327 \, \cos\left(d x + c\right)^{4} - 41 \, \cos\left(d x + c\right)^{2} - 5\right)} \sin\left(d x + c\right) + 25}{105 \, {\left(2 \, a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3} + {\left(a^{2} d \cos\left(d x + c\right)^{5} - 2 \, a^{2} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/105*(432*cos(d*x + c)^6 - 660*cos(d*x + c)^4 + 98*cos(d*x + c)^2 - 105*(2*cos(d*x + c)^5 - 2*cos(d*x + c)^3 + (cos(d*x + c)^5 - 2*cos(d*x + c)^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 105*(2*cos(d*x + c)^5 - 2*cos(d*x + c)^3 + (cos(d*x + c)^5 - 2*cos(d*x + c)^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(327*cos(d*x + c)^4 - 41*cos(d*x + c)^2 - 5)*sin(d*x + c) + 25)/(2*a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3 + (a^2*d*cos(d*x + c)^5 - 2*a^2*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
838,1,292,0,1.016882," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3834 \, \cos\left(d x + c\right)^{6} - 3056 \, \cos\left(d x + c\right)^{4} - 468 \, \cos\left(d x + c\right)^{2} + 1155 \, {\left(\cos\left(d x + c\right)^{7} - 3 \, \cos\left(d x + c\right)^{5} + 2 \, \cos\left(d x + c\right)^{3} - 2 \, {\left(\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 1155 \, {\left(\cos\left(d x + c\right)^{7} - 3 \, \cos\left(d x + c\right)^{5} + 2 \, \cos\left(d x + c\right)^{3} - 2 \, {\left(\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(768 \, \cos\left(d x + c\right)^{6} - 765 \, \cos\left(d x + c\right)^{4} - 98 \, \cos\left(d x + c\right)^{2} - 10\right)} \sin\left(d x + c\right) - 100}{420 \, {\left(a^{2} d \cos\left(d x + c\right)^{7} - 3 \, a^{2} d \cos\left(d x + c\right)^{5} + 2 \, a^{2} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{2} d \cos\left(d x + c\right)^{5} - a^{2} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/420*(3834*cos(d*x + c)^6 - 3056*cos(d*x + c)^4 - 468*cos(d*x + c)^2 + 1155*(cos(d*x + c)^7 - 3*cos(d*x + c)^5 + 2*cos(d*x + c)^3 - 2*(cos(d*x + c)^5 - cos(d*x + c)^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 1155*(cos(d*x + c)^7 - 3*cos(d*x + c)^5 + 2*cos(d*x + c)^3 - 2*(cos(d*x + c)^5 - cos(d*x + c)^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(768*cos(d*x + c)^6 - 765*cos(d*x + c)^4 - 98*cos(d*x + c)^2 - 10)*sin(d*x + c) - 100)/(a^2*d*cos(d*x + c)^7 - 3*a^2*d*cos(d*x + c)^5 + 2*a^2*d*cos(d*x + c)^3 - 2*(a^2*d*cos(d*x + c)^5 - a^2*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
839,1,177,0,1.082182," ","integrate(sec(d*x+c)^4*sin(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{945 \, d x \cos\left(d x + c\right)^{5} + 668 \, \cos\left(d x + c\right)^{6} - 1260 \, d x \cos\left(d x + c\right)^{3} - 1431 \, \cos\left(d x + c\right)^{4} + 465 \, \cos\left(d x + c\right)^{2} + {\left(315 \, d x \cos\left(d x + c\right)^{5} - 1260 \, d x \cos\left(d x + c\right)^{3} - 1059 \, \cos\left(d x + c\right)^{4} + 305 \, \cos\left(d x + c\right)^{2} - 35\right)} \sin\left(d x + c\right) - 70}{315 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/315*(945*d*x*cos(d*x + c)^5 + 668*cos(d*x + c)^6 - 1260*d*x*cos(d*x + c)^3 - 1431*cos(d*x + c)^4 + 465*cos(d*x + c)^2 + (315*d*x*cos(d*x + c)^5 - 1260*d*x*cos(d*x + c)^3 - 1059*cos(d*x + c)^4 + 305*cos(d*x + c)^2 - 35)*sin(d*x + c) - 70)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
840,1,130,0,1.069137," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{19 \, \cos\left(d x + c\right)^{6} + 9 \, \cos\left(d x + c\right)^{4} - 51 \, \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, \cos\left(d x + c\right)^{4} - 34 \, \cos\left(d x + c\right)^{2} + 7\right)} \sin\left(d x + c\right) + 7}{63 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/63*(19*cos(d*x + c)^6 + 9*cos(d*x + c)^4 - 51*cos(d*x + c)^2 + 2*(3*cos(d*x + c)^4 - 34*cos(d*x + c)^2 + 7)*sin(d*x + c) + 7)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
841,1,128,0,1.145138," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{\cos\left(d x + c\right)^{6} - 36 \, \cos\left(d x + c\right)^{4} + 57 \, \cos\left(d x + c\right)^{2} - {\left(3 \, \cos\left(d x + c\right)^{4} - 34 \, \cos\left(d x + c\right)^{2} + 7\right)} \sin\left(d x + c\right) - 14}{63 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/63*(cos(d*x + c)^6 - 36*cos(d*x + c)^4 + 57*cos(d*x + c)^2 - (3*cos(d*x + c)^4 - 34*cos(d*x + c)^2 + 7)*sin(d*x + c) - 14)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
842,1,130,0,1.201275," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{22 \, \cos\left(d x + c\right)^{6} - 99 \, \cos\left(d x + c\right)^{4} + 120 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(33 \, \cos\left(d x + c\right)^{4} - 80 \, \cos\left(d x + c\right)^{2} + 35\right)} \sin\left(d x + c\right) - 35}{315 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/315*(22*cos(d*x + c)^6 - 99*cos(d*x + c)^4 + 120*cos(d*x + c)^2 - 2*(33*cos(d*x + c)^4 - 80*cos(d*x + c)^2 + 35)*sin(d*x + c) - 35)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
843,1,130,0,0.998526," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, \cos\left(d x + c\right)^{6} - 9 \, \cos\left(d x + c\right)^{4} + 15 \, \cos\left(d x + c\right)^{2} - {\left(6 \, \cos\left(d x + c\right)^{4} - 5 \, \cos\left(d x + c\right)^{2} + 5\right)} \sin\left(d x + c\right) - 10}{45 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/45*(2*cos(d*x + c)^6 - 9*cos(d*x + c)^4 + 15*cos(d*x + c)^2 - (6*cos(d*x + c)^4 - 5*cos(d*x + c)^2 + 5)*sin(d*x + c) - 10)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
844,1,130,0,0.773737," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{6} - 36 \, \cos\left(d x + c\right)^{4} + 15 \, \cos\left(d x + c\right)^{2} - 2 \, {\left(12 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} - 35\right)} \sin\left(d x + c\right) + 35}{315 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/315*(8*cos(d*x + c)^6 - 36*cos(d*x + c)^4 + 15*cos(d*x + c)^2 - 2*(12*cos(d*x + c)^4 - 10*cos(d*x + c)^2 - 35)*sin(d*x + c) + 35)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
845,1,130,0,0.586453," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, \cos\left(d x + c\right)^{6} - 36 \, \cos\left(d x + c\right)^{4} + 15 \, \cos\left(d x + c\right)^{2} - {\left(24 \, \cos\left(d x + c\right)^{4} - 20 \, \cos\left(d x + c\right)^{2} - 7\right)} \sin\left(d x + c\right) + 14}{63 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/63*(8*cos(d*x + c)^6 - 36*cos(d*x + c)^4 + 15*cos(d*x + c)^2 - (24*cos(d*x + c)^4 - 20*cos(d*x + c)^2 - 7)*sin(d*x + c) + 14)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
846,1,250,0,0.952041," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{736 \, \cos\left(d x + c\right)^{6} - 1422 \, \cos\left(d x + c\right)^{4} - 510 \, \cos\left(d x + c\right)^{2} - 315 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 315 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3} + {\left(\cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(789 \, \cos\left(d x + c\right)^{4} + 235 \, \cos\left(d x + c\right)^{2} + 35\right)} \sin\left(d x + c\right) - 140}{630 \, {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3} + {\left(a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/630*(736*cos(d*x + c)^6 - 1422*cos(d*x + c)^4 - 510*cos(d*x + c)^2 - 315*(3*cos(d*x + c)^5 - 4*cos(d*x + c)^3 + (cos(d*x + c)^5 - 4*cos(d*x + c)^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 315*(3*cos(d*x + c)^5 - 4*cos(d*x + c)^3 + (cos(d*x + c)^5 - 4*cos(d*x + c)^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(789*cos(d*x + c)^4 + 235*cos(d*x + c)^2 + 35)*sin(d*x + c) - 140)/(3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3 + (a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
847,1,297,0,2.006965," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8094 \, \cos\left(d x + c\right)^{6} - 9484 \, \cos\left(d x + c\right)^{4} + 620 \, \cos\left(d x + c\right)^{2} + 945 \, {\left(\cos\left(d x + c\right)^{7} - 5 \, \cos\left(d x + c\right)^{5} + 4 \, \cos\left(d x + c\right)^{3} - {\left(3 \, \cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 945 \, {\left(\cos\left(d x + c\right)^{7} - 5 \, \cos\left(d x + c\right)^{5} + 4 \, \cos\left(d x + c\right)^{3} - {\left(3 \, \cos\left(d x + c\right)^{5} - 4 \, \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(1664 \, \cos\left(d x + c\right)^{6} - 4653 \, \cos\left(d x + c\right)^{4} + 285 \, \cos\left(d x + c\right)^{2} + 35\right)} \sin\left(d x + c\right) + 140}{630 \, {\left(a^{3} d \cos\left(d x + c\right)^{7} - 5 \, a^{3} d \cos\left(d x + c\right)^{5} + 4 \, a^{3} d \cos\left(d x + c\right)^{3} - {\left(3 \, a^{3} d \cos\left(d x + c\right)^{5} - 4 \, a^{3} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/630*(8094*cos(d*x + c)^6 - 9484*cos(d*x + c)^4 + 620*cos(d*x + c)^2 + 945*(cos(d*x + c)^7 - 5*cos(d*x + c)^5 + 4*cos(d*x + c)^3 - (3*cos(d*x + c)^5 - 4*cos(d*x + c)^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 945*(cos(d*x + c)^7 - 5*cos(d*x + c)^5 + 4*cos(d*x + c)^3 - (3*cos(d*x + c)^5 - 4*cos(d*x + c)^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(1664*cos(d*x + c)^6 - 4653*cos(d*x + c)^4 + 285*cos(d*x + c)^2 + 35)*sin(d*x + c) + 140)/(a^3*d*cos(d*x + c)^7 - 5*a^3*d*cos(d*x + c)^5 + 4*a^3*d*cos(d*x + c)^3 - (3*a^3*d*cos(d*x + c)^5 - 4*a^3*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
848,1,153,0,1.080792," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{488 \, \cos\left(d x + c\right)^{6} - 1220 \, \cos\left(d x + c\right)^{4} + 1120 \, \cos\left(d x + c\right)^{2} + {\left(122 \, \cos\left(d x + c\right)^{6} - 915 \, \cos\left(d x + c\right)^{4} + 1400 \, \cos\left(d x + c\right)^{2} - 735\right)} \sin\left(d x + c\right) - 420}{3465 \, {\left(a^{4} d \cos\left(d x + c\right)^{7} - 8 \, a^{4} d \cos\left(d x + c\right)^{5} + 8 \, a^{4} d \cos\left(d x + c\right)^{3} - 4 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} - 2 \, a^{4} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3465*(488*cos(d*x + c)^6 - 1220*cos(d*x + c)^4 + 1120*cos(d*x + c)^2 + (122*cos(d*x + c)^6 - 915*cos(d*x + c)^4 + 1400*cos(d*x + c)^2 - 735)*sin(d*x + c) - 420)/(a^4*d*cos(d*x + c)^7 - 8*a^4*d*cos(d*x + c)^5 + 8*a^4*d*cos(d*x + c)^3 - 4*(a^4*d*cos(d*x + c)^5 - 2*a^4*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
849,1,154,0,1.054260," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","-\frac{128 \, \cos\left(d x + c\right)^{6} - 320 \, \cos\left(d x + c\right)^{4} + 805 \, \cos\left(d x + c\right)^{2} + 4 \, {\left(8 \, \cos\left(d x + c\right)^{6} - 60 \, \cos\left(d x + c\right)^{4} + 35 \, \cos\left(d x + c\right)^{2} - 105\right)} \sin\left(d x + c\right) - 735}{3465 \, {\left(a^{4} d \cos\left(d x + c\right)^{7} - 8 \, a^{4} d \cos\left(d x + c\right)^{5} + 8 \, a^{4} d \cos\left(d x + c\right)^{3} - 4 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} - 2 \, a^{4} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/3465*(128*cos(d*x + c)^6 - 320*cos(d*x + c)^4 + 805*cos(d*x + c)^2 + 4*(8*cos(d*x + c)^6 - 60*cos(d*x + c)^4 + 35*cos(d*x + c)^2 - 105)*sin(d*x + c) - 735)/(a^4*d*cos(d*x + c)^7 - 8*a^4*d*cos(d*x + c)^5 + 8*a^4*d*cos(d*x + c)^3 - 4*(a^4*d*cos(d*x + c)^5 - 2*a^4*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
850,1,153,0,1.181684," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""fricas"")","\frac{32 \, \cos\left(d x + c\right)^{6} - 80 \, \cos\left(d x + c\right)^{4} + 28 \, \cos\left(d x + c\right)^{2} + {\left(8 \, \cos\left(d x + c\right)^{6} - 60 \, \cos\left(d x + c\right)^{4} + 35 \, \cos\left(d x + c\right)^{2} + 49\right)} \sin\left(d x + c\right) + 28}{231 \, {\left(a^{4} d \cos\left(d x + c\right)^{7} - 8 \, a^{4} d \cos\left(d x + c\right)^{5} + 8 \, a^{4} d \cos\left(d x + c\right)^{3} - 4 \, {\left(a^{4} d \cos\left(d x + c\right)^{5} - 2 \, a^{4} d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/231*(32*cos(d*x + c)^6 - 80*cos(d*x + c)^4 + 28*cos(d*x + c)^2 + (8*cos(d*x + c)^6 - 60*cos(d*x + c)^4 + 35*cos(d*x + c)^2 + 49)*sin(d*x + c) + 28)/(a^4*d*cos(d*x + c)^7 - 8*a^4*d*cos(d*x + c)^5 + 8*a^4*d*cos(d*x + c)^3 - 4*(a^4*d*cos(d*x + c)^5 - 2*a^4*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
851,1,172,0,0.849663," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, a \cos\left(d x + c\right)^{4} + 6 \, a \cos\left(d x + c\right)^{2} - 9 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 39 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(4 \, a \cos\left(d x + c\right)^{4} + 6 \, a \cos\left(d x + c\right)^{2} - 3 \, a\right)} \sin\left(d x + c\right) + 2 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(8*a*cos(d*x + c)^4 + 6*a*cos(d*x + c)^2 - 9*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 39*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(4*a*cos(d*x + c)^4 + 6*a*cos(d*x + c)^2 - 3*a)*sin(d*x + c) + 2*a)/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
852,1,159,0,1.147311," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, a \cos\left(d x + c\right)^{4} + 2 \, a \cos\left(d x + c\right)^{2} + 7 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 23 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) - 6 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(16*a*cos(d*x + c)^4 + 2*a*cos(d*x + c)^2 + 7*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 23*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(8*a*cos(d*x + c)^2 + a)*sin(d*x + c) - 6*a)/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
853,1,136,0,1.042503," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, a \cos\left(d x + c\right)^{2} - 5 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 11 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 6 \, a \sin\left(d x + c\right) + 2 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(10*a*cos(d*x + c)^2 - 5*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 11*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 6*a*sin(d*x + c) + 2*a)/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
854,1,136,0,1.602404," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, a \cos\left(d x + c\right)^{2} + 3 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, a \sin\left(d x + c\right) - 6 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(10*a*cos(d*x + c)^2 + 3*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*a*sin(d*x + c) - 6*a)/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
855,1,135,0,0.977144," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 6 \, a \sin\left(d x + c\right) + 2 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(2*a*cos(d*x + c)^2 - (a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 6*a*sin(d*x + c) + 2*a)/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
856,1,135,0,1.115965," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, a \sin\left(d x + c\right) - 6 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/16*(2*a*cos(d*x + c)^2 - (a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*a*sin(d*x + c) - 6*a)/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","B",0
857,1,175,0,1.101586," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, a \cos\left(d x + c\right)^{2} - 16 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 5 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 11 \, {\left(a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, a \sin\left(d x + c\right) + 6 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(6*a*cos(d*x + c)^2 - 16*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(1/2*sin(d*x + c)) + 5*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 11*(a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*a*sin(d*x + c) + 6*a)/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
858,1,229,0,1.107620," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{22 \, a \cos\left(d x + c\right)^{2} - 16 \, {\left(a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 7 \, {\left(a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 23 \, {\left(a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15 \, a \cos\left(d x + c\right)^{2} - a\right)} \sin\left(d x + c\right) - 6 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(22*a*cos(d*x + c)^2 - 16*(a*cos(d*x + c)^4 + a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(1/2*sin(d*x + c)) - 7*(a*cos(d*x + c)^4 + a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 23*(a*cos(d*x + c)^4 + a*cos(d*x + c)^2*sin(d*x + c) - a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(15*a*cos(d*x + c)^2 - a)*sin(d*x + c) - 6*a)/(d*cos(d*x + c)^4 + d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
859,1,294,0,0.801322," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, a \cos\left(d x + c\right)^{4} - 16 \, a \cos\left(d x + c\right)^{2} + 48 \, {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 9 \, {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 39 \, {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2} - {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, a \cos\left(d x + c\right)^{2} + a\right)} \sin\left(d x + c\right) - 6 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/16*(30*a*cos(d*x + c)^4 - 16*a*cos(d*x + c)^2 + 48*(a*cos(d*x + c)^4 - a*cos(d*x + c)^2 - (a*cos(d*x + c)^4 - a*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*sin(d*x + c)) - 9*(a*cos(d*x + c)^4 - a*cos(d*x + c)^2 - (a*cos(d*x + c)^4 - a*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) - 39*(a*cos(d*x + c)^4 - a*cos(d*x + c)^2 - (a*cos(d*x + c)^4 - a*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 2*(3*a*cos(d*x + c)^2 + a)*sin(d*x + c) - 6*a)/(d*cos(d*x + c)^4 - d*cos(d*x + c)^2 - (d*cos(d*x + c)^4 - d*cos(d*x + c)^2)*sin(d*x + c))","B",0
860,1,343,0,1.331558," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{138 \, a \cos\left(d x + c\right)^{4} - 172 \, a \cos\left(d x + c\right)^{2} - 144 \, {\left(a \cos\left(d x + c\right)^{6} - 2 \, a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{2} + {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 33 \, {\left(a \cos\left(d x + c\right)^{6} - 2 \, a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{2} + {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 177 \, {\left(a \cos\left(d x + c\right)^{6} - 2 \, a \cos\left(d x + c\right)^{4} + a \cos\left(d x + c\right)^{2} + {\left(a \cos\left(d x + c\right)^{4} - a \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(105 \, a \cos\left(d x + c\right)^{4} - 104 \, a \cos\left(d x + c\right)^{2} + 3 \, a\right)} \sin\left(d x + c\right) + 18 \, a}{48 \, {\left(d \cos\left(d x + c\right)^{6} - 2 \, d \cos\left(d x + c\right)^{4} + d \cos\left(d x + c\right)^{2} + {\left(d \cos\left(d x + c\right)^{4} - d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/48*(138*a*cos(d*x + c)^4 - 172*a*cos(d*x + c)^2 - 144*(a*cos(d*x + c)^6 - 2*a*cos(d*x + c)^4 + a*cos(d*x + c)^2 + (a*cos(d*x + c)^4 - a*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*sin(d*x + c)) - 33*(a*cos(d*x + c)^6 - 2*a*cos(d*x + c)^4 + a*cos(d*x + c)^2 + (a*cos(d*x + c)^4 - a*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) + 177*(a*cos(d*x + c)^6 - 2*a*cos(d*x + c)^4 + a*cos(d*x + c)^2 + (a*cos(d*x + c)^4 - a*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) - 2*(105*a*cos(d*x + c)^4 - 104*a*cos(d*x + c)^2 + 3*a)*sin(d*x + c) + 18*a)/(d*cos(d*x + c)^6 - 2*d*cos(d*x + c)^4 + d*cos(d*x + c)^2 + (d*cos(d*x + c)^4 - d*cos(d*x + c)^2)*sin(d*x + c))","B",0
861,1,168,0,1.590410," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, a^{2} \cos\left(d x + c\right)^{4} + 22 \, a^{2} \cos\left(d x + c\right)^{2} - 12 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 31 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, a^{2} \cos\left(d x + c\right)^{2} - 5 \, a^{2}\right)} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/8*(4*a^2*cos(d*x + c)^4 + 22*a^2*cos(d*x + c)^2 - 12*a^2 - (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(sin(d*x + c) + 1) - 31*(a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(-sin(d*x + c) + 1) - 2*(4*a^2*cos(d*x + c)^2 - 5*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
862,1,154,0,1.587838," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, a^{2} \cos\left(d x + c\right)^{2} - 4 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 17 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/8*(16*a^2*cos(d*x + c)^2 - 4*a^2 + (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(sin(d*x + c) + 1) - 17*(a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(-sin(d*x + c) + 1) - 2*(4*a^2*cos(d*x + c)^2 - a^2)*sin(d*x + c))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
863,1,125,0,2.060694," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{10 \, a^{2} \sin\left(d x + c\right) - 8 \, a^{2} + {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 7 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/8*(10*a^2*sin(d*x + c) - 8*a^2 + (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(sin(d*x + c) + 1) + 7*(a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
864,1,125,0,0.983455," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, a^{2} \sin\left(d x + c\right) - 4 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/8*(6*a^2*sin(d*x + c) - 4*a^2 - (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(sin(d*x + c) + 1) + (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","B",0
865,1,120,0,1.244734," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a^{2} \sin\left(d x + c\right) + {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/8*(2*a^2*sin(d*x + c) + (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(sin(d*x + c) + 1) - (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
866,1,166,0,1.040394," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, a^{2} \sin\left(d x + c\right) - 8 \, a^{2} + 8 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 7 \, {\left(a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/8*(6*a^2*sin(d*x + c) - 8*a^2 + 8*(a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(1/2*sin(d*x + c)) - (a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(sin(d*x + c) + 1) - 7*(a^2*cos(d*x + c)^2 + 2*a^2*sin(d*x + c) - 2*a^2)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
867,1,240,0,1.367579," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{18 \, a^{2} \cos\left(d x + c\right)^{2} + 28 \, a^{2} \sin\left(d x + c\right) - 26 \, a^{2} + 16 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 17 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{8 \, {\left(2 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{2} - 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/8*(18*a^2*cos(d*x + c)^2 + 28*a^2*sin(d*x + c) - 26*a^2 + 16*(2*a^2*cos(d*x + c)^2 - 2*a^2 - (a^2*cos(d*x + c)^2 - 2*a^2)*sin(d*x + c))*log(1/2*sin(d*x + c)) + (2*a^2*cos(d*x + c)^2 - 2*a^2 - (a^2*cos(d*x + c)^2 - 2*a^2)*sin(d*x + c))*log(sin(d*x + c) + 1) - 17*(2*a^2*cos(d*x + c)^2 - 2*a^2 - (a^2*cos(d*x + c)^2 - 2*a^2)*sin(d*x + c))*log(-sin(d*x + c) + 1))/(2*d*cos(d*x + c)^2 - (d*cos(d*x + c)^2 - 2*d)*sin(d*x + c) - 2*d)","B",0
868,1,302,0,1.211693," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{44 \, a^{2} \cos\left(d x + c\right)^{2} - 40 \, a^{2} - 32 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 3 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + {\left(a^{2} \cos\left(d x + c\right)^{4} - 3 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 31 \, {\left(a^{2} \cos\left(d x + c\right)^{4} - 3 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, {\left(a^{2} \cos\left(d x + c\right)^{2} - a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15 \, a^{2} \cos\left(d x + c\right)^{2} - 19 \, a^{2}\right)} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right)^{4} - 3 \, d \cos\left(d x + c\right)^{2} + 2 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) + 2 \, d\right)}}"," ",0,"-1/8*(44*a^2*cos(d*x + c)^2 - 40*a^2 - 32*(a^2*cos(d*x + c)^4 - 3*a^2*cos(d*x + c)^2 + 2*a^2 + 2*(a^2*cos(d*x + c)^2 - a^2)*sin(d*x + c))*log(1/2*sin(d*x + c)) + (a^2*cos(d*x + c)^4 - 3*a^2*cos(d*x + c)^2 + 2*a^2 + 2*(a^2*cos(d*x + c)^2 - a^2)*sin(d*x + c))*log(sin(d*x + c) + 1) + 31*(a^2*cos(d*x + c)^4 - 3*a^2*cos(d*x + c)^2 + 2*a^2 + 2*(a^2*cos(d*x + c)^2 - a^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) - 2*(15*a^2*cos(d*x + c)^2 - 19*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4 - 3*d*cos(d*x + c)^2 + 2*(d*cos(d*x + c)^2 - d)*sin(d*x + c) + 2*d)","B",0
869,1,370,0,1.046972," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{150 \, a^{2} \cos\left(d x + c\right)^{4} - 356 \, a^{2} \cos\left(d x + c\right)^{2} + 214 \, a^{2} + 144 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{4} - 3 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 3 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{4} - 3 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 147 \, {\left(2 \, a^{2} \cos\left(d x + c\right)^{4} - 4 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} - {\left(a^{2} \cos\left(d x + c\right)^{4} - 3 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, {\left(57 \, a^{2} \cos\left(d x + c\right)^{2} - 55 \, a^{2}\right)} \sin\left(d x + c\right)}{24 \, {\left(2 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{4} - 3 \, d \cos\left(d x + c\right)^{2} + 2 \, d\right)} \sin\left(d x + c\right) + 2 \, d\right)}}"," ",0,"1/24*(150*a^2*cos(d*x + c)^4 - 356*a^2*cos(d*x + c)^2 + 214*a^2 + 144*(2*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + 2*a^2 - (a^2*cos(d*x + c)^4 - 3*a^2*cos(d*x + c)^2 + 2*a^2)*sin(d*x + c))*log(1/2*sin(d*x + c)) + 3*(2*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + 2*a^2 - (a^2*cos(d*x + c)^4 - 3*a^2*cos(d*x + c)^2 + 2*a^2)*sin(d*x + c))*log(sin(d*x + c) + 1) - 147*(2*a^2*cos(d*x + c)^4 - 4*a^2*cos(d*x + c)^2 + 2*a^2 - (a^2*cos(d*x + c)^4 - 3*a^2*cos(d*x + c)^2 + 2*a^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 4*(57*a^2*cos(d*x + c)^2 - 55*a^2)*sin(d*x + c))/(2*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 - (d*cos(d*x + c)^4 - 3*d*cos(d*x + c)^2 + 2*d)*sin(d*x + c) + 2*d)","B",0
870,1,141,0,1.566196," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{10 \, a^{3} \cos\left(d x + c\right)^{4} + 115 \, a^{3} \cos\left(d x + c\right)^{2} - 80 \, a^{3} - 120 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, a^{3} \cos\left(d x + c\right)^{4} - 24 \, a^{3} \cos\left(d x + c\right)^{2} + 37 \, a^{3}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/12*(10*a^3*cos(d*x + c)^4 + 115*a^3*cos(d*x + c)^2 - 80*a^3 - 120*(a^3*cos(d*x + c)^2 + 2*a^3*sin(d*x + c) - 2*a^3)*log(-sin(d*x + c) + 1) + 2*(2*a^3*cos(d*x + c)^4 - 24*a^3*cos(d*x + c)^2 + 37*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
871,1,128,0,0.790930," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} \cos\left(d x + c\right)^{4} + 19 \, a^{3} \cos\left(d x + c\right)^{2} - 8 \, a^{3} - 24 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(4 \, a^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/4*(2*a^3*cos(d*x + c)^4 + 19*a^3*cos(d*x + c)^2 - 8*a^3 - 24*(a^3*cos(d*x + c)^2 + 2*a^3*sin(d*x + c) - 2*a^3)*log(-sin(d*x + c) + 1) - 2*(4*a^3*cos(d*x + c)^2 - 3*a^3)*sin(d*x + c))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
872,1,110,0,0.612630," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, a^{3} \cos\left(d x + c\right)^{2} + a^{3} - 6 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + a^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/2*(4*a^3*cos(d*x + c)^2 + a^3 - 6*(a^3*cos(d*x + c)^2 + 2*a^3*sin(d*x + c) - 2*a^3)*log(-sin(d*x + c) + 1) - 2*(a^3*cos(d*x + c)^2 + a^3)*sin(d*x + c))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
873,1,86,0,1.146350," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4 \, a^{3} \sin\left(d x + c\right) - 3 \, a^{3} + 2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/2*(4*a^3*sin(d*x + c) - 3*a^3 + 2*(a^3*cos(d*x + c)^2 + 2*a^3*sin(d*x + c) - 2*a^3)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
874,1,44,0,1.204745," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, a^{3} \sin\left(d x + c\right) - a^{3}}{2 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/2*(2*a^3*sin(d*x + c) - a^3)/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
875,1,126,0,0.970958," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{2 \, a^{3} \sin\left(d x + c\right) - 3 \, a^{3} + 2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) - 2 \, a^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/2*(2*a^3*sin(d*x + c) - 3*a^3 + 2*(a^3*cos(d*x + c)^2 + 2*a^3*sin(d*x + c) - 2*a^3)*log(1/2*sin(d*x + c)) - 2*(a^3*cos(d*x + c)^2 + 2*a^3*sin(d*x + c) - 2*a^3)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
876,1,185,0,1.234307," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, a^{3} \cos\left(d x + c\right)^{2} + 9 \, a^{3} \sin\left(d x + c\right) - 8 \, a^{3} + 6 \, {\left(2 \, a^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 6 \, {\left(2 \, a^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{3} - {\left(a^{3} \cos\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(2 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{2} - 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/2*(6*a^3*cos(d*x + c)^2 + 9*a^3*sin(d*x + c) - 8*a^3 + 6*(2*a^3*cos(d*x + c)^2 - 2*a^3 - (a^3*cos(d*x + c)^2 - 2*a^3)*sin(d*x + c))*log(1/2*sin(d*x + c)) - 6*(2*a^3*cos(d*x + c)^2 - 2*a^3 - (a^3*cos(d*x + c)^2 - 2*a^3)*sin(d*x + c))*log(-sin(d*x + c) + 1))/(2*d*cos(d*x + c)^2 - (d*cos(d*x + c)^2 - 2*d)*sin(d*x + c) - 2*d)","A",0
877,1,235,0,0.997395," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{18 \, a^{3} \cos\left(d x + c\right)^{2} - 17 \, a^{3} - 12 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 3 \, a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} + 2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 12 \, {\left(a^{3} \cos\left(d x + c\right)^{4} - 3 \, a^{3} \cos\left(d x + c\right)^{2} + 2 \, a^{3} + 2 \, {\left(a^{3} \cos\left(d x + c\right)^{2} - a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 4 \, {\left(3 \, a^{3} \cos\left(d x + c\right)^{2} - 4 \, a^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right)^{4} - 3 \, d \cos\left(d x + c\right)^{2} + 2 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right) + 2 \, d\right)}}"," ",0,"-1/2*(18*a^3*cos(d*x + c)^2 - 17*a^3 - 12*(a^3*cos(d*x + c)^4 - 3*a^3*cos(d*x + c)^2 + 2*a^3 + 2*(a^3*cos(d*x + c)^2 - a^3)*sin(d*x + c))*log(1/2*sin(d*x + c)) + 12*(a^3*cos(d*x + c)^4 - 3*a^3*cos(d*x + c)^2 + 2*a^3 + 2*(a^3*cos(d*x + c)^2 - a^3)*sin(d*x + c))*log(-sin(d*x + c) + 1) - 4*(3*a^3*cos(d*x + c)^2 - 4*a^3)*sin(d*x + c))/(d*cos(d*x + c)^4 - 3*d*cos(d*x + c)^2 + 2*(d*cos(d*x + c)^2 - d)*sin(d*x + c) + 2*d)","B",0
878,1,207,0,2.025280," ","integrate(sec(d*x+c)^7*sin(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{256 \, \cos\left(d x + c\right)^{10} - 3968 \, \cos\left(d x + c\right)^{8} - 686 \, \cos\left(d x + c\right)^{6} + 2810 \, \cos\left(d x + c\right)^{4} - 796 \, \cos\left(d x + c\right)^{2} - 5385 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 1545 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(64 \, \cos\left(d x + c\right)^{8} + 1952 \, \cos\left(d x + c\right)^{6} + 375 \, \cos\left(d x + c\right)^{4} - 70 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 112}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/768*(256*cos(d*x + c)^10 - 3968*cos(d*x + c)^8 - 686*cos(d*x + c)^6 + 2810*cos(d*x + c)^4 - 796*cos(d*x + c)^2 - 5385*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 1545*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) + 2*(64*cos(d*x + c)^8 + 1952*cos(d*x + c)^6 + 375*cos(d*x + c)^4 - 70*cos(d*x + c)^2 + 8)*sin(d*x + c) + 112)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
879,1,197,0,1.239260," ","integrate(sec(d*x+c)^7*sin(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{384 \, \cos\left(d x + c\right)^{8} + 1374 \, \cos\left(d x + c\right)^{6} + 630 \, \cos\left(d x + c\right)^{4} - 132 \, \cos\left(d x + c\right)^{2} + 2865 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 975 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(192 \, \cos\left(d x + c\right)^{8} + 288 \, \cos\left(d x + c\right)^{6} - 945 \, \cos\left(d x + c\right)^{4} + 330 \, \cos\left(d x + c\right)^{2} - 56\right)} \sin\left(d x + c\right) + 16}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/768*(384*cos(d*x + c)^8 + 1374*cos(d*x + c)^6 + 630*cos(d*x + c)^4 - 132*cos(d*x + c)^2 + 2865*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 975*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(192*cos(d*x + c)^8 + 288*cos(d*x + c)^6 - 945*cos(d*x + c)^4 + 330*cos(d*x + c)^2 - 56)*sin(d*x + c) + 16)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
880,1,187,0,1.267406," ","integrate(sec(d*x+c)^7*sin(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{768 \, \cos\left(d x + c\right)^{8} + 1182 \, \cos\left(d x + c\right)^{6} - 1674 \, \cos\left(d x + c\right)^{4} + 636 \, \cos\left(d x + c\right)^{2} + 1329 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 561 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(384 \, \cos\left(d x + c\right)^{6} + 207 \, \cos\left(d x + c\right)^{4} - 54 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) - 112}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"-1/768*(768*cos(d*x + c)^8 + 1182*cos(d*x + c)^6 - 1674*cos(d*x + c)^4 + 636*cos(d*x + c)^2 + 1329*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) - 561*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(384*cos(d*x + c)^6 + 207*cos(d*x + c)^4 - 54*cos(d*x + c)^2 + 8)*sin(d*x + c) - 112)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
881,1,167,0,0.680758," ","integrate(sec(d*x+c)^7*sin(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{558 \, \cos\left(d x + c\right)^{6} + 326 \, \cos\left(d x + c\right)^{4} - 100 \, \cos\left(d x + c\right)^{2} + 489 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 279 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(489 \, \cos\left(d x + c\right)^{4} - 250 \, \cos\left(d x + c\right)^{2} + 56\right)} \sin\left(d x + c\right) + 16}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/768*(558*cos(d*x + c)^6 + 326*cos(d*x + c)^4 - 100*cos(d*x + c)^2 + 489*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 279*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) + 2*(489*cos(d*x + c)^4 - 250*cos(d*x + c)^2 + 56)*sin(d*x + c) + 16)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
882,1,167,0,2.578666," ","integrate(sec(d*x+c)^7*sin(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{558 \, \cos\left(d x + c\right)^{6} - 826 \, \cos\left(d x + c\right)^{4} + 476 \, \cos\left(d x + c\right)^{2} + 105 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(87 \, \cos\left(d x + c\right)^{4} - 38 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) - 112}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"-1/768*(558*cos(d*x + c)^6 - 826*cos(d*x + c)^4 + 476*cos(d*x + c)^2 + 105*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) - 105*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(87*cos(d*x + c)^4 - 38*cos(d*x + c)^2 + 8)*sin(d*x + c) - 112)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
883,1,167,0,1.204412," ","integrate(sec(d*x+c)^7*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{6} + 118 \, \cos\left(d x + c\right)^{4} - 68 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(177 \, \cos\left(d x + c\right)^{4} - 170 \, \cos\left(d x + c\right)^{2} + 56\right)} \sin\left(d x + c\right) + 16}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/768*(30*cos(d*x + c)^6 + 118*cos(d*x + c)^4 - 68*cos(d*x + c)^2 - 15*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 15*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) + 2*(177*cos(d*x + c)^4 - 170*cos(d*x + c)^2 + 56)*sin(d*x + c) + 16)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
884,1,167,0,0.810674," ","integrate(sec(d*x+c)^7*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{30 \, \cos\left(d x + c\right)^{6} - 266 \, \cos\left(d x + c\right)^{4} + 316 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 22 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) - 112}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"-1/768*(30*cos(d*x + c)^6 - 266*cos(d*x + c)^4 + 316*cos(d*x + c)^2 - 15*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 15*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(15*cos(d*x + c)^4 - 22*cos(d*x + c)^2 + 8)*sin(d*x + c) - 112)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
885,1,167,0,0.912517," ","integrate(sec(d*x+c)^7*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{18 \, \cos\left(d x + c\right)^{6} - 6 \, \cos\left(d x + c\right)^{4} + 36 \, \cos\left(d x + c\right)^{2} - 9 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 9 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(9 \, \cos\left(d x + c\right)^{4} - 90 \, \cos\left(d x + c\right)^{2} + 56\right)} \sin\left(d x + c\right) - 16}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"-1/768*(18*cos(d*x + c)^6 - 6*cos(d*x + c)^4 + 36*cos(d*x + c)^2 - 9*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 9*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(9*cos(d*x + c)^4 - 90*cos(d*x + c)^2 + 56)*sin(d*x + c) - 16)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
886,1,167,0,1.020566," ","integrate(sec(d*x+c)^7*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{18 \, \cos\left(d x + c\right)^{6} - 6 \, \cos\left(d x + c\right)^{4} - 156 \, \cos\left(d x + c\right)^{2} - 9 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 9 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(9 \, \cos\left(d x + c\right)^{4} + 6 \, \cos\left(d x + c\right)^{2} - 8\right)} \sin\left(d x + c\right) + 112}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/768*(18*cos(d*x + c)^6 - 6*cos(d*x + c)^4 - 156*cos(d*x + c)^2 - 9*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 9*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(9*cos(d*x + c)^4 + 6*cos(d*x + c)^2 - 8)*sin(d*x + c) + 112)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
887,1,167,0,1.864224," ","integrate(sec(d*x+c)^7*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{2} - 56\right)} \sin\left(d x + c\right) + 16}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/768*(30*cos(d*x + c)^6 - 10*cos(d*x + c)^4 - 4*cos(d*x + c)^2 - 15*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 15*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(15*cos(d*x + c)^4 + 10*cos(d*x + c)^2 - 56)*sin(d*x + c) + 16)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
888,1,167,0,1.082488," ","integrate(sec(d*x+c)^7*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{30 \, \cos\left(d x + c\right)^{6} - 10 \, \cos\left(d x + c\right)^{4} - 4 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) - 112}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"-1/768*(30*cos(d*x + c)^6 - 10*cos(d*x + c)^4 - 4*cos(d*x + c)^2 - 15*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 15*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(15*cos(d*x + c)^4 + 10*cos(d*x + c)^2 + 8)*sin(d*x + c) - 112)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
889,1,167,0,0.963285," ","integrate(sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{210 \, \cos\left(d x + c\right)^{6} - 70 \, \cos\left(d x + c\right)^{4} - 28 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 14 \, {\left(15 \, \cos\left(d x + c\right)^{4} + 10 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) - 16}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"-1/768*(210*cos(d*x + c)^6 - 70*cos(d*x + c)^4 - 28*cos(d*x + c)^2 - 105*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 105*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 14*(15*cos(d*x + c)^4 + 10*cos(d*x + c)^2 + 8)*sin(d*x + c) - 16)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
890,1,202,0,1.180438," ","integrate(csc(d*x+c)*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{210 \, \cos\left(d x + c\right)^{6} + 314 \, \cos\left(d x + c\right)^{4} + 164 \, \cos\left(d x + c\right)^{2} + 768 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 489 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 279 \, {\left(\cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(87 \, \cos\left(d x + c\right)^{4} + 26 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 112}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/768*(210*cos(d*x + c)^6 + 314*cos(d*x + c)^4 + 164*cos(d*x + c)^2 + 768*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(1/2*sin(d*x + c)) - 489*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(sin(d*x + c) + 1) - 279*(cos(d*x + c)^6*sin(d*x + c) + cos(d*x + c)^6)*log(-sin(d*x + c) + 1) + 2*(87*cos(d*x + c)^4 + 26*cos(d*x + c)^2 + 8)*sin(d*x + c) + 112)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
891,1,258,0,1.134823," ","integrate(csc(d*x+c)^2*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{1506 \, \cos\left(d x + c\right)^{6} - 438 \, \cos\left(d x + c\right)^{4} - 188 \, \cos\left(d x + c\right)^{2} - 768 \, {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{6}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 1329 \, {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 561 \, {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(945 \, \cos\left(d x + c\right)^{6} - 123 \, \cos\left(d x + c\right)^{4} - 30 \, \cos\left(d x + c\right)^{2} - 8\right)} \sin\left(d x + c\right) - 112}{768 \, {\left(a d \cos\left(d x + c\right)^{8} - a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/768*(1506*cos(d*x + c)^6 - 438*cos(d*x + c)^4 - 188*cos(d*x + c)^2 - 768*(cos(d*x + c)^8 - cos(d*x + c)^6*sin(d*x + c) - cos(d*x + c)^6)*log(1/2*sin(d*x + c)) + 1329*(cos(d*x + c)^8 - cos(d*x + c)^6*sin(d*x + c) - cos(d*x + c)^6)*log(sin(d*x + c) + 1) - 561*(cos(d*x + c)^8 - cos(d*x + c)^6*sin(d*x + c) - cos(d*x + c)^6)*log(-sin(d*x + c) + 1) + 2*(945*cos(d*x + c)^6 - 123*cos(d*x + c)^4 - 30*cos(d*x + c)^2 - 8)*sin(d*x + c) - 112)/(a*d*cos(d*x + c)^8 - a*d*cos(d*x + c)^6*sin(d*x + c) - a*d*cos(d*x + c)^6)","A",0
892,1,311,0,1.602259," ","integrate(csc(d*x+c)^3*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{1890 \, \cos\left(d x + c\right)^{8} - 600 \, \cos\left(d x + c\right)^{6} - 582 \, \cos\left(d x + c\right)^{4} - 212 \, \cos\left(d x + c\right)^{2} + 3840 \, {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6} + {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 2865 \, {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6} + {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 975 \, {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6} + {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(15 \, \cos\left(d x + c\right)^{6} - 165 \, \cos\left(d x + c\right)^{4} - 34 \, \cos\left(d x + c\right)^{2} - 8\right)} \sin\left(d x + c\right) - 112}{768 \, {\left(a d \cos\left(d x + c\right)^{8} - a d \cos\left(d x + c\right)^{6} + {\left(a d \cos\left(d x + c\right)^{8} - a d \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/768*(1890*cos(d*x + c)^8 - 600*cos(d*x + c)^6 - 582*cos(d*x + c)^4 - 212*cos(d*x + c)^2 + 3840*(cos(d*x + c)^8 - cos(d*x + c)^6 + (cos(d*x + c)^8 - cos(d*x + c)^6)*sin(d*x + c))*log(1/2*sin(d*x + c)) - 2865*(cos(d*x + c)^8 - cos(d*x + c)^6 + (cos(d*x + c)^8 - cos(d*x + c)^6)*sin(d*x + c))*log(sin(d*x + c) + 1) - 975*(cos(d*x + c)^8 - cos(d*x + c)^6 + (cos(d*x + c)^8 - cos(d*x + c)^6)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 2*(15*cos(d*x + c)^6 - 165*cos(d*x + c)^4 - 34*cos(d*x + c)^2 - 8)*sin(d*x + c) - 112)/(a*d*cos(d*x + c)^8 - a*d*cos(d*x + c)^6 + (a*d*cos(d*x + c)^8 - a*d*cos(d*x + c)^6)*sin(d*x + c))","A",0
893,1,360,0,0.997278," ","integrate(csc(d*x+c)^4*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{5010 \, \cos\left(d x + c\right)^{8} - 6360 \, \cos\left(d x + c\right)^{6} + 746 \, \cos\left(d x + c\right)^{4} + 236 \, \cos\left(d x + c\right)^{2} - 3840 \, {\left(\cos\left(d x + c\right)^{10} - 2 \, \cos\left(d x + c\right)^{8} + \cos\left(d x + c\right)^{6} - {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 5385 \, {\left(\cos\left(d x + c\right)^{10} - 2 \, \cos\left(d x + c\right)^{8} + \cos\left(d x + c\right)^{6} - {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 1545 \, {\left(\cos\left(d x + c\right)^{10} - 2 \, \cos\left(d x + c\right)^{8} + \cos\left(d x + c\right)^{6} - {\left(\cos\left(d x + c\right)^{8} - \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3465 \, \cos\left(d x + c\right)^{8} - 3660 \, \cos\left(d x + c\right)^{6} + 213 \, \cos\left(d x + c\right)^{4} + 38 \, \cos\left(d x + c\right)^{2} + 8\right)} \sin\left(d x + c\right) + 112}{768 \, {\left(a d \cos\left(d x + c\right)^{10} - 2 \, a d \cos\left(d x + c\right)^{8} + a d \cos\left(d x + c\right)^{6} - {\left(a d \cos\left(d x + c\right)^{8} - a d \cos\left(d x + c\right)^{6}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/768*(5010*cos(d*x + c)^8 - 6360*cos(d*x + c)^6 + 746*cos(d*x + c)^4 + 236*cos(d*x + c)^2 - 3840*(cos(d*x + c)^10 - 2*cos(d*x + c)^8 + cos(d*x + c)^6 - (cos(d*x + c)^8 - cos(d*x + c)^6)*sin(d*x + c))*log(1/2*sin(d*x + c)) + 5385*(cos(d*x + c)^10 - 2*cos(d*x + c)^8 + cos(d*x + c)^6 - (cos(d*x + c)^8 - cos(d*x + c)^6)*sin(d*x + c))*log(sin(d*x + c) + 1) - 1545*(cos(d*x + c)^10 - 2*cos(d*x + c)^8 + cos(d*x + c)^6 - (cos(d*x + c)^8 - cos(d*x + c)^6)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 2*(3465*cos(d*x + c)^8 - 3660*cos(d*x + c)^6 + 213*cos(d*x + c)^4 + 38*cos(d*x + c)^2 + 8)*sin(d*x + c) + 112)/(a*d*cos(d*x + c)^10 - 2*a*d*cos(d*x + c)^8 + a*d*cos(d*x + c)^6 - (a*d*cos(d*x + c)^8 - a*d*cos(d*x + c)^6)*sin(d*x + c))","A",0
894,1,115,0,1.101754," ","integrate(sec(d*x+c)^8*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{24 \, a^{2} \cos\left(d x + c\right)^{4} - 47 \, a^{2} \cos\left(d x + c\right)^{2} + 25 \, a^{2} - 2 \, {\left(6 \, a^{2} \cos\left(d x + c\right)^{4} - 9 \, a^{2} \cos\left(d x + c\right)^{2} + 5 \, a^{2}\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{5} + 2 \, d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/105*(24*a^2*cos(d*x + c)^4 - 47*a^2*cos(d*x + c)^2 + 25*a^2 - 2*(6*a^2*cos(d*x + c)^4 - 9*a^2*cos(d*x + c)^2 + 5*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5 + 2*d*cos(d*x + c)^3*sin(d*x + c) - 2*d*cos(d*x + c)^3)","A",0
895,1,217,0,1.299675," ","integrate(sec(d*x+c)^9*sin(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{1280 \, \cos\left(d x + c\right)^{10} + 6510 \, \cos\left(d x + c\right)^{8} + 3590 \, \cos\left(d x + c\right)^{6} - 1124 \, \cos\left(d x + c\right)^{4} + 272 \, \cos\left(d x + c\right)^{2} + 11145 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 4215 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(640 \, \cos\left(d x + c\right)^{10} + 960 \, \cos\left(d x + c\right)^{8} - 5385 \, \cos\left(d x + c\right)^{6} + 2810 \, \cos\left(d x + c\right)^{4} - 952 \, \cos\left(d x + c\right)^{2} + 144\right)} \sin\left(d x + c\right) - 32}{2560 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"-1/2560*(1280*cos(d*x + c)^10 + 6510*cos(d*x + c)^8 + 3590*cos(d*x + c)^6 - 1124*cos(d*x + c)^4 + 272*cos(d*x + c)^2 + 11145*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 4215*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(640*cos(d*x + c)^10 + 960*cos(d*x + c)^8 - 5385*cos(d*x + c)^6 + 2810*cos(d*x + c)^4 - 952*cos(d*x + c)^2 + 144)*sin(d*x + c) - 32)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
896,1,207,0,1.403397," ","integrate(sec(d*x+c)^9*sin(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{7680 \, \cos\left(d x + c\right)^{10} + 17610 \, \cos\left(d x + c\right)^{8} - 27630 \, \cos\left(d x + c\right)^{6} + 15828 \, \cos\left(d x + c\right)^{4} - 5584 \, \cos\left(d x + c\right)^{2} + 14235 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6555 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3840 \, \cos\left(d x + c\right)^{8} + 3045 \, \cos\left(d x + c\right)^{6} - 1170 \, \cos\left(d x + c\right)^{4} + 344 \, \cos\left(d x + c\right)^{2} - 48\right)} \sin\left(d x + c\right) + 864}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"1/7680*(7680*cos(d*x + c)^10 + 17610*cos(d*x + c)^8 - 27630*cos(d*x + c)^6 + 15828*cos(d*x + c)^4 - 5584*cos(d*x + c)^2 + 14235*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) - 6555*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(3840*cos(d*x + c)^8 + 3045*cos(d*x + c)^6 - 1170*cos(d*x + c)^4 + 344*cos(d*x + c)^2 - 48)*sin(d*x + c) + 864)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
897,1,187,0,1.168900," ","integrate(sec(d*x+c)^9*sin(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{5790 \, \cos\left(d x + c\right)^{8} + 4470 \, \cos\left(d x + c\right)^{6} - 2052 \, \cos\left(d x + c\right)^{4} + 656 \, \cos\left(d x + c\right)^{2} + 4785 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 2895 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(6705 \, \cos\left(d x + c\right)^{6} - 5130 \, \cos\left(d x + c\right)^{4} + 2296 \, \cos\left(d x + c\right)^{2} - 432\right)} \sin\left(d x + c\right) - 96}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"-1/7680*(5790*cos(d*x + c)^8 + 4470*cos(d*x + c)^6 - 2052*cos(d*x + c)^4 + 656*cos(d*x + c)^2 + 4785*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 2895*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) + 2*(6705*cos(d*x + c)^6 - 5130*cos(d*x + c)^4 + 2296*cos(d*x + c)^2 - 432)*sin(d*x + c) - 96)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
898,1,187,0,1.823808," ","integrate(sec(d*x+c)^9*sin(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{1930 \, \cos\left(d x + c\right)^{8} - 3630 \, \cos\left(d x + c\right)^{6} + 3156 \, \cos\left(d x + c\right)^{4} - 1488 \, \cos\left(d x + c\right)^{2} + 315 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 315 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(325 \, \cos\left(d x + c\right)^{6} - 210 \, \cos\left(d x + c\right)^{4} + 88 \, \cos\left(d x + c\right)^{2} - 16\right)} \sin\left(d x + c\right) + 288}{2560 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"1/2560*(1930*cos(d*x + c)^8 - 3630*cos(d*x + c)^6 + 3156*cos(d*x + c)^4 - 1488*cos(d*x + c)^2 + 315*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) - 315*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(325*cos(d*x + c)^6 - 210*cos(d*x + c)^4 + 88*cos(d*x + c)^2 - 16)*sin(d*x + c) + 288)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
899,1,187,0,1.293204," ","integrate(sec(d*x+c)^9*sin(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{210 \, \cos\left(d x + c\right)^{8} + 1210 \, \cos\left(d x + c\right)^{6} - 1052 \, \cos\left(d x + c\right)^{4} + 496 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(1815 \, \cos\left(d x + c\right)^{6} - 2630 \, \cos\left(d x + c\right)^{4} + 1736 \, \cos\left(d x + c\right)^{2} - 432\right)} \sin\left(d x + c\right) - 96}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"-1/7680*(210*cos(d*x + c)^8 + 1210*cos(d*x + c)^6 - 1052*cos(d*x + c)^4 + 496*cos(d*x + c)^2 - 105*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 105*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) + 2*(1815*cos(d*x + c)^6 - 2630*cos(d*x + c)^4 + 1736*cos(d*x + c)^2 - 432)*sin(d*x + c) - 96)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
900,1,187,0,1.352890," ","integrate(sec(d*x+c)^9*sin(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{210 \, \cos\left(d x + c\right)^{8} - 2630 \, \cos\left(d x + c\right)^{6} + 4708 \, \cos\left(d x + c\right)^{4} - 3344 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(105 \, \cos\left(d x + c\right)^{6} - 250 \, \cos\left(d x + c\right)^{4} + 184 \, \cos\left(d x + c\right)^{2} - 48\right)} \sin\left(d x + c\right) + 864}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"1/7680*(210*cos(d*x + c)^8 - 2630*cos(d*x + c)^6 + 4708*cos(d*x + c)^4 - 3344*cos(d*x + c)^2 - 105*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 105*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(105*cos(d*x + c)^6 - 250*cos(d*x + c)^4 + 184*cos(d*x + c)^2 - 48)*sin(d*x + c) + 864)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
901,1,187,0,1.304096," ","integrate(sec(d*x+c)^9*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{8} - 10 \, \cos\left(d x + c\right)^{6} + 124 \, \cos\left(d x + c\right)^{4} - 112 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15 \, \cos\left(d x + c\right)^{6} - 310 \, \cos\left(d x + c\right)^{4} + 392 \, \cos\left(d x + c\right)^{2} - 144\right)} \sin\left(d x + c\right) + 32}{2560 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"1/2560*(30*cos(d*x + c)^8 - 10*cos(d*x + c)^6 + 124*cos(d*x + c)^4 - 112*cos(d*x + c)^2 - 15*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 15*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(15*cos(d*x + c)^6 - 310*cos(d*x + c)^4 + 392*cos(d*x + c)^2 - 144)*sin(d*x + c) + 32)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
902,1,187,0,1.182273," ","integrate(sec(d*x+c)^9*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{90 \, \cos\left(d x + c\right)^{8} - 30 \, \cos\left(d x + c\right)^{6} - 1548 \, \cos\left(d x + c\right)^{4} + 2224 \, \cos\left(d x + c\right)^{2} - 45 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 45 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(45 \, \cos\left(d x + c\right)^{6} + 30 \, \cos\left(d x + c\right)^{4} - 104 \, \cos\left(d x + c\right)^{2} + 48\right)} \sin\left(d x + c\right) - 864}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"-1/7680*(90*cos(d*x + c)^8 - 30*cos(d*x + c)^6 - 1548*cos(d*x + c)^4 + 2224*cos(d*x + c)^2 - 45*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 45*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(45*cos(d*x + c)^6 + 30*cos(d*x + c)^4 - 104*cos(d*x + c)^2 + 48)*sin(d*x + c) - 864)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
903,1,187,0,1.008366," ","integrate(sec(d*x+c)^9*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{90 \, \cos\left(d x + c\right)^{8} - 30 \, \cos\left(d x + c\right)^{6} - 12 \, \cos\left(d x + c\right)^{4} + 176 \, \cos\left(d x + c\right)^{2} - 45 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 45 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(45 \, \cos\left(d x + c\right)^{6} + 30 \, \cos\left(d x + c\right)^{4} - 616 \, \cos\left(d x + c\right)^{2} + 432\right)} \sin\left(d x + c\right) - 96}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"-1/7680*(90*cos(d*x + c)^8 - 30*cos(d*x + c)^6 - 12*cos(d*x + c)^4 + 176*cos(d*x + c)^2 - 45*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 45*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(45*cos(d*x + c)^6 + 30*cos(d*x + c)^4 - 616*cos(d*x + c)^2 + 432)*sin(d*x + c) - 96)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
904,1,187,0,1.173476," ","integrate(sec(d*x+c)^9*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{30 \, \cos\left(d x + c\right)^{8} - 10 \, \cos\left(d x + c\right)^{6} - 4 \, \cos\left(d x + c\right)^{4} - 368 \, \cos\left(d x + c\right)^{2} - 15 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15 \, \cos\left(d x + c\right)^{6} + 10 \, \cos\left(d x + c\right)^{4} + 8 \, \cos\left(d x + c\right)^{2} - 16\right)} \sin\left(d x + c\right) + 288}{2560 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"1/2560*(30*cos(d*x + c)^8 - 10*cos(d*x + c)^6 - 4*cos(d*x + c)^4 - 368*cos(d*x + c)^2 - 15*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 15*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(15*cos(d*x + c)^6 + 10*cos(d*x + c)^4 + 8*cos(d*x + c)^2 - 16)*sin(d*x + c) + 288)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
905,1,187,0,1.270392," ","integrate(sec(d*x+c)^9*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{210 \, \cos\left(d x + c\right)^{8} - 70 \, \cos\left(d x + c\right)^{6} - 28 \, \cos\left(d x + c\right)^{4} - 16 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(105 \, \cos\left(d x + c\right)^{6} + 70 \, \cos\left(d x + c\right)^{4} + 56 \, \cos\left(d x + c\right)^{2} - 432\right)} \sin\left(d x + c\right) + 96}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"1/7680*(210*cos(d*x + c)^8 - 70*cos(d*x + c)^6 - 28*cos(d*x + c)^4 - 16*cos(d*x + c)^2 - 105*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 105*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(105*cos(d*x + c)^6 + 70*cos(d*x + c)^4 + 56*cos(d*x + c)^2 - 432)*sin(d*x + c) + 96)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
906,1,187,0,1.114659," ","integrate(sec(d*x+c)^9*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{210 \, \cos\left(d x + c\right)^{8} - 70 \, \cos\left(d x + c\right)^{6} - 28 \, \cos\left(d x + c\right)^{4} - 16 \, \cos\left(d x + c\right)^{2} - 105 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 105 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(105 \, \cos\left(d x + c\right)^{6} + 70 \, \cos\left(d x + c\right)^{4} + 56 \, \cos\left(d x + c\right)^{2} + 48\right)} \sin\left(d x + c\right) - 864}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"-1/7680*(210*cos(d*x + c)^8 - 70*cos(d*x + c)^6 - 28*cos(d*x + c)^4 - 16*cos(d*x + c)^2 - 105*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 105*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 2*(105*cos(d*x + c)^6 + 70*cos(d*x + c)^4 + 56*cos(d*x + c)^2 + 48)*sin(d*x + c) - 864)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
907,1,187,0,1.247468," ","integrate(sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{630 \, \cos\left(d x + c\right)^{8} - 210 \, \cos\left(d x + c\right)^{6} - 84 \, \cos\left(d x + c\right)^{4} - 48 \, \cos\left(d x + c\right)^{2} - 315 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 315 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 6 \, {\left(105 \, \cos\left(d x + c\right)^{6} + 70 \, \cos\left(d x + c\right)^{4} + 56 \, \cos\left(d x + c\right)^{2} + 48\right)} \sin\left(d x + c\right) - 32}{2560 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"-1/2560*(630*cos(d*x + c)^8 - 210*cos(d*x + c)^6 - 84*cos(d*x + c)^4 - 48*cos(d*x + c)^2 - 315*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) + 315*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) - 6*(105*cos(d*x + c)^6 + 70*cos(d*x + c)^4 + 56*cos(d*x + c)^2 + 48)*sin(d*x + c) - 32)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
908,1,222,0,1.119246," ","integrate(csc(d*x+c)*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{1890 \, \cos\left(d x + c\right)^{8} + 3210 \, \cos\left(d x + c\right)^{6} + 1668 \, \cos\left(d x + c\right)^{4} + 1136 \, \cos\left(d x + c\right)^{2} + 7680 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4785 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2895 \, {\left(\cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(975 \, \cos\left(d x + c\right)^{6} + 330 \, \cos\left(d x + c\right)^{4} + 136 \, \cos\left(d x + c\right)^{2} + 48\right)} \sin\left(d x + c\right) + 864}{7680 \, {\left(a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"1/7680*(1890*cos(d*x + c)^8 + 3210*cos(d*x + c)^6 + 1668*cos(d*x + c)^4 + 1136*cos(d*x + c)^2 + 7680*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(1/2*sin(d*x + c)) - 4785*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(sin(d*x + c) + 1) - 2895*(cos(d*x + c)^8*sin(d*x + c) + cos(d*x + c)^8)*log(-sin(d*x + c) + 1) + 2*(975*cos(d*x + c)^6 + 330*cos(d*x + c)^4 + 136*cos(d*x + c)^2 + 48)*sin(d*x + c) + 864)/(a*d*cos(d*x + c)^8*sin(d*x + c) + a*d*cos(d*x + c)^8)","A",0
909,1,278,0,1.129344," ","integrate(csc(d*x+c)^2*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16950 \, \cos\left(d x + c\right)^{8} - 5010 \, \cos\left(d x + c\right)^{6} - 2132 \, \cos\left(d x + c\right)^{4} - 1264 \, \cos\left(d x + c\right)^{2} - 7680 \, {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{8}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 14235 \, {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{8}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 6555 \, {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) - \cos\left(d x + c\right)^{8}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(10395 \, \cos\left(d x + c\right)^{8} - 1545 \, \cos\left(d x + c\right)^{6} - 426 \, \cos\left(d x + c\right)^{4} - 152 \, \cos\left(d x + c\right)^{2} - 48\right)} \sin\left(d x + c\right) - 864}{7680 \, {\left(a d \cos\left(d x + c\right)^{10} - a d \cos\left(d x + c\right)^{8} \sin\left(d x + c\right) - a d \cos\left(d x + c\right)^{8}\right)}}"," ",0,"1/7680*(16950*cos(d*x + c)^8 - 5010*cos(d*x + c)^6 - 2132*cos(d*x + c)^4 - 1264*cos(d*x + c)^2 - 7680*(cos(d*x + c)^10 - cos(d*x + c)^8*sin(d*x + c) - cos(d*x + c)^8)*log(1/2*sin(d*x + c)) + 14235*(cos(d*x + c)^10 - cos(d*x + c)^8*sin(d*x + c) - cos(d*x + c)^8)*log(sin(d*x + c) + 1) - 6555*(cos(d*x + c)^10 - cos(d*x + c)^8*sin(d*x + c) - cos(d*x + c)^8)*log(-sin(d*x + c) + 1) + 2*(10395*cos(d*x + c)^8 - 1545*cos(d*x + c)^6 - 426*cos(d*x + c)^4 - 152*cos(d*x + c)^2 - 48)*sin(d*x + c) - 864)/(a*d*cos(d*x + c)^10 - a*d*cos(d*x + c)^8*sin(d*x + c) - a*d*cos(d*x + c)^8)","A",0
910,1,331,0,1.490090," ","integrate(csc(d*x+c)^3*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6930 \, \cos\left(d x + c\right)^{10} - 1560 \, \cos\left(d x + c\right)^{8} - 2454 \, \cos\left(d x + c\right)^{6} - 884 \, \cos\left(d x + c\right)^{4} - 464 \, \cos\left(d x + c\right)^{2} + 15360 \, {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8} + {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 11145 \, {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8} + {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 4215 \, {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8} + {\left(\cos\left(d x + c\right)^{10} - \cos\left(d x + c\right)^{8}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(375 \, \cos\left(d x + c\right)^{8} - 765 \, \cos\left(d x + c\right)^{6} - 178 \, \cos\left(d x + c\right)^{4} - 56 \, \cos\left(d x + c\right)^{2} - 16\right)} \sin\left(d x + c\right) - 288}{2560 \, {\left(a d \cos\left(d x + c\right)^{10} - a d \cos\left(d x + c\right)^{8} + {\left(a d \cos\left(d x + c\right)^{10} - a d \cos\left(d x + c\right)^{8}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/2560*(6930*cos(d*x + c)^10 - 1560*cos(d*x + c)^8 - 2454*cos(d*x + c)^6 - 884*cos(d*x + c)^4 - 464*cos(d*x + c)^2 + 15360*(cos(d*x + c)^10 - cos(d*x + c)^8 + (cos(d*x + c)^10 - cos(d*x + c)^8)*sin(d*x + c))*log(1/2*sin(d*x + c)) - 11145*(cos(d*x + c)^10 - cos(d*x + c)^8 + (cos(d*x + c)^10 - cos(d*x + c)^8)*sin(d*x + c))*log(sin(d*x + c) + 1) - 4215*(cos(d*x + c)^10 - cos(d*x + c)^8 + (cos(d*x + c)^10 - cos(d*x + c)^8)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 2*(375*cos(d*x + c)^8 - 765*cos(d*x + c)^6 - 178*cos(d*x + c)^4 - 56*cos(d*x + c)^2 - 16)*sin(d*x + c) - 288)/(a*d*cos(d*x + c)^10 - a*d*cos(d*x + c)^8 + (a*d*cos(d*x + c)^10 - a*d*cos(d*x + c)^8)*sin(d*x + c))","A",0
911,0,0,0,1.413508," ","integrate((g*sec(f*x+e))^p*(d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(\left(g \sec\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
912,0,0,0,0.964387," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right), x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e), x)","F",0
913,1,902,0,1.688785," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^4*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left(24 \, a^{4} c^{5} - 120 \, a^{4} c^{4} d + 240 \, a^{4} c^{3} d^{2} - 240 \, a^{4} c^{2} d^{3} + 120 \, a^{4} c d^{4} + 360 \, a^{4} d^{5} + 8 \, {\left(a^{4} c d^{4} + a^{4} d^{5}\right)} n^{4} + {\left(120 \, a^{4} d^{5} + {\left(a^{4} c d^{4} + 4 \, a^{4} d^{5}\right)} n^{4} + 2 \, {\left(3 \, a^{4} c d^{4} + 22 \, a^{4} d^{5}\right)} n^{3} + {\left(11 \, a^{4} c d^{4} + 164 \, a^{4} d^{5}\right)} n^{2} + 2 \, {\left(3 \, a^{4} c d^{4} + 122 \, a^{4} d^{5}\right)} n\right)} \cos\left(f x + e\right)^{4} - 16 \, {\left(a^{4} c^{2} d^{3} - 5 \, a^{4} c d^{4} - 6 \, a^{4} d^{5}\right)} n^{3} + 8 \, {\left(3 \, a^{4} c^{3} d^{2} - 15 \, a^{4} c^{2} d^{3} + 32 \, a^{4} c d^{4} + 50 \, a^{4} d^{5}\right)} n^{2} - 4 \, {\left(120 \, a^{4} d^{5} + {\left(2 \, a^{4} c d^{4} + 3 \, a^{4} d^{5}\right)} n^{4} - {\left(3 \, a^{4} c^{2} d^{3} - 18 \, a^{4} c d^{4} - 35 \, a^{4} d^{5}\right)} n^{3} + {\left(3 \, a^{4} c^{3} d^{2} - 18 \, a^{4} c^{2} d^{3} + 49 \, a^{4} c d^{4} + 141 \, a^{4} d^{5}\right)} n^{2} + {\left(3 \, a^{4} c^{3} d^{2} - 15 \, a^{4} c^{2} d^{3} + 33 \, a^{4} c d^{4} + 229 \, a^{4} d^{5}\right)} n\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left(3 \, a^{4} c^{4} d - 15 \, a^{4} c^{3} d^{2} + 31 \, a^{4} c^{2} d^{3} - 35 \, a^{4} c d^{4} - 84 \, a^{4} d^{5}\right)} n + {\left(384 \, a^{4} d^{5} + 8 \, {\left(a^{4} c d^{4} + a^{4} d^{5}\right)} n^{4} + {\left(a^{4} d^{5} n^{4} + 10 \, a^{4} d^{5} n^{3} + 35 \, a^{4} d^{5} n^{2} + 50 \, a^{4} d^{5} n + 24 \, a^{4} d^{5}\right)} \cos\left(f x + e\right)^{4} - 16 \, {\left(a^{4} c^{2} d^{3} - 5 \, a^{4} c d^{4} - 6 \, a^{4} d^{5}\right)} n^{3} + 8 \, {\left(3 \, a^{4} c^{3} d^{2} - 15 \, a^{4} c^{2} d^{3} + 32 \, a^{4} c d^{4} + 50 \, a^{4} d^{5}\right)} n^{2} - 4 \, {\left(72 \, a^{4} d^{5} + {\left(a^{4} c d^{4} + 2 \, a^{4} d^{5}\right)} n^{4} - {\left(a^{4} c^{2} d^{3} - 8 \, a^{4} c d^{4} - 23 \, a^{4} d^{5}\right)} n^{3} - {\left(3 \, a^{4} c^{2} d^{3} - 17 \, a^{4} c d^{4} - 91 \, a^{4} d^{5}\right)} n^{2} - 2 \, {\left(a^{4} c^{2} d^{3} - 5 \, a^{4} c d^{4} - 71 \, a^{4} d^{5}\right)} n\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left(3 \, a^{4} c^{4} d - 15 \, a^{4} c^{3} d^{2} + 31 \, a^{4} c^{2} d^{3} - 35 \, a^{4} c d^{4} - 84 \, a^{4} d^{5}\right)} n\right)} \sin\left(f x + e\right)\right)} {\left(d \sin\left(f x + e\right) + c\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}"," ",0,"(24*a^4*c^5 - 120*a^4*c^4*d + 240*a^4*c^3*d^2 - 240*a^4*c^2*d^3 + 120*a^4*c*d^4 + 360*a^4*d^5 + 8*(a^4*c*d^4 + a^4*d^5)*n^4 + (120*a^4*d^5 + (a^4*c*d^4 + 4*a^4*d^5)*n^4 + 2*(3*a^4*c*d^4 + 22*a^4*d^5)*n^3 + (11*a^4*c*d^4 + 164*a^4*d^5)*n^2 + 2*(3*a^4*c*d^4 + 122*a^4*d^5)*n)*cos(f*x + e)^4 - 16*(a^4*c^2*d^3 - 5*a^4*c*d^4 - 6*a^4*d^5)*n^3 + 8*(3*a^4*c^3*d^2 - 15*a^4*c^2*d^3 + 32*a^4*c*d^4 + 50*a^4*d^5)*n^2 - 4*(120*a^4*d^5 + (2*a^4*c*d^4 + 3*a^4*d^5)*n^4 - (3*a^4*c^2*d^3 - 18*a^4*c*d^4 - 35*a^4*d^5)*n^3 + (3*a^4*c^3*d^2 - 18*a^4*c^2*d^3 + 49*a^4*c*d^4 + 141*a^4*d^5)*n^2 + (3*a^4*c^3*d^2 - 15*a^4*c^2*d^3 + 33*a^4*c*d^4 + 229*a^4*d^5)*n)*cos(f*x + e)^2 - 8*(3*a^4*c^4*d - 15*a^4*c^3*d^2 + 31*a^4*c^2*d^3 - 35*a^4*c*d^4 - 84*a^4*d^5)*n + (384*a^4*d^5 + 8*(a^4*c*d^4 + a^4*d^5)*n^4 + (a^4*d^5*n^4 + 10*a^4*d^5*n^3 + 35*a^4*d^5*n^2 + 50*a^4*d^5*n + 24*a^4*d^5)*cos(f*x + e)^4 - 16*(a^4*c^2*d^3 - 5*a^4*c*d^4 - 6*a^4*d^5)*n^3 + 8*(3*a^4*c^3*d^2 - 15*a^4*c^2*d^3 + 32*a^4*c*d^4 + 50*a^4*d^5)*n^2 - 4*(72*a^4*d^5 + (a^4*c*d^4 + 2*a^4*d^5)*n^4 - (a^4*c^2*d^3 - 8*a^4*c*d^4 - 23*a^4*d^5)*n^3 - (3*a^4*c^2*d^3 - 17*a^4*c*d^4 - 91*a^4*d^5)*n^2 - 2*(a^4*c^2*d^3 - 5*a^4*c*d^4 - 71*a^4*d^5)*n)*cos(f*x + e)^2 - 8*(3*a^4*c^4*d - 15*a^4*c^3*d^2 + 31*a^4*c^2*d^3 - 35*a^4*c*d^4 - 84*a^4*d^5)*n)*sin(f*x + e))*(d*sin(f*x + e) + c)^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)","B",0
914,1,545,0,1.579200," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","-\frac{{\left(6 \, a^{3} c^{4} - 24 \, a^{3} c^{3} d + 36 \, a^{3} c^{2} d^{2} - 24 \, a^{3} c d^{3} - 42 \, a^{3} d^{4} - {\left(a^{3} d^{4} n^{3} + 6 \, a^{3} d^{4} n^{2} + 11 \, a^{3} d^{4} n + 6 \, a^{3} d^{4}\right)} \cos\left(f x + e\right)^{4} - 4 \, {\left(a^{3} c d^{3} + a^{3} d^{4}\right)} n^{3} + 6 \, {\left(a^{3} c^{2} d^{2} - 4 \, a^{3} c d^{3} - 5 \, a^{3} d^{4}\right)} n^{2} + {\left(48 \, a^{3} d^{4} + {\left(3 \, a^{3} c d^{3} + 5 \, a^{3} d^{4}\right)} n^{3} - 3 \, {\left(a^{3} c^{2} d^{2} - 5 \, a^{3} c d^{3} - 12 \, a^{3} d^{4}\right)} n^{2} - {\left(3 \, a^{3} c^{2} d^{2} - 12 \, a^{3} c d^{3} - 79 \, a^{3} d^{4}\right)} n\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, a^{3} c^{3} d - 12 \, a^{3} c^{2} d^{2} + 19 \, a^{3} c d^{3} + 34 \, a^{3} d^{4}\right)} n - {\left(48 \, a^{3} d^{4} + 4 \, {\left(a^{3} c d^{3} + a^{3} d^{4}\right)} n^{3} - 6 \, {\left(a^{3} c^{2} d^{2} - 4 \, a^{3} c d^{3} - 5 \, a^{3} d^{4}\right)} n^{2} - {\left(24 \, a^{3} d^{4} + {\left(a^{3} c d^{3} + 3 \, a^{3} d^{4}\right)} n^{3} + 3 \, {\left(a^{3} c d^{3} + 7 \, a^{3} d^{4}\right)} n^{2} + 2 \, {\left(a^{3} c d^{3} + 21 \, a^{3} d^{4}\right)} n\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, a^{3} c^{3} d - 12 \, a^{3} c^{2} d^{2} + 19 \, a^{3} c d^{3} + 34 \, a^{3} d^{4}\right)} n\right)} \sin\left(f x + e\right)\right)} {\left(d \sin\left(f x + e\right) + c\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}"," ",0,"-(6*a^3*c^4 - 24*a^3*c^3*d + 36*a^3*c^2*d^2 - 24*a^3*c*d^3 - 42*a^3*d^4 - (a^3*d^4*n^3 + 6*a^3*d^4*n^2 + 11*a^3*d^4*n + 6*a^3*d^4)*cos(f*x + e)^4 - 4*(a^3*c*d^3 + a^3*d^4)*n^3 + 6*(a^3*c^2*d^2 - 4*a^3*c*d^3 - 5*a^3*d^4)*n^2 + (48*a^3*d^4 + (3*a^3*c*d^3 + 5*a^3*d^4)*n^3 - 3*(a^3*c^2*d^2 - 5*a^3*c*d^3 - 12*a^3*d^4)*n^2 - (3*a^3*c^2*d^2 - 12*a^3*c*d^3 - 79*a^3*d^4)*n)*cos(f*x + e)^2 - 2*(3*a^3*c^3*d - 12*a^3*c^2*d^2 + 19*a^3*c*d^3 + 34*a^3*d^4)*n - (48*a^3*d^4 + 4*(a^3*c*d^3 + a^3*d^4)*n^3 - 6*(a^3*c^2*d^2 - 4*a^3*c*d^3 - 5*a^3*d^4)*n^2 - (24*a^3*d^4 + (a^3*c*d^3 + 3*a^3*d^4)*n^3 + 3*(a^3*c*d^3 + 7*a^3*d^4)*n^2 + 2*(a^3*c*d^3 + 21*a^3*d^4)*n)*cos(f*x + e)^2 + 2*(3*a^3*c^3*d - 12*a^3*c^2*d^2 + 19*a^3*c*d^3 + 34*a^3*d^4)*n)*sin(f*x + e))*(d*sin(f*x + e) + c)^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)","B",0
915,1,294,0,1.463816," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","\frac{{\left(2 \, a^{2} c^{3} - 6 \, a^{2} c^{2} d + 6 \, a^{2} c d^{2} + 6 \, a^{2} d^{3} + 2 \, {\left(a^{2} c d^{2} + a^{2} d^{3}\right)} n^{2} - {\left(6 \, a^{2} d^{3} + {\left(a^{2} c d^{2} + 2 \, a^{2} d^{3}\right)} n^{2} + {\left(a^{2} c d^{2} + 8 \, a^{2} d^{3}\right)} n\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{2} c^{2} d - 3 \, a^{2} c d^{2} - 4 \, a^{2} d^{3}\right)} n + {\left(8 \, a^{2} d^{3} + 2 \, {\left(a^{2} c d^{2} + a^{2} d^{3}\right)} n^{2} - {\left(a^{2} d^{3} n^{2} + 3 \, a^{2} d^{3} n + 2 \, a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{2} c^{2} d - 3 \, a^{2} c d^{2} - 4 \, a^{2} d^{3}\right)} n\right)} \sin\left(f x + e\right)\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{d^{3} f n^{3} + 6 \, d^{3} f n^{2} + 11 \, d^{3} f n + 6 \, d^{3} f}"," ",0,"(2*a^2*c^3 - 6*a^2*c^2*d + 6*a^2*c*d^2 + 6*a^2*d^3 + 2*(a^2*c*d^2 + a^2*d^3)*n^2 - (6*a^2*d^3 + (a^2*c*d^2 + 2*a^2*d^3)*n^2 + (a^2*c*d^2 + 8*a^2*d^3)*n)*cos(f*x + e)^2 - 2*(a^2*c^2*d - 3*a^2*c*d^2 - 4*a^2*d^3)*n + (8*a^2*d^3 + 2*(a^2*c*d^2 + a^2*d^3)*n^2 - (a^2*d^3*n^2 + 3*a^2*d^3*n + 2*a^2*d^3)*cos(f*x + e)^2 - 2*(a^2*c^2*d - 3*a^2*c*d^2 - 4*a^2*d^3)*n)*sin(f*x + e))*(d*sin(f*x + e) + c)^n/(d^3*f*n^3 + 6*d^3*f*n^2 + 11*d^3*f*n + 6*d^3*f)","B",0
916,1,116,0,1.273890," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","-\frac{{\left(a c^{2} - 2 \, a c d - a d^{2} + {\left(a d^{2} n + a d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(a c d + a d^{2}\right)} n - {\left(2 \, a d^{2} + {\left(a c d + a d^{2}\right)} n\right)} \sin\left(f x + e\right)\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{d^{2} f n^{2} + 3 \, d^{2} f n + 2 \, d^{2} f}"," ",0,"-(a*c^2 - 2*a*c*d - a*d^2 + (a*d^2*n + a*d^2)*cos(f*x + e)^2 - (a*c*d + a*d^2)*n - (2*a*d^2 + (a*c*d + a*d^2)*n)*sin(f*x + e))*(d*sin(f*x + e) + c)^n/(d^2*f*n^2 + 3*d^2*f*n + 2*d^2*f)","A",0
917,0,0,0,1.197682," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)}{a \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*sin(f*x + e) + c)^n*cos(f*x + e)/(a*sin(f*x + e) + a), x)","F",0
918,0,0,0,1.238081," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(d*sin(f*x + e) + c)^n*cos(f*x + e)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
919,0,0,0,1.885530," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(d*sin(f*x + e) + c)^n*cos(f*x + e)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
920,1,744,0,1.241625," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left({\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} m^{4} + {\left({\left(4 \, c d^{3} + d^{4}\right)} m^{4} + 120 \, c d^{3} + 2 \, {\left(22 \, c d^{3} + 3 \, d^{4}\right)} m^{3} + {\left(164 \, c d^{3} + 11 \, d^{4}\right)} m^{2} + 2 \, {\left(122 \, c d^{3} + 3 \, d^{4}\right)} m\right)} \cos\left(f x + e\right)^{4} + 120 \, c^{4} + 240 \, c^{2} d^{2} + 24 \, d^{4} + 2 \, {\left(7 \, c^{4} + 24 \, c^{3} d + 30 \, c^{2} d^{2} + 16 \, c d^{3} + 3 \, d^{4}\right)} m^{3} + {\left(71 \, c^{4} + 188 \, c^{3} d + 186 \, c^{2} d^{2} + 92 \, c d^{3} + 23 \, d^{4}\right)} m^{2} - 2 \, {\left({\left(2 \, c^{3} d + 3 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} m^{4} + 120 \, c^{3} d + 120 \, c d^{3} + 2 \, {\left(13 \, c^{3} d + 15 \, c^{2} d^{2} + 19 \, c d^{3} + 3 \, d^{4}\right)} m^{3} + {\left(118 \, c^{3} d + 87 \, c^{2} d^{2} + 128 \, c d^{3} + 17 \, d^{4}\right)} m^{2} + 2 \, {\left(107 \, c^{3} d + 30 \, c^{2} d^{2} + 107 \, c d^{3} + 6 \, d^{4}\right)} m\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(77 \, c^{4} + 120 \, c^{3} d + 114 \, c^{2} d^{2} + 80 \, c d^{3} + 9 \, d^{4}\right)} m + {\left({\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} m^{4} + {\left(d^{4} m^{4} + 10 \, d^{4} m^{3} + 35 \, d^{4} m^{2} + 50 \, d^{4} m + 24 \, d^{4}\right)} \cos\left(f x + e\right)^{4} + 120 \, c^{4} + 240 \, c^{2} d^{2} + 24 \, d^{4} + 2 \, {\left(7 \, c^{4} + 24 \, c^{3} d + 30 \, c^{2} d^{2} + 16 \, c d^{3} + 3 \, d^{4}\right)} m^{3} + {\left(71 \, c^{4} + 188 \, c^{3} d + 186 \, c^{2} d^{2} + 92 \, c d^{3} + 23 \, d^{4}\right)} m^{2} - 2 \, {\left({\left(3 \, c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} m^{4} + 120 \, c^{2} d^{2} + 24 \, d^{4} + 4 \, {\left(9 \, c^{2} d^{2} + 4 \, c d^{3} + 2 \, d^{4}\right)} m^{3} + {\left(147 \, c^{2} d^{2} + 34 \, c d^{3} + 29 \, d^{4}\right)} m^{2} + 2 \, {\left(117 \, c^{2} d^{2} + 10 \, c d^{3} + 23 \, d^{4}\right)} m\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(77 \, c^{4} + 120 \, c^{3} d + 114 \, c^{2} d^{2} + 80 \, c d^{3} + 9 \, d^{4}\right)} m\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f m^{5} + 15 \, f m^{4} + 85 \, f m^{3} + 225 \, f m^{2} + 274 \, f m + 120 \, f}"," ",0,"((c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*m^4 + ((4*c*d^3 + d^4)*m^4 + 120*c*d^3 + 2*(22*c*d^3 + 3*d^4)*m^3 + (164*c*d^3 + 11*d^4)*m^2 + 2*(122*c*d^3 + 3*d^4)*m)*cos(f*x + e)^4 + 120*c^4 + 240*c^2*d^2 + 24*d^4 + 2*(7*c^4 + 24*c^3*d + 30*c^2*d^2 + 16*c*d^3 + 3*d^4)*m^3 + (71*c^4 + 188*c^3*d + 186*c^2*d^2 + 92*c*d^3 + 23*d^4)*m^2 - 2*((2*c^3*d + 3*c^2*d^2 + 4*c*d^3 + d^4)*m^4 + 120*c^3*d + 120*c*d^3 + 2*(13*c^3*d + 15*c^2*d^2 + 19*c*d^3 + 3*d^4)*m^3 + (118*c^3*d + 87*c^2*d^2 + 128*c*d^3 + 17*d^4)*m^2 + 2*(107*c^3*d + 30*c^2*d^2 + 107*c*d^3 + 6*d^4)*m)*cos(f*x + e)^2 + 2*(77*c^4 + 120*c^3*d + 114*c^2*d^2 + 80*c*d^3 + 9*d^4)*m + ((c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*m^4 + (d^4*m^4 + 10*d^4*m^3 + 35*d^4*m^2 + 50*d^4*m + 24*d^4)*cos(f*x + e)^4 + 120*c^4 + 240*c^2*d^2 + 24*d^4 + 2*(7*c^4 + 24*c^3*d + 30*c^2*d^2 + 16*c*d^3 + 3*d^4)*m^3 + (71*c^4 + 188*c^3*d + 186*c^2*d^2 + 92*c*d^3 + 23*d^4)*m^2 - 2*((3*c^2*d^2 + 2*c*d^3 + d^4)*m^4 + 120*c^2*d^2 + 24*d^4 + 4*(9*c^2*d^2 + 4*c*d^3 + 2*d^4)*m^3 + (147*c^2*d^2 + 34*c*d^3 + 29*d^4)*m^2 + 2*(117*c^2*d^2 + 10*c*d^3 + 23*d^4)*m)*cos(f*x + e)^2 + 2*(77*c^4 + 120*c^3*d + 114*c^2*d^2 + 80*c*d^3 + 9*d^4)*m)*sin(f*x + e))*(a*sin(f*x + e) + a)^m/(f*m^5 + 15*f*m^4 + 85*f*m^3 + 225*f*m^2 + 274*f*m + 120*f)","B",0
921,1,403,0,1.297538," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left({\left(d^{3} m^{3} + 6 \, d^{3} m^{2} + 11 \, d^{3} m + 6 \, d^{3}\right)} \cos\left(f x + e\right)^{4} + {\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} m^{3} + 24 \, c^{3} + 24 \, c d^{2} + 3 \, {\left(3 \, c^{3} + 7 \, c^{2} d + 5 \, c d^{2} + d^{3}\right)} m^{2} - {\left({\left(3 \, c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} m^{3} + 36 \, c^{2} d + 12 \, d^{3} + 3 \, {\left(8 \, c^{2} d + 5 \, c d^{2} + 3 \, d^{3}\right)} m^{2} + {\left(57 \, c^{2} d + 12 \, c d^{2} + 19 \, d^{3}\right)} m\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{3} + 18 \, c^{2} d + 9 \, c d^{2} + 4 \, d^{3}\right)} m + {\left({\left(c^{3} + 3 \, c^{2} d + 3 \, c d^{2} + d^{3}\right)} m^{3} + 24 \, c^{3} + 24 \, c d^{2} + 3 \, {\left(3 \, c^{3} + 7 \, c^{2} d + 5 \, c d^{2} + d^{3}\right)} m^{2} - {\left({\left(3 \, c d^{2} + d^{3}\right)} m^{3} + 24 \, c d^{2} + 3 \, {\left(7 \, c d^{2} + d^{3}\right)} m^{2} + 2 \, {\left(21 \, c d^{2} + d^{3}\right)} m\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{3} + 18 \, c^{2} d + 9 \, c d^{2} + 4 \, d^{3}\right)} m\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f m^{4} + 10 \, f m^{3} + 35 \, f m^{2} + 50 \, f m + 24 \, f}"," ",0,"((d^3*m^3 + 6*d^3*m^2 + 11*d^3*m + 6*d^3)*cos(f*x + e)^4 + (c^3 + 3*c^2*d + 3*c*d^2 + d^3)*m^3 + 24*c^3 + 24*c*d^2 + 3*(3*c^3 + 7*c^2*d + 5*c*d^2 + d^3)*m^2 - ((3*c^2*d + 3*c*d^2 + 2*d^3)*m^3 + 36*c^2*d + 12*d^3 + 3*(8*c^2*d + 5*c*d^2 + 3*d^3)*m^2 + (57*c^2*d + 12*c*d^2 + 19*d^3)*m)*cos(f*x + e)^2 + 2*(13*c^3 + 18*c^2*d + 9*c*d^2 + 4*d^3)*m + ((c^3 + 3*c^2*d + 3*c*d^2 + d^3)*m^3 + 24*c^3 + 24*c*d^2 + 3*(3*c^3 + 7*c^2*d + 5*c*d^2 + d^3)*m^2 - ((3*c*d^2 + d^3)*m^3 + 24*c*d^2 + 3*(7*c*d^2 + d^3)*m^2 + 2*(21*c*d^2 + d^3)*m)*cos(f*x + e)^2 + 2*(13*c^3 + 18*c^2*d + 9*c*d^2 + 4*d^3)*m)*sin(f*x + e))*(a*sin(f*x + e) + a)^m/(f*m^4 + 10*f*m^3 + 35*f*m^2 + 50*f*m + 24*f)","B",0
922,1,189,0,1.357969," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left({\left(c^{2} + 2 \, c d + d^{2}\right)} m^{2} - {\left({\left(2 \, c d + d^{2}\right)} m^{2} + 6 \, c d + {\left(8 \, c d + d^{2}\right)} m\right)} \cos\left(f x + e\right)^{2} + 6 \, c^{2} + 2 \, d^{2} + {\left(5 \, c^{2} + 6 \, c d + d^{2}\right)} m + {\left({\left(c^{2} + 2 \, c d + d^{2}\right)} m^{2} - {\left(d^{2} m^{2} + 3 \, d^{2} m + 2 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + 6 \, c^{2} + 2 \, d^{2} + {\left(5 \, c^{2} + 6 \, c d + d^{2}\right)} m\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f m^{3} + 6 \, f m^{2} + 11 \, f m + 6 \, f}"," ",0,"((c^2 + 2*c*d + d^2)*m^2 - ((2*c*d + d^2)*m^2 + 6*c*d + (8*c*d + d^2)*m)*cos(f*x + e)^2 + 6*c^2 + 2*d^2 + (5*c^2 + 6*c*d + d^2)*m + ((c^2 + 2*c*d + d^2)*m^2 - (d^2*m^2 + 3*d^2*m + 2*d^2)*cos(f*x + e)^2 + 6*c^2 + 2*d^2 + (5*c^2 + 6*c*d + d^2)*m)*sin(f*x + e))*(a*sin(f*x + e) + a)^m/(f*m^3 + 6*f*m^2 + 11*f*m + 6*f)","A",0
923,1,70,0,1.297645," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left({\left(d m + d\right)} \cos\left(f x + e\right)^{2} - {\left(c + d\right)} m - {\left({\left(c + d\right)} m + 2 \, c\right)} \sin\left(f x + e\right) - 2 \, c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f m^{2} + 3 \, f m + 2 \, f}"," ",0,"-((d*m + d)*cos(f*x + e)^2 - (c + d)*m - ((c + d)*m + 2*c)*sin(f*x + e) - 2*c)*(a*sin(f*x + e) + a)^m/(f*m^2 + 3*f*m + 2*f)","A",0
924,0,0,0,1.158025," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)}{d \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*cos(f*x + e)/(d*sin(f*x + e) + c), x)","F",0
925,0,0,0,1.134350," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}, x\right)"," ",0,"integral(-(a*sin(f*x + e) + a)^m*cos(f*x + e)/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2), x)","F",0
926,0,0,0,1.276115," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)}{3 \, c d^{2} \cos\left(f x + e\right)^{2} - c^{3} - 3 \, c d^{2} + {\left(d^{3} \cos\left(f x + e\right)^{2} - 3 \, c^{2} d - d^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(a*sin(f*x + e) + a)^m*cos(f*x + e)/(3*c*d^2*cos(f*x + e)^2 - c^3 - 3*c*d^2 + (d^3*cos(f*x + e)^2 - 3*c^2*d - d^3)*sin(f*x + e)), x)","F",0
927,0,0,0,1.439869," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right), x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*sin(d*x + c)^n*cos(d*x + c), x)","F",0
928,1,197,0,1.277734," ","integrate(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left({\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} \cos\left(d x + c\right)^{4} + m^{4} + 6 \, m^{3} - 2 \, {\left(m^{4} + 6 \, m^{3} + 17 \, m^{2} + 12 \, m\right)} \cos\left(d x + c\right)^{2} + 23 \, m^{2} + {\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} \cos\left(d x + c\right)^{4} + m^{4} + 6 \, m^{3} - 2 \, {\left(m^{4} + 8 \, m^{3} + 29 \, m^{2} + 46 \, m + 24\right)} \cos\left(d x + c\right)^{2} + 23 \, m^{2} + 18 \, m + 24\right)} \sin\left(d x + c\right) + 18 \, m + 24\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{5} + 15 \, d m^{4} + 85 \, d m^{3} + 225 \, d m^{2} + 274 \, d m + 120 \, d}"," ",0,"((m^4 + 6*m^3 + 11*m^2 + 6*m)*cos(d*x + c)^4 + m^4 + 6*m^3 - 2*(m^4 + 6*m^3 + 17*m^2 + 12*m)*cos(d*x + c)^2 + 23*m^2 + ((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*cos(d*x + c)^4 + m^4 + 6*m^3 - 2*(m^4 + 8*m^3 + 29*m^2 + 46*m + 24)*cos(d*x + c)^2 + 23*m^2 + 18*m + 24)*sin(d*x + c) + 18*m + 24)*(a*sin(d*x + c) + a)^m/(d*m^5 + 15*d*m^4 + 85*d*m^3 + 225*d*m^2 + 274*d*m + 120*d)","A",0
929,1,140,0,1.341180," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","\frac{{\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} \cos\left(d x + c\right)^{4} + m^{3} - {\left(2 \, m^{3} + 9 \, m^{2} + 19 \, m + 12\right)} \cos\left(d x + c\right)^{2} + 3 \, m^{2} + {\left(m^{3} - {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} \cos\left(d x + c\right)^{2} + 3 \, m^{2} + 8 \, m\right)} \sin\left(d x + c\right) + 8 \, m\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{4} + 10 \, d m^{3} + 35 \, d m^{2} + 50 \, d m + 24 \, d}"," ",0,"((m^3 + 6*m^2 + 11*m + 6)*cos(d*x + c)^4 + m^3 - (2*m^3 + 9*m^2 + 19*m + 12)*cos(d*x + c)^2 + 3*m^2 + (m^3 - (m^3 + 3*m^2 + 2*m)*cos(d*x + c)^2 + 3*m^2 + 8*m)*sin(d*x + c) + 8*m)*(a*sin(d*x + c) + a)^m/(d*m^4 + 10*d*m^3 + 35*d*m^2 + 50*d*m + 24*d)","A",0
930,1,93,0,1.085442," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","-\frac{{\left({\left(m^{2} + m\right)} \cos\left(d x + c\right)^{2} - m^{2} + {\left({\left(m^{2} + 3 \, m + 2\right)} \cos\left(d x + c\right)^{2} - m^{2} - m - 2\right)} \sin\left(d x + c\right) - m - 2\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{3} + 6 \, d m^{2} + 11 \, d m + 6 \, d}"," ",0,"-((m^2 + m)*cos(d*x + c)^2 - m^2 + ((m^2 + 3*m + 2)*cos(d*x + c)^2 - m^2 - m - 2)*sin(d*x + c) - m - 2)*(a*sin(d*x + c) + a)^m/(d*m^3 + 6*d*m^2 + 11*d*m + 6*d)","A",0
931,1,54,0,1.302306," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","-\frac{{\left({\left(m + 1\right)} \cos\left(d x + c\right)^{2} - m \sin\left(d x + c\right) - m\right)} {\left(a \sin\left(d x + c\right) + a\right)}^{m}}{d m^{2} + 3 \, d m + 2 \, d}"," ",0,"-((m + 1)*cos(d*x + c)^2 - m*sin(d*x + c) - m)*(a*sin(d*x + c) + a)^m/(d*m^2 + 3*d*m + 2*d)","A",0
932,0,0,0,1.304661," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right), x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c), x)","F",0
933,0,0,0,0.985089," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right)^{2}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c)^2, x)","F",0
934,0,0,0,1.376486," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right)^{3}, x\right)"," ",0,"integral((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c)^3, x)","F",0
935,1,72,0,1.264234," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{8 \, {\left(a c + a d\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(4 \, a c + a d\right)} f x + 3 \, {\left(2 \, a d \cos\left(f x + e\right)^{3} - {\left(4 \, a c + a d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, f}"," ",0,"-1/24*(8*(a*c + a*d)*cos(f*x + e)^3 - 3*(4*a*c + a*d)*f*x + 3*(2*a*d*cos(f*x + e)^3 - (4*a*c + a*d)*cos(f*x + e))*sin(f*x + e))/f","A",0
936,1,667,0,1.614545," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{\sqrt{\frac{c + d}{a d}} \log\left(\frac{d^{2} \cos\left(f x + e\right)^{3} - {\left(6 \, c d + 7 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} - 2 \, c d - d^{2} - 4 \, {\left(d^{2} \cos\left(f x + e\right)^{2} - c d - 3 \, d^{2} - {\left(c d + 2 \, d^{2}\right)} \cos\left(f x + e\right) + {\left(d^{2} \cos\left(f x + e\right) + c d + 3 \, d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{\frac{c + d}{a d}} - {\left(c^{2} + 8 \, c d + 9 \, d^{2}\right)} \cos\left(f x + e\right) + {\left(d^{2} \cos\left(f x + e\right)^{2} - c^{2} - 2 \, c d - d^{2} + 2 \, {\left(3 \, c d + 4 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{d^{2} \cos\left(f x + e\right)^{3} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} - 2 \, c d - d^{2} - {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right) + {\left(d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \cos\left(f x + e\right) - c^{2} - 2 \, c d - d^{2}\right)} \sin\left(f x + e\right)}\right) + \frac{2 \, \sqrt{2} \log\left(-\frac{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) - 2\right)} \sin\left(f x + e\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(f x + e\right) + 2}{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2}\right)}{\sqrt{a}}}{2 \, {\left(a c - a d\right)} f}, \frac{\sqrt{-\frac{c + d}{a d}} \arctan\left(\frac{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) - c - 2 \, d\right)} \sqrt{-\frac{c + d}{a d}}}{2 \, {\left(c + d\right)} \cos\left(f x + e\right)}\right) - \frac{\sqrt{2} \log\left(-\frac{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) - 2\right)} \sin\left(f x + e\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(f x + e\right) + 2}{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2}\right)}{\sqrt{a}}}{{\left(a c - a d\right)} f}\right]"," ",0,"[-1/2*(sqrt((c + d)/(a*d))*log((d^2*cos(f*x + e)^3 - (6*c*d + 7*d^2)*cos(f*x + e)^2 - c^2 - 2*c*d - d^2 - 4*(d^2*cos(f*x + e)^2 - c*d - 3*d^2 - (c*d + 2*d^2)*cos(f*x + e) + (d^2*cos(f*x + e) + c*d + 3*d^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt((c + d)/(a*d)) - (c^2 + 8*c*d + 9*d^2)*cos(f*x + e) + (d^2*cos(f*x + e)^2 - c^2 - 2*c*d - d^2 + 2*(3*c*d + 4*d^2)*cos(f*x + e))*sin(f*x + e))/(d^2*cos(f*x + e)^3 + (2*c*d + d^2)*cos(f*x + e)^2 - c^2 - 2*c*d - d^2 - (c^2 + d^2)*cos(f*x + e) + (d^2*cos(f*x + e)^2 - 2*c*d*cos(f*x + e) - c^2 - 2*c*d - d^2)*sin(f*x + e))) + 2*sqrt(2)*log(-(cos(f*x + e)^2 - (cos(f*x + e) - 2)*sin(f*x + e) + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*(cos(f*x + e) - sin(f*x + e) + 1)/sqrt(a) + 3*cos(f*x + e) + 2)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2))/sqrt(a))/((a*c - a*d)*f), (sqrt(-(c + d)/(a*d))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-(c + d)/(a*d))/((c + d)*cos(f*x + e))) - sqrt(2)*log(-(cos(f*x + e)^2 - (cos(f*x + e) - 2)*sin(f*x + e) + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*(cos(f*x + e) - sin(f*x + e) + 1)/sqrt(a) + 3*cos(f*x + e) + 2)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2))/sqrt(a))/((a*c - a*d)*f)]","B",0
937,1,2071,0,3.121366," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\frac{4 \, \sqrt{2} a d \log\left(-\frac{{\left(c - 3 \, d\right)} \cos\left(f x + e\right)^{2} - \frac{2 \, \sqrt{2} {\left({\left(c - d\right)} \cos\left(f x + e\right) - {\left(c - d\right)} \sin\left(f x + e\right) + c - d\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{a c - a d}} + {\left(3 \, c - d\right)} \cos\left(f x + e\right) - {\left({\left(c - 3 \, d\right)} \cos\left(f x + e\right) - 2 \, c - 2 \, d\right)} \sin\left(f x + e\right) + 2 \, c + 2 \, d}{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2}\right)}{\sqrt{a c - a d}} - \sqrt{-a d} \log\left(\frac{128 \, a d^{4} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + 128 \, {\left(2 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 32 \, {\left(5 \, a c^{2} d^{2} - 14 \, a c d^{3} + 13 \, a d^{4}\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(a c^{3} d - 2 \, a c^{2} d^{2} + 9 \, a c d^{3} - 4 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left(16 \, d^{3} \cos\left(f x + e\right)^{4} + 24 \, {\left(c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - c^{3} + 17 \, c^{2} d - 59 \, c d^{2} + 51 \, d^{3} - 2 \, {\left(5 \, c^{2} d - 26 \, c d^{2} + 33 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{3} - 7 \, c^{2} d + 31 \, c d^{2} - 25 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(16 \, d^{3} \cos\left(f x + e\right)^{3} + c^{3} - 17 \, c^{2} d + 59 \, c d^{2} - 51 \, d^{3} - 8 \, {\left(3 \, c d^{2} - 5 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, c^{2} d - 14 \, c d^{2} + 13 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-a d} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} + {\left(a c^{4} - 28 \, a c^{3} d + 230 \, a c^{2} d^{2} - 476 \, a c d^{3} + 289 \, a d^{4}\right)} \cos\left(f x + e\right) + {\left(128 \, a d^{4} \cos\left(f x + e\right)^{4} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - 256 \, {\left(a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(5 \, a c^{2} d^{2} - 6 \, a c d^{3} + 5 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} + 32 \, {\left(a c^{3} d - 7 \, a c^{2} d^{2} + 15 \, a c d^{3} - 9 \, a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1}\right)}{4 \, a^{2} d f}, \frac{\frac{2 \, \sqrt{2} a d \log\left(-\frac{{\left(c - 3 \, d\right)} \cos\left(f x + e\right)^{2} - \frac{2 \, \sqrt{2} {\left({\left(c - d\right)} \cos\left(f x + e\right) - {\left(c - d\right)} \sin\left(f x + e\right) + c - d\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{a c - a d}} + {\left(3 \, c - d\right)} \cos\left(f x + e\right) - {\left({\left(c - 3 \, d\right)} \cos\left(f x + e\right) - 2 \, c - 2 \, d\right)} \sin\left(f x + e\right) + 2 \, c + 2 \, d}{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2}\right)}{\sqrt{a c - a d}} - \sqrt{a d} \arctan\left(\frac{{\left(8 \, d^{2} \cos\left(f x + e\right)^{2} - c^{2} + 6 \, c d - 9 \, d^{2} - 8 \, {\left(c d - d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a d} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{4 \, {\left(2 \, a d^{3} \cos\left(f x + e\right)^{3} - {\left(3 \, a c d^{2} - a d^{3}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} d - a c d^{2} + 2 \, a d^{3}\right)} \cos\left(f x + e\right)\right)}}\right)}{2 \, a^{2} d f}, \frac{8 \, \sqrt{2} a d \sqrt{-\frac{1}{a c - a d}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{1}{a c - a d}}}{\cos\left(f x + e\right)}\right) - \sqrt{-a d} \log\left(\frac{128 \, a d^{4} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + 128 \, {\left(2 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 32 \, {\left(5 \, a c^{2} d^{2} - 14 \, a c d^{3} + 13 \, a d^{4}\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(a c^{3} d - 2 \, a c^{2} d^{2} + 9 \, a c d^{3} - 4 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left(16 \, d^{3} \cos\left(f x + e\right)^{4} + 24 \, {\left(c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - c^{3} + 17 \, c^{2} d - 59 \, c d^{2} + 51 \, d^{3} - 2 \, {\left(5 \, c^{2} d - 26 \, c d^{2} + 33 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{3} - 7 \, c^{2} d + 31 \, c d^{2} - 25 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(16 \, d^{3} \cos\left(f x + e\right)^{3} + c^{3} - 17 \, c^{2} d + 59 \, c d^{2} - 51 \, d^{3} - 8 \, {\left(3 \, c d^{2} - 5 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, c^{2} d - 14 \, c d^{2} + 13 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-a d} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} + {\left(a c^{4} - 28 \, a c^{3} d + 230 \, a c^{2} d^{2} - 476 \, a c d^{3} + 289 \, a d^{4}\right)} \cos\left(f x + e\right) + {\left(128 \, a d^{4} \cos\left(f x + e\right)^{4} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - 256 \, {\left(a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(5 \, a c^{2} d^{2} - 6 \, a c d^{3} + 5 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} + 32 \, {\left(a c^{3} d - 7 \, a c^{2} d^{2} + 15 \, a c d^{3} - 9 \, a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1}\right)}{4 \, a^{2} d f}, \frac{4 \, \sqrt{2} a d \sqrt{-\frac{1}{a c - a d}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{1}{a c - a d}}}{\cos\left(f x + e\right)}\right) - \sqrt{a d} \arctan\left(\frac{{\left(8 \, d^{2} \cos\left(f x + e\right)^{2} - c^{2} + 6 \, c d - 9 \, d^{2} - 8 \, {\left(c d - d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a d} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{4 \, {\left(2 \, a d^{3} \cos\left(f x + e\right)^{3} - {\left(3 \, a c d^{2} - a d^{3}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} d - a c d^{2} + 2 \, a d^{3}\right)} \cos\left(f x + e\right)\right)}}\right)}{2 \, a^{2} d f}\right]"," ",0,"[1/4*(4*sqrt(2)*a*d*log(-((c - 3*d)*cos(f*x + e)^2 - 2*sqrt(2)*((c - d)*cos(f*x + e) - (c - d)*sin(f*x + e) + c - d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/sqrt(a*c - a*d) + (3*c - d)*cos(f*x + e) - ((c - 3*d)*cos(f*x + e) - 2*c - 2*d)*sin(f*x + e) + 2*c + 2*d)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2))/sqrt(a*c - a*d) - sqrt(-a*d)*log((128*a*d^4*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + 128*(2*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 32*(5*a*c^2*d^2 - 14*a*c*d^3 + 13*a*d^4)*cos(f*x + e)^3 - 32*(a*c^3*d - 2*a*c^2*d^2 + 9*a*c*d^3 - 4*a*d^4)*cos(f*x + e)^2 - 8*(16*d^3*cos(f*x + e)^4 + 24*(c*d^2 - d^3)*cos(f*x + e)^3 - c^3 + 17*c^2*d - 59*c*d^2 + 51*d^3 - 2*(5*c^2*d - 26*c*d^2 + 33*d^3)*cos(f*x + e)^2 - (c^3 - 7*c^2*d + 31*c*d^2 - 25*d^3)*cos(f*x + e) + (16*d^3*cos(f*x + e)^3 + c^3 - 17*c^2*d + 59*c*d^2 - 51*d^3 - 8*(3*c*d^2 - 5*d^3)*cos(f*x + e)^2 - 2*(5*c^2*d - 14*c*d^2 + 13*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-a*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c) + (a*c^4 - 28*a*c^3*d + 230*a*c^2*d^2 - 476*a*c*d^3 + 289*a*d^4)*cos(f*x + e) + (128*a*d^4*cos(f*x + e)^4 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - 256*(a*c*d^3 - a*d^4)*cos(f*x + e)^3 - 32*(5*a*c^2*d^2 - 6*a*c*d^3 + 5*a*d^4)*cos(f*x + e)^2 + 32*(a*c^3*d - 7*a*c^2*d^2 + 15*a*c*d^3 - 9*a*d^4)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e) + sin(f*x + e) + 1)))/(a^2*d*f), 1/2*(2*sqrt(2)*a*d*log(-((c - 3*d)*cos(f*x + e)^2 - 2*sqrt(2)*((c - d)*cos(f*x + e) - (c - d)*sin(f*x + e) + c - d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/sqrt(a*c - a*d) + (3*c - d)*cos(f*x + e) - ((c - 3*d)*cos(f*x + e) - 2*c - 2*d)*sin(f*x + e) + 2*c + 2*d)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2))/sqrt(a*c - a*d) - sqrt(a*d)*arctan(1/4*(8*d^2*cos(f*x + e)^2 - c^2 + 6*c*d - 9*d^2 - 8*(c*d - d^2)*sin(f*x + e))*sqrt(a*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(2*a*d^3*cos(f*x + e)^3 - (3*a*c*d^2 - a*d^3)*cos(f*x + e)*sin(f*x + e) - (a*c^2*d - a*c*d^2 + 2*a*d^3)*cos(f*x + e))))/(a^2*d*f), 1/4*(8*sqrt(2)*a*d*sqrt(-1/(a*c - a*d))*arctan(sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt(-1/(a*c - a*d))/cos(f*x + e)) - sqrt(-a*d)*log((128*a*d^4*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + 128*(2*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 32*(5*a*c^2*d^2 - 14*a*c*d^3 + 13*a*d^4)*cos(f*x + e)^3 - 32*(a*c^3*d - 2*a*c^2*d^2 + 9*a*c*d^3 - 4*a*d^4)*cos(f*x + e)^2 - 8*(16*d^3*cos(f*x + e)^4 + 24*(c*d^2 - d^3)*cos(f*x + e)^3 - c^3 + 17*c^2*d - 59*c*d^2 + 51*d^3 - 2*(5*c^2*d - 26*c*d^2 + 33*d^3)*cos(f*x + e)^2 - (c^3 - 7*c^2*d + 31*c*d^2 - 25*d^3)*cos(f*x + e) + (16*d^3*cos(f*x + e)^3 + c^3 - 17*c^2*d + 59*c*d^2 - 51*d^3 - 8*(3*c*d^2 - 5*d^3)*cos(f*x + e)^2 - 2*(5*c^2*d - 14*c*d^2 + 13*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-a*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c) + (a*c^4 - 28*a*c^3*d + 230*a*c^2*d^2 - 476*a*c*d^3 + 289*a*d^4)*cos(f*x + e) + (128*a*d^4*cos(f*x + e)^4 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - 256*(a*c*d^3 - a*d^4)*cos(f*x + e)^3 - 32*(5*a*c^2*d^2 - 6*a*c*d^3 + 5*a*d^4)*cos(f*x + e)^2 + 32*(a*c^3*d - 7*a*c^2*d^2 + 15*a*c*d^3 - 9*a*d^4)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e) + sin(f*x + e) + 1)))/(a^2*d*f), 1/2*(4*sqrt(2)*a*d*sqrt(-1/(a*c - a*d))*arctan(sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt(-1/(a*c - a*d))/cos(f*x + e)) - sqrt(a*d)*arctan(1/4*(8*d^2*cos(f*x + e)^2 - c^2 + 6*c*d - 9*d^2 - 8*(c*d - d^2)*sin(f*x + e))*sqrt(a*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(2*a*d^3*cos(f*x + e)^3 - (3*a*c*d^2 - a*d^3)*cos(f*x + e)*sin(f*x + e) - (a*c^2*d - a*c*d^2 + 2*a*d^3)*cos(f*x + e))))/(a^2*d*f)]","B",0
938,0,0,0,1.540179," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
939,0,0,0,1.455737," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2} + {\left(a^{3} \cos\left(f x + e\right)^{4} - 4 \, a^{3} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(3*a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2 + (a^3*cos(f*x + e)^4 - 4*a^3*cos(f*x + e)^2)*sin(f*x + e))*(d*sin(f*x + e) + c)^n, x)","F",0
940,0,0,0,1.470282," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(f x + e\right)^{4} - 2 \, a^{2} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - 2 \, a^{2} \cos\left(f x + e\right)^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(a^2*cos(f*x + e)^4 - 2*a^2*cos(f*x + e)^2*sin(f*x + e) - 2*a^2*cos(f*x + e)^2)*(d*sin(f*x + e) + c)^n, x)","F",0
941,0,0,0,1.291184," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) + a \cos\left(f x + e\right)^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a*cos(f*x + e)^2*sin(f*x + e) + a*cos(f*x + e)^2)*(d*sin(f*x + e) + c)^n, x)","F",0
942,0,0,0,1.223770," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{a \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(a*sin(f*x + e) + a), x)","F",0
943,0,0,0,1.007554," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
944,0,0,0,1.276293," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
945,0,0,0,1.716753," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e)^4, x)","F",0
946,0,0,0,1.941682," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(f x + e\right)^{6} - 2 \, a^{2} \cos\left(f x + e\right)^{4} \sin\left(f x + e\right) - 2 \, a^{2} \cos\left(f x + e\right)^{4}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(a^2*cos(f*x + e)^6 - 2*a^2*cos(f*x + e)^4*sin(f*x + e) - 2*a^2*cos(f*x + e)^4)*(d*sin(f*x + e) + c)^n, x)","F",0
947,0,0,0,1.428355," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \cos\left(f x + e\right)^{4} \sin\left(f x + e\right) + a \cos\left(f x + e\right)^{4}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a*cos(f*x + e)^4*sin(f*x + e) + a*cos(f*x + e)^4)*(d*sin(f*x + e) + c)^n, x)","F",0
948,0,0,0,1.490014," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{a \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a), x)","F",0
949,0,0,0,1.074317," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
950,0,0,0,1.505307," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
951,0,0,0,1.252470," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{a^{4} \cos\left(f x + e\right)^{4} - 8 \, a^{4} \cos\left(f x + e\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(f x + e\right)^{2} - 2 \, a^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a^4*cos(f*x + e)^4 - 8*a^4*cos(f*x + e)^2 + 8*a^4 - 4*(a^4*cos(f*x + e)^2 - 2*a^4)*sin(f*x + e)), x)","F",0
952,0,0,0,1.546028," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^5,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{5 \, a^{5} \cos\left(f x + e\right)^{4} - 20 \, a^{5} \cos\left(f x + e\right)^{2} + 16 \, a^{5} + {\left(a^{5} \cos\left(f x + e\right)^{4} - 12 \, a^{5} \cos\left(f x + e\right)^{2} + 16 \, a^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(5*a^5*cos(f*x + e)^4 - 20*a^5*cos(f*x + e)^2 + 16*a^5 + (a^5*cos(f*x + e)^4 - 12*a^5*cos(f*x + e)^2 + 16*a^5)*sin(f*x + e)), x)","F",0
953,1,97,0,1.354274," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{315 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{8} + 8 \, {\left(35 \, B a \cos\left(d x + c\right)^{8} - 5 \, {\left(9 \, A + B\right)} a \cos\left(d x + c\right)^{6} - 6 \, {\left(9 \, A + B\right)} a \cos\left(d x + c\right)^{4} - 8 \, {\left(9 \, A + B\right)} a \cos\left(d x + c\right)^{2} - 16 \, {\left(9 \, A + B\right)} a\right)} \sin\left(d x + c\right)}{2520 \, d}"," ",0,"-1/2520*(315*(A + B)*a*cos(d*x + c)^8 + 8*(35*B*a*cos(d*x + c)^8 - 5*(9*A + B)*a*cos(d*x + c)^6 - 6*(9*A + B)*a*cos(d*x + c)^4 - 8*(9*A + B)*a*cos(d*x + c)^2 - 16*(9*A + B)*a)*sin(d*x + c))/d","A",0
954,1,81,0,1.325033," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{35 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{6} + 2 \, {\left(15 \, B a \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, A + B\right)} a \cos\left(d x + c\right)^{4} - 4 \, {\left(7 \, A + B\right)} a \cos\left(d x + c\right)^{2} - 8 \, {\left(7 \, A + B\right)} a\right)} \sin\left(d x + c\right)}{210 \, d}"," ",0,"-1/210*(35*(A + B)*a*cos(d*x + c)^6 + 2*(15*B*a*cos(d*x + c)^6 - 3*(7*A + B)*a*cos(d*x + c)^4 - 4*(7*A + B)*a*cos(d*x + c)^2 - 8*(7*A + B)*a)*sin(d*x + c))/d","A",0
955,1,65,0,1.191445," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{4} + 4 \, {\left(3 \, B a \cos\left(d x + c\right)^{4} - {\left(5 \, A + B\right)} a \cos\left(d x + c\right)^{2} - 2 \, {\left(5 \, A + B\right)} a\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(15*(A + B)*a*cos(d*x + c)^4 + 4*(3*B*a*cos(d*x + c)^4 - (5*A + B)*a*cos(d*x + c)^2 - 2*(5*A + B)*a)*sin(d*x + c))/d","A",0
956,1,48,0,1.306115," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(B a \cos\left(d x + c\right)^{2} - {\left(3 \, A + B\right)} a\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(3*(A + B)*a*cos(d*x + c)^2 + 2*(B*a*cos(d*x + c)^2 - (3*A + B)*a)*sin(d*x + c))/d","A",0
957,1,31,0,1.029097," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(A + B\right)} a \log\left(-\sin\left(d x + c\right) + 1\right) + B a \sin\left(d x + c\right)}{d}"," ",0,"-((A + B)*a*log(-sin(d*x + c) + 1) + B*a*sin(d*x + c))/d","A",0
958,1,90,0,1.384854," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(A + B\right)} a - {\left({\left(A - B\right)} a \sin\left(d x + c\right) - {\left(A - B\right)} a\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A - B\right)} a \sin\left(d x + c\right) - {\left(A - B\right)} a\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{4 \, {\left(d \sin\left(d x + c\right) - d\right)}}"," ",0,"-1/4*(2*(A + B)*a - ((A - B)*a*sin(d*x + c) - (A - B)*a)*log(sin(d*x + c) + 1) + ((A - B)*a*sin(d*x + c) - (A - B)*a)*log(-sin(d*x + c) + 1))/(d*sin(d*x + c) - d)","B",0
959,1,182,0,1.354186," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A - B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, A - B\right)} a \sin\left(d x + c\right) - 2 \, {\left(A - 3 \, B\right)} a - {\left({\left(3 \, A - B\right)} a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(3 \, A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, A - B\right)} a \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(3 \, A - B\right)} a \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{16 \, {\left(d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(2*(3*A - B)*a*cos(d*x + c)^2 + 2*(3*A - B)*a*sin(d*x + c) - 2*(A - 3*B)*a - ((3*A - B)*a*cos(d*x + c)^2*sin(d*x + c) - (3*A - B)*a*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((3*A - B)*a*cos(d*x + c)^2*sin(d*x + c) - (3*A - B)*a*cos(d*x + c)^2)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2*sin(d*x + c) - d*cos(d*x + c)^2)","A",0
960,1,222,0,1.431460," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, {\left(5 \, A - B\right)} a \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, A - B\right)} a \cos\left(d x + c\right)^{2} - 4 \, {\left(A - 5 \, B\right)} a - 3 \, {\left({\left(5 \, A - B\right)} a \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(5 \, A - B\right)} a \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(5 \, A - B\right)} a \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(5 \, A - B\right)} a \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, {\left(5 \, A - B\right)} a \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A - B\right)} a\right)} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"-1/96*(6*(5*A - B)*a*cos(d*x + c)^4 - 2*(5*A - B)*a*cos(d*x + c)^2 - 4*(A - 5*B)*a - 3*((5*A - B)*a*cos(d*x + c)^4*sin(d*x + c) - (5*A - B)*a*cos(d*x + c)^4)*log(sin(d*x + c) + 1) + 3*((5*A - B)*a*cos(d*x + c)^4*sin(d*x + c) - (5*A - B)*a*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) + 2*(3*(5*A - B)*a*cos(d*x + c)^2 + 2*(5*A - B)*a)*sin(d*x + c))/(d*cos(d*x + c)^4*sin(d*x + c) - d*cos(d*x + c)^4)","A",0
961,1,97,0,1.691044," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{384 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{7} - 105 \, {\left(8 \, A + B\right)} a d x + 7 \, {\left(48 \, B a \cos\left(d x + c\right)^{7} - 8 \, {\left(8 \, A + B\right)} a \cos\left(d x + c\right)^{5} - 10 \, {\left(8 \, A + B\right)} a \cos\left(d x + c\right)^{3} - 15 \, {\left(8 \, A + B\right)} a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2688 \, d}"," ",0,"-1/2688*(384*(A + B)*a*cos(d*x + c)^7 - 105*(8*A + B)*a*d*x + 7*(48*B*a*cos(d*x + c)^7 - 8*(8*A + B)*a*cos(d*x + c)^5 - 10*(8*A + B)*a*cos(d*x + c)^3 - 15*(8*A + B)*a*cos(d*x + c))*sin(d*x + c))/d","A",0
962,1,81,0,1.339286," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{48 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{5} - 15 \, {\left(6 \, A + B\right)} a d x + 5 \, {\left(8 \, B a \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, A + B\right)} a \cos\left(d x + c\right)^{3} - 3 \, {\left(6 \, A + B\right)} a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(48*(A + B)*a*cos(d*x + c)^5 - 15*(6*A + B)*a*d*x + 5*(8*B*a*cos(d*x + c)^5 - 2*(6*A + B)*a*cos(d*x + c)^3 - 3*(6*A + B)*a*cos(d*x + c))*sin(d*x + c))/d","A",0
963,1,65,0,0.789678," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, {\left(A + B\right)} a \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, A + B\right)} a d x + 3 \, {\left(2 \, B a \cos\left(d x + c\right)^{3} - {\left(4 \, A + B\right)} a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"-1/24*(8*(A + B)*a*cos(d*x + c)^3 - 3*(4*A + B)*a*d*x + 3*(2*B*a*cos(d*x + c)^3 - (4*A + B)*a*cos(d*x + c))*sin(d*x + c))/d","A",0
964,1,73,0,1.274935," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{B a d x - {\left(A + B\right)} a + {\left(B a d x - {\left(A + B\right)} a\right)} \cos\left(d x + c\right) - {\left(B a d x + {\left(A + B\right)} a\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d}"," ",0,"-(B*a*d*x - (A + B)*a + (B*a*d*x - (A + B)*a)*cos(d*x + c) - (B*a*d*x + (A + B)*a)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","B",0
965,1,69,0,1.273085," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(2 \, A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} a \sin\left(d x + c\right) - {\left(A - 2 \, B\right)} a}{3 \, {\left(d \cos\left(d x + c\right) \sin\left(d x + c\right) - d \cos\left(d x + c\right)\right)}}"," ",0,"-1/3*((2*A - B)*a*cos(d*x + c)^2 + (2*A - B)*a*sin(d*x + c) - (A - 2*B)*a)/(d*cos(d*x + c)*sin(d*x + c) - d*cos(d*x + c))","A",0
966,1,112,0,1.363168," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, A - B\right)} a \cos\left(d x + c\right)^{4} - {\left(4 \, A - B\right)} a \cos\left(d x + c\right)^{2} - {\left(A - 4 \, B\right)} a + {\left(2 \, {\left(4 \, A - B\right)} a \cos\left(d x + c\right)^{2} + {\left(4 \, A - B\right)} a\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/15*(2*(4*A - B)*a*cos(d*x + c)^4 - (4*A - B)*a*cos(d*x + c)^2 - (A - 4*B)*a + (2*(4*A - B)*a*cos(d*x + c)^2 + (4*A - B)*a)*sin(d*x + c))/(d*cos(d*x + c)^3*sin(d*x + c) - d*cos(d*x + c)^3)","A",0
967,1,149,0,0.908573," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, {\left(6 \, A - B\right)} a \cos\left(d x + c\right)^{6} - 4 \, {\left(6 \, A - B\right)} a \cos\left(d x + c\right)^{4} - {\left(6 \, A - B\right)} a \cos\left(d x + c\right)^{2} - 3 \, {\left(A - 6 \, B\right)} a + {\left(8 \, {\left(6 \, A - B\right)} a \cos\left(d x + c\right)^{4} + 4 \, {\left(6 \, A - B\right)} a \cos\left(d x + c\right)^{2} + 3 \, {\left(6 \, A - B\right)} a\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"-1/105*(8*(6*A - B)*a*cos(d*x + c)^6 - 4*(6*A - B)*a*cos(d*x + c)^4 - (6*A - B)*a*cos(d*x + c)^2 - 3*(A - 6*B)*a + (8*(6*A - B)*a*cos(d*x + c)^4 + 4*(6*A - B)*a*cos(d*x + c)^2 + 3*(6*A - B)*a)*sin(d*x + c))/(d*cos(d*x + c)^5*sin(d*x + c) - d*cos(d*x + c)^5)","A",0
968,1,185,0,1.465702," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, {\left(8 \, A - B\right)} a \cos\left(d x + c\right)^{8} - 8 \, {\left(8 \, A - B\right)} a \cos\left(d x + c\right)^{6} - 2 \, {\left(8 \, A - B\right)} a \cos\left(d x + c\right)^{4} - {\left(8 \, A - B\right)} a \cos\left(d x + c\right)^{2} - 5 \, {\left(A - 8 \, B\right)} a + {\left(16 \, {\left(8 \, A - B\right)} a \cos\left(d x + c\right)^{6} + 8 \, {\left(8 \, A - B\right)} a \cos\left(d x + c\right)^{4} + 6 \, {\left(8 \, A - B\right)} a \cos\left(d x + c\right)^{2} + 5 \, {\left(8 \, A - B\right)} a\right)} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{7} \sin\left(d x + c\right) - d \cos\left(d x + c\right)^{7}\right)}}"," ",0,"-1/315*(16*(8*A - B)*a*cos(d*x + c)^8 - 8*(8*A - B)*a*cos(d*x + c)^6 - 2*(8*A - B)*a*cos(d*x + c)^4 - (8*A - B)*a*cos(d*x + c)^2 - 5*(A - 8*B)*a + (16*(8*A - B)*a*cos(d*x + c)^6 + 8*(8*A - B)*a*cos(d*x + c)^4 + 6*(8*A - B)*a*cos(d*x + c)^2 + 5*(8*A - B)*a)*sin(d*x + c))/(d*cos(d*x + c)^7*sin(d*x + c) - d*cos(d*x + c)^7)","A",0
969,1,127,0,1.168203," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{126 \, B a^{2} \cos\left(d x + c\right)^{10} - 315 \, {\left(A + B\right)} a^{2} \cos\left(d x + c\right)^{8} - 4 \, {\left(35 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{8} - 10 \, {\left(5 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{6} - 12 \, {\left(5 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{4} - 16 \, {\left(5 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{2} - 32 \, {\left(5 \, A + B\right)} a^{2}\right)} \sin\left(d x + c\right)}{1260 \, d}"," ",0,"1/1260*(126*B*a^2*cos(d*x + c)^10 - 315*(A + B)*a^2*cos(d*x + c)^8 - 4*(35*(A + 2*B)*a^2*cos(d*x + c)^8 - 10*(5*A + B)*a^2*cos(d*x + c)^6 - 12*(5*A + B)*a^2*cos(d*x + c)^4 - 16*(5*A + B)*a^2*cos(d*x + c)^2 - 32*(5*A + B)*a^2)*sin(d*x + c))/d","A",0
970,1,109,0,1.205974," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, B a^{2} \cos\left(d x + c\right)^{8} - 280 \, {\left(A + B\right)} a^{2} \cos\left(d x + c\right)^{6} - 8 \, {\left(15 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} - 6 \, {\left(4 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{4} - 8 \, {\left(4 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{2} - 16 \, {\left(4 \, A + B\right)} a^{2}\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*B*a^2*cos(d*x + c)^8 - 280*(A + B)*a^2*cos(d*x + c)^6 - 8*(15*(A + 2*B)*a^2*cos(d*x + c)^6 - 6*(4*A + B)*a^2*cos(d*x + c)^4 - 8*(4*A + B)*a^2*cos(d*x + c)^2 - 16*(4*A + B)*a^2)*sin(d*x + c))/d","A",0
971,1,91,0,1.289670," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{5 \, B a^{2} \cos\left(d x + c\right)^{6} - 15 \, {\left(A + B\right)} a^{2} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, A + B\right)} a^{2} \cos\left(d x + c\right)^{2} - 4 \, {\left(3 \, A + B\right)} a^{2}\right)} \sin\left(d x + c\right)}{30 \, d}"," ",0,"1/30*(5*B*a^2*cos(d*x + c)^6 - 15*(A + B)*a^2*cos(d*x + c)^4 - 2*(3*(A + 2*B)*a^2*cos(d*x + c)^4 - 2*(3*A + B)*a^2*cos(d*x + c)^2 - 4*(3*A + B)*a^2)*sin(d*x + c))/d","A",0
972,1,72,0,1.276601," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, B a^{2} \cos\left(d x + c\right)^{4} - 12 \, {\left(A + B\right)} a^{2} \cos\left(d x + c\right)^{2} - 4 \, {\left({\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, A + B\right)} a^{2}\right)} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*a^2*cos(d*x + c)^4 - 12*(A + B)*a^2*cos(d*x + c)^2 - 4*((A + 2*B)*a^2*cos(d*x + c)^2 - 2*(2*A + B)*a^2)*sin(d*x + c))/d","A",0
973,1,54,0,1.333298," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{B a^{2} \cos\left(d x + c\right)^{2} - 4 \, {\left(A + B\right)} a^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A + 2 \, B\right)} a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*a^2*cos(d*x + c)^2 - 4*(A + B)*a^2*log(-sin(d*x + c) + 1) - 2*(A + 2*B)*a^2*sin(d*x + c))/d","A",0
974,1,55,0,1.372960," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(A + B\right)} a^{2} - {\left(B a^{2} \sin\left(d x + c\right) - B a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{d \sin\left(d x + c\right) - d}"," ",0,"-((A + B)*a^2 - (B*a^2*sin(d*x + c) - B*a^2)*log(-sin(d*x + c) + 1))/(d*sin(d*x + c) - d)","A",0
975,1,161,0,1.501734," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(A - B\right)} a^{2} \sin\left(d x + c\right) - 4 \, A a^{2} + {\left({\left(A - B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - B\right)} a^{2} \sin\left(d x + c\right) - 2 \, {\left(A - B\right)} a^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A - B\right)} a^{2} \cos\left(d x + c\right)^{2} + 2 \, {\left(A - B\right)} a^{2} \sin\left(d x + c\right) - 2 \, {\left(A - B\right)} a^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"1/8*(2*(A - B)*a^2*sin(d*x + c) - 4*A*a^2 + ((A - B)*a^2*cos(d*x + c)^2 + 2*(A - B)*a^2*sin(d*x + c) - 2*(A - B)*a^2)*log(sin(d*x + c) + 1) - ((A - B)*a^2*cos(d*x + c)^2 + 2*(A - B)*a^2*sin(d*x + c) - 2*(A - B)*a^2)*log(-sin(d*x + c) + 1))/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","B",0
976,1,271,0,1.288590," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, {\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right)^{2} - 8 \, {\left(A - 2 \, B\right)} a^{2} - 3 \, {\left({\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, {\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right)^{4} + 2 \, {\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, {\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, {\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right)^{2} - 4 \, {\left(2 \, A - B\right)} a^{2}\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} + 2 \, d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/48*(12*(2*A - B)*a^2*cos(d*x + c)^2 - 8*(A - 2*B)*a^2 - 3*((2*A - B)*a^2*cos(d*x + c)^4 + 2*(2*A - B)*a^2*cos(d*x + c)^2*sin(d*x + c) - 2*(2*A - B)*a^2*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + 3*((2*A - B)*a^2*cos(d*x + c)^4 + 2*(2*A - B)*a^2*cos(d*x + c)^2*sin(d*x + c) - 2*(2*A - B)*a^2*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(3*(2*A - B)*a^2*cos(d*x + c)^2 - 4*(2*A - B)*a^2)*sin(d*x + c))/(d*cos(d*x + c)^4 + 2*d*cos(d*x + c)^2*sin(d*x + c) - 2*d*cos(d*x + c)^2)","B",0
977,1,135,0,1.115797," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{896 \, B a^{2} \cos\left(d x + c\right)^{9} - 2304 \, {\left(A + B\right)} a^{2} \cos\left(d x + c\right)^{7} + 315 \, {\left(9 \, A + 2 \, B\right)} a^{2} d x - 21 \, {\left(48 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{7} - 8 \, {\left(9 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} - 10 \, {\left(9 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} - 15 \, {\left(9 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8064 \, d}"," ",0,"1/8064*(896*B*a^2*cos(d*x + c)^9 - 2304*(A + B)*a^2*cos(d*x + c)^7 + 315*(9*A + 2*B)*a^2*d*x - 21*(48*(A + 2*B)*a^2*cos(d*x + c)^7 - 8*(9*A + 2*B)*a^2*cos(d*x + c)^5 - 10*(9*A + 2*B)*a^2*cos(d*x + c)^3 - 15*(9*A + 2*B)*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
978,1,115,0,1.260963," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{240 \, B a^{2} \cos\left(d x + c\right)^{7} - 672 \, {\left(A + B\right)} a^{2} \cos\left(d x + c\right)^{5} + 105 \, {\left(7 \, A + 2 \, B\right)} a^{2} d x - 35 \, {\left(8 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{5} - 2 \, {\left(7 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} - 3 \, {\left(7 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(240*B*a^2*cos(d*x + c)^7 - 672*(A + B)*a^2*cos(d*x + c)^5 + 105*(7*A + 2*B)*a^2*d*x - 35*(8*(A + 2*B)*a^2*cos(d*x + c)^5 - 2*(7*A + 2*B)*a^2*cos(d*x + c)^3 - 3*(7*A + 2*B)*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
979,1,95,0,1.265484," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{24 \, B a^{2} \cos\left(d x + c\right)^{5} - 80 \, {\left(A + B\right)} a^{2} \cos\left(d x + c\right)^{3} + 15 \, {\left(5 \, A + 2 \, B\right)} a^{2} d x - 15 \, {\left(2 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{3} - {\left(5 \, A + 2 \, B\right)} a^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(24*B*a^2*cos(d*x + c)^5 - 80*(A + B)*a^2*cos(d*x + c)^3 + 15*(5*A + 2*B)*a^2*d*x - 15*(2*(A + 2*B)*a^2*cos(d*x + c)^3 - (5*A + 2*B)*a^2*cos(d*x + c))*sin(d*x + c))/d","A",0
980,1,128,0,1.395293," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(A + 2 \, B\right)} a^{2} d x - B a^{2} \cos\left(d x + c\right)^{2} - 2 \, {\left(A + B\right)} a^{2} + {\left({\left(A + 2 \, B\right)} a^{2} d x - {\left(2 \, A + 3 \, B\right)} a^{2}\right)} \cos\left(d x + c\right) - {\left({\left(A + 2 \, B\right)} a^{2} d x - B a^{2} \cos\left(d x + c\right) + 2 \, {\left(A + B\right)} a^{2}\right)} \sin\left(d x + c\right)}{d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d}"," ",0,"-((A + 2*B)*a^2*d*x - B*a^2*cos(d*x + c)^2 - 2*(A + B)*a^2 + ((A + 2*B)*a^2*d*x - (2*A + 3*B)*a^2)*cos(d*x + c) - ((A + 2*B)*a^2*d*x - B*a^2*cos(d*x + c) + 2*(A + B)*a^2)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","B",0
981,1,120,0,1.345972," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} a^{2} \cos\left(d x + c\right) + {\left(A + B\right)} a^{2} - {\left({\left(A - 2 \, B\right)} a^{2} \cos\left(d x + c\right) - {\left(A + B\right)} a^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/3*((A - 2*B)*a^2*cos(d*x + c)^2 + (2*A - B)*a^2*cos(d*x + c) + (A + B)*a^2 - ((A - 2*B)*a^2*cos(d*x + c) - (A + B)*a^2)*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","A",0
982,1,113,0,1.201891," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 3 \, {\left(2 \, A - 3 \, B\right)} a^{2} - {\left(2 \, {\left(3 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 3 \, {\left(3 \, A - 2 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + 2 \, d \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)\right)}}"," ",0,"-1/15*(4*(3*A - 2*B)*a^2*cos(d*x + c)^2 - 3*(2*A - 3*B)*a^2 - (2*(3*A - 2*B)*a^2*cos(d*x + c)^2 - 3*(3*A - 2*B)*a^2)*sin(d*x + c))/(d*cos(d*x + c)^3 + 2*d*cos(d*x + c)*sin(d*x + c) - 2*d*cos(d*x + c))","A",0
983,1,157,0,0.926499," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, {\left(5 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} - 8 \, {\left(5 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 5 \, {\left(2 \, A - 5 \, B\right)} a^{2} - {\left(8 \, {\left(5 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} - 12 \, {\left(5 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 5 \, {\left(5 \, A - 2 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{5} + 2 \, d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)^{3}\right)}}"," ",0,"-1/105*(16*(5*A - 2*B)*a^2*cos(d*x + c)^4 - 8*(5*A - 2*B)*a^2*cos(d*x + c)^2 - 5*(2*A - 5*B)*a^2 - (8*(5*A - 2*B)*a^2*cos(d*x + c)^4 - 12*(5*A - 2*B)*a^2*cos(d*x + c)^2 - 5*(5*A - 2*B)*a^2)*sin(d*x + c))/(d*cos(d*x + c)^5 + 2*d*cos(d*x + c)^3*sin(d*x + c) - 2*d*cos(d*x + c)^3)","A",0
984,1,197,0,1.278195," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{32 \, {\left(7 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} - 16 \, {\left(7 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} - 4 \, {\left(7 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 7 \, {\left(2 \, A - 7 \, B\right)} a^{2} - {\left(16 \, {\left(7 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} - 24 \, {\left(7 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} - 10 \, {\left(7 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 7 \, {\left(7 \, A - 2 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{315 \, {\left(d \cos\left(d x + c\right)^{7} + 2 \, d \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)^{5}\right)}}"," ",0,"-1/315*(32*(7*A - 2*B)*a^2*cos(d*x + c)^6 - 16*(7*A - 2*B)*a^2*cos(d*x + c)^4 - 4*(7*A - 2*B)*a^2*cos(d*x + c)^2 - 7*(2*A - 7*B)*a^2 - (16*(7*A - 2*B)*a^2*cos(d*x + c)^6 - 24*(7*A - 2*B)*a^2*cos(d*x + c)^4 - 10*(7*A - 2*B)*a^2*cos(d*x + c)^2 - 7*(7*A - 2*B)*a^2)*sin(d*x + c))/(d*cos(d*x + c)^7 + 2*d*cos(d*x + c)^5*sin(d*x + c) - 2*d*cos(d*x + c)^5)","A",0
985,1,237,0,0.878654," ","integrate(sec(d*x+c)^12*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{256 \, {\left(9 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{8} - 128 \, {\left(9 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} - 32 \, {\left(9 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} - 16 \, {\left(9 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 45 \, {\left(2 \, A - 9 \, B\right)} a^{2} - {\left(128 \, {\left(9 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{8} - 192 \, {\left(9 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{6} - 80 \, {\left(9 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{4} - 56 \, {\left(9 \, A - 2 \, B\right)} a^{2} \cos\left(d x + c\right)^{2} - 45 \, {\left(9 \, A - 2 \, B\right)} a^{2}\right)} \sin\left(d x + c\right)}{3465 \, {\left(d \cos\left(d x + c\right)^{9} + 2 \, d \cos\left(d x + c\right)^{7} \sin\left(d x + c\right) - 2 \, d \cos\left(d x + c\right)^{7}\right)}}"," ",0,"-1/3465*(256*(9*A - 2*B)*a^2*cos(d*x + c)^8 - 128*(9*A - 2*B)*a^2*cos(d*x + c)^6 - 32*(9*A - 2*B)*a^2*cos(d*x + c)^4 - 16*(9*A - 2*B)*a^2*cos(d*x + c)^2 - 45*(2*A - 9*B)*a^2 - (128*(9*A - 2*B)*a^2*cos(d*x + c)^8 - 192*(9*A - 2*B)*a^2*cos(d*x + c)^6 - 80*(9*A - 2*B)*a^2*cos(d*x + c)^4 - 56*(9*A - 2*B)*a^2*cos(d*x + c)^2 - 45*(9*A - 2*B)*a^2)*sin(d*x + c))/(d*cos(d*x + c)^9 + 2*d*cos(d*x + c)^7*sin(d*x + c) - 2*d*cos(d*x + c)^7)","A",0
986,1,155,0,1.417625," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{231 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{10} - 1155 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{8} + 2 \, {\left(105 \, B a^{3} \cos\left(d x + c\right)^{10} - 35 \, {\left(11 \, A + 15 \, B\right)} a^{3} \cos\left(d x + c\right)^{8} + 20 \, {\left(11 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{6} + 24 \, {\left(11 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} + 32 \, {\left(11 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 64 \, {\left(11 \, A + 3 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{2310 \, d}"," ",0,"1/2310*(231*(A + 3*B)*a^3*cos(d*x + c)^10 - 1155*(A + B)*a^3*cos(d*x + c)^8 + 2*(105*B*a^3*cos(d*x + c)^10 - 35*(11*A + 15*B)*a^3*cos(d*x + c)^8 + 20*(11*A + 3*B)*a^3*cos(d*x + c)^6 + 24*(11*A + 3*B)*a^3*cos(d*x + c)^4 + 32*(11*A + 3*B)*a^3*cos(d*x + c)^2 + 64*(11*A + 3*B)*a^3)*sin(d*x + c))/d","A",0
987,1,129,0,1.571647," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{63 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{8} - 336 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{6} + 8 \, {\left(7 \, B a^{3} \cos\left(d x + c\right)^{8} - {\left(27 \, A + 37 \, B\right)} a^{3} \cos\left(d x + c\right)^{6} + 6 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{4} + 8 \, {\left(3 \, A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + 16 \, {\left(3 \, A + B\right)} a^{3}\right)} \sin\left(d x + c\right)}{504 \, d}"," ",0,"1/504*(63*(A + 3*B)*a^3*cos(d*x + c)^8 - 336*(A + B)*a^3*cos(d*x + c)^6 + 8*(7*B*a^3*cos(d*x + c)^8 - (27*A + 37*B)*a^3*cos(d*x + c)^6 + 6*(3*A + B)*a^3*cos(d*x + c)^4 + 8*(3*A + B)*a^3*cos(d*x + c)^2 + 16*(3*A + B)*a^3)*sin(d*x + c))/d","A",0
988,1,115,0,1.040610," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{35 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{6} - 210 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{4} + 2 \, {\left(15 \, B a^{3} \cos\left(d x + c\right)^{6} - 3 \, {\left(21 \, A + 29 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} + 8 \, {\left(7 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 16 \, {\left(7 \, A + 3 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{210 \, d}"," ",0,"1/210*(35*(A + 3*B)*a^3*cos(d*x + c)^6 - 210*(A + B)*a^3*cos(d*x + c)^4 + 2*(15*B*a^3*cos(d*x + c)^6 - 3*(21*A + 29*B)*a^3*cos(d*x + c)^4 + 8*(7*A + 3*B)*a^3*cos(d*x + c)^2 + 16*(7*A + 3*B)*a^3)*sin(d*x + c))/d","A",0
989,1,94,0,1.308137," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{5 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} - 40 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{2} + 4 \, {\left(B a^{3} \cos\left(d x + c\right)^{4} - {\left(5 \, A + 7 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, A + 3 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{20 \, d}"," ",0,"1/20*(5*(A + 3*B)*a^3*cos(d*x + c)^4 - 40*(A + B)*a^3*cos(d*x + c)^2 + 4*(B*a^3*cos(d*x + c)^4 - (5*A + 7*B)*a^3*cos(d*x + c)^2 + 2*(5*A + 3*B)*a^3)*sin(d*x + c))/d","A",0
990,1,77,0,1.350947," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} - 24 \, {\left(A + B\right)} a^{3} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(B a^{3} \cos\left(d x + c\right)^{2} - {\left(9 \, A + 13 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(3*(A + 3*B)*a^3*cos(d*x + c)^2 - 24*(A + B)*a^3*log(-sin(d*x + c) + 1) + 2*(B*a^3*cos(d*x + c)^2 - (9*A + 13*B)*a^3)*sin(d*x + c))/d","A",0
991,1,89,0,1.364450," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{B a^{3} \cos\left(d x + c\right)^{2} + B a^{3} \sin\left(d x + c\right) + {\left(2 \, A + B\right)} a^{3} - {\left({\left(A + 3 \, B\right)} a^{3} \sin\left(d x + c\right) - {\left(A + 3 \, B\right)} a^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{d \sin\left(d x + c\right) - d}"," ",0,"-(B*a^3*cos(d*x + c)^2 + B*a^3*sin(d*x + c) + (2*A + B)*a^3 - ((A + 3*B)*a^3*sin(d*x + c) - (A + 3*B)*a^3)*log(-sin(d*x + c) + 1))/(d*sin(d*x + c) - d)","A",0
992,1,49,0,1.348348," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, B a^{3} \sin\left(d x + c\right) + {\left(A - B\right)} a^{3}}{2 \, {\left(d \cos\left(d x + c\right)^{2} + 2 \, d \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/2*(2*B*a^3*sin(d*x + c) + (A - B)*a^3)/(d*cos(d*x + c)^2 + 2*d*sin(d*x + c) - 2*d)","A",0
993,1,242,0,1.437982," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(A - B\right)} a^{3} \cos\left(d x + c\right)^{2} + 18 \, {\left(A - B\right)} a^{3} \sin\left(d x + c\right) - 2 \, {\left(13 \, A - 5 \, B\right)} a^{3} + 3 \, {\left(3 \, {\left(A - B\right)} a^{3} \cos\left(d x + c\right)^{2} - 4 \, {\left(A - B\right)} a^{3} - {\left({\left(A - B\right)} a^{3} \cos\left(d x + c\right)^{2} - 4 \, {\left(A - B\right)} a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, {\left(A - B\right)} a^{3} \cos\left(d x + c\right)^{2} - 4 \, {\left(A - B\right)} a^{3} - {\left({\left(A - B\right)} a^{3} \cos\left(d x + c\right)^{2} - 4 \, {\left(A - B\right)} a^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{48 \, {\left(3 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{2} - 4 \, d\right)} \sin\left(d x + c\right) - 4 \, d\right)}}"," ",0,"1/48*(6*(A - B)*a^3*cos(d*x + c)^2 + 18*(A - B)*a^3*sin(d*x + c) - 2*(13*A - 5*B)*a^3 + 3*(3*(A - B)*a^3*cos(d*x + c)^2 - 4*(A - B)*a^3 - ((A - B)*a^3*cos(d*x + c)^2 - 4*(A - B)*a^3)*sin(d*x + c))*log(sin(d*x + c) + 1) - 3*(3*(A - B)*a^3*cos(d*x + c)^2 - 4*(A - B)*a^3 - ((A - B)*a^3*cos(d*x + c)^2 - 4*(A - B)*a^3)*sin(d*x + c))*log(-sin(d*x + c) + 1))/(3*d*cos(d*x + c)^2 - (d*cos(d*x + c)^2 - 4*d)*sin(d*x + c) - 4*d)","B",0
994,1,353,0,1.039472," ","integrate(sec(d*x+c)^9*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} - 26 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 12 \, {\left(3 \, A - 5 \, B\right)} a^{3} + 3 \, {\left(3 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} - {\left({\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} - {\left({\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 6 \, {\left(3 \, {\left(5 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} - 2 \, {\left(5 \, A - 3 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{192 \, {\left(3 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} - {\left(d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/192*(6*(5*A - 3*B)*a^3*cos(d*x + c)^4 - 26*(5*A - 3*B)*a^3*cos(d*x + c)^2 + 12*(3*A - 5*B)*a^3 + 3*(3*(5*A - 3*B)*a^3*cos(d*x + c)^4 - 4*(5*A - 3*B)*a^3*cos(d*x + c)^2 - ((5*A - 3*B)*a^3*cos(d*x + c)^4 - 4*(5*A - 3*B)*a^3*cos(d*x + c)^2)*sin(d*x + c))*log(sin(d*x + c) + 1) - 3*(3*(5*A - 3*B)*a^3*cos(d*x + c)^4 - 4*(5*A - 3*B)*a^3*cos(d*x + c)^2 - ((5*A - 3*B)*a^3*cos(d*x + c)^4 - 4*(5*A - 3*B)*a^3*cos(d*x + c)^2)*sin(d*x + c))*log(-sin(d*x + c) + 1) + 6*(3*(5*A - 3*B)*a^3*cos(d*x + c)^2 - 2*(5*A - 3*B)*a^3)*sin(d*x + c))/(3*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 - (d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2)*sin(d*x + c))","B",0
995,1,155,0,1.255352," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8960 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{9} - 46080 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{7} + 3465 \, {\left(10 \, A + 3 \, B\right)} a^{3} d x + 21 \, {\left(384 \, B a^{3} \cos\left(d x + c\right)^{9} - 48 \, {\left(30 \, A + 41 \, B\right)} a^{3} \cos\left(d x + c\right)^{7} + 88 \, {\left(10 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{5} + 110 \, {\left(10 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 165 \, {\left(10 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(8960*(A + 3*B)*a^3*cos(d*x + c)^9 - 46080*(A + B)*a^3*cos(d*x + c)^7 + 3465*(10*A + 3*B)*a^3*d*x + 21*(384*B*a^3*cos(d*x + c)^9 - 48*(30*A + 41*B)*a^3*cos(d*x + c)^7 + 88*(10*A + 3*B)*a^3*cos(d*x + c)^5 + 110*(10*A + 3*B)*a^3*cos(d*x + c)^3 + 165*(10*A + 3*B)*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
996,1,135,0,1.467517," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{640 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{7} - 3584 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{5} + 315 \, {\left(8 \, A + 3 \, B\right)} a^{3} d x + 35 \, {\left(16 \, B a^{3} \cos\left(d x + c\right)^{7} - 8 \, {\left(8 \, A + 11 \, B\right)} a^{3} \cos\left(d x + c\right)^{5} + 6 \, {\left(8 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 9 \, {\left(8 \, A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4480 \, d}"," ",0,"1/4480*(640*(A + 3*B)*a^3*cos(d*x + c)^7 - 3584*(A + B)*a^3*cos(d*x + c)^5 + 315*(8*A + 3*B)*a^3*d*x + 35*(16*B*a^3*cos(d*x + c)^7 - 8*(8*A + 11*B)*a^3*cos(d*x + c)^5 + 6*(8*A + 3*B)*a^3*cos(d*x + c)^3 + 9*(8*A + 3*B)*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
997,1,111,0,1.358401," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{5} - 320 \, {\left(A + B\right)} a^{3} \cos\left(d x + c\right)^{3} + 105 \, {\left(2 \, A + B\right)} a^{3} d x + 5 \, {\left(8 \, B a^{3} \cos\left(d x + c\right)^{5} - 2 \, {\left(18 \, A + 25 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} + 21 \, {\left(2 \, A + B\right)} a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(48*(A + 3*B)*a^3*cos(d*x + c)^5 - 320*(A + B)*a^3*cos(d*x + c)^3 + 105*(2*A + B)*a^3*d*x + 5*(8*B*a^3*cos(d*x + c)^5 - 2*(18*A + 25*B)*a^3*cos(d*x + c)^3 + 21*(2*A + B)*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
998,1,173,0,1.184772," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{B a^{3} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, A + 3 \, B\right)} a^{3} d x + 2 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 8 \, {\left(A + B\right)} a^{3} - {\left(3 \, {\left(2 \, A + 3 \, B\right)} a^{3} d x - {\left(10 \, A + 13 \, B\right)} a^{3}\right)} \cos\left(d x + c\right) + {\left(3 \, {\left(2 \, A + 3 \, B\right)} a^{3} d x + B a^{3} \cos\left(d x + c\right)^{2} - {\left(2 \, A + 5 \, B\right)} a^{3} \cos\left(d x + c\right) + 8 \, {\left(A + B\right)} a^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(d \cos\left(d x + c\right) - d \sin\left(d x + c\right) + d\right)}}"," ",0,"1/2*(B*a^3*cos(d*x + c)^3 - 3*(2*A + 3*B)*a^3*d*x + 2*(A + 3*B)*a^3*cos(d*x + c)^2 + 8*(A + B)*a^3 - (3*(2*A + 3*B)*a^3*d*x - (10*A + 13*B)*a^3)*cos(d*x + c) + (3*(2*A + 3*B)*a^3*d*x + B*a^3*cos(d*x + c)^2 - (2*A + 5*B)*a^3*cos(d*x + c) + 8*(A + B)*a^3)*sin(d*x + c))/(d*cos(d*x + c) - d*sin(d*x + c) + d)","A",0
999,1,167,0,1.244110," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, B a^{3} d x + 2 \, {\left(A + B\right)} a^{3} - {\left(3 \, B a^{3} d x + {\left(A + 7 \, B\right)} a^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, B a^{3} d x + {\left(A - 5 \, B\right)} a^{3}\right)} \cos\left(d x + c\right) - {\left(6 \, B a^{3} d x - 2 \, {\left(A + B\right)} a^{3} + {\left(3 \, B a^{3} d x - {\left(A + 7 \, B\right)} a^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left(d \cos\left(d x + c\right)^{2} - d \cos\left(d x + c\right) + {\left(d \cos\left(d x + c\right) + 2 \, d\right)} \sin\left(d x + c\right) - 2 \, d\right)}}"," ",0,"-1/3*(6*B*a^3*d*x + 2*(A + B)*a^3 - (3*B*a^3*d*x + (A + 7*B)*a^3)*cos(d*x + c)^2 + (3*B*a^3*d*x + (A - 5*B)*a^3)*cos(d*x + c) - (6*B*a^3*d*x - 2*(A + B)*a^3 + (3*B*a^3*d*x - (A + 7*B)*a^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d*cos(d*x + c) + (d*cos(d*x + c) + 2*d)*sin(d*x + c) - 2*d)","B",0
1000,1,188,0,1.455490," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(2 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{3} - 2 \, {\left(2 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} - 3 \, {\left(3 \, A - 2 \, B\right)} a^{3} \cos\left(d x + c\right) - 3 \, {\left(A + B\right)} a^{3} + {\left({\left(2 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 3 \, {\left(2 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right) - 3 \, {\left(A + B\right)} a^{3}\right)} \sin\left(d x + c\right)}{15 \, {\left(d \cos\left(d x + c\right)^{3} + 3 \, d \cos\left(d x + c\right)^{2} - 2 \, d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{2} - 2 \, d \cos\left(d x + c\right) - 4 \, d\right)} \sin\left(d x + c\right) - 4 \, d\right)}}"," ",0,"1/15*((2*A - 3*B)*a^3*cos(d*x + c)^3 - 2*(2*A - 3*B)*a^3*cos(d*x + c)^2 - 3*(3*A - 2*B)*a^3*cos(d*x + c) - 3*(A + B)*a^3 + ((2*A - 3*B)*a^3*cos(d*x + c)^2 + 3*(2*A - 3*B)*a^3*cos(d*x + c) - 3*(A + B)*a^3)*sin(d*x + c))/(d*cos(d*x + c)^3 + 3*d*cos(d*x + c)^2 - 2*d*cos(d*x + c) - (d*cos(d*x + c)^2 - 2*d*cos(d*x + c) - 4*d)*sin(d*x + c) - 4*d)","A",0
1001,1,146,0,1.227069," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{4} - 9 \, {\left(4 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} + 5 \, {\left(3 \, A - 4 \, B\right)} a^{3} + {\left(6 \, {\left(4 \, A - 3 \, B\right)} a^{3} \cos\left(d x + c\right)^{2} - 5 \, {\left(4 \, A - 3 \, B\right)} a^{3}\right)} \sin\left(d x + c\right)}{35 \, {\left(3 \, d \cos\left(d x + c\right)^{3} - 4 \, d \cos\left(d x + c\right) - {\left(d \cos\left(d x + c\right)^{3} - 4 \, d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/35*(2*(4*A - 3*B)*a^3*cos(d*x + c)^4 - 9*(4*A - 3*B)*a^3*cos(d*x + c)^2 + 5*(3*A - 4*B)*a^3 + (6*(4*A - 3*B)*a^3*cos(d*x + c)^2 - 5*(4*A - 3*B)*a^3)*sin(d*x + c))/(3*d*cos(d*x + c)^3 - 4*d*cos(d*x + c) - (d*cos(d*x + c)^3 - 4*d*cos(d*x + c))*sin(d*x + c))","A",0
1002,1,188,0,1.239772," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, {\left(2 \, A - B\right)} a^{3} \cos\left(d x + c\right)^{6} - 36 \, {\left(2 \, A - B\right)} a^{3} \cos\left(d x + c\right)^{4} + 15 \, {\left(2 \, A - B\right)} a^{3} \cos\left(d x + c\right)^{2} + 7 \, {\left(A - 2 \, B\right)} a^{3} + {\left(24 \, {\left(2 \, A - B\right)} a^{3} \cos\left(d x + c\right)^{4} - 20 \, {\left(2 \, A - B\right)} a^{3} \cos\left(d x + c\right)^{2} - 7 \, {\left(2 \, A - B\right)} a^{3}\right)} \sin\left(d x + c\right)}{63 \, {\left(3 \, d \cos\left(d x + c\right)^{5} - 4 \, d \cos\left(d x + c\right)^{3} - {\left(d \cos\left(d x + c\right)^{5} - 4 \, d \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/63*(8*(2*A - B)*a^3*cos(d*x + c)^6 - 36*(2*A - B)*a^3*cos(d*x + c)^4 + 15*(2*A - B)*a^3*cos(d*x + c)^2 + 7*(A - 2*B)*a^3 + (24*(2*A - B)*a^3*cos(d*x + c)^4 - 20*(2*A - B)*a^3*cos(d*x + c)^2 - 7*(2*A - B)*a^3)*sin(d*x + c))/(3*d*cos(d*x + c)^5 - 4*d*cos(d*x + c)^3 - (d*cos(d*x + c)^5 - 4*d*cos(d*x + c)^3)*sin(d*x + c))","A",0
1003,1,84,0,1.679538," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{35 \, {\left(A - B\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(15 \, B \cos\left(d x + c\right)^{6} + 3 \, {\left(7 \, A - B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(7 \, A - B\right)} \cos\left(d x + c\right)^{2} + 56 \, A - 8 \, B\right)} \sin\left(d x + c\right)}{210 \, a d}"," ",0,"1/210*(35*(A - B)*cos(d*x + c)^6 + 2*(15*B*cos(d*x + c)^6 + 3*(7*A - B)*cos(d*x + c)^4 + 4*(7*A - B)*cos(d*x + c)^2 + 56*A - 8*B)*sin(d*x + c))/(a*d)","A",0
1004,1,66,0,1.373341," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, {\left(A - B\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3 \, B \cos\left(d x + c\right)^{4} + {\left(5 \, A - B\right)} \cos\left(d x + c\right)^{2} + 10 \, A - 2 \, B\right)} \sin\left(d x + c\right)}{60 \, a d}"," ",0,"1/60*(15*(A - B)*cos(d*x + c)^4 + 4*(3*B*cos(d*x + c)^4 + (5*A - B)*cos(d*x + c)^2 + 10*A - 2*B)*sin(d*x + c))/(a*d)","A",0
1005,1,49,0,1.363338," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(A - B\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B \cos\left(d x + c\right)^{2} + 3 \, A - B\right)} \sin\left(d x + c\right)}{6 \, a d}"," ",0,"1/6*(3*(A - B)*cos(d*x + c)^2 + 2*(B*cos(d*x + c)^2 + 3*A - B)*sin(d*x + c))/(a*d)","A",0
1006,1,31,0,1.696546," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(A - B\right)} \log\left(\sin\left(d x + c\right) + 1\right) + B \sin\left(d x + c\right)}{a d}"," ",0,"((A - B)*log(sin(d*x + c) + 1) + B*sin(d*x + c))/(a*d)","A",0
1007,1,73,0,1.546252," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left({\left(A + B\right)} \sin\left(d x + c\right) + A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A + B\right)} \sin\left(d x + c\right) + A + B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, A + 2 \, B}{4 \, {\left(a d \sin\left(d x + c\right) + a d\right)}}"," ",0,"1/4*(((A + B)*sin(d*x + c) + A + B)*log(sin(d*x + c) + 1) - ((A + B)*sin(d*x + c) + A + B)*log(-sin(d*x + c) + 1) - 2*A + 2*B)/(a*d*sin(d*x + c) + a*d)","A",0
1008,1,161,0,1.094005," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} - {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, A + B\right)} \sin\left(d x + c\right) - 2 \, A - 6 \, B}{16 \, {\left(a d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/16*(2*(3*A + B)*cos(d*x + c)^2 - ((3*A + B)*cos(d*x + c)^2*sin(d*x + c) + (3*A + B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((3*A + B)*cos(d*x + c)^2*sin(d*x + c) + (3*A + B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(3*A + B)*sin(d*x + c) - 2*A - 6*B)/(a*d*cos(d*x + c)^2*sin(d*x + c) + a*d*cos(d*x + c)^2)","A",0
1009,1,194,0,1.476038," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, {\left(5 \, A + B\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, A + B\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(5 \, A + B\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(5 \, A + B\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left({\left(5 \, A + B\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(5 \, A + B\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(3 \, {\left(5 \, A + B\right)} \cos\left(d x + c\right)^{2} + 10 \, A + 2 \, B\right)} \sin\left(d x + c\right) - 4 \, A - 20 \, B}{96 \, {\left(a d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"-1/96*(6*(5*A + B)*cos(d*x + c)^4 - 2*(5*A + B)*cos(d*x + c)^2 - 3*((5*A + B)*cos(d*x + c)^4*sin(d*x + c) + (5*A + B)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) + 3*((5*A + B)*cos(d*x + c)^4*sin(d*x + c) + (5*A + B)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) - 2*(3*(5*A + B)*cos(d*x + c)^2 + 10*A + 2*B)*sin(d*x + c) - 4*A - 20*B)/(a*d*cos(d*x + c)^4*sin(d*x + c) + a*d*cos(d*x + c)^4)","A",0
1010,1,224,0,1.709785," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{30 \, {\left(7 \, A + B\right)} \cos\left(d x + c\right)^{6} - 10 \, {\left(7 \, A + B\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(7 \, A + B\right)} \cos\left(d x + c\right)^{2} - 15 \, {\left({\left(7 \, A + B\right)} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + {\left(7 \, A + B\right)} \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 15 \, {\left({\left(7 \, A + B\right)} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + {\left(7 \, A + B\right)} \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(15 \, {\left(7 \, A + B\right)} \cos\left(d x + c\right)^{4} + 10 \, {\left(7 \, A + B\right)} \cos\left(d x + c\right)^{2} + 56 \, A + 8 \, B\right)} \sin\left(d x + c\right) - 16 \, A - 112 \, B}{768 \, {\left(a d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + a d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"-1/768*(30*(7*A + B)*cos(d*x + c)^6 - 10*(7*A + B)*cos(d*x + c)^4 - 4*(7*A + B)*cos(d*x + c)^2 - 15*((7*A + B)*cos(d*x + c)^6*sin(d*x + c) + (7*A + B)*cos(d*x + c)^6)*log(sin(d*x + c) + 1) + 15*((7*A + B)*cos(d*x + c)^6*sin(d*x + c) + (7*A + B)*cos(d*x + c)^6)*log(-sin(d*x + c) + 1) - 2*(15*(7*A + B)*cos(d*x + c)^4 + 10*(7*A + B)*cos(d*x + c)^2 + 56*A + 8*B)*sin(d*x + c) - 16*A - 112*B)/(a*d*cos(d*x + c)^6*sin(d*x + c) + a*d*cos(d*x + c)^6)","A",0
1011,1,82,0,1.439546," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5 \, B \cos\left(d x + c\right)^{6} + 15 \, {\left(A - B\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, {\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, A - B\right)} \cos\left(d x + c\right)^{2} - 12 \, A + 4 \, B\right)} \sin\left(d x + c\right)}{30 \, a^{2} d}"," ",0,"1/30*(5*B*cos(d*x + c)^6 + 15*(A - B)*cos(d*x + c)^4 - 2*(3*(A - 2*B)*cos(d*x + c)^4 - 2*(3*A - B)*cos(d*x + c)^2 - 12*A + 4*B)*sin(d*x + c))/(a^2*d)","A",0
1012,1,64,0,1.062524," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, B \cos\left(d x + c\right)^{4} + 12 \, {\left(A - B\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left({\left(A - 2 \, B\right)} \cos\left(d x + c\right)^{2} - 4 \, A + 2 \, B\right)} \sin\left(d x + c\right)}{12 \, a^{2} d}"," ",0,"1/12*(3*B*cos(d*x + c)^4 + 12*(A - B)*cos(d*x + c)^2 - 4*((A - 2*B)*cos(d*x + c)^2 - 4*A + 2*B)*sin(d*x + c))/(a^2*d)","A",0
1013,1,48,0,1.361506," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{B \cos\left(d x + c\right)^{2} + 4 \, {\left(A - B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 2 \, {\left(A - 2 \, B\right)} \sin\left(d x + c\right)}{2 \, a^{2} d}"," ",0,"1/2*(B*cos(d*x + c)^2 + 4*(A - B)*log(sin(d*x + c) + 1) - 2*(A - 2*B)*sin(d*x + c))/(a^2*d)","A",0
1014,1,45,0,0.933160," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(B \sin\left(d x + c\right) + B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - A + B}{a^{2} d \sin\left(d x + c\right) + a^{2} d}"," ",0,"((B*sin(d*x + c) + B)*log(sin(d*x + c) + 1) - A + B)/(a^2*d*sin(d*x + c) + a^2*d)","A",0
1015,1,134,0,0.816251," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left({\left(A + B\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(A + B\right)} \sin\left(d x + c\right) - 2 \, A - 2 \, B\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A + B\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(A + B\right)} \sin\left(d x + c\right) - 2 \, A - 2 \, B\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A + B\right)} \sin\left(d x + c\right) + 4 \, A}{8 \, {\left(a^{2} d \cos\left(d x + c\right)^{2} - 2 \, a^{2} d \sin\left(d x + c\right) - 2 \, a^{2} d\right)}}"," ",0,"1/8*(((A + B)*cos(d*x + c)^2 - 2*(A + B)*sin(d*x + c) - 2*A - 2*B)*log(sin(d*x + c) + 1) - ((A + B)*cos(d*x + c)^2 - 2*(A + B)*sin(d*x + c) - 2*A - 2*B)*log(-sin(d*x + c) + 1) + 2*(A + B)*sin(d*x + c) + 4*A)/(a^2*d*cos(d*x + c)^2 - 2*a^2*d*sin(d*x + c) - 2*a^2*d)","B",0
1016,1,230,0,1.150862," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{12 \, {\left(2 \, A + B\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, A + B\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, A + B\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, {\left(2 \, A + B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(2 \, A + B\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, A + B\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, {\left(2 \, A + B\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, {\left(2 \, A + B\right)} \cos\left(d x + c\right)^{2} - 8 \, A - 4 \, B\right)} \sin\left(d x + c\right) - 8 \, A - 16 \, B}{48 \, {\left(a^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{2} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/48*(12*(2*A + B)*cos(d*x + c)^2 + 3*((2*A + B)*cos(d*x + c)^4 - 2*(2*A + B)*cos(d*x + c)^2*sin(d*x + c) - 2*(2*A + B)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - 3*((2*A + B)*cos(d*x + c)^4 - 2*(2*A + B)*cos(d*x + c)^2*sin(d*x + c) - 2*(2*A + B)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(3*(2*A + B)*cos(d*x + c)^2 - 8*A - 4*B)*sin(d*x + c) - 8*A - 16*B)/(a^2*d*cos(d*x + c)^4 - 2*a^2*d*cos(d*x + c)^2*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^2)","B",0
1017,1,260,0,1.189164," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{60 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{4} - 20 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} + 15 \, {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 15 \, {\left({\left(3 \, A + B\right)} \cos\left(d x + c\right)^{6} - 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(15 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{4} - 20 \, {\left(3 \, A + B\right)} \cos\left(d x + c\right)^{2} - 36 \, A - 12 \, B\right)} \sin\left(d x + c\right) - 24 \, A - 72 \, B}{384 \, {\left(a^{2} d \cos\left(d x + c\right)^{6} - 2 \, a^{2} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/384*(60*(3*A + B)*cos(d*x + c)^4 - 20*(3*A + B)*cos(d*x + c)^2 + 15*((3*A + B)*cos(d*x + c)^6 - 2*(3*A + B)*cos(d*x + c)^4*sin(d*x + c) - 2*(3*A + B)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - 15*((3*A + B)*cos(d*x + c)^6 - 2*(3*A + B)*cos(d*x + c)^4*sin(d*x + c) - 2*(3*A + B)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) + 2*(15*(3*A + B)*cos(d*x + c)^4 - 20*(3*A + B)*cos(d*x + c)^2 - 36*A - 12*B)*sin(d*x + c) - 24*A - 72*B)/(a^2*d*cos(d*x + c)^6 - 2*a^2*d*cos(d*x + c)^4*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^4)","A",0
1018,1,290,0,1.032134," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{420 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{6} - 140 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{4} - 56 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{2} + 105 \, {\left({\left(4 \, A + B\right)} \cos\left(d x + c\right)^{8} - 2 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - 2 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 105 \, {\left({\left(4 \, A + B\right)} \cos\left(d x + c\right)^{8} - 2 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - 2 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(105 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{6} - 140 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{4} - 84 \, {\left(4 \, A + B\right)} \cos\left(d x + c\right)^{2} - 256 \, A - 64 \, B\right)} \sin\left(d x + c\right) - 128 \, A - 512 \, B}{3840 \, {\left(a^{2} d \cos\left(d x + c\right)^{8} - 2 \, a^{2} d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) - 2 \, a^{2} d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/3840*(420*(4*A + B)*cos(d*x + c)^6 - 140*(4*A + B)*cos(d*x + c)^4 - 56*(4*A + B)*cos(d*x + c)^2 + 105*((4*A + B)*cos(d*x + c)^8 - 2*(4*A + B)*cos(d*x + c)^6*sin(d*x + c) - 2*(4*A + B)*cos(d*x + c)^6)*log(sin(d*x + c) + 1) - 105*((4*A + B)*cos(d*x + c)^8 - 2*(4*A + B)*cos(d*x + c)^6*sin(d*x + c) - 2*(4*A + B)*cos(d*x + c)^6)*log(-sin(d*x + c) + 1) + 2*(105*(4*A + B)*cos(d*x + c)^6 - 140*(4*A + B)*cos(d*x + c)^4 - 84*(4*A + B)*cos(d*x + c)^2 - 256*A - 64*B)*sin(d*x + c) - 128*A - 512*B)/(a^2*d*cos(d*x + c)^8 - 2*a^2*d*cos(d*x + c)^6*sin(d*x + c) - 2*a^2*d*cos(d*x + c)^6)","A",0
1019,0,0,0,1.168328," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m, x)","F",0
1020,1,333,0,1.275614," ","integrate(cos(f*x+e)^7*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left({\left(B m^{4} + 22 \, B m^{3} + 179 \, B m^{2} + 638 \, B m + 840 \, B\right)} \cos\left(f x + e\right)^{8} - {\left({\left(A + B\right)} m^{4} + {\left(17 \, A + 9 \, B\right)} m^{3} + 4 \, {\left(23 \, A + 5 \, B\right)} m^{2} + 160 \, A m\right)} \cos\left(f x + e\right)^{6} - 12 \, {\left({\left(A + B\right)} m^{3} + {\left(11 \, A + 3 \, B\right)} m^{2} + 24 \, A m\right)} \cos\left(f x + e\right)^{4} - 96 \, {\left({\left(A + B\right)} m^{2} + 8 \, A m\right)} \cos\left(f x + e\right)^{2} - 384 \, {\left(A + B\right)} m - {\left({\left({\left(A + B\right)} m^{4} + {\left(23 \, A + 15 \, B\right)} m^{3} + 2 \, {\left(97 \, A + 37 \, B\right)} m^{2} + 8 \, {\left(89 \, A + 15 \, B\right)} m + 960 \, A\right)} \cos\left(f x + e\right)^{6} + 12 \, {\left({\left(A + B\right)} m^{3} + {\left(15 \, A + 7 \, B\right)} m^{2} + 4 \, {\left(17 \, A + 3 \, B\right)} m + 96 \, A\right)} \cos\left(f x + e\right)^{4} + 96 \, {\left({\left(A + B\right)} m^{2} + 2 \, {\left(5 \, A + B\right)} m + 16 \, A\right)} \cos\left(f x + e\right)^{2} + 384 \, {\left(A + B\right)} m + 3072 \, A\right)} \sin\left(f x + e\right) - 3072 \, A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f m^{5} + 30 \, f m^{4} + 355 \, f m^{3} + 2070 \, f m^{2} + 5944 \, f m + 6720 \, f}"," ",0,"-((B*m^4 + 22*B*m^3 + 179*B*m^2 + 638*B*m + 840*B)*cos(f*x + e)^8 - ((A + B)*m^4 + (17*A + 9*B)*m^3 + 4*(23*A + 5*B)*m^2 + 160*A*m)*cos(f*x + e)^6 - 12*((A + B)*m^3 + (11*A + 3*B)*m^2 + 24*A*m)*cos(f*x + e)^4 - 96*((A + B)*m^2 + 8*A*m)*cos(f*x + e)^2 - 384*(A + B)*m - (((A + B)*m^4 + (23*A + 15*B)*m^3 + 2*(97*A + 37*B)*m^2 + 8*(89*A + 15*B)*m + 960*A)*cos(f*x + e)^6 + 12*((A + B)*m^3 + (15*A + 7*B)*m^2 + 4*(17*A + 3*B)*m + 96*A)*cos(f*x + e)^4 + 96*((A + B)*m^2 + 2*(5*A + B)*m + 16*A)*cos(f*x + e)^2 + 384*(A + B)*m + 3072*A)*sin(f*x + e) - 3072*A)*(a*sin(f*x + e) + a)^m/(f*m^5 + 30*f*m^4 + 355*f*m^3 + 2070*f*m^2 + 5944*f*m + 6720*f)","B",0
1021,1,221,0,1.241580," ","integrate(cos(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left({\left(B m^{3} + 12 \, B m^{2} + 47 \, B m + 60 \, B\right)} \cos\left(f x + e\right)^{6} - {\left({\left(A + B\right)} m^{3} + 3 \, {\left(3 \, A + B\right)} m^{2} + 18 \, A m\right)} \cos\left(f x + e\right)^{4} - 8 \, {\left({\left(A + B\right)} m^{2} + 6 \, A m\right)} \cos\left(f x + e\right)^{2} - 32 \, {\left(A + B\right)} m - {\left({\left({\left(A + B\right)} m^{3} + {\left(13 \, A + 7 \, B\right)} m^{2} + 6 \, {\left(9 \, A + 2 \, B\right)} m + 72 \, A\right)} \cos\left(f x + e\right)^{4} + 8 \, {\left({\left(A + B\right)} m^{2} + 2 \, {\left(4 \, A + B\right)} m + 12 \, A\right)} \cos\left(f x + e\right)^{2} + 32 \, {\left(A + B\right)} m + 192 \, A\right)} \sin\left(f x + e\right) - 192 \, A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f m^{4} + 18 \, f m^{3} + 119 \, f m^{2} + 342 \, f m + 360 \, f}"," ",0,"-((B*m^3 + 12*B*m^2 + 47*B*m + 60*B)*cos(f*x + e)^6 - ((A + B)*m^3 + 3*(3*A + B)*m^2 + 18*A*m)*cos(f*x + e)^4 - 8*((A + B)*m^2 + 6*A*m)*cos(f*x + e)^2 - 32*(A + B)*m - (((A + B)*m^3 + (13*A + 7*B)*m^2 + 6*(9*A + 2*B)*m + 72*A)*cos(f*x + e)^4 + 8*((A + B)*m^2 + 2*(4*A + B)*m + 12*A)*cos(f*x + e)^2 + 32*(A + B)*m + 192*A)*sin(f*x + e) - 192*A)*(a*sin(f*x + e) + a)^m/(f*m^4 + 18*f*m^3 + 119*f*m^2 + 342*f*m + 360*f)","A",0
1022,1,135,0,1.178395," ","integrate(cos(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left({\left(B m^{2} + 5 \, B m + 6 \, B\right)} \cos\left(f x + e\right)^{4} - {\left({\left(A + B\right)} m^{2} + 4 \, A m\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + B\right)} m - {\left({\left({\left(A + B\right)} m^{2} + 2 \, {\left(3 \, A + B\right)} m + 8 \, A\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(A + B\right)} m + 16 \, A\right)} \sin\left(f x + e\right) - 16 \, A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f m^{3} + 9 \, f m^{2} + 26 \, f m + 24 \, f}"," ",0,"-((B*m^2 + 5*B*m + 6*B)*cos(f*x + e)^4 - ((A + B)*m^2 + 4*A*m)*cos(f*x + e)^2 - 4*(A + B)*m - (((A + B)*m^2 + 2*(3*A + B)*m + 8*A)*cos(f*x + e)^2 + 4*(A + B)*m + 16*A)*sin(f*x + e) - 16*A)*(a*sin(f*x + e) + a)^m/(f*m^3 + 9*f*m^2 + 26*f*m + 24*f)","A",0
1023,1,70,0,1.122574," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left({\left(B m + B\right)} \cos\left(f x + e\right)^{2} - {\left(A + B\right)} m - {\left({\left(A + B\right)} m + 2 \, A\right)} \sin\left(f x + e\right) - 2 \, A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f m^{2} + 3 \, f m + 2 \, f}"," ",0,"-((B*m + B)*cos(f*x + e)^2 - (A + B)*m - ((A + B)*m + 2*A)*sin(f*x + e) - 2*A)*(a*sin(f*x + e) + a)^m/(f*m^2 + 3*f*m + 2*f)","A",0
1024,0,0,0,0.935739," ","integrate(sec(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(f x + e\right) \sin\left(f x + e\right) + A \sec\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sec(f*x + e)*sin(f*x + e) + A*sec(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
1025,0,0,0,1.041873," ","integrate(sec(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(f x + e\right)^{3} \sin\left(f x + e\right) + A \sec\left(f x + e\right)^{3}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sec(f*x + e)^3*sin(f*x + e) + A*sec(f*x + e)^3)*(a*sin(f*x + e) + a)^m, x)","F",0
1026,0,0,0,1.142802," ","integrate(sec(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(f x + e\right)^{5} \sin\left(f x + e\right) + A \sec\left(f x + e\right)^{5}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sec(f*x + e)^5*sin(f*x + e) + A*sec(f*x + e)^5)*(a*sin(f*x + e) + a)^m, x)","F",0
1027,0,0,0,1.250662," ","integrate(cos(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(f x + e\right)^{6} \sin\left(f x + e\right) + A \cos\left(f x + e\right)^{6}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*cos(f*x + e)^6*sin(f*x + e) + A*cos(f*x + e)^6)*(a*sin(f*x + e) + a)^m, x)","F",0
1028,0,0,0,0.996182," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(f x + e\right)^{4} \sin\left(f x + e\right) + A \cos\left(f x + e\right)^{4}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*cos(f*x + e)^4*sin(f*x + e) + A*cos(f*x + e)^4)*(a*sin(f*x + e) + a)^m, x)","F",0
1029,0,0,0,1.237765," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) + A \cos\left(f x + e\right)^{2}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*cos(f*x + e)^2*sin(f*x + e) + A*cos(f*x + e)^2)*(a*sin(f*x + e) + a)^m, x)","F",0
1030,0,0,0,0.983674," ","integrate(sec(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(f x + e\right)^{2} \sin\left(f x + e\right) + A \sec\left(f x + e\right)^{2}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sec(f*x + e)^2*sin(f*x + e) + A*sec(f*x + e)^2)*(a*sin(f*x + e) + a)^m, x)","F",0
1031,0,0,0,0.991228," ","integrate(sec(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(f x + e\right)^{4} \sin\left(f x + e\right) + A \sec\left(f x + e\right)^{4}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sec(f*x + e)^4*sin(f*x + e) + A*sec(f*x + e)^4)*(a*sin(f*x + e) + a)^m, x)","F",0
1032,0,0,0,1.271662," ","integrate(sec(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sec\left(f x + e\right)^{6} \sin\left(f x + e\right) + A \sec\left(f x + e\right)^{6}\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sec(f*x + e)^6*sin(f*x + e) + A*sec(f*x + e)^6)*(a*sin(f*x + e) + a)^m, x)","F",0
1033,1,197,0,0.617311," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-p),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(B p^{2} - {\left(3 \, A - 8 \, B\right)} p - 12 \, A + 16 \, B\right)} \cos\left(f x + e\right)^{3} + {\left(A p^{3} + 3 \, {\left(4 \, A - B\right)} p^{2} + {\left(47 \, A - 24 \, B\right)} p + 60 \, A - 45 \, B\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(B p - 3 \, A + 4 \, B\right)} \cos\left(f x + e\right)^{3} - {\left(B p^{3} - 3 \, {\left(A - 4 \, B\right)} p^{2} - {\left(24 \, A - 47 \, B\right)} p - 45 \, A + 60 \, B\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p - 4}}{f p^{4} + 16 \, f p^{3} + 86 \, f p^{2} + 176 \, f p + 105 \, f}"," ",0,"(2*(B*p^2 - (3*A - 8*B)*p - 12*A + 16*B)*cos(f*x + e)^3 + (A*p^3 + 3*(4*A - B)*p^2 + (47*A - 24*B)*p + 60*A - 45*B)*cos(f*x + e) - (2*(B*p - 3*A + 4*B)*cos(f*x + e)^3 - (B*p^3 - 3*(A - 4*B)*p^2 - (24*A - 47*B)*p - 45*A + 60*B)*cos(f*x + e))*sin(f*x + e))*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 4)/(f*p^4 + 16*f*p^3 + 86*f*p^2 + 176*f*p + 105*f)","A",0
1034,1,131,0,0.641958," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-p),x, algorithm=""fricas"")","\frac{{\left({\left(B p - 2 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{3} + {\left(B p^{2} - 2 \, {\left(A - 3 \, B\right)} p - 6 \, A + 9 \, B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(A p^{2} + 2 \, {\left(3 \, A - B\right)} p + 9 \, A - 6 \, B\right)} \cos\left(f x + e\right)\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p - 3}}{f p^{3} + 9 \, f p^{2} + 23 \, f p + 15 \, f}"," ",0,"((B*p - 2*A + 3*B)*cos(f*x + e)^3 + (B*p^2 - 2*(A - 3*B)*p - 6*A + 9*B)*cos(f*x + e)*sin(f*x + e) + (A*p^2 + 2*(3*A - B)*p + 9*A - 6*B)*cos(f*x + e))*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 3)/(f*p^3 + 9*f*p^2 + 23*f*p + 15*f)","A",0
1035,1,84,0,1.072170," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-p),x, algorithm=""fricas"")","\frac{{\left({\left(B p - A + 2 \, B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(A p + 2 \, A - B\right)} \cos\left(f x + e\right)\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p - 2}}{f p^{2} + 4 \, f p + 3 \, f}"," ",0,"((B*p - A + 2*B)*cos(f*x + e)*sin(f*x + e) + (A*p + 2*A - B)*cos(f*x + e))*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 2)/(f*p^2 + 4*f*p + 3*f)","A",0
1036,0,0,0,1.178170," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-p),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p - 1}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 1), x)","F",0
1037,0,0,0,0.928272," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^p),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{p}}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p/(-c*sin(f*x + e) + c)^p, x)","F",0
1038,0,0,0,1.115522," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-p),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p + 1}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p + 1), x)","F",0
1039,0,0,0,1.165642," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-p),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-c \sin\left(f x + e\right) + c\right)}^{-p + 2}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p + 2), x)","F",0
1040,1,33,0,1.137030," ","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, algorithm=""fricas"")","\frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} A \cos\left(f x + e\right)}{f}"," ",0,"(g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m*A*cos(f*x + e)/f","A",0
1041,1,35,0,1.114293," ","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, algorithm=""fricas"")","-\frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(-a \sin\left(f x + e\right) + a\right)}^{m} A \cos\left(f x + e\right)}{f}"," ",0,"-(g*cos(f*x + e))^p*(-a*sin(f*x + e) + a)^m*A*cos(f*x + e)/f","A",0
1042,0,0,0,1.947548," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(g \cos\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
1043,0,0,0,1.507604," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2)*(g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n, x)","F",0
1044,0,0,0,1.589461," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(a \sin\left(f x + e\right) + a\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((a*sin(f*x + e) + a)*(g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n, x)","F",0
1045,0,0,0,1.201105," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a), x)","F",0
1046,0,0,0,1.966511," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
1047,0,0,0,1.632978," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
1048,0,0,0,1.760085," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a^{4} \cos\left(f x + e\right)^{4} - 8 \, a^{4} \cos\left(f x + e\right)^{2} + 8 \, a^{4} - 4 \, {\left(a^{4} \cos\left(f x + e\right)^{2} - 2 \, a^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a^4*cos(f*x + e)^4 - 8*a^4*cos(f*x + e)^2 + 8*a^4 - 4*(a^4*cos(f*x + e)^2 - 2*a^4)*sin(f*x + e)), x)","F",0
1049,0,0,0,1.951024," ","integrate((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(\left(g \sec\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
1050,1,73,0,0.737909," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, a \cos\left(d x + c\right)^{5} - 80 \, a \cos\left(d x + c\right)^{3} + 15 \, b d x + 5 \, {\left(8 \, b \cos\left(d x + c\right)^{5} - 14 \, b \cos\left(d x + c\right)^{3} + 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(48*a*cos(d*x + c)^5 - 80*a*cos(d*x + c)^3 + 15*b*d*x + 5*(8*b*cos(d*x + c)^5 - 14*b*cos(d*x + c)^3 + 3*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1051,1,62,0,1.068730," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{24 \, b \cos\left(d x + c\right)^{5} - 40 \, b \cos\left(d x + c\right)^{3} + 15 \, a d x - 15 \, {\left(2 \, a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, d}"," ",0,"1/120*(24*b*cos(d*x + c)^5 - 40*b*cos(d*x + c)^3 + 15*a*d*x - 15*(2*a*cos(d*x + c)^3 - a*cos(d*x + c))*sin(d*x + c))/d","A",0
1052,1,51,0,0.712095," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, a \cos\left(d x + c\right)^{3} - 3 \, b d x + 3 \, {\left(2 \, b \cos\left(d x + c\right)^{3} - b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"-1/24*(8*a*cos(d*x + c)^3 - 3*b*d*x + 3*(2*b*cos(d*x + c)^3 - b*cos(d*x + c))*sin(d*x + c))/d","A",0
1053,1,60,0,2.178311," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{b d x + b \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, a \cos\left(d x + c\right) - a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, d}"," ",0,"1/2*(b*d*x + b*cos(d*x + c)*sin(d*x + c) + 2*a*cos(d*x + c) - a*log(1/2*cos(d*x + c) + 1/2) + a*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
1054,1,84,0,1.168221," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, a \cos\left(d x + c\right) + 2 \, {\left(a d x - b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, d \sin\left(d x + c\right)}"," ",0,"-1/2*(b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*a*cos(d*x + c) + 2*(a*d*x - b*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","B",0
1055,1,114,0,1.200327," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, b d x \cos\left(d x + c\right)^{2} - 4 \, b d x - 4 \, b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right) - {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(4*b*d*x*cos(d*x + c)^2 - 4*b*d*x - 4*b*cos(d*x + c)*sin(d*x + c) - 2*a*cos(d*x + c) - (a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + (a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
1056,1,119,0,1.096211," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, a \cos\left(d x + c\right)^{3} + 6 \, b \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(4*a*cos(d*x + c)^3 + 6*b*cos(d*x + c)*sin(d*x + c) + 3*(b*cos(d*x + c)^2 - b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(b*cos(d*x + c)^2 - b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
1057,1,137,0,0.771949," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, b \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + 6 \, a \cos\left(d x + c\right)^{3} + 6 \, a \cos\left(d x + c\right) - 3 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/48*(16*b*cos(d*x + c)^3*sin(d*x + c) + 6*a*cos(d*x + c)^3 + 6*a*cos(d*x + c) - 3*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 3*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
1058,1,169,0,0.926453," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{32 \, a \cos\left(d x + c\right)^{5} - 80 \, a \cos\left(d x + c\right)^{3} + 15 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left(b \cos\left(d x + c\right)^{3} + b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/240*(32*a*cos(d*x + c)^5 - 80*a*cos(d*x + c)^3 + 15*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*(b*cos(d*x + c)^3 + b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
1059,1,104,0,0.904561," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{120 \, b^{2} \cos\left(d x + c\right)^{7} - 168 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 105 \, a b d x + 280 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{3} - 35 \, {\left(8 \, a b \cos\left(d x + c\right)^{5} - 14 \, a b \cos\left(d x + c\right)^{3} + 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"-1/840*(120*b^2*cos(d*x + c)^7 - 168*(a^2 + 2*b^2)*cos(d*x + c)^5 - 105*a*b*d*x + 280*(a^2 + b^2)*cos(d*x + c)^3 - 35*(8*a*b*cos(d*x + c)^5 - 14*a*b*cos(d*x + c)^3 + 3*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1060,1,103,0,0.776280," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{96 \, a b \cos\left(d x + c\right)^{5} - 160 \, a b \cos\left(d x + c\right)^{3} + 15 \, {\left(2 \, a^{2} + b^{2}\right)} d x + 5 \, {\left(8 \, b^{2} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{2} + 7 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(96*a*b*cos(d*x + c)^5 - 160*a*b*cos(d*x + c)^3 + 15*(2*a^2 + b^2)*d*x + 5*(8*b^2*cos(d*x + c)^5 - 2*(6*a^2 + 7*b^2)*cos(d*x + c)^3 + 3*(2*a^2 + b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
1061,1,73,0,0.994898," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{12 \, b^{2} \cos\left(d x + c\right)^{5} + 15 \, a b d x - 20 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(2 \, a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*b^2*cos(d*x + c)^5 + 15*a*b*d*x - 20*(a^2 + b^2)*cos(d*x + c)^3 - 15*(2*a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1062,1,84,0,0.804183," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, b^{2} \cos\left(d x + c\right)^{3} - 6 \, a b d x - 6 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, a^{2} \cos\left(d x + c\right) + 3 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{6 \, d}"," ",0,"-1/6*(2*b^2*cos(d*x + c)^3 - 6*a*b*d*x - 6*a*b*cos(d*x + c)*sin(d*x + c) - 6*a^2*cos(d*x + c) + 3*a^2*log(1/2*cos(d*x + c) + 1/2) - 3*a^2*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
1063,1,118,0,1.135830," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{b^{2} \cos\left(d x + c\right)^{3} + 2 \, a b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, a b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right) + {\left({\left(2 \, a^{2} - b^{2}\right)} d x - 4 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, d \sin\left(d x + c\right)}"," ",0,"-1/2*(b^2*cos(d*x + c)^3 + 2*a*b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*a*b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + (2*a^2 - b^2)*cos(d*x + c) + ((2*a^2 - b^2)*d*x - 4*a*b*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
1064,1,168,0,1.409881," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, a b d x \cos\left(d x + c\right)^{2} - 4 \, b^{2} \cos\left(d x + c\right)^{3} - 8 \, a b d x - 8 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right) - {\left({\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + 2 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + 2 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(8*a*b*d*x*cos(d*x + c)^2 - 4*b^2*cos(d*x + c)^3 - 8*a*b*d*x - 8*a*b*cos(d*x + c)*sin(d*x + c) - 2*(a^2 - 2*b^2)*cos(d*x + c) - ((a^2 - 2*b^2)*cos(d*x + c)^2 - a^2 + 2*b^2)*log(1/2*cos(d*x + c) + 1/2) + ((a^2 - 2*b^2)*cos(d*x + c)^2 - a^2 + 2*b^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
1065,1,167,0,1.383528," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, b^{2} \cos\left(d x + c\right) + 3 \, {\left(a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 6 \, {\left(b^{2} d x \cos\left(d x + c\right)^{2} - b^{2} d x - a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/6*(2*(a^2 - 3*b^2)*cos(d*x + c)^3 + 6*b^2*cos(d*x + c) + 3*(a*b*cos(d*x + c)^2 - a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(a*b*cos(d*x + c)^2 - a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 6*(b^2*d*x*cos(d*x + c)^2 - b^2*d*x - a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1066,1,200,0,1.058106," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{32 \, a b \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) + 6 \, {\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right) - 3 \, {\left({\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} + 4 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} + 4 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/48*(32*a*b*cos(d*x + c)^3*sin(d*x + c) + 6*(a^2 - 4*b^2)*cos(d*x + c)^3 + 6*(a^2 + 4*b^2)*cos(d*x + c) - 3*((a^2 + 4*b^2)*cos(d*x + c)^4 - 2*(a^2 + 4*b^2)*cos(d*x + c)^2 + a^2 + 4*b^2)*log(1/2*cos(d*x + c) + 1/2) + 3*((a^2 + 4*b^2)*cos(d*x + c)^4 - 2*(a^2 + 4*b^2)*cos(d*x + c)^2 + a^2 + 4*b^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
1067,1,195,0,0.653479," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{8 \, {\left(2 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 40 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(a b \cos\left(d x + c\right)^{4} - 2 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(a b \cos\left(d x + c\right)^{4} - 2 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left(a b \cos\left(d x + c\right)^{3} + a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/120*(8*(2*a^2 + 5*b^2)*cos(d*x + c)^5 - 40*(a^2 + b^2)*cos(d*x + c)^3 + 15*(a*b*cos(d*x + c)^4 - 2*a*b*cos(d*x + c)^2 + a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(a*b*cos(d*x + c)^4 - 2*a*b*cos(d*x + c)^2 + a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*(a*b*cos(d*x + c)^3 + a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
1068,1,283,0,0.772191," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{30 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 80 \, a^{2} \cos\left(d x + c\right)^{3} - 30 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right) - 15 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} - 2 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left({\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} - 2 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 64 \, {\left(2 \, a b \cos\left(d x + c\right)^{5} - 5 \, a b \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/480*(30*(a^2 + 2*b^2)*cos(d*x + c)^5 - 80*a^2*cos(d*x + c)^3 - 30*(a^2 + 2*b^2)*cos(d*x + c) - 15*((a^2 + 2*b^2)*cos(d*x + c)^6 - 3*(a^2 + 2*b^2)*cos(d*x + c)^4 + 3*(a^2 + 2*b^2)*cos(d*x + c)^2 - a^2 - 2*b^2)*log(1/2*cos(d*x + c) + 1/2) + 15*((a^2 + 2*b^2)*cos(d*x + c)^6 - 3*(a^2 + 2*b^2)*cos(d*x + c)^4 + 3*(a^2 + 2*b^2)*cos(d*x + c)^2 - a^2 - 2*b^2)*log(-1/2*cos(d*x + c) + 1/2) + 64*(2*a*b*cos(d*x + c)^5 - 5*a*b*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
1069,1,141,0,1.202278," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{240 \, b^{3} \cos\left(d x + c\right)^{7} - 336 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{5} + 560 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} d x - 105 \, {\left(8 \, a b^{2} \cos\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{3} + 7 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"-1/1680*(240*b^3*cos(d*x + c)^7 - 336*(3*a^2*b + 2*b^3)*cos(d*x + c)^5 + 560*(3*a^2*b + b^3)*cos(d*x + c)^3 - 105*(2*a^3 + 3*a*b^2)*d*x - 105*(8*a*b^2*cos(d*x + c)^5 - 2*(2*a^3 + 7*a*b^2)*cos(d*x + c)^3 + (2*a^3 + 3*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
1070,1,116,0,1.224357," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{144 \, a b^{2} \cos\left(d x + c\right)^{5} - 80 \, {\left(a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(6 \, a^{2} b + b^{3}\right)} d x + 5 \, {\left(8 \, b^{3} \cos\left(d x + c\right)^{5} - 2 \, {\left(18 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(144*a*b^2*cos(d*x + c)^5 - 80*(a^3 + 3*a*b^2)*cos(d*x + c)^3 + 15*(6*a^2*b + b^3)*d*x + 5*(8*b^3*cos(d*x + c)^5 - 2*(18*a^2*b + 7*b^3)*cos(d*x + c)^3 + 3*(6*a^2*b + b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
1071,1,116,0,0.863343," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, a b^{2} \cos\left(d x + c\right)^{3} - 8 \, a^{3} \cos\left(d x + c\right) + 4 \, a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(12 \, a^{2} b + b^{3}\right)} d x + {\left(2 \, b^{3} \cos\left(d x + c\right)^{3} - {\left(12 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, d}"," ",0,"-1/8*(8*a*b^2*cos(d*x + c)^3 - 8*a^3*cos(d*x + c) + 4*a^3*log(1/2*cos(d*x + c) + 1/2) - 4*a^3*log(-1/2*cos(d*x + c) + 1/2) - (12*a^2*b + b^3)*d*x + (2*b^3*cos(d*x + c)^3 - (12*a^2*b + b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
1072,1,143,0,1.188320," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{9 \, a b^{2} \cos\left(d x + c\right)^{3} + 9 \, a^{2} b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, a^{2} b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right) + {\left(2 \, b^{3} \cos\left(d x + c\right)^{3} - 18 \, a^{2} b \cos\left(d x + c\right) + 3 \, {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d x\right)} \sin\left(d x + c\right)}{6 \, d \sin\left(d x + c\right)}"," ",0,"-1/6*(9*a*b^2*cos(d*x + c)^3 + 9*a^2*b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*a^2*b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(2*a^3 - 3*a*b^2)*cos(d*x + c) + (2*b^3*cos(d*x + c)^3 - 18*a^2*b*cos(d*x + c) + 3*(2*a^3 - 3*a*b^2)*d*x)*sin(d*x + c))/(d*sin(d*x + c))","A",0
1073,1,216,0,0.969229," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{12 \, a b^{2} \cos\left(d x + c\right)^{3} - 2 \, {\left(6 \, a^{2} b - b^{3}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{2} b - b^{3}\right)} d x + 2 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cos\left(d x + c\right) - {\left(a^{3} - 6 \, a b^{2} - {\left(a^{3} - 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{3} - 6 \, a b^{2} - {\left(a^{3} - 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(b^{3} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/4*(12*a*b^2*cos(d*x + c)^3 - 2*(6*a^2*b - b^3)*d*x*cos(d*x + c)^2 + 2*(6*a^2*b - b^3)*d*x + 2*(a^3 - 6*a*b^2)*cos(d*x + c) - (a^3 - 6*a*b^2 - (a^3 - 6*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + (a^3 - 6*a*b^2 - (a^3 - 6*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) + 2*(b^3*cos(d*x + c)^3 + (6*a^2*b - b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
1074,1,231,0,0.807084," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{36 \, a b^{2} \cos\left(d x + c\right) + 4 \, {\left(a^{3} - 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 6 \, {\left(6 \, a b^{2} d x \cos\left(d x + c\right)^{2} - 2 \, b^{3} \cos\left(d x + c\right)^{3} - 6 \, a b^{2} d x - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(36*a*b^2*cos(d*x + c) + 4*(a^3 - 9*a*b^2)*cos(d*x + c)^3 - 3*(3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 6*(6*a*b^2*d*x*cos(d*x + c)^2 - 2*b^3*cos(d*x + c)^3 - 6*a*b^2*d*x - (3*a^2*b - 2*b^3)*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1075,1,265,0,1.117398," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{16 \, b^{3} d x \cos\left(d x + c\right)^{4} - 32 \, b^{3} d x \cos\left(d x + c\right)^{2} + 16 \, b^{3} d x + 2 \, {\left(a^{3} - 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right) - {\left({\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + a^{3} + 12 \, a b^{2} - 2 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + a^{3} + 12 \, a b^{2} - 2 \, {\left(a^{3} + 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 16 \, {\left(b^{3} \cos\left(d x + c\right) + {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/16*(16*b^3*d*x*cos(d*x + c)^4 - 32*b^3*d*x*cos(d*x + c)^2 + 16*b^3*d*x + 2*(a^3 - 12*a*b^2)*cos(d*x + c)^3 + 2*(a^3 + 12*a*b^2)*cos(d*x + c) - ((a^3 + 12*a*b^2)*cos(d*x + c)^4 + a^3 + 12*a*b^2 - 2*(a^3 + 12*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + ((a^3 + 12*a*b^2)*cos(d*x + c)^4 + a^3 + 12*a*b^2 - 2*(a^3 + 12*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) + 16*(b^3*cos(d*x + c) + (a^2*b - b^3)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
1076,1,275,0,1.282169," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{16 \, {\left(2 \, a^{3} + 15 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} - 80 \, {\left(a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left({\left(3 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b + 4 \, b^{3} - 2 \, {\left(3 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left({\left(3 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b + 4 \, b^{3} - 2 \, {\left(3 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left({\left(3 \, a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(3 \, a^{2} b + 4 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/240*(16*(2*a^3 + 15*a*b^2)*cos(d*x + c)^5 - 80*(a^3 + 3*a*b^2)*cos(d*x + c)^3 + 15*((3*a^2*b + 4*b^3)*cos(d*x + c)^4 + 3*a^2*b + 4*b^3 - 2*(3*a^2*b + 4*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*((3*a^2*b + 4*b^3)*cos(d*x + c)^4 + 3*a^2*b + 4*b^3 - 2*(3*a^2*b + 4*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*((3*a^2*b - 4*b^3)*cos(d*x + c)^3 + (3*a^2*b + 4*b^3)*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
1077,1,310,0,1.154314," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{80 \, a^{3} \cos\left(d x + c\right)^{3} - 30 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 30 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} - a^{3} - 6 \, a b^{2} + 3 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} - a^{3} - 6 \, a b^{2} + 3 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left({\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/480*(80*a^3*cos(d*x + c)^3 - 30*(a^3 + 6*a*b^2)*cos(d*x + c)^5 + 30*(a^3 + 6*a*b^2)*cos(d*x + c) + 15*((a^3 + 6*a*b^2)*cos(d*x + c)^6 - 3*(a^3 + 6*a*b^2)*cos(d*x + c)^4 - a^3 - 6*a*b^2 + 3*(a^3 + 6*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - 15*((a^3 + 6*a*b^2)*cos(d*x + c)^6 - 3*(a^3 + 6*a*b^2)*cos(d*x + c)^4 - a^3 - 6*a*b^2 + 3*(a^3 + 6*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 32*((6*a^2*b + 5*b^3)*cos(d*x + c)^5 - 5*(3*a^2*b + b^3)*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
1078,1,643,0,0.937545," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{6} - 5 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x + 3 \, {\left(4 \, a^{5} - 3 \, a^{3} b^{2} + {\left(4 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 6 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} d x - 6 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{2} b^{6} - b^{8}\right)} d \sin\left(d x + c\right) + {\left(a^{3} b^{5} - a b^{7}\right)} d\right)}}, \frac{2 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{6} - 5 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x + 3 \, {\left(4 \, a^{5} - 3 \, a^{3} b^{2} + {\left(4 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 3 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - {\left({\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} d x - 6 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left({\left(a^{2} b^{6} - b^{8}\right)} d \sin\left(d x + c\right) + {\left(a^{3} b^{5} - a b^{7}\right)} d\right)}}\right]"," ",0,"[1/6*(4*(a^3*b^3 - a*b^5)*cos(d*x + c)^3 + 6*(4*a^6 - 5*a^4*b^2 + a^2*b^4)*d*x + 3*(4*a^5 - 3*a^3*b^2 + (4*a^4*b - 3*a^2*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 6*(4*a^5*b - 5*a^3*b^3 + a*b^5)*cos(d*x + c) - 2*((a^2*b^4 - b^6)*cos(d*x + c)^3 - 3*(4*a^5*b - 5*a^3*b^3 + a*b^5)*d*x - 6*(a^4*b^2 - a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^6 - b^8)*d*sin(d*x + c) + (a^3*b^5 - a*b^7)*d), 1/3*(2*(a^3*b^3 - a*b^5)*cos(d*x + c)^3 + 3*(4*a^6 - 5*a^4*b^2 + a^2*b^4)*d*x + 3*(4*a^5 - 3*a^3*b^2 + (4*a^4*b - 3*a^2*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 3*(4*a^5*b - 5*a^3*b^3 + a*b^5)*cos(d*x + c) - ((a^2*b^4 - b^6)*cos(d*x + c)^3 - 3*(4*a^5*b - 5*a^3*b^3 + a*b^5)*d*x - 6*(a^4*b^2 - a^2*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^6 - b^8)*d*sin(d*x + c) + (a^3*b^5 - a*b^7)*d)]","A",0
1079,1,568,0,1.091702," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{5} - 7 \, a^{3} b^{2} + a b^{4}\right)} d x - {\left(3 \, a^{4} - 2 \, a^{2} b^{2} + {\left(3 \, a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + {\left(6 \, a^{4} b - 7 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + {\left({\left(6 \, a^{4} b - 7 \, a^{2} b^{3} + b^{5}\right)} d x + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{5} - b^{7}\right)} d \sin\left(d x + c\right) + {\left(a^{3} b^{4} - a b^{6}\right)} d\right)}}, -\frac{{\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{5} - 7 \, a^{3} b^{2} + a b^{4}\right)} d x + 2 \, {\left(3 \, a^{4} - 2 \, a^{2} b^{2} + {\left(3 \, a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left(6 \, a^{4} b - 7 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) + {\left({\left(6 \, a^{4} b - 7 \, a^{2} b^{3} + b^{5}\right)} d x + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{5} - b^{7}\right)} d \sin\left(d x + c\right) + {\left(a^{3} b^{4} - a b^{6}\right)} d\right)}}\right]"," ",0,"[-1/2*((a^2*b^3 - b^5)*cos(d*x + c)^3 + (6*a^5 - 7*a^3*b^2 + a*b^4)*d*x - (3*a^4 - 2*a^2*b^2 + (3*a^3*b - 2*a*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + (6*a^4*b - 7*a^2*b^3 + b^5)*cos(d*x + c) + ((6*a^4*b - 7*a^2*b^3 + b^5)*d*x + 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d*sin(d*x + c) + (a^3*b^4 - a*b^6)*d), -1/2*((a^2*b^3 - b^5)*cos(d*x + c)^3 + (6*a^5 - 7*a^3*b^2 + a*b^4)*d*x + 2*(3*a^4 - 2*a^2*b^2 + (3*a^3*b - 2*a*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + (6*a^4*b - 7*a^2*b^3 + b^5)*cos(d*x + c) + ((6*a^4*b - 7*a^2*b^3 + b^5)*d*x + 3*(a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^5 - b^7)*d*sin(d*x + c) + (a^3*b^4 - a*b^6)*d)]","A",0
1080,1,479,0,0.832785," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{4} - a^{2} b^{2}\right)} d x + {\left(2 \, a^{3} - a b^{2} + {\left(2 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 4 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) + 2 \, {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d x + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{4} - b^{6}\right)} d \sin\left(d x + c\right) + {\left(a^{3} b^{3} - a b^{5}\right)} d\right)}}, \frac{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d x + {\left(2 \, a^{3} - a b^{2} + {\left(2 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) + {\left(2 \, {\left(a^{3} b - a b^{3}\right)} d x + {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{2} b^{4} - b^{6}\right)} d \sin\left(d x + c\right) + {\left(a^{3} b^{3} - a b^{5}\right)} d}\right]"," ",0,"[1/2*(4*(a^4 - a^2*b^2)*d*x + (2*a^3 - a*b^2 + (2*a^2*b - b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 4*(a^3*b - a*b^3)*cos(d*x + c) + 2*(2*(a^3*b - a*b^3)*d*x + (a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*sin(d*x + c) + (a^3*b^3 - a*b^5)*d), (2*(a^4 - a^2*b^2)*d*x + (2*a^3 - a*b^2 + (2*a^2*b - b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 2*(a^3*b - a*b^3)*cos(d*x + c) + (2*(a^3*b - a*b^3)*d*x + (a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/((a^2*b^4 - b^6)*d*sin(d*x + c) + (a^3*b^3 - a*b^5)*d)]","A",0
1081,1,483,0,0.891260," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} \sin\left(d x + c\right) + a b\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) + {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left({\left(a^{4} b - a^{2} b^{3}\right)} d \sin\left(d x + c\right) + {\left(a^{5} - a^{3} b^{2}\right)} d\right)}}, \frac{2 \, {\left(b^{2} \sin\left(d x + c\right) + a b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 2 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right) - {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left({\left(a^{4} b - a^{2} b^{3}\right)} d \sin\left(d x + c\right) + {\left(a^{5} - a^{3} b^{2}\right)} d\right)}}\right]"," ",0,"[-1/2*((b^2*sin(d*x + c) + a*b)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(a^3 - a*b^2)*cos(d*x + c) + (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^4*b - a^2*b^3)*d*sin(d*x + c) + (a^5 - a^3*b^2)*d), 1/2*(2*(b^2*sin(d*x + c) + a*b)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 2*(a^3 - a*b^2)*cos(d*x + c) - (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^4*b - a^2*b^3)*d*sin(d*x + c) + (a^5 - a^3*b^2)*d)]","B",0
1082,1,768,0,1.881219," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} \cos\left(d x + c\right) - 2 \, {\left(a^{2} b^{2} - b^{4} - {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(a^{2} b^{2} - b^{4} - {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left({\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} - a^{4} b^{2}\right)} d \sin\left(d x + c\right) - {\left(a^{5} b - a^{3} b^{3}\right)} d\right)}}, \frac{2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left(a^{4} - a^{2} b^{2}\right)} \cos\left(d x + c\right) - {\left(a^{2} b^{2} - b^{4} - {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{2} b^{2} - b^{4} - {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{{\left(a^{5} b - a^{3} b^{3}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} - a^{4} b^{2}\right)} d \sin\left(d x + c\right) - {\left(a^{5} b - a^{3} b^{3}\right)} d}\right]"," ",0,"[1/2*(4*(a^3*b - a*b^3)*cos(d*x + c)*sin(d*x + c) - (a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2 + (a^3 - 2*a*b^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(a^4 - a^2*b^2)*cos(d*x + c) - 2*(a^2*b^2 - b^4 - (a^2*b^2 - b^4)*cos(d*x + c)^2 + (a^3*b - a*b^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 2*(a^2*b^2 - b^4 - (a^2*b^2 - b^4)*cos(d*x + c)^2 + (a^3*b - a*b^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^5*b - a^3*b^3)*d*cos(d*x + c)^2 - (a^6 - a^4*b^2)*d*sin(d*x + c) - (a^5*b - a^3*b^3)*d), (2*(a^3*b - a*b^3)*cos(d*x + c)*sin(d*x + c) - (a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2 + (a^3 - 2*a*b^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + (a^4 - a^2*b^2)*cos(d*x + c) - (a^2*b^2 - b^4 - (a^2*b^2 - b^4)*cos(d*x + c)^2 + (a^3*b - a*b^3)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^2*b^2 - b^4 - (a^2*b^2 - b^4)*cos(d*x + c)^2 + (a^3*b - a*b^3)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^5*b - a^3*b^3)*d*cos(d*x + c)^2 - (a^6 - a^4*b^2)*d*sin(d*x + c) - (a^5*b - a^3*b^3)*d)]","B",0
1083,1,1130,0,2.310277," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, {\left(2 \, a^{3} b - 3 \, a b^{3} - {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{2} - 3 \, b^{4} - {\left(2 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4} - {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5} - {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4} - {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5} - {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{7} - a^{5} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} - a^{5} b^{2}\right)} d + {\left({\left(a^{6} b - a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b - a^{4} b^{3}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{12 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, {\left(2 \, a^{3} b - 3 \, a b^{3} - {\left(2 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{2} - 3 \, b^{4} - {\left(2 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 2 \, {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4} - {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5} - {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4} - {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5} - {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{7} - a^{5} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{7} - a^{5} b^{2}\right)} d + {\left({\left(a^{6} b - a^{4} b^{3}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b - a^{4} b^{3}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(12*(a^3*b^2 - a*b^4)*cos(d*x + c)^3 - 6*(a^4*b - a^2*b^3)*cos(d*x + c)*sin(d*x + c) - 2*(2*a^3*b - 3*a*b^3 - (2*a^3*b - 3*a*b^3)*cos(d*x + c)^2 + (2*a^2*b^2 - 3*b^4 - (2*a^2*b^2 - 3*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c) - (a^5 - 7*a^3*b^2 + 6*a*b^4 - (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2 + (a^4*b - 7*a^2*b^3 + 6*b^5 - (a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^5 - 7*a^3*b^2 + 6*a*b^4 - (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2 + (a^4*b - 7*a^2*b^3 + 6*b^5 - (a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^7 - a^5*b^2)*d*cos(d*x + c)^2 - (a^7 - a^5*b^2)*d + ((a^6*b - a^4*b^3)*d*cos(d*x + c)^2 - (a^6*b - a^4*b^3)*d)*sin(d*x + c)), 1/4*(12*(a^3*b^2 - a*b^4)*cos(d*x + c)^3 - 6*(a^4*b - a^2*b^3)*cos(d*x + c)*sin(d*x + c) + 4*(2*a^3*b - 3*a*b^3 - (2*a^3*b - 3*a*b^3)*cos(d*x + c)^2 + (2*a^2*b^2 - 3*b^4 - (2*a^2*b^2 - 3*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 2*(a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c) - (a^5 - 7*a^3*b^2 + 6*a*b^4 - (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2 + (a^4*b - 7*a^2*b^3 + 6*b^5 - (a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^5 - 7*a^3*b^2 + 6*a*b^4 - (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2 + (a^4*b - 7*a^2*b^3 + 6*b^5 - (a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^7 - a^5*b^2)*d*cos(d*x + c)^2 - (a^7 - a^5*b^2)*d + ((a^6*b - a^4*b^3)*d*cos(d*x + c)^2 - (a^6*b - a^4*b^3)*d)*sin(d*x + c))]","B",0
1084,1,1471,0,1.567935," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{6} - 7 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} b^{3} - 4 \, b^{5} + {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{2} - 4 \, a b^{4} - {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 12 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6} + {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6} + {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(a^{5} b - 13 \, a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{7} b - a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{7} b - a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{7} b - a^{5} b^{3}\right)} d - {\left({\left(a^{8} - a^{6} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} - a^{6} b^{2}\right)} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{2 \, {\left(a^{6} - 7 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(3 \, a^{2} b^{3} - 4 \, b^{5} + {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{2} - 4 \, a b^{4} - {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 12 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6} + {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6} + {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(a^{5} b - 13 \, a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{7} b - a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{7} b - a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{7} b - a^{5} b^{3}\right)} d - {\left({\left(a^{8} - a^{6} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} - a^{6} b^{2}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/6*(2*(a^6 - 7*a^4*b^2 + 6*a^2*b^4)*cos(d*x + c)^3 - 3*(3*a^2*b^3 - 4*b^5 + (3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - 2*(3*a^2*b^3 - 4*b^5)*cos(d*x + c)^2 + (3*a^3*b^2 - 4*a*b^4 - (3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 12*(a^4*b^2 - a^2*b^4)*cos(d*x + c) + 3*(a^4*b^2 - 5*a^2*b^4 + 4*b^6 + (a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 - 2*(a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^2 + (a^5*b - 5*a^3*b^3 + 4*a*b^5 - (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^4*b^2 - 5*a^2*b^4 + 4*b^6 + (a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 - 2*(a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^2 + (a^5*b - 5*a^3*b^3 + 4*a*b^5 - (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*((a^5*b - 13*a^3*b^3 + 12*a*b^5)*cos(d*x + c)^3 - 3*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b - a^5*b^3)*d*cos(d*x + c)^4 - 2*(a^7*b - a^5*b^3)*d*cos(d*x + c)^2 + (a^7*b - a^5*b^3)*d - ((a^8 - a^6*b^2)*d*cos(d*x + c)^2 - (a^8 - a^6*b^2)*d)*sin(d*x + c)), -1/6*(2*(a^6 - 7*a^4*b^2 + 6*a^2*b^4)*cos(d*x + c)^3 - 6*(3*a^2*b^3 - 4*b^5 + (3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - 2*(3*a^2*b^3 - 4*b^5)*cos(d*x + c)^2 + (3*a^3*b^2 - 4*a*b^4 - (3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 12*(a^4*b^2 - a^2*b^4)*cos(d*x + c) + 3*(a^4*b^2 - 5*a^2*b^4 + 4*b^6 + (a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 - 2*(a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^2 + (a^5*b - 5*a^3*b^3 + 4*a*b^5 - (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^4*b^2 - 5*a^2*b^4 + 4*b^6 + (a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 - 2*(a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^2 + (a^5*b - 5*a^3*b^3 + 4*a*b^5 - (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*((a^5*b - 13*a^3*b^3 + 12*a*b^5)*cos(d*x + c)^3 - 3*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b - a^5*b^3)*d*cos(d*x + c)^4 - 2*(a^7*b - a^5*b^3)*d*cos(d*x + c)^2 + (a^7*b - a^5*b^3)*d - ((a^8 - a^6*b^2)*d*cos(d*x + c)^2 - (a^8 - a^6*b^2)*d)*sin(d*x + c))]","B",0
1085,1,1058,0,1.552948," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(12 \, a^{6} b^{2} - 25 \, a^{4} b^{4} + 14 \, a^{2} b^{6} - b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(12 \, a^{8} - 13 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 13 \, a^{2} b^{6} - b^{8}\right)} d x + {\left(12 \, a^{7} - 7 \, a^{5} b^{2} - 13 \, a^{3} b^{4} + 6 \, a b^{6} - {\left(12 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{6} b - 19 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(12 \, a^{7} b - 19 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + 4 \, a b^{7}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(12 \, a^{7} b - 25 \, a^{5} b^{3} + 14 \, a^{3} b^{5} - a b^{7}\right)} d x + {\left(18 \, a^{6} b^{2} - 36 \, a^{4} b^{4} + 19 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{4} b^{7} - 2 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{6} - 2 \, a^{3} b^{8} + a b^{10}\right)} d \sin\left(d x + c\right) - {\left(a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9} + b^{11}\right)} d\right)}}, -\frac{{\left(12 \, a^{6} b^{2} - 25 \, a^{4} b^{4} + 14 \, a^{2} b^{6} - b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(12 \, a^{8} - 13 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 13 \, a^{2} b^{6} - b^{8}\right)} d x - {\left(12 \, a^{7} - 7 \, a^{5} b^{2} - 13 \, a^{3} b^{4} + 6 \, a b^{6} - {\left(12 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{6} b - 19 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(12 \, a^{7} b - 19 \, a^{5} b^{3} + 3 \, a^{3} b^{5} + 4 \, a b^{7}\right)} \cos\left(d x + c\right) - {\left({\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(12 \, a^{7} b - 25 \, a^{5} b^{3} + 14 \, a^{3} b^{5} - a b^{7}\right)} d x + {\left(18 \, a^{6} b^{2} - 36 \, a^{4} b^{4} + 19 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{7} - 2 \, a^{2} b^{9} + b^{11}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{6} - 2 \, a^{3} b^{8} + a b^{10}\right)} d \sin\left(d x + c\right) - {\left(a^{6} b^{5} - a^{4} b^{7} - a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[-1/4*(2*(12*a^6*b^2 - 25*a^4*b^4 + 14*a^2*b^6 - b^8)*d*x*cos(d*x + c)^2 + 8*(a^5*b^3 - 2*a^3*b^5 + a*b^7)*cos(d*x + c)^3 - 2*(12*a^8 - 13*a^6*b^2 - 11*a^4*b^4 + 13*a^2*b^6 - b^8)*d*x + (12*a^7 - 7*a^5*b^2 - 13*a^3*b^4 + 6*a*b^6 - (12*a^5*b^2 - 19*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + 2*(12*a^6*b - 19*a^4*b^3 + 6*a^2*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(12*a^7*b - 19*a^5*b^3 + 3*a^3*b^5 + 4*a*b^7)*cos(d*x + c) - 2*((a^4*b^4 - 2*a^2*b^6 + b^8)*cos(d*x + c)^3 + 2*(12*a^7*b - 25*a^5*b^3 + 14*a^3*b^5 - a*b^7)*d*x + (18*a^6*b^2 - 36*a^4*b^4 + 19*a^2*b^6 - b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^7 - 2*a^2*b^9 + b^11)*d*cos(d*x + c)^2 - 2*(a^5*b^6 - 2*a^3*b^8 + a*b^10)*d*sin(d*x + c) - (a^6*b^5 - a^4*b^7 - a^2*b^9 + b^11)*d), -1/2*((12*a^6*b^2 - 25*a^4*b^4 + 14*a^2*b^6 - b^8)*d*x*cos(d*x + c)^2 + 4*(a^5*b^3 - 2*a^3*b^5 + a*b^7)*cos(d*x + c)^3 - (12*a^8 - 13*a^6*b^2 - 11*a^4*b^4 + 13*a^2*b^6 - b^8)*d*x - (12*a^7 - 7*a^5*b^2 - 13*a^3*b^4 + 6*a*b^6 - (12*a^5*b^2 - 19*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + 2*(12*a^6*b - 19*a^4*b^3 + 6*a^2*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (12*a^7*b - 19*a^5*b^3 + 3*a^3*b^5 + 4*a*b^7)*cos(d*x + c) - ((a^4*b^4 - 2*a^2*b^6 + b^8)*cos(d*x + c)^3 + 2*(12*a^7*b - 25*a^5*b^3 + 14*a^3*b^5 - a*b^7)*d*x + (18*a^6*b^2 - 36*a^4*b^4 + 19*a^2*b^6 - b^8)*cos(d*x + c))*sin(d*x + c))/((a^4*b^7 - 2*a^2*b^9 + b^11)*d*cos(d*x + c)^2 - 2*(a^5*b^6 - 2*a^3*b^8 + a*b^10)*d*sin(d*x + c) - (a^6*b^5 - a^4*b^7 - a^2*b^9 + b^11)*d)]","A",0
1086,1,919,0,2.345652," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} - 12 \, {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d x - {\left(6 \, a^{6} - 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4} + 2 \, b^{6} - {\left(6 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b - 9 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(6 \, a^{6} b - 9 \, a^{4} b^{3} + a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right) - 2 \, {\left(12 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d x + {\left(9 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + 8 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d \sin\left(d x + c\right) - {\left(a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8} + b^{10}\right)} d\right)}}, \frac{6 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(a^{7} - a^{5} b^{2} - a^{3} b^{4} + a b^{6}\right)} d x - {\left(6 \, a^{6} - 3 \, a^{4} b^{2} - 7 \, a^{2} b^{4} + 2 \, b^{6} - {\left(6 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b - 9 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(6 \, a^{6} b - 9 \, a^{4} b^{3} + a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right) - {\left(12 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} d x + {\left(9 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + 8 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{6} - 2 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{5} - 2 \, a^{3} b^{7} + a b^{9}\right)} d \sin\left(d x + c\right) - {\left(a^{6} b^{4} - a^{4} b^{6} - a^{2} b^{8} + b^{10}\right)} d\right)}}\right]"," ",0,"[1/4*(12*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*d*x*cos(d*x + c)^2 + 4*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^3 - 12*(a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*x - (6*a^6 - 3*a^4*b^2 - 7*a^2*b^4 + 2*b^6 - (6*a^4*b^2 - 9*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(6*a^5*b - 9*a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(6*a^6*b - 9*a^4*b^3 + a^2*b^5 + 2*b^7)*cos(d*x + c) - 2*(12*(a^6*b - 2*a^4*b^3 + a^2*b^5)*d*x + (9*a^5*b^2 - 17*a^3*b^4 + 8*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - 2*(a^5*b^5 - 2*a^3*b^7 + a*b^9)*d*sin(d*x + c) - (a^6*b^4 - a^4*b^6 - a^2*b^8 + b^10)*d), 1/2*(6*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*d*x*cos(d*x + c)^2 + 2*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^3 - 6*(a^7 - a^5*b^2 - a^3*b^4 + a*b^6)*d*x - (6*a^6 - 3*a^4*b^2 - 7*a^2*b^4 + 2*b^6 - (6*a^4*b^2 - 9*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(6*a^5*b - 9*a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (6*a^6*b - 9*a^4*b^3 + a^2*b^5 + 2*b^7)*cos(d*x + c) - (12*(a^6*b - 2*a^4*b^3 + a^2*b^5)*d*x + (9*a^5*b^2 - 17*a^3*b^4 + 8*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^6 - 2*a^2*b^8 + b^10)*d*cos(d*x + c)^2 - 2*(a^5*b^5 - 2*a^3*b^7 + a*b^9)*d*sin(d*x + c) - (a^6*b^4 - a^4*b^6 - a^2*b^8 + b^10)*d)]","B",0
1087,1,793,0,0.929952," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d x \cos\left(d x + c\right)^{2} - 4 \, {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d x - {\left(2 \, a^{5} - a^{3} b^{2} - 3 \, a b^{4} - {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - 2 \, {\left(4 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x + {\left(3 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d \sin\left(d x + c\right) - {\left(a^{6} b^{3} - a^{4} b^{5} - a^{2} b^{7} + b^{9}\right)} d\right)}}, -\frac{2 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6}\right)} d x - {\left(2 \, a^{5} - a^{3} b^{2} - 3 \, a b^{4} - {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - {\left(4 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} d x + {\left(3 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{4} b^{5} - 2 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b^{4} - 2 \, a^{3} b^{6} + a b^{8}\right)} d \sin\left(d x + c\right) - {\left(a^{6} b^{3} - a^{4} b^{5} - a^{2} b^{7} + b^{9}\right)} d\right)}}\right]"," ",0,"[-1/4*(4*(a^4*b^2 - 2*a^2*b^4 + b^6)*d*x*cos(d*x + c)^2 - 4*(a^6 - a^4*b^2 - a^2*b^4 + b^6)*d*x - (2*a^5 - a^3*b^2 - 3*a*b^4 - (2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + 2*(2*a^4*b - 3*a^2*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(d*x + c) - 2*(4*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x + (3*a^4*b^2 - 5*a^2*b^4 + 2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c)^2 - 2*(a^5*b^4 - 2*a^3*b^6 + a*b^8)*d*sin(d*x + c) - (a^6*b^3 - a^4*b^5 - a^2*b^7 + b^9)*d), -1/2*(2*(a^4*b^2 - 2*a^2*b^4 + b^6)*d*x*cos(d*x + c)^2 - 2*(a^6 - a^4*b^2 - a^2*b^4 + b^6)*d*x - (2*a^5 - a^3*b^2 - 3*a*b^4 - (2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + 2*(2*a^4*b - 3*a^2*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(d*x + c) - (4*(a^5*b - 2*a^3*b^3 + a*b^5)*d*x + (3*a^4*b^2 - 5*a^2*b^4 + 2*b^6)*cos(d*x + c))*sin(d*x + c))/((a^4*b^5 - 2*a^2*b^7 + b^9)*d*cos(d*x + c)^2 - 2*(a^5*b^4 - 2*a^3*b^6 + a*b^8)*d*sin(d*x + c) - (a^6*b^3 - a^4*b^5 - a^2*b^7 + b^9)*d)]","B",0
1088,1,996,0,1.710539," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(3 \, a^{4} b + a^{2} b^{3} - 2 \, b^{5} - {\left(3 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) - 2 \, {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left({\left(a^{7} b^{2} - 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \sin\left(d x + c\right) - {\left(a^{9} - a^{7} b^{2} - a^{5} b^{4} + a^{3} b^{6}\right)} d\right)}}, -\frac{{\left(a^{5} b - 3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(3 \, a^{4} b + a^{2} b^{3} - 2 \, b^{5} - {\left(3 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - 2 \, a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left(2 \, a^{6} - 5 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) - {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{6} - a^{4} b^{2} - a^{2} b^{4} + b^{6} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left({\left(a^{7} b^{2} - 2 \, a^{5} b^{4} + a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{8} b - 2 \, a^{6} b^{3} + a^{4} b^{5}\right)} d \sin\left(d x + c\right) - {\left(a^{9} - a^{7} b^{2} - a^{5} b^{4} + a^{3} b^{6}\right)} d\right)}}\right]"," ",0,"[-1/4*(2*(a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(d*x + c)*sin(d*x + c) - (3*a^4*b + a^2*b^3 - 2*b^5 - (3*a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - 2*a*b^4)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(2*a^6 - 5*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c) - 2*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 2*(a^6 - a^4*b^2 - a^2*b^4 + b^6 - (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^7*b^2 - 2*a^5*b^4 + a^3*b^6)*d*cos(d*x + c)^2 - 2*(a^8*b - 2*a^6*b^3 + a^4*b^5)*d*sin(d*x + c) - (a^9 - a^7*b^2 - a^5*b^4 + a^3*b^6)*d), -1/2*((a^5*b - 3*a^3*b^3 + 2*a*b^5)*cos(d*x + c)*sin(d*x + c) + (3*a^4*b + a^2*b^3 - 2*b^5 - (3*a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - 2*a*b^4)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + (2*a^6 - 5*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c) - (a^6 - a^4*b^2 - a^2*b^4 + b^6 - (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^6 - a^4*b^2 - a^2*b^4 + b^6 - (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/((a^7*b^2 - 2*a^5*b^4 + a^3*b^6)*d*cos(d*x + c)^2 - 2*(a^8*b - 2*a^6*b^3 + a^4*b^5)*d*sin(d*x + c) - (a^9 - a^7*b^2 - a^5*b^4 + a^3*b^6)*d)]","B",0
1089,1,1394,0,2.007857," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(8 \, a^{6} b - 17 \, a^{4} b^{3} + 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(4 \, a^{5} b - 18 \, a^{3} b^{3} + 12 \, a b^{5} - 2 \, {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} - 7 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 6 \, b^{6} - {\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 6 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{7} + a^{5} b^{2} - 9 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right) + 6 \, {\left(2 \, a^{5} b^{2} - 4 \, a^{3} b^{4} + 2 \, a b^{6} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 6 \, {\left(2 \, a^{5} b^{2} - 4 \, a^{3} b^{4} + 2 \, a b^{6} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(2 \, {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d + {\left({\left(a^{8} b^{2} - 2 \, a^{6} b^{4} + a^{4} b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} - a^{8} b^{2} - a^{6} b^{4} + a^{4} b^{6}\right)} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{{\left(5 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(8 \, a^{6} b - 17 \, a^{4} b^{3} + 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(4 \, a^{5} b - 18 \, a^{3} b^{3} + 12 \, a b^{5} - 2 \, {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} - 7 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 6 \, b^{6} - {\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 6 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{7} + a^{5} b^{2} - 9 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right) + 3 \, {\left(2 \, a^{5} b^{2} - 4 \, a^{3} b^{4} + 2 \, a b^{6} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(2 \, a^{5} b^{2} - 4 \, a^{3} b^{4} + 2 \, a b^{6} - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{6} b - a^{4} b^{3} - a^{2} b^{5} + b^{7} - {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(2 \, {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{9} b - 2 \, a^{7} b^{3} + a^{5} b^{5}\right)} d + {\left({\left(a^{8} b^{2} - 2 \, a^{6} b^{4} + a^{4} b^{6}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} - a^{8} b^{2} - a^{6} b^{4} + a^{4} b^{6}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(2*(5*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^3 - 2*(8*a^6*b - 17*a^4*b^3 + 9*a^2*b^5)*cos(d*x + c)*sin(d*x + c) + (4*a^5*b - 18*a^3*b^3 + 12*a*b^5 - 2*(2*a^5*b - 9*a^3*b^3 + 6*a*b^5)*cos(d*x + c)^2 + (2*a^6 - 7*a^4*b^2 - 3*a^2*b^4 + 6*b^6 - (2*a^4*b^2 - 9*a^2*b^4 + 6*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^7 + a^5*b^2 - 9*a^3*b^4 + 6*a*b^6)*cos(d*x + c) + 6*(2*a^5*b^2 - 4*a^3*b^4 + 2*a*b^6 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + (a^6*b - a^4*b^3 - a^2*b^5 + b^7 - (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 6*(2*a^5*b^2 - 4*a^3*b^4 + 2*a*b^6 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + (a^6*b - a^4*b^3 - a^2*b^5 + b^7 - (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(2*(a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^2 - 2*(a^9*b - 2*a^7*b^3 + a^5*b^5)*d + ((a^8*b^2 - 2*a^6*b^4 + a^4*b^6)*d*cos(d*x + c)^2 - (a^10 - a^8*b^2 - a^6*b^4 + a^4*b^6)*d)*sin(d*x + c)), -1/2*((5*a^5*b^2 - 11*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^3 - (8*a^6*b - 17*a^4*b^3 + 9*a^2*b^5)*cos(d*x + c)*sin(d*x + c) + (4*a^5*b - 18*a^3*b^3 + 12*a*b^5 - 2*(2*a^5*b - 9*a^3*b^3 + 6*a*b^5)*cos(d*x + c)^2 + (2*a^6 - 7*a^4*b^2 - 3*a^2*b^4 + 6*b^6 - (2*a^4*b^2 - 9*a^2*b^4 + 6*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^7 + a^5*b^2 - 9*a^3*b^4 + 6*a*b^6)*cos(d*x + c) + 3*(2*a^5*b^2 - 4*a^3*b^4 + 2*a*b^6 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + (a^6*b - a^4*b^3 - a^2*b^5 + b^7 - (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(2*a^5*b^2 - 4*a^3*b^4 + 2*a*b^6 - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + (a^6*b - a^4*b^3 - a^2*b^5 + b^7 - (a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(2*(a^9*b - 2*a^7*b^3 + a^5*b^5)*d*cos(d*x + c)^2 - 2*(a^9*b - 2*a^7*b^3 + a^5*b^5)*d + ((a^8*b^2 - 2*a^6*b^4 + a^4*b^6)*d*cos(d*x + c)^2 - (a^10 - a^8*b^2 - a^6*b^4 + a^4*b^6)*d)*sin(d*x + c))]","B",0
1090,1,1922,0,2.411105," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(17 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(6 \, a^{6} b - 13 \, a^{4} b^{3} - 7 \, a^{2} b^{5} + 12 \, b^{7} + {\left(6 \, a^{4} b^{3} - 19 \, a^{2} b^{5} + 12 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(6 \, a^{6} b - 7 \, a^{4} b^{3} - 26 \, a^{2} b^{5} + 24 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 12 \, a b^{6} - {\left(6 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 12 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(a^{8} - 19 \, a^{6} b^{2} + 36 \, a^{4} b^{4} - 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right) - {\left(a^{8} - 13 \, a^{6} b^{2} + 11 \, a^{4} b^{4} + 13 \, a^{2} b^{6} - 12 \, b^{8} + {\left(a^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{8} - 12 \, a^{6} b^{2} - 3 \, a^{4} b^{4} + 38 \, a^{2} b^{6} - 24 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7} - {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{8} - 13 \, a^{6} b^{2} + 11 \, a^{4} b^{4} + 13 \, a^{2} b^{6} - 12 \, b^{8} + {\left(a^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{8} - 12 \, a^{6} b^{2} - 3 \, a^{4} b^{4} + 38 \, a^{2} b^{6} - 24 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7} - {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(11 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{7} b + 3 \, a^{5} b^{3} - 19 \, a^{3} b^{5} + 12 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{9} b^{2} - 2 \, a^{7} b^{4} + a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{11} - 3 \, a^{7} b^{4} + 2 \, a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{11} - a^{9} b^{2} - a^{7} b^{4} + a^{5} b^{6}\right)} d - 2 \, {\left({\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{2 \, {\left(17 \, a^{6} b^{2} - 35 \, a^{4} b^{4} + 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{6} b - 13 \, a^{4} b^{3} - 7 \, a^{2} b^{5} + 12 \, b^{7} + {\left(6 \, a^{4} b^{3} - 19 \, a^{2} b^{5} + 12 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(6 \, a^{6} b - 7 \, a^{4} b^{3} - 26 \, a^{2} b^{5} + 24 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 12 \, a b^{6} - {\left(6 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 12 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 2 \, {\left(a^{8} - 19 \, a^{6} b^{2} + 36 \, a^{4} b^{4} - 18 \, a^{2} b^{6}\right)} \cos\left(d x + c\right) - {\left(a^{8} - 13 \, a^{6} b^{2} + 11 \, a^{4} b^{4} + 13 \, a^{2} b^{6} - 12 \, b^{8} + {\left(a^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{8} - 12 \, a^{6} b^{2} - 3 \, a^{4} b^{4} + 38 \, a^{2} b^{6} - 24 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7} - {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{8} - 13 \, a^{6} b^{2} + 11 \, a^{4} b^{4} + 13 \, a^{2} b^{6} - 12 \, b^{8} + {\left(a^{6} b^{2} - 14 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - 12 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{8} - 12 \, a^{6} b^{2} - 3 \, a^{4} b^{4} + 38 \, a^{2} b^{6} - 24 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7} - {\left(a^{7} b - 14 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(11 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 12 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{7} b + 3 \, a^{5} b^{3} - 19 \, a^{3} b^{5} + 12 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{9} b^{2} - 2 \, a^{7} b^{4} + a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{11} - 3 \, a^{7} b^{4} + 2 \, a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{11} - a^{9} b^{2} - a^{7} b^{4} + a^{5} b^{6}\right)} d - 2 \, {\left({\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} b - 2 \, a^{8} b^{3} + a^{6} b^{5}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(2*(17*a^6*b^2 - 35*a^4*b^4 + 18*a^2*b^6)*cos(d*x + c)^3 - (6*a^6*b - 13*a^4*b^3 - 7*a^2*b^5 + 12*b^7 + (6*a^4*b^3 - 19*a^2*b^5 + 12*b^7)*cos(d*x + c)^4 - (6*a^6*b - 7*a^4*b^3 - 26*a^2*b^5 + 24*b^7)*cos(d*x + c)^2 + 2*(6*a^5*b^2 - 19*a^3*b^4 + 12*a*b^6 - (6*a^5*b^2 - 19*a^3*b^4 + 12*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(a^8 - 19*a^6*b^2 + 36*a^4*b^4 - 18*a^2*b^6)*cos(d*x + c) - (a^8 - 13*a^6*b^2 + 11*a^4*b^4 + 13*a^2*b^6 - 12*b^8 + (a^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*cos(d*x + c)^4 - (a^8 - 12*a^6*b^2 - 3*a^4*b^4 + 38*a^2*b^6 - 24*b^8)*cos(d*x + c)^2 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7 - (a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^8 - 13*a^6*b^2 + 11*a^4*b^4 + 13*a^2*b^6 - 12*b^8 + (a^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*cos(d*x + c)^4 - (a^8 - 12*a^6*b^2 - 3*a^4*b^4 + 38*a^2*b^6 - 24*b^8)*cos(d*x + c)^2 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7 - (a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*((11*a^5*b^3 - 23*a^3*b^5 + 12*a*b^7)*cos(d*x + c)^3 - (4*a^7*b + 3*a^5*b^3 - 19*a^3*b^5 + 12*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - 2*a^7*b^4 + a^5*b^6)*d*cos(d*x + c)^4 - (a^11 - 3*a^7*b^4 + 2*a^5*b^6)*d*cos(d*x + c)^2 + (a^11 - a^9*b^2 - a^7*b^4 + a^5*b^6)*d - 2*((a^10*b - 2*a^8*b^3 + a^6*b^5)*d*cos(d*x + c)^2 - (a^10*b - 2*a^8*b^3 + a^6*b^5)*d)*sin(d*x + c)), -1/4*(2*(17*a^6*b^2 - 35*a^4*b^4 + 18*a^2*b^6)*cos(d*x + c)^3 + 2*(6*a^6*b - 13*a^4*b^3 - 7*a^2*b^5 + 12*b^7 + (6*a^4*b^3 - 19*a^2*b^5 + 12*b^7)*cos(d*x + c)^4 - (6*a^6*b - 7*a^4*b^3 - 26*a^2*b^5 + 24*b^7)*cos(d*x + c)^2 + 2*(6*a^5*b^2 - 19*a^3*b^4 + 12*a*b^6 - (6*a^5*b^2 - 19*a^3*b^4 + 12*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 2*(a^8 - 19*a^6*b^2 + 36*a^4*b^4 - 18*a^2*b^6)*cos(d*x + c) - (a^8 - 13*a^6*b^2 + 11*a^4*b^4 + 13*a^2*b^6 - 12*b^8 + (a^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*cos(d*x + c)^4 - (a^8 - 12*a^6*b^2 - 3*a^4*b^4 + 38*a^2*b^6 - 24*b^8)*cos(d*x + c)^2 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7 - (a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (a^8 - 13*a^6*b^2 + 11*a^4*b^4 + 13*a^2*b^6 - 12*b^8 + (a^6*b^2 - 14*a^4*b^4 + 25*a^2*b^6 - 12*b^8)*cos(d*x + c)^4 - (a^8 - 12*a^6*b^2 - 3*a^4*b^4 + 38*a^2*b^6 - 24*b^8)*cos(d*x + c)^2 + 2*(a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7 - (a^7*b - 14*a^5*b^3 + 25*a^3*b^5 - 12*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*((11*a^5*b^3 - 23*a^3*b^5 + 12*a*b^7)*cos(d*x + c)^3 - (4*a^7*b + 3*a^5*b^3 - 19*a^3*b^5 + 12*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - 2*a^7*b^4 + a^5*b^6)*d*cos(d*x + c)^4 - (a^11 - 3*a^7*b^4 + 2*a^5*b^6)*d*cos(d*x + c)^2 + (a^11 - a^9*b^2 - a^7*b^4 + a^5*b^6)*d - 2*((a^10*b - 2*a^8*b^3 + a^6*b^5)*d*cos(d*x + c)^2 - (a^10*b - 2*a^8*b^3 + a^6*b^5)*d)*sin(d*x + c))]","B",0
1091,0,0,0,0.938532," ","integrate(cos(f*x+e)^2/(a+b*sin(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right)} \cos\left(f x + e\right)^{2}}{b^{3} d \cos\left(f x + e\right)^{4} - {\left(3 \, a^{2} b + 2 \, b^{3}\right)} d \cos\left(f x + e\right)^{2} + {\left(3 \, a^{2} b + b^{3}\right)} d - {\left(3 \, a b^{2} d \cos\left(f x + e\right)^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} d\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))*cos(f*x + e)^2/(b^3*d*cos(f*x + e)^4 - (3*a^2*b + 2*b^3)*d*cos(f*x + e)^2 + (3*a^2*b + b^3)*d - (3*a*b^2*d*cos(f*x + e)^2 - (a^3 + 3*a*b^2)*d)*sin(f*x + e)), x)","F",0
1092,1,95,0,0.949589," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4480 \, b \cos\left(d x + c\right)^{9} - 11520 \, b \cos\left(d x + c\right)^{7} + 8064 \, b \cos\left(d x + c\right)^{5} - 945 \, a d x - 315 \, {\left(16 \, a \cos\left(d x + c\right)^{7} - 24 \, a \cos\left(d x + c\right)^{5} + 2 \, a \cos\left(d x + c\right)^{3} + 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40320 \, d}"," ",0,"-1/40320*(4480*b*cos(d*x + c)^9 - 11520*b*cos(d*x + c)^7 + 8064*b*cos(d*x + c)^5 - 945*a*d*x - 315*(16*a*cos(d*x + c)^7 - 24*a*cos(d*x + c)^5 + 2*a*cos(d*x + c)^3 + 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
1093,1,84,0,0.966822," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{640 \, a \cos\left(d x + c\right)^{7} - 896 \, a \cos\left(d x + c\right)^{5} + 105 \, b d x + 35 \, {\left(16 \, b \cos\left(d x + c\right)^{7} - 24 \, b \cos\left(d x + c\right)^{5} + 2 \, b \cos\left(d x + c\right)^{3} + 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4480 \, d}"," ",0,"1/4480*(640*a*cos(d*x + c)^7 - 896*a*cos(d*x + c)^5 + 105*b*d*x + 35*(16*b*cos(d*x + c)^7 - 24*b*cos(d*x + c)^5 + 2*b*cos(d*x + c)^3 + 3*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1094,1,73,0,0.790220," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{240 \, b \cos\left(d x + c\right)^{7} - 336 \, b \cos\left(d x + c\right)^{5} + 105 \, a d x - 35 \, {\left(8 \, a \cos\left(d x + c\right)^{5} - 2 \, a \cos\left(d x + c\right)^{3} - 3 \, a \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, d}"," ",0,"1/1680*(240*b*cos(d*x + c)^7 - 336*b*cos(d*x + c)^5 + 105*a*d*x - 35*(8*a*cos(d*x + c)^5 - 2*a*cos(d*x + c)^3 - 3*a*cos(d*x + c))*sin(d*x + c))/d","A",0
1095,1,62,0,0.713790," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{48 \, a \cos\left(d x + c\right)^{5} - 15 \, b d x + 5 \, {\left(8 \, b \cos\left(d x + c\right)^{5} - 2 \, b \cos\left(d x + c\right)^{3} - 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(48*a*cos(d*x + c)^5 - 15*b*d*x + 5*(8*b*cos(d*x + c)^5 - 2*b*cos(d*x + c)^3 - 3*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1096,1,88,0,1.000290," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, a \cos\left(d x + c\right)^{3} + 9 \, b d x + 24 \, a \cos\left(d x + c\right) - 12 \, a \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, a \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(2 \, b \cos\left(d x + c\right)^{3} + 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"1/24*(8*a*cos(d*x + c)^3 + 9*b*d*x + 24*a*cos(d*x + c) - 12*a*log(1/2*cos(d*x + c) + 1/2) + 12*a*log(-1/2*cos(d*x + c) + 1/2) + 3*(2*b*cos(d*x + c)^3 + 3*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1097,1,107,0,0.981404," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a \cos\left(d x + c\right)^{3} - 3 \, b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, a \cos\left(d x + c\right) + {\left(2 \, b \cos\left(d x + c\right)^{3} - 9 \, a d x + 6 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, d \sin\left(d x + c\right)}"," ",0,"1/6*(3*a*cos(d*x + c)^3 - 3*b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*a*cos(d*x + c) + (2*b*cos(d*x + c)^3 - 9*a*d*x + 6*b*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
1098,1,139,0,0.994030," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, b d x \cos\left(d x + c\right)^{2} + 4 \, a \cos\left(d x + c\right)^{3} - 6 \, b d x - 6 \, a \cos\left(d x + c\right) - 3 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(b \cos\left(d x + c\right)^{3} - 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(6*b*d*x*cos(d*x + c)^2 + 4*a*cos(d*x + c)^3 - 6*b*d*x - 6*a*cos(d*x + c) - 3*(a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + 3*(a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2) + 2*(b*cos(d*x + c)^3 - 3*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
1099,1,160,0,1.138458," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, a \cos\left(d x + c\right)^{3} + 9 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 12 \, a \cos\left(d x + c\right) + 6 \, {\left(2 \, a d x \cos\left(d x + c\right)^{2} - 2 \, b \cos\left(d x + c\right)^{3} - 2 \, a d x + 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(16*a*cos(d*x + c)^3 + 9*(b*cos(d*x + c)^2 - b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*(b*cos(d*x + c)^2 - b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 12*a*cos(d*x + c) + 6*(2*a*d*x*cos(d*x + c)^2 - 2*b*cos(d*x + c)^3 - 2*a*d*x + 3*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
1100,1,180,0,1.094417," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{48 \, b d x \cos\left(d x + c\right)^{4} - 96 \, b d x \cos\left(d x + c\right)^{2} - 30 \, a \cos\left(d x + c\right)^{3} + 48 \, b d x + 18 \, a \cos\left(d x + c\right) - 9 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(4 \, b \cos\left(d x + c\right)^{3} - 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/48*(48*b*d*x*cos(d*x + c)^4 - 96*b*d*x*cos(d*x + c)^2 - 30*a*cos(d*x + c)^3 + 48*b*d*x + 18*a*cos(d*x + c) - 9*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 9*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2) - 16*(4*b*cos(d*x + c)^3 - 3*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
1101,1,160,0,1.032733," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a \cos\left(d x + c\right)^{5} + 15 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 10 \, {\left(5 \, b \cos\left(d x + c\right)^{3} - 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/80*(16*a*cos(d*x + c)^5 + 15*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 10*(5*b*cos(d*x + c)^3 - 3*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
1102,1,187,0,1.050982," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{96 \, b \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + 30 \, a \cos\left(d x + c\right)^{5} + 80 \, a \cos\left(d x + c\right)^{3} - 30 \, a \cos\left(d x + c\right) - 15 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} + 3 \, a \cos\left(d x + c\right)^{2} - a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/480*(96*b*cos(d*x + c)^5*sin(d*x + c) + 30*a*cos(d*x + c)^5 + 80*a*cos(d*x + c)^3 - 30*a*cos(d*x + c) - 15*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(1/2*cos(d*x + c) + 1/2) + 15*(a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 + 3*a*cos(d*x + c)^2 - a)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
1103,1,221,0,0.761626," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{192 \, a \cos\left(d x + c\right)^{7} - 672 \, a \cos\left(d x + c\right)^{5} + 105 \, {\left(b \cos\left(d x + c\right)^{6} - 3 \, b \cos\left(d x + c\right)^{4} + 3 \, b \cos\left(d x + c\right)^{2} - b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 105 \, {\left(b \cos\left(d x + c\right)^{6} - 3 \, b \cos\left(d x + c\right)^{4} + 3 \, b \cos\left(d x + c\right)^{2} - b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 70 \, {\left(3 \, b \cos\left(d x + c\right)^{5} + 8 \, b \cos\left(d x + c\right)^{3} - 3 \, b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3360 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/3360*(192*a*cos(d*x + c)^7 - 672*a*cos(d*x + c)^5 + 105*(b*cos(d*x + c)^6 - 3*b*cos(d*x + c)^4 + 3*b*cos(d*x + c)^2 - b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 105*(b*cos(d*x + c)^6 - 3*b*cos(d*x + c)^4 + 3*b*cos(d*x + c)^2 - b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 70*(3*b*cos(d*x + c)^5 + 8*b*cos(d*x + c)^3 - 3*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
1104,1,239,0,0.981712," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{210 \, a \cos\left(d x + c\right)^{7} - 770 \, a \cos\left(d x + c\right)^{5} - 770 \, a \cos\left(d x + c\right)^{3} + 210 \, a \cos\left(d x + c\right) - 105 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(a \cos\left(d x + c\right)^{8} - 4 \, a \cos\left(d x + c\right)^{6} + 6 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 256 \, {\left(2 \, b \cos\left(d x + c\right)^{7} - 7 \, b \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)}{8960 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/8960*(210*a*cos(d*x + c)^7 - 770*a*cos(d*x + c)^5 - 770*a*cos(d*x + c)^3 + 210*a*cos(d*x + c) - 105*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*log(1/2*cos(d*x + c) + 1/2) + 105*(a*cos(d*x + c)^8 - 4*a*cos(d*x + c)^6 + 6*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 + a)*log(-1/2*cos(d*x + c) + 1/2) + 256*(2*b*cos(d*x + c)^7 - 7*b*cos(d*x + c)^5)*sin(d*x + c))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
1105,1,116,0,0.781880," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2240 \, b^{2} \cos\left(d x + c\right)^{9} - 2880 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{7} + 4032 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{5} - 945 \, a b d x - 315 \, {\left(16 \, a b \cos\left(d x + c\right)^{7} - 24 \, a b \cos\left(d x + c\right)^{5} + 2 \, a b \cos\left(d x + c\right)^{3} + 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{20160 \, d}"," ",0,"-1/20160*(2240*b^2*cos(d*x + c)^9 - 2880*(a^2 + 2*b^2)*cos(d*x + c)^7 + 4032*(a^2 + b^2)*cos(d*x + c)^5 - 945*a*b*d*x - 315*(16*a*b*cos(d*x + c)^7 - 24*a*b*cos(d*x + c)^5 + 2*a*b*cos(d*x + c)^3 + 3*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1106,1,128,0,0.803324," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3840 \, a b \cos\left(d x + c\right)^{7} - 5376 \, a b \cos\left(d x + c\right)^{5} + 105 \, {\left(8 \, a^{2} + 3 \, b^{2}\right)} d x + 35 \, {\left(48 \, b^{2} \cos\left(d x + c\right)^{7} - 8 \, {\left(8 \, a^{2} + 9 \, b^{2}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{13440 \, d}"," ",0,"1/13440*(3840*a*b*cos(d*x + c)^7 - 5376*a*b*cos(d*x + c)^5 + 105*(8*a^2 + 3*b^2)*d*x + 35*(48*b^2*cos(d*x + c)^7 - 8*(8*a^2 + 9*b^2)*cos(d*x + c)^5 + 2*(8*a^2 + 3*b^2)*cos(d*x + c)^3 + 3*(8*a^2 + 3*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
1107,1,85,0,0.927289," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{120 \, b^{2} \cos\left(d x + c\right)^{7} - 168 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{5} + 105 \, a b d x - 35 \, {\left(8 \, a b \cos\left(d x + c\right)^{5} - 2 \, a b \cos\left(d x + c\right)^{3} - 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(120*b^2*cos(d*x + c)^7 - 168*(a^2 + b^2)*cos(d*x + c)^5 + 105*a*b*d*x - 35*(8*a*b*cos(d*x + c)^5 - 2*a*b*cos(d*x + c)^3 - 3*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1108,1,112,0,0.719240," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{12 \, b^{2} \cos\left(d x + c\right)^{5} - 20 \, a^{2} \cos\left(d x + c\right)^{3} - 45 \, a b d x - 60 \, a^{2} \cos\left(d x + c\right) + 30 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 30 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(2 \, a b \cos\left(d x + c\right)^{3} + 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(12*b^2*cos(d*x + c)^5 - 20*a^2*cos(d*x + c)^3 - 45*a*b*d*x - 60*a^2*cos(d*x + c) + 30*a^2*log(1/2*cos(d*x + c) + 1/2) - 30*a^2*log(-1/2*cos(d*x + c) + 1/2) - 15*(2*a*b*cos(d*x + c)^3 + 3*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1109,1,155,0,0.927649," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, b^{2} \cos\left(d x + c\right)^{5} - 3 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{3} + 24 \, a b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 24 \, a b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 9 \, {\left(4 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right) - {\left(16 \, a b \cos\left(d x + c\right)^{3} - 9 \, {\left(4 \, a^{2} - b^{2}\right)} d x + 48 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d \sin\left(d x + c\right)}"," ",0,"-1/24*(6*b^2*cos(d*x + c)^5 - 3*(4*a^2 - b^2)*cos(d*x + c)^3 + 24*a*b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 24*a*b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 9*(4*a^2 - b^2)*cos(d*x + c) - (16*a*b*cos(d*x + c)^3 - 9*(4*a^2 - b^2)*d*x + 48*a*b*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
1110,1,210,0,0.633142," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, b^{2} \cos\left(d x + c\right)^{5} - 36 \, a b d x \cos\left(d x + c\right)^{2} + 36 \, a b d x - 4 \, {\left(3 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(3 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left({\left(3 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, a^{2} + 2 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(3 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, a^{2} + 2 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 12 \, {\left(a b \cos\left(d x + c\right)^{3} - 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/12*(4*b^2*cos(d*x + c)^5 - 36*a*b*d*x*cos(d*x + c)^2 + 36*a*b*d*x - 4*(3*a^2 - 2*b^2)*cos(d*x + c)^3 + 6*(3*a^2 - 2*b^2)*cos(d*x + c) + 3*((3*a^2 - 2*b^2)*cos(d*x + c)^2 - 3*a^2 + 2*b^2)*log(1/2*cos(d*x + c) + 1/2) - 3*((3*a^2 - 2*b^2)*cos(d*x + c)^2 - 3*a^2 + 2*b^2)*log(-1/2*cos(d*x + c) + 1/2) - 12*(a*b*cos(d*x + c)^3 - 3*a*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
1111,1,218,0,0.740059," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cos\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 9 \, {\left(a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, {\left(a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left({\left(2 \, a^{2} - 3 \, b^{2}\right)} d x \cos\left(d x + c\right)^{2} - 4 \, a b \cos\left(d x + c\right)^{3} - {\left(2 \, a^{2} - 3 \, b^{2}\right)} d x + 6 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/6*(3*b^2*cos(d*x + c)^5 + 4*(2*a^2 - 3*b^2)*cos(d*x + c)^3 + 9*(a*b*cos(d*x + c)^2 - a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*(a*b*cos(d*x + c)^2 - a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(2*a^2 - 3*b^2)*cos(d*x + c) + 3*((2*a^2 - 3*b^2)*d*x*cos(d*x + c)^2 - 4*a*b*cos(d*x + c)^3 - (2*a^2 - 3*b^2)*d*x + 6*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1112,1,260,0,0.494994," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{96 \, a b d x \cos\left(d x + c\right)^{4} - 48 \, b^{2} \cos\left(d x + c\right)^{5} - 192 \, a b d x \cos\left(d x + c\right)^{2} + 96 \, a b d x - 30 \, {\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 18 \, {\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right) - 9 \, {\left({\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} - 4 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 9 \, {\left({\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} - 4 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left(4 \, a b \cos\left(d x + c\right)^{3} - 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/48*(96*a*b*d*x*cos(d*x + c)^4 - 48*b^2*cos(d*x + c)^5 - 192*a*b*d*x*cos(d*x + c)^2 + 96*a*b*d*x - 30*(a^2 - 4*b^2)*cos(d*x + c)^3 + 18*(a^2 - 4*b^2)*cos(d*x + c) - 9*((a^2 - 4*b^2)*cos(d*x + c)^4 - 2*(a^2 - 4*b^2)*cos(d*x + c)^2 + a^2 - 4*b^2)*log(1/2*cos(d*x + c) + 1/2) + 9*((a^2 - 4*b^2)*cos(d*x + c)^4 - 2*(a^2 - 4*b^2)*cos(d*x + c)^2 + a^2 - 4*b^2)*log(-1/2*cos(d*x + c) + 1/2) - 32*(4*a*b*cos(d*x + c)^3 - 3*a*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
1113,1,241,0,0.553952," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(3 \, a^{2} - 20 \, b^{2}\right)} \cos\left(d x + c\right)^{5} + 280 \, b^{2} \cos\left(d x + c\right)^{3} - 120 \, b^{2} \cos\left(d x + c\right) + 45 \, {\left(a b \cos\left(d x + c\right)^{4} - 2 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 45 \, {\left(a b \cos\left(d x + c\right)^{4} - 2 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left(4 \, b^{2} d x \cos\left(d x + c\right)^{4} - 8 \, b^{2} d x \cos\left(d x + c\right)^{2} - 5 \, a b \cos\left(d x + c\right)^{3} + 4 \, b^{2} d x + 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/120*(8*(3*a^2 - 20*b^2)*cos(d*x + c)^5 + 280*b^2*cos(d*x + c)^3 - 120*b^2*cos(d*x + c) + 45*(a*b*cos(d*x + c)^4 - 2*a*b*cos(d*x + c)^2 + a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 45*(a*b*cos(d*x + c)^4 - 2*a*b*cos(d*x + c)^2 + a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*(4*b^2*d*x*cos(d*x + c)^4 - 8*b^2*d*x*cos(d*x + c)^2 - 5*a*b*cos(d*x + c)^3 + 4*b^2*d*x + 3*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
1114,1,274,0,0.516426," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{192 \, a b \cos\left(d x + c\right)^{5} \sin\left(d x + c\right) + 30 \, {\left(a^{2} - 10 \, b^{2}\right)} \cos\left(d x + c\right)^{5} + 80 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right) - 15 \, {\left({\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} - 6 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left({\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 6 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} - 6 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/480*(192*a*b*cos(d*x + c)^5*sin(d*x + c) + 30*(a^2 - 10*b^2)*cos(d*x + c)^5 + 80*(a^2 + 6*b^2)*cos(d*x + c)^3 - 30*(a^2 + 6*b^2)*cos(d*x + c) - 15*((a^2 + 6*b^2)*cos(d*x + c)^6 - 3*(a^2 + 6*b^2)*cos(d*x + c)^4 + 3*(a^2 + 6*b^2)*cos(d*x + c)^2 - a^2 - 6*b^2)*log(1/2*cos(d*x + c) + 1/2) + 15*((a^2 + 6*b^2)*cos(d*x + c)^6 - 3*(a^2 + 6*b^2)*cos(d*x + c)^4 + 3*(a^2 + 6*b^2)*cos(d*x + c)^2 - a^2 - 6*b^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
1115,1,248,0,0.621919," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{48 \, {\left(2 \, a^{2} + 7 \, b^{2}\right)} \cos\left(d x + c\right)^{7} - 336 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{5} + 105 \, {\left(a b \cos\left(d x + c\right)^{6} - 3 \, a b \cos\left(d x + c\right)^{4} + 3 \, a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 105 \, {\left(a b \cos\left(d x + c\right)^{6} - 3 \, a b \cos\left(d x + c\right)^{4} + 3 \, a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 70 \, {\left(3 \, a b \cos\left(d x + c\right)^{5} + 8 \, a b \cos\left(d x + c\right)^{3} - 3 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/1680*(48*(2*a^2 + 7*b^2)*cos(d*x + c)^7 - 336*(a^2 + b^2)*cos(d*x + c)^5 + 105*(a*b*cos(d*x + c)^6 - 3*a*b*cos(d*x + c)^4 + 3*a*b*cos(d*x + c)^2 - a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 105*(a*b*cos(d*x + c)^6 - 3*a*b*cos(d*x + c)^4 + 3*a*b*cos(d*x + c)^2 - a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 70*(3*a*b*cos(d*x + c)^5 + 8*a*b*cos(d*x + c)^3 - 3*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1116,1,164,0,0.532365," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4480 \, b^{3} \cos\left(d x + c\right)^{9} - 5760 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{7} + 8064 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{5} - 315 \, {\left(8 \, a^{3} + 9 \, a b^{2}\right)} d x - 105 \, {\left(144 \, a b^{2} \cos\left(d x + c\right)^{7} - 8 \, {\left(8 \, a^{3} + 27 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{40320 \, d}"," ",0,"-1/40320*(4480*b^3*cos(d*x + c)^9 - 5760*(3*a^2*b + 2*b^3)*cos(d*x + c)^7 + 8064*(3*a^2*b + b^3)*cos(d*x + c)^5 - 315*(8*a^3 + 9*a*b^2)*d*x - 105*(144*a*b^2*cos(d*x + c)^7 - 8*(8*a^3 + 27*a*b^2)*cos(d*x + c)^5 + 2*(8*a^3 + 9*a*b^2)*cos(d*x + c)^3 + 3*(8*a^3 + 9*a*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
1117,1,136,0,0.799155," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{1920 \, a b^{2} \cos\left(d x + c\right)^{7} - 896 \, {\left(a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 105 \, {\left(8 \, a^{2} b + b^{3}\right)} d x + 35 \, {\left(16 \, b^{3} \cos\left(d x + c\right)^{7} - 8 \, {\left(8 \, a^{2} b + 3 \, b^{3}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4480 \, d}"," ",0,"1/4480*(1920*a*b^2*cos(d*x + c)^7 - 896*(a^3 + 3*a*b^2)*cos(d*x + c)^5 + 105*(8*a^2*b + b^3)*d*x + 35*(16*b^3*cos(d*x + c)^7 - 8*(8*a^2*b + 3*b^3)*cos(d*x + c)^5 + 2*(8*a^2*b + b^3)*cos(d*x + c)^3 + 3*(8*a^2*b + b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
1118,1,150,0,0.708490," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{144 \, a b^{2} \cos\left(d x + c\right)^{5} - 80 \, a^{3} \cos\left(d x + c\right)^{3} - 240 \, a^{3} \cos\left(d x + c\right) + 120 \, a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 120 \, a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(18 \, a^{2} b + b^{3}\right)} d x + 5 \, {\left(8 \, b^{3} \cos\left(d x + c\right)^{5} - 2 \, {\left(18 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(18 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"-1/240*(144*a*b^2*cos(d*x + c)^5 - 80*a^3*cos(d*x + c)^3 - 240*a^3*cos(d*x + c) + 120*a^3*log(1/2*cos(d*x + c) + 1/2) - 120*a^3*log(-1/2*cos(d*x + c) + 1/2) - 15*(18*a^2*b + b^3)*d*x + 5*(8*b^3*cos(d*x + c)^5 - 2*(18*a^2*b + b^3)*cos(d*x + c)^3 - 3*(18*a^2*b + b^3)*cos(d*x + c))*sin(d*x + c))/d","A",0
1119,1,179,0,0.669592," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{30 \, a b^{2} \cos\left(d x + c\right)^{5} + 60 \, a^{2} b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 60 \, a^{2} b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 5 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right) + {\left(8 \, b^{3} \cos\left(d x + c\right)^{5} - 40 \, a^{2} b \cos\left(d x + c\right)^{3} - 120 \, a^{2} b \cos\left(d x + c\right) + 15 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} d x\right)} \sin\left(d x + c\right)}{40 \, d \sin\left(d x + c\right)}"," ",0,"-1/40*(30*a*b^2*cos(d*x + c)^5 + 60*a^2*b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 60*a^2*b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 5*(4*a^3 - 3*a*b^2)*cos(d*x + c)^3 + 15*(4*a^3 - 3*a*b^2)*cos(d*x + c) + (8*b^3*cos(d*x + c)^5 - 40*a^2*b*cos(d*x + c)^3 - 120*a^2*b*cos(d*x + c) + 15*(4*a^3 - 3*a*b^2)*d*x)*sin(d*x + c))/(d*sin(d*x + c))","A",0
1120,1,260,0,0.743083," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, a b^{2} \cos\left(d x + c\right)^{5} - 3 \, {\left(12 \, a^{2} b - b^{3}\right)} d x \cos\left(d x + c\right)^{2} - 8 \, {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(12 \, a^{2} b - b^{3}\right)} d x + 12 \, {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right) - 6 \, {\left(a^{3} - 2 \, a b^{2} - {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 6 \, {\left(a^{3} - 2 \, a b^{2} - {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(2 \, b^{3} \cos\left(d x + c\right)^{5} - {\left(12 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(12 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/8*(8*a*b^2*cos(d*x + c)^5 - 3*(12*a^2*b - b^3)*d*x*cos(d*x + c)^2 - 8*(a^3 - 2*a*b^2)*cos(d*x + c)^3 + 3*(12*a^2*b - b^3)*d*x + 12*(a^3 - 2*a*b^2)*cos(d*x + c) - 6*(a^3 - 2*a*b^2 - (a^3 - 2*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 6*(a^3 - 2*a*b^2 - (a^3 - 2*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) + (2*b^3*cos(d*x + c)^5 - (12*a^2*b - b^3)*cos(d*x + c)^3 + 3*(12*a^2*b - b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
1121,1,293,0,0.657123," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{18 \, a b^{2} \cos\left(d x + c\right)^{5} + 8 \, {\left(2 \, a^{3} - 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(9 \, a^{2} b - 2 \, b^{3} - {\left(9 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(9 \, a^{2} b - 2 \, b^{3} - {\left(9 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 6 \, {\left(2 \, a^{3} - 9 \, a b^{2}\right)} \cos\left(d x + c\right) + 2 \, {\left(2 \, b^{3} \cos\left(d x + c\right)^{5} + 3 \, {\left(2 \, a^{3} - 9 \, a b^{2}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(9 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} - 9 \, a b^{2}\right)} d x + 3 \, {\left(9 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/12*(18*a*b^2*cos(d*x + c)^5 + 8*(2*a^3 - 9*a*b^2)*cos(d*x + c)^3 - 3*(9*a^2*b - 2*b^3 - (9*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(9*a^2*b - 2*b^3 - (9*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 6*(2*a^3 - 9*a*b^2)*cos(d*x + c) + 2*(2*b^3*cos(d*x + c)^5 + 3*(2*a^3 - 9*a*b^2)*d*x*cos(d*x + c)^2 - 2*(9*a^2*b - 2*b^3)*cos(d*x + c)^3 - 3*(2*a^3 - 9*a*b^2)*d*x + 3*(9*a^2*b - 2*b^3)*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1122,1,331,0,0.554245," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{48 \, a b^{2} \cos\left(d x + c\right)^{5} - 24 \, {\left(2 \, a^{2} b - b^{3}\right)} d x \cos\left(d x + c\right)^{4} + 48 \, {\left(2 \, a^{2} b - b^{3}\right)} d x \cos\left(d x + c\right)^{2} + 10 \, {\left(a^{3} - 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 24 \, {\left(2 \, a^{2} b - b^{3}\right)} d x - 6 \, {\left(a^{3} - 12 \, a b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left({\left(a^{3} - 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + a^{3} - 12 \, a b^{2} - 2 \, {\left(a^{3} - 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(a^{3} - 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + a^{3} - 12 \, a b^{2} - 2 \, {\left(a^{3} - 12 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 8 \, {\left(b^{3} \cos\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/16*(48*a*b^2*cos(d*x + c)^5 - 24*(2*a^2*b - b^3)*d*x*cos(d*x + c)^4 + 48*(2*a^2*b - b^3)*d*x*cos(d*x + c)^2 + 10*(a^3 - 12*a*b^2)*cos(d*x + c)^3 - 24*(2*a^2*b - b^3)*d*x - 6*(a^3 - 12*a*b^2)*cos(d*x + c) + 3*((a^3 - 12*a*b^2)*cos(d*x + c)^4 + a^3 - 12*a*b^2 - 2*(a^3 - 12*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - 3*((a^3 - 12*a*b^2)*cos(d*x + c)^4 + a^3 - 12*a*b^2 - 2*(a^3 - 12*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) + 8*(b^3*cos(d*x + c)^5 + 4*(2*a^2*b - b^3)*cos(d*x + c)^3 - 3*(2*a^2*b - b^3)*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
1123,1,334,0,0.598820," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{560 \, a b^{2} \cos\left(d x + c\right)^{3} + 16 \, {\left(a^{3} - 20 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} - 240 \, a b^{2} \cos\left(d x + c\right) + 15 \, {\left({\left(3 \, a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b - 4 \, b^{3} - 2 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left({\left(3 \, a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b - 4 \, b^{3} - 2 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 10 \, {\left(24 \, a b^{2} d x \cos\left(d x + c\right)^{4} - 8 \, b^{3} \cos\left(d x + c\right)^{5} - 48 \, a b^{2} d x \cos\left(d x + c\right)^{2} + 24 \, a b^{2} d x - 5 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/80*(560*a*b^2*cos(d*x + c)^3 + 16*(a^3 - 20*a*b^2)*cos(d*x + c)^5 - 240*a*b^2*cos(d*x + c) + 15*((3*a^2*b - 4*b^3)*cos(d*x + c)^4 + 3*a^2*b - 4*b^3 - 2*(3*a^2*b - 4*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*((3*a^2*b - 4*b^3)*cos(d*x + c)^4 + 3*a^2*b - 4*b^3 - 2*(3*a^2*b - 4*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 10*(24*a*b^2*d*x*cos(d*x + c)^4 - 8*b^3*cos(d*x + c)^5 - 48*a*b^2*d*x*cos(d*x + c)^2 + 24*a*b^2*d*x - 5*(3*a^2*b - 4*b^3)*cos(d*x + c)^3 + 3*(3*a^2*b - 4*b^3)*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
1124,1,373,0,0.672357," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{480 \, b^{3} d x \cos\left(d x + c\right)^{6} - 1440 \, b^{3} d x \cos\left(d x + c\right)^{4} + 1440 \, b^{3} d x \cos\left(d x + c\right)^{2} + 30 \, {\left(a^{3} - 30 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} - 480 \, b^{3} d x + 80 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right) - 15 \, {\left({\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} - a^{3} - 18 \, a b^{2} + 3 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left({\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} - a^{3} - 18 \, a b^{2} + 3 \, {\left(a^{3} + 18 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 32 \, {\left(35 \, b^{3} \cos\left(d x + c\right)^{3} + {\left(9 \, a^{2} b - 20 \, b^{3}\right)} \cos\left(d x + c\right)^{5} - 15 \, b^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/480*(480*b^3*d*x*cos(d*x + c)^6 - 1440*b^3*d*x*cos(d*x + c)^4 + 1440*b^3*d*x*cos(d*x + c)^2 + 30*(a^3 - 30*a*b^2)*cos(d*x + c)^5 - 480*b^3*d*x + 80*(a^3 + 18*a*b^2)*cos(d*x + c)^3 - 30*(a^3 + 18*a*b^2)*cos(d*x + c) - 15*((a^3 + 18*a*b^2)*cos(d*x + c)^6 - 3*(a^3 + 18*a*b^2)*cos(d*x + c)^4 - a^3 - 18*a*b^2 + 3*(a^3 + 18*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 15*((a^3 + 18*a*b^2)*cos(d*x + c)^6 - 3*(a^3 + 18*a*b^2)*cos(d*x + c)^4 - a^3 - 18*a*b^2 + 3*(a^3 + 18*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) + 32*(35*b^3*cos(d*x + c)^3 + (9*a^2*b - 20*b^3)*cos(d*x + c)^5 - 15*b^3*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
1125,1,347,0,0.614865," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{32 \, {\left(2 \, a^{3} + 21 \, a b^{2}\right)} \cos\left(d x + c\right)^{7} - 224 \, {\left(a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} + 105 \, {\left({\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - a^{2} b - 2 \, b^{3} + 3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 105 \, {\left({\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{4} - a^{2} b - 2 \, b^{3} + 3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 70 \, {\left({\left(3 \, a^{2} b - 10 \, b^{3}\right)} \cos\left(d x + c\right)^{5} + 8 \, {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1120 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/1120*(32*(2*a^3 + 21*a*b^2)*cos(d*x + c)^7 - 224*(a^3 + 3*a*b^2)*cos(d*x + c)^5 + 105*((a^2*b + 2*b^3)*cos(d*x + c)^6 - 3*(a^2*b + 2*b^3)*cos(d*x + c)^4 - a^2*b - 2*b^3 + 3*(a^2*b + 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 105*((a^2*b + 2*b^3)*cos(d*x + c)^6 - 3*(a^2*b + 2*b^3)*cos(d*x + c)^4 - a^2*b - 2*b^3 + 3*(a^2*b + 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 70*((3*a^2*b - 10*b^3)*cos(d*x + c)^5 + 8*(a^2*b + 2*b^3)*cos(d*x + c)^3 - 3*(a^2*b + 2*b^3)*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1126,1,384,0,0.652102," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{210 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{7} - 70 \, {\left(11 \, a^{3} - 40 \, a b^{2}\right)} \cos\left(d x + c\right)^{5} - 770 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 210 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right) - 105 \, {\left({\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{8} - 4 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + a^{3} + 8 \, a b^{2} - 4 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left({\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{8} - 4 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + a^{3} + 8 \, a b^{2} - 4 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 256 \, {\left({\left(6 \, a^{2} b + 7 \, b^{3}\right)} \cos\left(d x + c\right)^{7} - 7 \, {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)}{8960 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/8960*(210*(a^3 + 8*a*b^2)*cos(d*x + c)^7 - 70*(11*a^3 - 40*a*b^2)*cos(d*x + c)^5 - 770*(a^3 + 8*a*b^2)*cos(d*x + c)^3 + 210*(a^3 + 8*a*b^2)*cos(d*x + c) - 105*((a^3 + 8*a*b^2)*cos(d*x + c)^8 - 4*(a^3 + 8*a*b^2)*cos(d*x + c)^6 + 6*(a^3 + 8*a*b^2)*cos(d*x + c)^4 + a^3 + 8*a*b^2 - 4*(a^3 + 8*a*b^2)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 105*((a^3 + 8*a*b^2)*cos(d*x + c)^8 - 4*(a^3 + 8*a*b^2)*cos(d*x + c)^6 + 6*(a^3 + 8*a*b^2)*cos(d*x + c)^4 + a^3 + 8*a*b^2 - 4*(a^3 + 8*a*b^2)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) + 256*((6*a^2*b + 7*b^3)*cos(d*x + c)^7 - 7*(3*a^2*b + b^3)*cos(d*x + c)^5)*sin(d*x + c))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
1127,1,649,0,0.727830," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{6 \, a b^{5} \cos\left(d x + c\right)^{5} - 5 \, {\left(4 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(8 \, a^{6} - 8 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x - 30 \, {\left(2 \, a^{5} - a^{3} b^{2} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 15 \, {\left(8 \, a^{5} b - 8 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - {\left(4 \, b^{6} \cos\left(d x + c\right)^{5} - 10 \, a^{2} b^{4} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{5} b - 8 \, a^{3} b^{3} + a b^{5}\right)} d x + 15 \, {\left(4 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{20 \, {\left(b^{8} d \sin\left(d x + c\right) + a b^{7} d\right)}}, \frac{6 \, a b^{5} \cos\left(d x + c\right)^{5} - 5 \, {\left(4 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(8 \, a^{6} - 8 \, a^{4} b^{2} + a^{2} b^{4}\right)} d x - 60 \, {\left(2 \, a^{5} - a^{3} b^{2} + {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 15 \, {\left(8 \, a^{5} b - 8 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - {\left(4 \, b^{6} \cos\left(d x + c\right)^{5} - 10 \, a^{2} b^{4} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{5} b - 8 \, a^{3} b^{3} + a b^{5}\right)} d x + 15 \, {\left(4 \, a^{4} b^{2} - 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{20 \, {\left(b^{8} d \sin\left(d x + c\right) + a b^{7} d\right)}}\right]"," ",0,"[1/20*(6*a*b^5*cos(d*x + c)^5 - 5*(4*a^3*b^3 - a*b^5)*cos(d*x + c)^3 - 15*(8*a^6 - 8*a^4*b^2 + a^2*b^4)*d*x - 30*(2*a^5 - a^3*b^2 + (2*a^4*b - a^2*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 15*(8*a^5*b - 8*a^3*b^3 + a*b^5)*cos(d*x + c) - (4*b^6*cos(d*x + c)^5 - 10*a^2*b^4*cos(d*x + c)^3 + 15*(8*a^5*b - 8*a^3*b^3 + a*b^5)*d*x + 15*(4*a^4*b^2 - 3*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/(b^8*d*sin(d*x + c) + a*b^7*d), 1/20*(6*a*b^5*cos(d*x + c)^5 - 5*(4*a^3*b^3 - a*b^5)*cos(d*x + c)^3 - 15*(8*a^6 - 8*a^4*b^2 + a^2*b^4)*d*x - 60*(2*a^5 - a^3*b^2 + (2*a^4*b - a^2*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 15*(8*a^5*b - 8*a^3*b^3 + a*b^5)*cos(d*x + c) - (4*b^6*cos(d*x + c)^5 - 10*a^2*b^4*cos(d*x + c)^3 + 15*(8*a^5*b - 8*a^3*b^3 + a*b^5)*d*x + 15*(4*a^4*b^2 - 3*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/(b^8*d*sin(d*x + c) + a*b^7*d)]","A",0
1128,1,604,0,0.752266," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, b^{5} \cos\left(d x + c\right)^{5} - {\left(20 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(40 \, a^{5} - 36 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d x + 12 \, {\left(5 \, a^{4} - 2 \, a^{2} b^{2} + {\left(5 \, a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 3 \, {\left(40 \, a^{4} b - 36 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right) + {\left(10 \, a b^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(40 \, a^{4} b - 36 \, a^{2} b^{3} + 3 \, b^{5}\right)} d x - 3 \, {\left(20 \, a^{3} b^{2} - 13 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(b^{7} d \sin\left(d x + c\right) + a b^{6} d\right)}}, -\frac{6 \, b^{5} \cos\left(d x + c\right)^{5} - {\left(20 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(40 \, a^{5} - 36 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d x - 24 \, {\left(5 \, a^{4} - 2 \, a^{2} b^{2} + {\left(5 \, a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left(40 \, a^{4} b - 36 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right) + {\left(10 \, a b^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(40 \, a^{4} b - 36 \, a^{2} b^{3} + 3 \, b^{5}\right)} d x - 3 \, {\left(20 \, a^{3} b^{2} - 13 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(b^{7} d \sin\left(d x + c\right) + a b^{6} d\right)}}\right]"," ",0,"[-1/24*(6*b^5*cos(d*x + c)^5 - (20*a^2*b^3 - 3*b^5)*cos(d*x + c)^3 - 3*(40*a^5 - 36*a^3*b^2 + 3*a*b^4)*d*x + 12*(5*a^4 - 2*a^2*b^2 + (5*a^3*b - 2*a*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 3*(40*a^4*b - 36*a^2*b^3 + 3*b^5)*cos(d*x + c) + (10*a*b^4*cos(d*x + c)^3 - 3*(40*a^4*b - 36*a^2*b^3 + 3*b^5)*d*x - 3*(20*a^3*b^2 - 13*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^7*d*sin(d*x + c) + a*b^6*d), -1/24*(6*b^5*cos(d*x + c)^5 - (20*a^2*b^3 - 3*b^5)*cos(d*x + c)^3 - 3*(40*a^5 - 36*a^3*b^2 + 3*a*b^4)*d*x - 24*(5*a^4 - 2*a^2*b^2 + (5*a^3*b - 2*a*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*(40*a^4*b - 36*a^2*b^3 + 3*b^5)*cos(d*x + c) + (10*a*b^4*cos(d*x + c)^3 - 3*(40*a^4*b - 36*a^2*b^3 + 3*b^5)*d*x - 3*(20*a^3*b^2 - 13*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^7*d*sin(d*x + c) + a*b^6*d)]","A",0
1129,1,507,0,1.096810," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a b^{3} \cos\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} d x + 3 \, {\left(4 \, a^{3} - a b^{2} + {\left(4 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 6 \, {\left(4 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right) - 2 \, {\left(b^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} b - 3 \, a b^{3}\right)} d x - 3 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(b^{6} d \sin\left(d x + c\right) + a b^{5} d\right)}}, -\frac{2 \, a b^{3} \cos\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{4} - 3 \, a^{2} b^{2}\right)} d x + 3 \, {\left(4 \, a^{3} - a b^{2} + {\left(4 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 3 \, {\left(4 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right) - {\left(b^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} b - 3 \, a b^{3}\right)} d x - 3 \, {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3 \, {\left(b^{6} d \sin\left(d x + c\right) + a b^{5} d\right)}}\right]"," ",0,"[-1/6*(4*a*b^3*cos(d*x + c)^3 + 6*(4*a^4 - 3*a^2*b^2)*d*x + 3*(4*a^3 - a*b^2 + (4*a^2*b - b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 6*(4*a^3*b - 3*a*b^3)*cos(d*x + c) - 2*(b^4*cos(d*x + c)^3 - 3*(4*a^3*b - 3*a*b^3)*d*x - 3*(2*a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/(b^6*d*sin(d*x + c) + a*b^5*d), -1/3*(2*a*b^3*cos(d*x + c)^3 + 3*(4*a^4 - 3*a^2*b^2)*d*x + 3*(4*a^3 - a*b^2 + (4*a^2*b - b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 3*(4*a^3*b - 3*a*b^3)*cos(d*x + c) - (b^4*cos(d*x + c)^3 - 3*(4*a^3*b - 3*a*b^3)*d*x - 3*(2*a^2*b^2 - b^4)*cos(d*x + c))*sin(d*x + c))/(b^6*d*sin(d*x + c) + a*b^5*d)]","A",0
1130,1,516,0,1.268906," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{4} d x - {\left(2 \, a^{3} + a b^{2} + {\left(2 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) + {\left(b^{4} \sin\left(d x + c\right) + a b^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(b^{4} \sin\left(d x + c\right) + a b^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(2 \, a^{3} b d x + a^{2} b^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{4} d \sin\left(d x + c\right) + a^{3} b^{3} d\right)}}, -\frac{4 \, a^{4} d x + 2 \, {\left(2 \, a^{3} + a b^{2} + {\left(2 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 2 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) + {\left(b^{4} \sin\left(d x + c\right) + a b^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(b^{4} \sin\left(d x + c\right) + a b^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(2 \, a^{3} b d x + a^{2} b^{2} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{4} d \sin\left(d x + c\right) + a^{3} b^{3} d\right)}}\right]"," ",0,"[-1/2*(4*a^4*d*x - (2*a^3 + a*b^2 + (2*a^2*b + b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(2*a^3*b - a*b^3)*cos(d*x + c) + (b^4*sin(d*x + c) + a*b^3)*log(1/2*cos(d*x + c) + 1/2) - (b^4*sin(d*x + c) + a*b^3)*log(-1/2*cos(d*x + c) + 1/2) + 2*(2*a^3*b*d*x + a^2*b^2*cos(d*x + c))*sin(d*x + c))/(a^2*b^4*d*sin(d*x + c) + a^3*b^3*d), -1/2*(4*a^4*d*x + 2*(2*a^3 + a*b^2 + (2*a^2*b + b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 2*(2*a^3*b - a*b^3)*cos(d*x + c) + (b^4*sin(d*x + c) + a*b^3)*log(1/2*cos(d*x + c) + 1/2) - (b^4*sin(d*x + c) + a*b^3)*log(-1/2*cos(d*x + c) + 1/2) + 2*(2*a^3*b*d*x + a^2*b^2*cos(d*x + c))*sin(d*x + c))/(a^2*b^4*d*sin(d*x + c) + a^3*b^3*d)]","A",0
1131,1,675,0,1.242518," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{3} b d x \cos\left(d x + c\right)^{2} - 2 \, a^{3} b d x + 2 \, a^{2} b^{2} \cos\left(d x + c\right) - {\left(a^{2} b + 2 \, b^{3} - {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left(b^{4} \cos\left(d x + c\right)^{2} - a b^{3} \sin\left(d x + c\right) - b^{4}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(b^{4} \cos\left(d x + c\right)^{2} - a b^{3} \sin\left(d x + c\right) - b^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{4} d x + {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{3} b^{3} d \cos\left(d x + c\right)^{2} - a^{4} b^{2} d \sin\left(d x + c\right) - a^{3} b^{3} d\right)}}, \frac{a^{3} b d x \cos\left(d x + c\right)^{2} - a^{3} b d x + a^{2} b^{2} \cos\left(d x + c\right) - {\left(a^{2} b + 2 \, b^{3} - {\left(a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} + 2 \, a b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left(b^{4} \cos\left(d x + c\right)^{2} - a b^{3} \sin\left(d x + c\right) - b^{4}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(b^{4} \cos\left(d x + c\right)^{2} - a b^{3} \sin\left(d x + c\right) - b^{4}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{4} d x + {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{a^{3} b^{3} d \cos\left(d x + c\right)^{2} - a^{4} b^{2} d \sin\left(d x + c\right) - a^{3} b^{3} d}\right]"," ",0,"[1/2*(2*a^3*b*d*x*cos(d*x + c)^2 - 2*a^3*b*d*x + 2*a^2*b^2*cos(d*x + c) - (a^2*b + 2*b^3 - (a^2*b + 2*b^3)*cos(d*x + c)^2 + (a^3 + 2*a*b^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*(b^4*cos(d*x + c)^2 - a*b^3*sin(d*x + c) - b^4)*log(1/2*cos(d*x + c) + 1/2) - 2*(b^4*cos(d*x + c)^2 - a*b^3*sin(d*x + c) - b^4)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^4*d*x + (a^3*b - 2*a*b^3)*cos(d*x + c))*sin(d*x + c))/(a^3*b^3*d*cos(d*x + c)^2 - a^4*b^2*d*sin(d*x + c) - a^3*b^3*d), (a^3*b*d*x*cos(d*x + c)^2 - a^3*b*d*x + a^2*b^2*cos(d*x + c) - (a^2*b + 2*b^3 - (a^2*b + 2*b^3)*cos(d*x + c)^2 + (a^3 + 2*a*b^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + (b^4*cos(d*x + c)^2 - a*b^3*sin(d*x + c) - b^4)*log(1/2*cos(d*x + c) + 1/2) - (b^4*cos(d*x + c)^2 - a*b^3*sin(d*x + c) - b^4)*log(-1/2*cos(d*x + c) + 1/2) - (a^4*d*x + (a^3*b - 2*a*b^3)*cos(d*x + c))*sin(d*x + c))/(a^3*b^3*d*cos(d*x + c)^2 - a^4*b^2*d*sin(d*x + c) - a^3*b^3*d)]","A",0
1132,1,804,0,1.045609," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, a^{2} b \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(a b \cos\left(d x + c\right)^{2} - a b + {\left(b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left(a^{3} - 2 \, a b^{2} - {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{3} - 2 \, a b^{2} - {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(a^{5} d \cos\left(d x + c\right)^{2} - a^{5} d + {\left(a^{4} b d \cos\left(d x + c\right)^{2} - a^{4} b d\right)} \sin\left(d x + c\right)\right)}}, -\frac{6 \, a^{2} b \cos\left(d x + c\right) \sin\left(d x + c\right) + 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(a b \cos\left(d x + c\right)^{2} - a b + {\left(b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 6 \, {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left(a^{3} - 2 \, a b^{2} - {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{3} - 2 \, a b^{2} - {\left(a^{3} - 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(a^{5} d \cos\left(d x + c\right)^{2} - a^{5} d + {\left(a^{4} b d \cos\left(d x + c\right)^{2} - a^{4} b d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(6*a^2*b*cos(d*x + c)*sin(d*x + c) + 4*(a^3 - 3*a*b^2)*cos(d*x + c)^3 - 6*(a*b*cos(d*x + c)^2 - a*b + (b^2*cos(d*x + c)^2 - b^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(a^3 - 2*a*b^2)*cos(d*x + c) + 3*(a^3 - 2*a*b^2 - (a^3 - 2*a*b^2)*cos(d*x + c)^2 + (a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^3 - 2*a*b^2 - (a^3 - 2*a*b^2)*cos(d*x + c)^2 + (a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(a^5*d*cos(d*x + c)^2 - a^5*d + (a^4*b*d*cos(d*x + c)^2 - a^4*b*d)*sin(d*x + c)), -1/4*(6*a^2*b*cos(d*x + c)*sin(d*x + c) + 4*(a^3 - 3*a*b^2)*cos(d*x + c)^3 + 12*(a*b*cos(d*x + c)^2 - a*b + (b^2*cos(d*x + c)^2 - b^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 6*(a^3 - 2*a*b^2)*cos(d*x + c) + 3*(a^3 - 2*a*b^2 - (a^3 - 2*a*b^2)*cos(d*x + c)^2 + (a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^3 - 2*a*b^2 - (a^3 - 2*a*b^2)*cos(d*x + c)^2 + (a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(a^5*d*cos(d*x + c)^2 - a^5*d + (a^4*b*d*cos(d*x + c)^2 - a^4*b*d)*sin(d*x + c))]","B",0
1133,1,1149,0,1.341351," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + a^{2} b - 4 \, b^{3} - 2 \, {\left(a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} - 4 \, a b^{2} - {\left(a^{3} - 4 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left({\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} - 4 \, b^{4} - 2 \, {\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b - 4 \, a b^{3} - {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} - 4 \, b^{4} - 2 \, {\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b - 4 \, a b^{3} - {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(7 \, a^{3} b - 12 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{5} b d \cos\left(d x + c\right)^{4} - 2 \, a^{5} b d \cos\left(d x + c\right)^{2} + a^{5} b d - {\left(a^{6} d \cos\left(d x + c\right)^{2} - a^{6} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{4 \, {\left(2 \, a^{4} - 3 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left({\left(a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + a^{2} b - 4 \, b^{3} - 2 \, {\left(a^{2} b - 4 \, b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} - 4 \, a b^{2} - {\left(a^{3} - 4 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 6 \, {\left(a^{4} - 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left({\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} - 4 \, b^{4} - 2 \, {\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b - 4 \, a b^{3} - {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} - 4 \, b^{4} - 2 \, {\left(3 \, a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{3} b - 4 \, a b^{3} - {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(7 \, a^{3} b - 12 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{5} b d \cos\left(d x + c\right)^{4} - 2 \, a^{5} b d \cos\left(d x + c\right)^{2} + a^{5} b d - {\left(a^{6} d \cos\left(d x + c\right)^{2} - a^{6} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/6*(4*(2*a^4 - 3*a^2*b^2)*cos(d*x + c)^3 + 3*((a^2*b - 4*b^3)*cos(d*x + c)^4 + a^2*b - 4*b^3 - 2*(a^2*b - 4*b^3)*cos(d*x + c)^2 + (a^3 - 4*a*b^2 - (a^3 - 4*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(a^4 - 2*a^2*b^2)*cos(d*x + c) + 3*((3*a^2*b^2 - 4*b^4)*cos(d*x + c)^4 + 3*a^2*b^2 - 4*b^4 - 2*(3*a^2*b^2 - 4*b^4)*cos(d*x + c)^2 + (3*a^3*b - 4*a*b^3 - (3*a^3*b - 4*a*b^3)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*((3*a^2*b^2 - 4*b^4)*cos(d*x + c)^4 + 3*a^2*b^2 - 4*b^4 - 2*(3*a^2*b^2 - 4*b^4)*cos(d*x + c)^2 + (3*a^3*b - 4*a*b^3 - (3*a^3*b - 4*a*b^3)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*((7*a^3*b - 12*a*b^3)*cos(d*x + c)^3 - 3*(3*a^3*b - 4*a*b^3)*cos(d*x + c))*sin(d*x + c))/(a^5*b*d*cos(d*x + c)^4 - 2*a^5*b*d*cos(d*x + c)^2 + a^5*b*d - (a^6*d*cos(d*x + c)^2 - a^6*d)*sin(d*x + c)), -1/6*(4*(2*a^4 - 3*a^2*b^2)*cos(d*x + c)^3 + 6*((a^2*b - 4*b^3)*cos(d*x + c)^4 + a^2*b - 4*b^3 - 2*(a^2*b - 4*b^3)*cos(d*x + c)^2 + (a^3 - 4*a*b^2 - (a^3 - 4*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 6*(a^4 - 2*a^2*b^2)*cos(d*x + c) + 3*((3*a^2*b^2 - 4*b^4)*cos(d*x + c)^4 + 3*a^2*b^2 - 4*b^4 - 2*(3*a^2*b^2 - 4*b^4)*cos(d*x + c)^2 + (3*a^3*b - 4*a*b^3 - (3*a^3*b - 4*a*b^3)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*((3*a^2*b^2 - 4*b^4)*cos(d*x + c)^4 + 3*a^2*b^2 - 4*b^4 - 2*(3*a^2*b^2 - 4*b^4)*cos(d*x + c)^2 + (3*a^3*b - 4*a*b^3 - (3*a^3*b - 4*a*b^3)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*((7*a^3*b - 12*a*b^3)*cos(d*x + c)^3 - 3*(3*a^3*b - 4*a*b^3)*cos(d*x + c))*sin(d*x + c))/(a^5*b*d*cos(d*x + c)^4 - 2*a^5*b*d*cos(d*x + c)^2 + a^5*b*d - (a^6*d*cos(d*x + c)^2 - a^6*d)*sin(d*x + c))]","B",0
1134,1,1578,0,1.398298," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{16 \, {\left(11 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{5} - 196 \, a^{3} b^{2} + 240 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 24 \, {\left({\left(2 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{4} + 2 \, a^{3} b - 5 \, a b^{3} - 2 \, {\left(2 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, a^{2} b^{2} - 5 \, b^{4} - 2 \, {\left(2 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4} + {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5} + {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4} + {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5} + {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(49 \, a^{4} b - 60 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(13 \, a^{4} b - 20 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{7} d \cos\left(d x + c\right)^{4} - 2 \, a^{7} d \cos\left(d x + c\right)^{2} + a^{7} d + {\left(a^{6} b d \cos\left(d x + c\right)^{4} - 2 \, a^{6} b d \cos\left(d x + c\right)^{2} + a^{6} b d\right)} \sin\left(d x + c\right)\right)}}, -\frac{16 \, {\left(11 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{5} - 196 \, a^{3} b^{2} + 240 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 48 \, {\left({\left(2 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{4} + 2 \, a^{3} b - 5 \, a b^{3} - 2 \, {\left(2 \, a^{3} b - 5 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 2 \, a^{2} b^{2} - 5 \, b^{4} - 2 \, {\left(2 \, a^{2} b^{2} - 5 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 6 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4} + {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5} + {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4} + {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 36 \, a^{3} b^{2} + 40 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5} + {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 36 \, a^{2} b^{3} + 40 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(49 \, a^{4} b - 60 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(13 \, a^{4} b - 20 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{7} d \cos\left(d x + c\right)^{4} - 2 \, a^{7} d \cos\left(d x + c\right)^{2} + a^{7} d + {\left(a^{6} b d \cos\left(d x + c\right)^{4} - 2 \, a^{6} b d \cos\left(d x + c\right)^{2} + a^{6} b d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/48*(16*(11*a^3*b^2 - 15*a*b^4)*cos(d*x + c)^5 + 2*(15*a^5 - 196*a^3*b^2 + 240*a*b^4)*cos(d*x + c)^3 + 24*((2*a^3*b - 5*a*b^3)*cos(d*x + c)^4 + 2*a^3*b - 5*a*b^3 - 2*(2*a^3*b - 5*a*b^3)*cos(d*x + c)^2 + ((2*a^2*b^2 - 5*b^4)*cos(d*x + c)^4 + 2*a^2*b^2 - 5*b^4 - 2*(2*a^2*b^2 - 5*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c) + 3*(3*a^5 - 36*a^3*b^2 + 40*a*b^4 + (3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - 36*a^2*b^3 + 40*b^5 + (3*a^4*b - 36*a^2*b^3 + 40*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 36*a^2*b^3 + 40*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(3*a^5 - 36*a^3*b^2 + 40*a*b^4 + (3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - 36*a^2*b^3 + 40*b^5 + (3*a^4*b - 36*a^2*b^3 + 40*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 36*a^2*b^3 + 40*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*((49*a^4*b - 60*a^2*b^3)*cos(d*x + c)^3 - 3*(13*a^4*b - 20*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(a^7*d*cos(d*x + c)^4 - 2*a^7*d*cos(d*x + c)^2 + a^7*d + (a^6*b*d*cos(d*x + c)^4 - 2*a^6*b*d*cos(d*x + c)^2 + a^6*b*d)*sin(d*x + c)), -1/48*(16*(11*a^3*b^2 - 15*a*b^4)*cos(d*x + c)^5 + 2*(15*a^5 - 196*a^3*b^2 + 240*a*b^4)*cos(d*x + c)^3 - 48*((2*a^3*b - 5*a*b^3)*cos(d*x + c)^4 + 2*a^3*b - 5*a*b^3 - 2*(2*a^3*b - 5*a*b^3)*cos(d*x + c)^2 + ((2*a^2*b^2 - 5*b^4)*cos(d*x + c)^4 + 2*a^2*b^2 - 5*b^4 - 2*(2*a^2*b^2 - 5*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 6*(3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c) + 3*(3*a^5 - 36*a^3*b^2 + 40*a*b^4 + (3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - 36*a^2*b^3 + 40*b^5 + (3*a^4*b - 36*a^2*b^3 + 40*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 36*a^2*b^3 + 40*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(3*a^5 - 36*a^3*b^2 + 40*a*b^4 + (3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 36*a^3*b^2 + 40*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - 36*a^2*b^3 + 40*b^5 + (3*a^4*b - 36*a^2*b^3 + 40*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 36*a^2*b^3 + 40*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*((49*a^4*b - 60*a^2*b^3)*cos(d*x + c)^3 - 3*(13*a^4*b - 20*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(a^7*d*cos(d*x + c)^4 - 2*a^7*d*cos(d*x + c)^2 + a^7*d + (a^6*b*d*cos(d*x + c)^4 - 2*a^6*b*d*cos(d*x + c)^2 + a^6*b*d)*sin(d*x + c))]","B",0
1135,1,1110,0,1.085112," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right)^{5} - 3 \, {\left(40 \, a^{6} b^{2} - 64 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - b^{8}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(20 \, a^{5} b^{3} - 27 \, a^{3} b^{5} + 7 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(40 \, a^{8} - 24 \, a^{6} b^{2} - 39 \, a^{4} b^{4} + 24 \, a^{2} b^{6} - b^{8}\right)} d x - 6 \, {\left(10 \, a^{7} - a^{5} b^{2} - 9 \, a^{3} b^{4} + 2 \, a b^{6} - {\left(10 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(10 \, a^{6} b - 11 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 6 \, {\left(20 \, a^{7} b - 22 \, a^{5} b^{3} - a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right) - {\left(2 \, {\left(a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{5} - {\left(10 \, a^{4} b^{4} - 11 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(40 \, a^{7} b - 64 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - a b^{7}\right)} d x - 3 \, {\left(60 \, a^{6} b^{2} - 91 \, a^{4} b^{4} + 32 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left({\left(a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{8} - a b^{10}\right)} d \sin\left(d x + c\right) - {\left(a^{4} b^{7} - b^{11}\right)} d\right)}}, -\frac{4 \, {\left(a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right)^{5} - 3 \, {\left(40 \, a^{6} b^{2} - 64 \, a^{4} b^{4} + 25 \, a^{2} b^{6} - b^{8}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(20 \, a^{5} b^{3} - 27 \, a^{3} b^{5} + 7 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(40 \, a^{8} - 24 \, a^{6} b^{2} - 39 \, a^{4} b^{4} + 24 \, a^{2} b^{6} - b^{8}\right)} d x + 12 \, {\left(10 \, a^{7} - a^{5} b^{2} - 9 \, a^{3} b^{4} + 2 \, a b^{6} - {\left(10 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(10 \, a^{6} b - 11 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 6 \, {\left(20 \, a^{7} b - 22 \, a^{5} b^{3} - a^{3} b^{5} + 3 \, a b^{7}\right)} \cos\left(d x + c\right) - {\left(2 \, {\left(a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{5} - {\left(10 \, a^{4} b^{4} - 11 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(40 \, a^{7} b - 64 \, a^{5} b^{3} + 25 \, a^{3} b^{5} - a b^{7}\right)} d x - 3 \, {\left(60 \, a^{6} b^{2} - 91 \, a^{4} b^{4} + 32 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left({\left(a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{8} - a b^{10}\right)} d \sin\left(d x + c\right) - {\left(a^{4} b^{7} - b^{11}\right)} d\right)}}\right]"," ",0,"[-1/8*(4*(a^3*b^5 - a*b^7)*cos(d*x + c)^5 - 3*(40*a^6*b^2 - 64*a^4*b^4 + 25*a^2*b^6 - b^8)*d*x*cos(d*x + c)^2 - 2*(20*a^5*b^3 - 27*a^3*b^5 + 7*a*b^7)*cos(d*x + c)^3 + 3*(40*a^8 - 24*a^6*b^2 - 39*a^4*b^4 + 24*a^2*b^6 - b^8)*d*x - 6*(10*a^7 - a^5*b^2 - 9*a^3*b^4 + 2*a*b^6 - (10*a^5*b^2 - 11*a^3*b^4 + 2*a*b^6)*cos(d*x + c)^2 + 2*(10*a^6*b - 11*a^4*b^3 + 2*a^2*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 6*(20*a^7*b - 22*a^5*b^3 - a^3*b^5 + 3*a*b^7)*cos(d*x + c) - (2*(a^2*b^6 - b^8)*cos(d*x + c)^5 - (10*a^4*b^4 - 11*a^2*b^6 + b^8)*cos(d*x + c)^3 - 6*(40*a^7*b - 64*a^5*b^3 + 25*a^3*b^5 - a*b^7)*d*x - 3*(60*a^6*b^2 - 91*a^4*b^4 + 32*a^2*b^6 - b^8)*cos(d*x + c))*sin(d*x + c))/((a^2*b^9 - b^11)*d*cos(d*x + c)^2 - 2*(a^3*b^8 - a*b^10)*d*sin(d*x + c) - (a^4*b^7 - b^11)*d), -1/8*(4*(a^3*b^5 - a*b^7)*cos(d*x + c)^5 - 3*(40*a^6*b^2 - 64*a^4*b^4 + 25*a^2*b^6 - b^8)*d*x*cos(d*x + c)^2 - 2*(20*a^5*b^3 - 27*a^3*b^5 + 7*a*b^7)*cos(d*x + c)^3 + 3*(40*a^8 - 24*a^6*b^2 - 39*a^4*b^4 + 24*a^2*b^6 - b^8)*d*x + 12*(10*a^7 - a^5*b^2 - 9*a^3*b^4 + 2*a*b^6 - (10*a^5*b^2 - 11*a^3*b^4 + 2*a*b^6)*cos(d*x + c)^2 + 2*(10*a^6*b - 11*a^4*b^3 + 2*a^2*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 6*(20*a^7*b - 22*a^5*b^3 - a^3*b^5 + 3*a*b^7)*cos(d*x + c) - (2*(a^2*b^6 - b^8)*cos(d*x + c)^5 - (10*a^4*b^4 - 11*a^2*b^6 + b^8)*cos(d*x + c)^3 - 6*(40*a^7*b - 64*a^5*b^3 + 25*a^3*b^5 - a*b^7)*d*x - 3*(60*a^6*b^2 - 91*a^4*b^4 + 32*a^2*b^6 - b^8)*cos(d*x + c))*sin(d*x + c))/((a^2*b^9 - b^11)*d*cos(d*x + c)^2 - 2*(a^3*b^8 - a*b^10)*d*sin(d*x + c) - (a^4*b^7 - b^11)*d)]","A",0
1136,1,976,0,0.971131," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{5} - 6 \, {\left(20 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 9 \, a b^{6}\right)} d x \cos\left(d x + c\right)^{2} - 8 \, {\left(5 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(20 \, a^{7} - 9 \, a^{5} b^{2} - 20 \, a^{3} b^{4} + 9 \, a b^{6}\right)} d x + 3 \, {\left(20 \, a^{6} + a^{4} b^{2} - 17 \, a^{2} b^{4} + 2 \, b^{6} - {\left(20 \, a^{4} b^{2} - 19 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{5} b - 19 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 6 \, {\left(20 \, a^{6} b - 19 \, a^{4} b^{3} - 3 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right) + 2 \, {\left(5 \, {\left(a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(20 \, a^{6} b - 29 \, a^{4} b^{3} + 9 \, a^{2} b^{5}\right)} d x + 3 \, {\left(30 \, a^{5} b^{2} - 41 \, a^{3} b^{4} + 11 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{7} - a b^{9}\right)} d \sin\left(d x + c\right) - {\left(a^{4} b^{6} - b^{10}\right)} d\right)}}, \frac{2 \, {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{5} - 3 \, {\left(20 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 9 \, a b^{6}\right)} d x \cos\left(d x + c\right)^{2} - 4 \, {\left(5 \, a^{4} b^{3} - 6 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(20 \, a^{7} - 9 \, a^{5} b^{2} - 20 \, a^{3} b^{4} + 9 \, a b^{6}\right)} d x + 3 \, {\left(20 \, a^{6} + a^{4} b^{2} - 17 \, a^{2} b^{4} + 2 \, b^{6} - {\left(20 \, a^{4} b^{2} - 19 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{5} b - 19 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 3 \, {\left(20 \, a^{6} b - 19 \, a^{4} b^{3} - 3 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right) + {\left(5 \, {\left(a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(20 \, a^{6} b - 29 \, a^{4} b^{3} + 9 \, a^{2} b^{5}\right)} d x + 3 \, {\left(30 \, a^{5} b^{2} - 41 \, a^{3} b^{4} + 11 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left({\left(a^{2} b^{8} - b^{10}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{7} - a b^{9}\right)} d \sin\left(d x + c\right) - {\left(a^{4} b^{6} - b^{10}\right)} d\right)}}\right]"," ",0,"[1/12*(4*(a^2*b^5 - b^7)*cos(d*x + c)^5 - 6*(20*a^5*b^2 - 29*a^3*b^4 + 9*a*b^6)*d*x*cos(d*x + c)^2 - 8*(5*a^4*b^3 - 6*a^2*b^5 + b^7)*cos(d*x + c)^3 + 6*(20*a^7 - 9*a^5*b^2 - 20*a^3*b^4 + 9*a*b^6)*d*x + 3*(20*a^6 + a^4*b^2 - 17*a^2*b^4 + 2*b^6 - (20*a^4*b^2 - 19*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(20*a^5*b - 19*a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 6*(20*a^6*b - 19*a^4*b^3 - 3*a^2*b^5 + 2*b^7)*cos(d*x + c) + 2*(5*(a^3*b^4 - a*b^6)*cos(d*x + c)^3 + 6*(20*a^6*b - 29*a^4*b^3 + 9*a^2*b^5)*d*x + 3*(30*a^5*b^2 - 41*a^3*b^4 + 11*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^8 - b^10)*d*cos(d*x + c)^2 - 2*(a^3*b^7 - a*b^9)*d*sin(d*x + c) - (a^4*b^6 - b^10)*d), 1/6*(2*(a^2*b^5 - b^7)*cos(d*x + c)^5 - 3*(20*a^5*b^2 - 29*a^3*b^4 + 9*a*b^6)*d*x*cos(d*x + c)^2 - 4*(5*a^4*b^3 - 6*a^2*b^5 + b^7)*cos(d*x + c)^3 + 3*(20*a^7 - 9*a^5*b^2 - 20*a^3*b^4 + 9*a*b^6)*d*x + 3*(20*a^6 + a^4*b^2 - 17*a^2*b^4 + 2*b^6 - (20*a^4*b^2 - 19*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(20*a^5*b - 19*a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 3*(20*a^6*b - 19*a^4*b^3 - 3*a^2*b^5 + 2*b^7)*cos(d*x + c) + (5*(a^3*b^4 - a*b^6)*cos(d*x + c)^3 + 6*(20*a^6*b - 29*a^4*b^3 + 9*a^2*b^5)*d*x + 3*(30*a^5*b^2 - 41*a^3*b^4 + 11*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^8 - b^10)*d*cos(d*x + c)^2 - 2*(a^3*b^7 - a*b^9)*d*sin(d*x + c) - (a^4*b^6 - b^10)*d)]","A",0
1137,1,837,0,1.101558," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(4 \, a^{6} - a^{4} b^{2} - 4 \, a^{2} b^{4} + b^{6}\right)} d x - 3 \, {\left(4 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4} - {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(4 \, a^{5} b - 3 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} d x + 3 \, {\left(6 \, a^{4} b^{2} - 7 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{6} - a b^{8}\right)} d \sin\left(d x + c\right) - {\left(a^{4} b^{5} - b^{9}\right)} d\right)}}, \frac{3 \, {\left(4 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{6} - a^{4} b^{2} - 4 \, a^{2} b^{4} + b^{6}\right)} d x - 3 \, {\left(4 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4} - {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(4 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left(4 \, a^{5} b - 3 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right) - {\left({\left(a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} d x + 3 \, {\left(6 \, a^{4} b^{2} - 7 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{6} - a b^{8}\right)} d \sin\left(d x + c\right) - {\left(a^{4} b^{5} - b^{9}\right)} d\right)}}\right]"," ",0,"[1/4*(6*(4*a^4*b^2 - 5*a^2*b^4 + b^6)*d*x*cos(d*x + c)^2 + 8*(a^3*b^3 - a*b^5)*cos(d*x + c)^3 - 6*(4*a^6 - a^4*b^2 - 4*a^2*b^4 + b^6)*d*x - 3*(4*a^5 + a^3*b^2 - 3*a*b^4 - (4*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + 2*(4*a^4*b - 3*a^2*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(4*a^5*b - 3*a^3*b^3 - a*b^5)*cos(d*x + c) - 2*((a^2*b^4 - b^6)*cos(d*x + c)^3 + 6*(4*a^5*b - 5*a^3*b^3 + a*b^5)*d*x + 3*(6*a^4*b^2 - 7*a^2*b^4 + b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^7 - b^9)*d*cos(d*x + c)^2 - 2*(a^3*b^6 - a*b^8)*d*sin(d*x + c) - (a^4*b^5 - b^9)*d), 1/2*(3*(4*a^4*b^2 - 5*a^2*b^4 + b^6)*d*x*cos(d*x + c)^2 + 4*(a^3*b^3 - a*b^5)*cos(d*x + c)^3 - 3*(4*a^6 - a^4*b^2 - 4*a^2*b^4 + b^6)*d*x - 3*(4*a^5 + a^3*b^2 - 3*a*b^4 - (4*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + 2*(4*a^4*b - 3*a^2*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*(4*a^5*b - 3*a^3*b^3 - a*b^5)*cos(d*x + c) - ((a^2*b^4 - b^6)*cos(d*x + c)^3 + 6*(4*a^5*b - 5*a^3*b^3 + a*b^5)*d*x + 3*(6*a^4*b^2 - 7*a^2*b^4 + b^6)*cos(d*x + c))*sin(d*x + c))/((a^2*b^7 - b^9)*d*cos(d*x + c)^2 - 2*(a^3*b^6 - a*b^8)*d*sin(d*x + c) - (a^4*b^5 - b^9)*d)]","B",0
1138,1,1042,0,1.521037," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{5} b^{2} - a^{3} b^{4}\right)} d x \cos\left(d x + c\right)^{2} - 4 \, {\left(a^{7} - a^{3} b^{4}\right)} d x + {\left(2 \, a^{6} + a^{4} b^{2} + a^{2} b^{4} + 2 \, b^{6} - {\left(2 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{5} b - a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{6} b + a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right) + 2 \, {\left(a^{4} b^{3} - b^{7} - {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{4} b^{3} - b^{7} - {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(4 \, {\left(a^{6} b - a^{4} b^{3}\right)} d x + {\left(3 \, a^{5} b^{2} - a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{6} b^{4} - a^{4} b^{6}\right)} d \sin\left(d x + c\right) - {\left(a^{7} b^{3} - a^{3} b^{7}\right)} d\right)}}, \frac{2 \, {\left(a^{5} b^{2} - a^{3} b^{4}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{7} - a^{3} b^{4}\right)} d x - {\left(2 \, a^{6} + a^{4} b^{2} + a^{2} b^{4} + 2 \, b^{6} - {\left(2 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{5} b - a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{6} b + a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right) + {\left(a^{4} b^{3} - b^{7} - {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{4} b^{3} - b^{7} - {\left(a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(4 \, {\left(a^{6} b - a^{4} b^{3}\right)} d x + {\left(3 \, a^{5} b^{2} - a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{6} b^{4} - a^{4} b^{6}\right)} d \sin\left(d x + c\right) - {\left(a^{7} b^{3} - a^{3} b^{7}\right)} d\right)}}\right]"," ",0,"[1/4*(4*(a^5*b^2 - a^3*b^4)*d*x*cos(d*x + c)^2 - 4*(a^7 - a^3*b^4)*d*x + (2*a^6 + a^4*b^2 + a^2*b^4 + 2*b^6 - (2*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(2*a^5*b - a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^6*b + a^4*b^3 - 3*a^2*b^5)*cos(d*x + c) + 2*(a^4*b^3 - b^7 - (a^2*b^5 - b^7)*cos(d*x + c)^2 + 2*(a^3*b^4 - a*b^6)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 2*(a^4*b^3 - b^7 - (a^2*b^5 - b^7)*cos(d*x + c)^2 + 2*(a^3*b^4 - a*b^6)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(4*(a^6*b - a^4*b^3)*d*x + (3*a^5*b^2 - a^3*b^4 - 2*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^5*b^5 - a^3*b^7)*d*cos(d*x + c)^2 - 2*(a^6*b^4 - a^4*b^6)*d*sin(d*x + c) - (a^7*b^3 - a^3*b^7)*d), 1/2*(2*(a^5*b^2 - a^3*b^4)*d*x*cos(d*x + c)^2 - 2*(a^7 - a^3*b^4)*d*x - (2*a^6 + a^4*b^2 + a^2*b^4 + 2*b^6 - (2*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(2*a^5*b - a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^6*b + a^4*b^3 - 3*a^2*b^5)*cos(d*x + c) + (a^4*b^3 - b^7 - (a^2*b^5 - b^7)*cos(d*x + c)^2 + 2*(a^3*b^4 - a*b^6)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - (a^4*b^3 - b^7 - (a^2*b^5 - b^7)*cos(d*x + c)^2 + 2*(a^3*b^4 - a*b^6)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - (4*(a^6*b - a^4*b^3)*d*x + (3*a^5*b^2 - a^3*b^4 - 2*a*b^6)*cos(d*x + c))*sin(d*x + c))/((a^5*b^5 - a^3*b^7)*d*cos(d*x + c)^2 - 2*(a^6*b^4 - a^4*b^6)*d*sin(d*x + c) - (a^7*b^3 - a^3*b^7)*d)]","B",0
1139,1,1064,0,0.980479," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{5} + 5 \, a^{3} b^{2} - 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 18 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left(2 \, a^{3} b - 4 \, a b^{3} - 2 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4} - {\left(a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right) + 6 \, {\left(2 \, a^{3} b^{2} - 2 \, a b^{4} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - b^{5} - {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 6 \, {\left(2 \, a^{3} b^{2} - 2 \, a b^{4} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - b^{5} - {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(2 \, {\left(a^{7} b - a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{7} b - a^{5} b^{3}\right)} d + {\left({\left(a^{6} b^{2} - a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} - a^{4} b^{4}\right)} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{{\left(a^{5} + 5 \, a^{3} b^{2} - 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 9 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + 3 \, {\left(2 \, a^{3} b - 4 \, a b^{3} - 2 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2} - 2 \, b^{4} - {\left(a^{2} b^{2} - 2 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(2 \, a^{3} b^{2} - 2 \, a b^{4} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - b^{5} - {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(2 \, a^{3} b^{2} - 2 \, a b^{4} - 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - b^{5} - {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{2 \, {\left(2 \, {\left(a^{7} b - a^{5} b^{3}\right)} d \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{7} b - a^{5} b^{3}\right)} d + {\left({\left(a^{6} b^{2} - a^{4} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} - a^{4} b^{4}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(2*(a^5 + 5*a^3*b^2 - 6*a*b^4)*cos(d*x + c)^3 - 18*(a^4*b - a^2*b^3)*cos(d*x + c)*sin(d*x + c) + 3*(2*a^3*b - 4*a*b^3 - 2*(a^3*b - 2*a*b^3)*cos(d*x + c)^2 + (a^4 - a^2*b^2 - 2*b^4 - (a^2*b^2 - 2*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c) + 6*(2*a^3*b^2 - 2*a*b^4 - 2*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 + (a^4*b - b^5 - (a^2*b^3 - b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 6*(2*a^3*b^2 - 2*a*b^4 - 2*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 + (a^4*b - b^5 - (a^2*b^3 - b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(2*(a^7*b - a^5*b^3)*d*cos(d*x + c)^2 - 2*(a^7*b - a^5*b^3)*d + ((a^6*b^2 - a^4*b^4)*d*cos(d*x + c)^2 - (a^8 - a^4*b^4)*d)*sin(d*x + c)), -1/2*((a^5 + 5*a^3*b^2 - 6*a*b^4)*cos(d*x + c)^3 - 9*(a^4*b - a^2*b^3)*cos(d*x + c)*sin(d*x + c) + 3*(2*a^3*b - 4*a*b^3 - 2*(a^3*b - 2*a*b^3)*cos(d*x + c)^2 + (a^4 - a^2*b^2 - 2*b^4 - (a^2*b^2 - 2*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*(a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c) + 3*(2*a^3*b^2 - 2*a*b^4 - 2*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 + (a^4*b - b^5 - (a^2*b^3 - b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(2*a^3*b^2 - 2*a*b^4 - 2*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 + (a^4*b - b^5 - (a^2*b^3 - b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2))/(2*(a^7*b - a^5*b^3)*d*cos(d*x + c)^2 - 2*(a^7*b - a^5*b^3)*d + ((a^6*b^2 - a^4*b^4)*d*cos(d*x + c)^2 - (a^8 - a^4*b^4)*d)*sin(d*x + c))]","B",0
1140,1,1560,0,1.483192," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{6} - 10 \, a^{4} b^{2} + 9 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b - a^{2} b^{3} - 4 \, b^{5} + {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4} - {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(a^{6} - 7 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 4 \, b^{6} + {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{6} - 3 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 4 \, b^{6} + {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{6} - 3 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(a^{5} b - 13 \, a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b + 3 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{7} b^{2} - a^{5} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{9} + a^{7} b^{2} - 2 \, a^{5} b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{9} - a^{5} b^{4}\right)} d - 2 \, {\left({\left(a^{8} b - a^{6} b^{3}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} b - a^{6} b^{3}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{4 \, {\left(a^{6} - 10 \, a^{4} b^{2} + 9 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(3 \, a^{4} b - a^{2} b^{3} - 4 \, b^{5} + {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4} - {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 6 \, {\left(a^{6} - 7 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 4 \, b^{6} + {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{6} - 3 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 4 \, b^{6} + {\left(a^{4} b^{2} - 5 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(a^{6} - 3 \, a^{4} b^{2} - 6 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5} - {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(a^{5} b - 13 \, a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b + 3 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{7} b^{2} - a^{5} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{9} + a^{7} b^{2} - 2 \, a^{5} b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{9} - a^{5} b^{4}\right)} d - 2 \, {\left({\left(a^{8} b - a^{6} b^{3}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{8} b - a^{6} b^{3}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(a^6 - 10*a^4*b^2 + 9*a^2*b^4)*cos(d*x + c)^3 + 3*(3*a^4*b - a^2*b^3 - 4*b^5 + (3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - (3*a^4*b + 2*a^2*b^3 - 8*b^5)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - 4*a*b^4 - (3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(a^6 - 7*a^4*b^2 + 6*a^2*b^4)*cos(d*x + c) + 3*(a^6 - 4*a^4*b^2 - a^2*b^4 + 4*b^6 + (a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 - (a^6 - 3*a^4*b^2 - 6*a^2*b^4 + 8*b^6)*cos(d*x + c)^2 + 2*(a^5*b - 5*a^3*b^3 + 4*a*b^5 - (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^6 - 4*a^4*b^2 - a^2*b^4 + 4*b^6 + (a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 - (a^6 - 3*a^4*b^2 - 6*a^2*b^4 + 8*b^6)*cos(d*x + c)^2 + 2*(a^5*b - 5*a^3*b^3 + 4*a*b^5 - (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*((a^5*b - 13*a^3*b^3 + 12*a*b^5)*cos(d*x + c)^3 + 3*(a^5*b + 3*a^3*b^3 - 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b^2 - a^5*b^4)*d*cos(d*x + c)^4 - (a^9 + a^7*b^2 - 2*a^5*b^4)*d*cos(d*x + c)^2 + (a^9 - a^5*b^4)*d - 2*((a^8*b - a^6*b^3)*d*cos(d*x + c)^2 - (a^8*b - a^6*b^3)*d)*sin(d*x + c)), 1/4*(4*(a^6 - 10*a^4*b^2 + 9*a^2*b^4)*cos(d*x + c)^3 - 6*(3*a^4*b - a^2*b^3 - 4*b^5 + (3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - (3*a^4*b + 2*a^2*b^3 - 8*b^5)*cos(d*x + c)^2 + 2*(3*a^3*b^2 - 4*a*b^4 - (3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 6*(a^6 - 7*a^4*b^2 + 6*a^2*b^4)*cos(d*x + c) + 3*(a^6 - 4*a^4*b^2 - a^2*b^4 + 4*b^6 + (a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 - (a^6 - 3*a^4*b^2 - 6*a^2*b^4 + 8*b^6)*cos(d*x + c)^2 + 2*(a^5*b - 5*a^3*b^3 + 4*a*b^5 - (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^6 - 4*a^4*b^2 - a^2*b^4 + 4*b^6 + (a^4*b^2 - 5*a^2*b^4 + 4*b^6)*cos(d*x + c)^4 - (a^6 - 3*a^4*b^2 - 6*a^2*b^4 + 8*b^6)*cos(d*x + c)^2 + 2*(a^5*b - 5*a^3*b^3 + 4*a*b^5 - (a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*((a^5*b - 13*a^3*b^3 + 12*a*b^5)*cos(d*x + c)^3 + 3*(a^5*b + 3*a^3*b^3 - 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/((a^7*b^2 - a^5*b^4)*d*cos(d*x + c)^4 - (a^9 + a^7*b^2 - 2*a^5*b^4)*d*cos(d*x + c)^2 + (a^9 - a^5*b^4)*d - 2*((a^8*b - a^6*b^3)*d*cos(d*x + c)^2 - (a^8*b - a^6*b^3)*d)*sin(d*x + c))]","B",0
1141,1,2027,0,1.745664," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(17 \, a^{5} b^{2} - 77 \, a^{3} b^{4} + 60 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 4 \, {\left(4 \, a^{7} + 3 \, a^{5} b^{2} - 67 \, a^{3} b^{4} + 60 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{5} b - 38 \, a^{3} b^{3} + 40 \, a b^{5} + 2 \, {\left(2 \, a^{5} b - 19 \, a^{3} b^{3} + 20 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(2 \, a^{5} b - 19 \, a^{3} b^{3} + 20 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} - 17 \, a^{4} b^{2} + a^{2} b^{4} + 20 \, b^{6} + {\left(2 \, a^{4} b^{2} - 19 \, a^{2} b^{4} + 20 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{6} - 15 \, a^{4} b^{2} - 18 \, a^{2} b^{4} + 40 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 6 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right) - 3 \, {\left(18 \, a^{5} b^{2} - 58 \, a^{3} b^{4} + 40 \, a b^{6} + 2 \, {\left(9 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(9 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{6} b - 20 \, a^{4} b^{3} - 9 \, a^{2} b^{5} + 20 \, b^{7} + {\left(9 \, a^{4} b^{3} - 29 \, a^{2} b^{5} + 20 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(9 \, a^{6} b - 11 \, a^{4} b^{3} - 38 \, a^{2} b^{5} + 40 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(18 \, a^{5} b^{2} - 58 \, a^{3} b^{4} + 40 \, a b^{6} + 2 \, {\left(9 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(9 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{6} b - 20 \, a^{4} b^{3} - 9 \, a^{2} b^{5} + 20 \, b^{7} + {\left(9 \, a^{4} b^{3} - 29 \, a^{2} b^{5} + 20 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(9 \, a^{6} b - 11 \, a^{4} b^{3} - 38 \, a^{2} b^{5} + 40 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, {\left(14 \, a^{6} b - 59 \, a^{4} b^{3} + 45 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{6} b - 41 \, a^{4} b^{3} + 30 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(2 \, {\left(a^{9} b - a^{7} b^{3}\right)} d \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{9} b - a^{7} b^{3}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b - a^{7} b^{3}\right)} d + {\left({\left(a^{8} b^{2} - a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{10} + a^{8} b^{2} - 2 \, a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{10} - a^{6} b^{4}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{2 \, {\left(17 \, a^{5} b^{2} - 77 \, a^{3} b^{4} + 60 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 4 \, {\left(4 \, a^{7} + 3 \, a^{5} b^{2} - 67 \, a^{3} b^{4} + 60 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(4 \, a^{5} b - 38 \, a^{3} b^{3} + 40 \, a b^{5} + 2 \, {\left(2 \, a^{5} b - 19 \, a^{3} b^{3} + 20 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(2 \, a^{5} b - 19 \, a^{3} b^{3} + 20 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} - 17 \, a^{4} b^{2} + a^{2} b^{4} + 20 \, b^{6} + {\left(2 \, a^{4} b^{2} - 19 \, a^{2} b^{4} + 20 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{6} - 15 \, a^{4} b^{2} - 18 \, a^{2} b^{4} + 40 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 6 \, {\left(2 \, a^{7} - 3 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right) - 3 \, {\left(18 \, a^{5} b^{2} - 58 \, a^{3} b^{4} + 40 \, a b^{6} + 2 \, {\left(9 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(9 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{6} b - 20 \, a^{4} b^{3} - 9 \, a^{2} b^{5} + 20 \, b^{7} + {\left(9 \, a^{4} b^{3} - 29 \, a^{2} b^{5} + 20 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(9 \, a^{6} b - 11 \, a^{4} b^{3} - 38 \, a^{2} b^{5} + 40 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(18 \, a^{5} b^{2} - 58 \, a^{3} b^{4} + 40 \, a b^{6} + 2 \, {\left(9 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(9 \, a^{5} b^{2} - 29 \, a^{3} b^{4} + 20 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(9 \, a^{6} b - 20 \, a^{4} b^{3} - 9 \, a^{2} b^{5} + 20 \, b^{7} + {\left(9 \, a^{4} b^{3} - 29 \, a^{2} b^{5} + 20 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(9 \, a^{6} b - 11 \, a^{4} b^{3} - 38 \, a^{2} b^{5} + 40 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, {\left(14 \, a^{6} b - 59 \, a^{4} b^{3} + 45 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{6} b - 41 \, a^{4} b^{3} + 30 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(2 \, {\left(a^{9} b - a^{7} b^{3}\right)} d \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{9} b - a^{7} b^{3}\right)} d \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{9} b - a^{7} b^{3}\right)} d + {\left({\left(a^{8} b^{2} - a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{10} + a^{8} b^{2} - 2 \, a^{6} b^{4}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{10} - a^{6} b^{4}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(2*(17*a^5*b^2 - 77*a^3*b^4 + 60*a*b^6)*cos(d*x + c)^5 - 4*(4*a^7 + 3*a^5*b^2 - 67*a^3*b^4 + 60*a*b^6)*cos(d*x + c)^3 - 3*(4*a^5*b - 38*a^3*b^3 + 40*a*b^5 + 2*(2*a^5*b - 19*a^3*b^3 + 20*a*b^5)*cos(d*x + c)^4 - 4*(2*a^5*b - 19*a^3*b^3 + 20*a*b^5)*cos(d*x + c)^2 + (2*a^6 - 17*a^4*b^2 + a^2*b^4 + 20*b^6 + (2*a^4*b^2 - 19*a^2*b^4 + 20*b^6)*cos(d*x + c)^4 - (2*a^6 - 15*a^4*b^2 - 18*a^2*b^4 + 40*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 6*(2*a^7 - 3*a^5*b^2 - 19*a^3*b^4 + 20*a*b^6)*cos(d*x + c) - 3*(18*a^5*b^2 - 58*a^3*b^4 + 40*a*b^6 + 2*(9*a^5*b^2 - 29*a^3*b^4 + 20*a*b^6)*cos(d*x + c)^4 - 4*(9*a^5*b^2 - 29*a^3*b^4 + 20*a*b^6)*cos(d*x + c)^2 + (9*a^6*b - 20*a^4*b^3 - 9*a^2*b^5 + 20*b^7 + (9*a^4*b^3 - 29*a^2*b^5 + 20*b^7)*cos(d*x + c)^4 - (9*a^6*b - 11*a^4*b^3 - 38*a^2*b^5 + 40*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(18*a^5*b^2 - 58*a^3*b^4 + 40*a*b^6 + 2*(9*a^5*b^2 - 29*a^3*b^4 + 20*a*b^6)*cos(d*x + c)^4 - 4*(9*a^5*b^2 - 29*a^3*b^4 + 20*a*b^6)*cos(d*x + c)^2 + (9*a^6*b - 20*a^4*b^3 - 9*a^2*b^5 + 20*b^7 + (9*a^4*b^3 - 29*a^2*b^5 + 20*b^7)*cos(d*x + c)^4 - (9*a^6*b - 11*a^4*b^3 - 38*a^2*b^5 + 40*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*(14*a^6*b - 59*a^4*b^3 + 45*a^2*b^5)*cos(d*x + c)^3 - 3*(11*a^6*b - 41*a^4*b^3 + 30*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(2*(a^9*b - a^7*b^3)*d*cos(d*x + c)^4 - 4*(a^9*b - a^7*b^3)*d*cos(d*x + c)^2 + 2*(a^9*b - a^7*b^3)*d + ((a^8*b^2 - a^6*b^4)*d*cos(d*x + c)^4 - (a^10 + a^8*b^2 - 2*a^6*b^4)*d*cos(d*x + c)^2 + (a^10 - a^6*b^4)*d)*sin(d*x + c)), 1/12*(2*(17*a^5*b^2 - 77*a^3*b^4 + 60*a*b^6)*cos(d*x + c)^5 - 4*(4*a^7 + 3*a^5*b^2 - 67*a^3*b^4 + 60*a*b^6)*cos(d*x + c)^3 - 6*(4*a^5*b - 38*a^3*b^3 + 40*a*b^5 + 2*(2*a^5*b - 19*a^3*b^3 + 20*a*b^5)*cos(d*x + c)^4 - 4*(2*a^5*b - 19*a^3*b^3 + 20*a*b^5)*cos(d*x + c)^2 + (2*a^6 - 17*a^4*b^2 + a^2*b^4 + 20*b^6 + (2*a^4*b^2 - 19*a^2*b^4 + 20*b^6)*cos(d*x + c)^4 - (2*a^6 - 15*a^4*b^2 - 18*a^2*b^4 + 40*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 6*(2*a^7 - 3*a^5*b^2 - 19*a^3*b^4 + 20*a*b^6)*cos(d*x + c) - 3*(18*a^5*b^2 - 58*a^3*b^4 + 40*a*b^6 + 2*(9*a^5*b^2 - 29*a^3*b^4 + 20*a*b^6)*cos(d*x + c)^4 - 4*(9*a^5*b^2 - 29*a^3*b^4 + 20*a*b^6)*cos(d*x + c)^2 + (9*a^6*b - 20*a^4*b^3 - 9*a^2*b^5 + 20*b^7 + (9*a^4*b^3 - 29*a^2*b^5 + 20*b^7)*cos(d*x + c)^4 - (9*a^6*b - 11*a^4*b^3 - 38*a^2*b^5 + 40*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(18*a^5*b^2 - 58*a^3*b^4 + 40*a*b^6 + 2*(9*a^5*b^2 - 29*a^3*b^4 + 20*a*b^6)*cos(d*x + c)^4 - 4*(9*a^5*b^2 - 29*a^3*b^4 + 20*a*b^6)*cos(d*x + c)^2 + (9*a^6*b - 20*a^4*b^3 - 9*a^2*b^5 + 20*b^7 + (9*a^4*b^3 - 29*a^2*b^5 + 20*b^7)*cos(d*x + c)^4 - (9*a^6*b - 11*a^4*b^3 - 38*a^2*b^5 + 40*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*(14*a^6*b - 59*a^4*b^3 + 45*a^2*b^5)*cos(d*x + c)^3 - 3*(11*a^6*b - 41*a^4*b^3 + 30*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(2*(a^9*b - a^7*b^3)*d*cos(d*x + c)^4 - 4*(a^9*b - a^7*b^3)*d*cos(d*x + c)^2 + 2*(a^9*b - a^7*b^3)*d + ((a^8*b^2 - a^6*b^4)*d*cos(d*x + c)^4 - (a^10 + a^8*b^2 - 2*a^6*b^4)*d*cos(d*x + c)^2 + (a^10 - a^6*b^4)*d)*sin(d*x + c))]","B",0
1142,1,2592,0,2.442174," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(83 \, a^{6} b^{2} - 263 \, a^{4} b^{4} + 180 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{8} - 181 \, a^{6} b^{2} + 536 \, a^{4} b^{4} - 360 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left(2 \, a^{6} b - 9 \, a^{4} b^{3} - a^{2} b^{5} + 10 \, b^{7} - {\left(2 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 10 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} - 23 \, a^{2} b^{5} + 30 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{6} b - 16 \, a^{4} b^{3} - 13 \, a^{2} b^{5} + 30 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 10 \, a b^{6} + {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(a^{8} - 32 \, a^{6} b^{2} + 91 \, a^{4} b^{4} - 60 \, a^{2} b^{6}\right)} \cos\left(d x + c\right) + 3 \, {\left(a^{8} - 24 \, a^{6} b^{2} + 39 \, a^{4} b^{4} + 24 \, a^{2} b^{6} - 40 \, b^{8} - {\left(a^{6} b^{2} - 25 \, a^{4} b^{4} + 64 \, a^{2} b^{6} - 40 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + {\left(a^{8} - 22 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 152 \, a^{2} b^{6} - 120 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{8} - 47 \, a^{6} b^{2} + 53 \, a^{4} b^{4} + 112 \, a^{2} b^{6} - 120 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7} + {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{8} - 24 \, a^{6} b^{2} + 39 \, a^{4} b^{4} + 24 \, a^{2} b^{6} - 40 \, b^{8} - {\left(a^{6} b^{2} - 25 \, a^{4} b^{4} + 64 \, a^{2} b^{6} - 40 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + {\left(a^{8} - 22 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 152 \, a^{2} b^{6} - 120 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{8} - 47 \, a^{6} b^{2} + 53 \, a^{4} b^{4} + 112 \, a^{2} b^{6} - 120 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7} + {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(2 \, {\left(13 \, a^{5} b^{3} - 43 \, a^{3} b^{5} + 30 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} - {\left(11 \, a^{7} b + 21 \, a^{5} b^{3} - 152 \, a^{3} b^{5} + 120 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{7} b - a^{5} b^{3} - 22 \, a^{3} b^{5} + 20 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{9} b^{2} - a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{6} - {\left(a^{11} + 2 \, a^{9} b^{2} - 3 \, a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{4} + {\left(2 \, a^{11} + a^{9} b^{2} - 3 \, a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{11} - a^{7} b^{4}\right)} d - 2 \, {\left({\left(a^{10} b - a^{8} b^{3}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{10} b - a^{8} b^{3}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{10} b - a^{8} b^{3}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{2 \, {\left(83 \, a^{6} b^{2} - 263 \, a^{4} b^{4} + 180 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{8} - 181 \, a^{6} b^{2} + 536 \, a^{4} b^{4} - 360 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} - 24 \, {\left(2 \, a^{6} b - 9 \, a^{4} b^{3} - a^{2} b^{5} + 10 \, b^{7} - {\left(2 \, a^{4} b^{3} - 11 \, a^{2} b^{5} + 10 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + {\left(2 \, a^{6} b - 5 \, a^{4} b^{3} - 23 \, a^{2} b^{5} + 30 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{6} b - 16 \, a^{4} b^{3} - 13 \, a^{2} b^{5} + 30 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 10 \, a b^{6} + {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{5} b^{2} - 11 \, a^{3} b^{4} + 10 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 6 \, {\left(a^{8} - 32 \, a^{6} b^{2} + 91 \, a^{4} b^{4} - 60 \, a^{2} b^{6}\right)} \cos\left(d x + c\right) + 3 \, {\left(a^{8} - 24 \, a^{6} b^{2} + 39 \, a^{4} b^{4} + 24 \, a^{2} b^{6} - 40 \, b^{8} - {\left(a^{6} b^{2} - 25 \, a^{4} b^{4} + 64 \, a^{2} b^{6} - 40 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + {\left(a^{8} - 22 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 152 \, a^{2} b^{6} - 120 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{8} - 47 \, a^{6} b^{2} + 53 \, a^{4} b^{4} + 112 \, a^{2} b^{6} - 120 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7} + {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{8} - 24 \, a^{6} b^{2} + 39 \, a^{4} b^{4} + 24 \, a^{2} b^{6} - 40 \, b^{8} - {\left(a^{6} b^{2} - 25 \, a^{4} b^{4} + 64 \, a^{2} b^{6} - 40 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + {\left(a^{8} - 22 \, a^{6} b^{2} - 11 \, a^{4} b^{4} + 152 \, a^{2} b^{6} - 120 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{8} - 47 \, a^{6} b^{2} + 53 \, a^{4} b^{4} + 112 \, a^{2} b^{6} - 120 \, b^{8}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7} + {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{7} b - 25 \, a^{5} b^{3} + 64 \, a^{3} b^{5} - 40 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(2 \, {\left(13 \, a^{5} b^{3} - 43 \, a^{3} b^{5} + 30 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} - {\left(11 \, a^{7} b + 21 \, a^{5} b^{3} - 152 \, a^{3} b^{5} + 120 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{7} b - a^{5} b^{3} - 22 \, a^{3} b^{5} + 20 \, a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{9} b^{2} - a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{6} - {\left(a^{11} + 2 \, a^{9} b^{2} - 3 \, a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{4} + {\left(2 \, a^{11} + a^{9} b^{2} - 3 \, a^{7} b^{4}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{11} - a^{7} b^{4}\right)} d - 2 \, {\left({\left(a^{10} b - a^{8} b^{3}\right)} d \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{10} b - a^{8} b^{3}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{10} b - a^{8} b^{3}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(2*(83*a^6*b^2 - 263*a^4*b^4 + 180*a^2*b^6)*cos(d*x + c)^5 + 2*(5*a^8 - 181*a^6*b^2 + 536*a^4*b^4 - 360*a^2*b^6)*cos(d*x + c)^3 + 12*(2*a^6*b - 9*a^4*b^3 - a^2*b^5 + 10*b^7 - (2*a^4*b^3 - 11*a^2*b^5 + 10*b^7)*cos(d*x + c)^6 + (2*a^6*b - 5*a^4*b^3 - 23*a^2*b^5 + 30*b^7)*cos(d*x + c)^4 - (4*a^6*b - 16*a^4*b^3 - 13*a^2*b^5 + 30*b^7)*cos(d*x + c)^2 + 2*(2*a^5*b^2 - 11*a^3*b^4 + 10*a*b^6 + (2*a^5*b^2 - 11*a^3*b^4 + 10*a*b^6)*cos(d*x + c)^4 - 2*(2*a^5*b^2 - 11*a^3*b^4 + 10*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(a^8 - 32*a^6*b^2 + 91*a^4*b^4 - 60*a^2*b^6)*cos(d*x + c) + 3*(a^8 - 24*a^6*b^2 + 39*a^4*b^4 + 24*a^2*b^6 - 40*b^8 - (a^6*b^2 - 25*a^4*b^4 + 64*a^2*b^6 - 40*b^8)*cos(d*x + c)^6 + (a^8 - 22*a^6*b^2 - 11*a^4*b^4 + 152*a^2*b^6 - 120*b^8)*cos(d*x + c)^4 - (2*a^8 - 47*a^6*b^2 + 53*a^4*b^4 + 112*a^2*b^6 - 120*b^8)*cos(d*x + c)^2 + 2*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7 + (a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*cos(d*x + c)^4 - 2*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^8 - 24*a^6*b^2 + 39*a^4*b^4 + 24*a^2*b^6 - 40*b^8 - (a^6*b^2 - 25*a^4*b^4 + 64*a^2*b^6 - 40*b^8)*cos(d*x + c)^6 + (a^8 - 22*a^6*b^2 - 11*a^4*b^4 + 152*a^2*b^6 - 120*b^8)*cos(d*x + c)^4 - (2*a^8 - 47*a^6*b^2 + 53*a^4*b^4 + 112*a^2*b^6 - 120*b^8)*cos(d*x + c)^2 + 2*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7 + (a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*cos(d*x + c)^4 - 2*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(2*(13*a^5*b^3 - 43*a^3*b^5 + 30*a*b^7)*cos(d*x + c)^5 - (11*a^7*b + 21*a^5*b^3 - 152*a^3*b^5 + 120*a*b^7)*cos(d*x + c)^3 + 3*(3*a^7*b - a^5*b^3 - 22*a^3*b^5 + 20*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - a^7*b^4)*d*cos(d*x + c)^6 - (a^11 + 2*a^9*b^2 - 3*a^7*b^4)*d*cos(d*x + c)^4 + (2*a^11 + a^9*b^2 - 3*a^7*b^4)*d*cos(d*x + c)^2 - (a^11 - a^7*b^4)*d - 2*((a^10*b - a^8*b^3)*d*cos(d*x + c)^4 - 2*(a^10*b - a^8*b^3)*d*cos(d*x + c)^2 + (a^10*b - a^8*b^3)*d)*sin(d*x + c)), 1/16*(2*(83*a^6*b^2 - 263*a^4*b^4 + 180*a^2*b^6)*cos(d*x + c)^5 + 2*(5*a^8 - 181*a^6*b^2 + 536*a^4*b^4 - 360*a^2*b^6)*cos(d*x + c)^3 - 24*(2*a^6*b - 9*a^4*b^3 - a^2*b^5 + 10*b^7 - (2*a^4*b^3 - 11*a^2*b^5 + 10*b^7)*cos(d*x + c)^6 + (2*a^6*b - 5*a^4*b^3 - 23*a^2*b^5 + 30*b^7)*cos(d*x + c)^4 - (4*a^6*b - 16*a^4*b^3 - 13*a^2*b^5 + 30*b^7)*cos(d*x + c)^2 + 2*(2*a^5*b^2 - 11*a^3*b^4 + 10*a*b^6 + (2*a^5*b^2 - 11*a^3*b^4 + 10*a*b^6)*cos(d*x + c)^4 - 2*(2*a^5*b^2 - 11*a^3*b^4 + 10*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 6*(a^8 - 32*a^6*b^2 + 91*a^4*b^4 - 60*a^2*b^6)*cos(d*x + c) + 3*(a^8 - 24*a^6*b^2 + 39*a^4*b^4 + 24*a^2*b^6 - 40*b^8 - (a^6*b^2 - 25*a^4*b^4 + 64*a^2*b^6 - 40*b^8)*cos(d*x + c)^6 + (a^8 - 22*a^6*b^2 - 11*a^4*b^4 + 152*a^2*b^6 - 120*b^8)*cos(d*x + c)^4 - (2*a^8 - 47*a^6*b^2 + 53*a^4*b^4 + 112*a^2*b^6 - 120*b^8)*cos(d*x + c)^2 + 2*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7 + (a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*cos(d*x + c)^4 - 2*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(a^8 - 24*a^6*b^2 + 39*a^4*b^4 + 24*a^2*b^6 - 40*b^8 - (a^6*b^2 - 25*a^4*b^4 + 64*a^2*b^6 - 40*b^8)*cos(d*x + c)^6 + (a^8 - 22*a^6*b^2 - 11*a^4*b^4 + 152*a^2*b^6 - 120*b^8)*cos(d*x + c)^4 - (2*a^8 - 47*a^6*b^2 + 53*a^4*b^4 + 112*a^2*b^6 - 120*b^8)*cos(d*x + c)^2 + 2*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7 + (a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*cos(d*x + c)^4 - 2*(a^7*b - 25*a^5*b^3 + 64*a^3*b^5 - 40*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(2*(13*a^5*b^3 - 43*a^3*b^5 + 30*a*b^7)*cos(d*x + c)^5 - (11*a^7*b + 21*a^5*b^3 - 152*a^3*b^5 + 120*a*b^7)*cos(d*x + c)^3 + 3*(3*a^7*b - a^5*b^3 - 22*a^3*b^5 + 20*a*b^7)*cos(d*x + c))*sin(d*x + c))/((a^9*b^2 - a^7*b^4)*d*cos(d*x + c)^6 - (a^11 + 2*a^9*b^2 - 3*a^7*b^4)*d*cos(d*x + c)^4 + (2*a^11 + a^9*b^2 - 3*a^7*b^4)*d*cos(d*x + c)^2 - (a^11 - a^7*b^4)*d - 2*((a^10*b - a^8*b^3)*d*cos(d*x + c)^4 - 2*(a^10*b - a^8*b^3)*d*cos(d*x + c)^2 + (a^10*b - a^8*b^3)*d)*sin(d*x + c))]","B",0
1143,0,0,0,1.219914," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(\cos\left(d x + c\right)^{6} - \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(cos(d*x + c)^6 - cos(d*x + c)^4)*sqrt(b*sin(d*x + c) + a), x)","F",0
1144,0,0,0,1.015781," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right), x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
1145,0,0,0,84.170202," ","integrate(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{3} \cot\left(d x + c\right), x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^3*cot(d*x + c), x)","F",0
1146,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1147,-1,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1148,0,0,0,163.747131," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sin\left(d x + c\right) + a} \cot\left(d x + c\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sin(d*x + c) + a)*cot(d*x + c)^4, x)","F",0
1149,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1151,0,0,0,1.603261," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a \cos\left(d x + c\right)^{6} - a \cos\left(d x + c\right)^{4} + {\left(b \cos\left(d x + c\right)^{6} - b \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(a*cos(d*x + c)^6 - a*cos(d*x + c)^4 + (b*cos(d*x + c)^6 - b*cos(d*x + c)^4)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a), x)","F",0
1152,0,0,0,1.152175," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b \cos\left(d x + c\right)^{6} - a \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - b \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(b*cos(d*x + c)^6 - a*cos(d*x + c)^4*sin(d*x + c) - b*cos(d*x + c)^4)*sqrt(b*sin(d*x + c) + a), x)","F",0
1153,0,0,0,3.893800," ","integrate(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{3} \cot\left(d x + c\right) \sin\left(d x + c\right) + a \cos\left(d x + c\right)^{3} \cot\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((b*cos(d*x + c)^3*cot(d*x + c)*sin(d*x + c) + a*cos(d*x + c)^3*cot(d*x + c))*sqrt(b*sin(d*x + c) + a), x)","F",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1158,-2,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   failed of mode Union(SparseUnivariatePolynomial(SimpleAlgebraicExtension(InnerPrimeField(7),SparseUnivariatePolynomial(InnerPrimeField(7)),?^2+1)),failed) cannot be coerced to mode SparseUnivariatePolynomial(SimpleAlgebraicExtension(InnerPrimeField(7),SparseUnivariatePolynomial(InnerPrimeField(7)),?^2+1))","F(-2)",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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1160,0,0,0,1.599751," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(2 \, a b \cos\left(d x + c\right)^{6} - 2 \, a b \cos\left(d x + c\right)^{4} + {\left(b^{2} \cos\left(d x + c\right)^{6} - {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(-(2*a*b*cos(d*x + c)^6 - 2*a*b*cos(d*x + c)^4 + (b^2*cos(d*x + c)^6 - (a^2 + b^2)*cos(d*x + c)^4)*sin(d*x + c))*sqrt(b*sin(d*x + c) + a), x)","F",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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1162,0,0,0,158.100231," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a b \cos\left(d x + c\right)^{2} \cot\left(d x + c\right)^{2} \sin\left(d x + c\right) - {\left(b^{2} \cos\left(d x + c\right)^{4} - {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \cot\left(d x + c\right)^{2}\right)} \sqrt{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral((2*a*b*cos(d*x + c)^2*cot(d*x + c)^2*sin(d*x + c) - (b^2*cos(d*x + c)^4 - (a^2 + b^2)*cos(d*x + c)^2)*cot(d*x + c)^2)*sqrt(b*sin(d*x + c) + a), x)","F",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,0,0,0,1.505238," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(\cos\left(d x + c\right)^{6} - \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(-(cos(d*x + c)^6 - cos(d*x + c)^4)*sin(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1169,0,0,0,1.707757," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\cos\left(d x + c\right)^{6} - \cos\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(-(cos(d*x + c)^6 - cos(d*x + c)^4)/sqrt(b*sin(d*x + c) + a), x)","F",0
1170,0,0,0,1.192454," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^4*sin(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1171,0,0,0,5.484989," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{3} \cot\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^3*cot(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1172,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1173,0,0,0,10.370441," ","integrate(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right) \cot\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)*cot(d*x + c)^3/sqrt(b*sin(d*x + c) + a), x)","F",0
1174,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1175,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1176,0,0,0,2.328877," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(d x + c\right)^{6} - \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a} \sin\left(d x + c\right)}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral((cos(d*x + c)^6 - cos(d*x + c)^4)*sqrt(b*sin(d*x + c) + a)*sin(d*x + c)/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
1177,0,0,0,1.647240," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(d x + c\right)^{6} - \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral((cos(d*x + c)^6 - cos(d*x + c)^4)*sqrt(b*sin(d*x + c) + a)/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
1178,0,0,0,1.743521," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c)/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
1179,0,0,0,4.482228," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{3} \cot\left(d x + c\right)}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^3*cot(d*x + c)/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
1180,-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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1181,-2,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   failed of mode Union(SparseUnivariatePolynomial(SimpleAlgebraicExtension(InnerPrimeField(7),SparseUnivariatePolynomial(InnerPrimeField(7)),?^2+2)),failed) cannot be coerced to mode SparseUnivariatePolynomial(SimpleAlgebraicExtension(InnerPrimeField(7),SparseUnivariatePolynomial(InnerPrimeField(7)),?^2+2))","F(-2)",0
1182,0,0,0,1.773589," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cot\left(d x + c\right)^{4}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cot(d*x + c)^4/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
1183,0,0,0,1.378037," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(d x + c\right)^{6} - \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a} \sin\left(d x + c\right)}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral((cos(d*x + c)^6 - cos(d*x + c)^4)*sqrt(b*sin(d*x + c) + a)*sin(d*x + c)/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
1184,0,0,0,1.575324," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(\cos\left(d x + c\right)^{6} - \cos\left(d x + c\right)^{4}\right)} \sqrt{b \sin\left(d x + c\right) + a}}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral((cos(d*x + c)^6 - cos(d*x + c)^4)*sqrt(b*sin(d*x + c) + a)/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
1185,0,0,0,1.183458," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c)/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
1186,0,0,0,102.413784," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{3} \cot\left(d x + c\right)}{3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^3*cot(d*x + c)/(3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2 + (b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c)), x)","F",0
1187,-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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1188,-1,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1189,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1190,0,0,0,1.546972," ","integrate(cos(f*x+e)^4/(a+b*sin(f*x+e))^(9/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right)} \cos\left(f x + e\right)^{4}}{b^{5} d \cos\left(f x + e\right)^{6} - {\left(10 \, a^{2} b^{3} + 3 \, b^{5}\right)} d \cos\left(f x + e\right)^{4} + {\left(5 \, a^{4} b + 20 \, a^{2} b^{3} + 3 \, b^{5}\right)} d \cos\left(f x + e\right)^{2} - {\left(5 \, a^{4} b + 10 \, a^{2} b^{3} + b^{5}\right)} d - {\left(5 \, a b^{4} d \cos\left(f x + e\right)^{4} - 10 \, {\left(a^{3} b^{2} + a b^{4}\right)} d \cos\left(f x + e\right)^{2} + {\left(a^{5} + 10 \, a^{3} b^{2} + 5 \, a b^{4}\right)} d\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))*cos(f*x + e)^4/(b^5*d*cos(f*x + e)^6 - (10*a^2*b^3 + 3*b^5)*d*cos(f*x + e)^4 + (5*a^4*b + 20*a^2*b^3 + 3*b^5)*d*cos(f*x + e)^2 - (5*a^4*b + 10*a^2*b^3 + b^5)*d - (5*a*b^4*d*cos(f*x + e)^4 - 10*(a^3*b^2 + a*b^4)*d*cos(f*x + e)^2 + (a^5 + 10*a^3*b^2 + 5*a*b^4)*d)*sin(f*x + e)), x)","F",0
1191,0,0,0,44.013892," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(1/3)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{\frac{1}{3}}}{\sqrt{b \sin\left(d x + c\right) + a}}, x\right)"," ",0,"integral(cos(d*x + c)^4*sin(d*x + c)^(1/3)/sqrt(b*sin(d*x + c) + a), x)","F",0
1192,0,0,0,2.037047," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{p} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^p*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
1193,0,0,0,1.589529," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(-3-p)*(a+b*sin(d*x+c))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{p} \sin\left(d x + c\right)^{-p - 3} \cos\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^p*sin(d*x + c)^(-p - 3)*cos(d*x + c)^4, x)","F",0
1194,0,0,0,1.633507," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(-4-p)*(a+b*sin(d*x+c))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{p} \sin\left(d x + c\right)^{-p - 4} \cos\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^p*sin(d*x + c)^(-p - 4)*cos(d*x + c)^4, x)","F",0
1195,0,0,0,1.362251," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(3 \, a b^{2} \cos\left(d x + c\right)^{6} - {\left(a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + {\left(b^{3} \cos\left(d x + c\right)^{6} - {\left(3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-(3*a*b^2*cos(d*x + c)^6 - (a^3 + 3*a*b^2)*cos(d*x + c)^4 + (b^3*cos(d*x + c)^6 - (3*a^2*b + b^3)*cos(d*x + c)^4)*sin(d*x + c))*sin(d*x + c)^n, x)","F",0
1196,0,0,0,1.433158," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(d x + c\right)^{6} - 2 \, a b \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) - {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-(b^2*cos(d*x + c)^6 - 2*a*b*cos(d*x + c)^4*sin(d*x + c) - (a^2 + b^2)*cos(d*x + c)^4)*sin(d*x + c)^n, x)","F",0
1197,0,0,0,1.427893," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + a \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral((b*cos(d*x + c)^4*sin(d*x + c) + a*cos(d*x + c)^4)*sin(d*x + c)^n, x)","F",0
1198,1,106,0,1.420683," ","integrate(cos(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{1386 \, a \cos\left(d x + c\right)^{10} - 3465 \, a \cos\left(d x + c\right)^{8} + 2310 \, a \cos\left(d x + c\right)^{6} + 20 \, {\left(63 \, b \cos\left(d x + c\right)^{10} - 161 \, b \cos\left(d x + c\right)^{8} + 113 \, b \cos\left(d x + c\right)^{6} - 3 \, b \cos\left(d x + c\right)^{4} - 4 \, b \cos\left(d x + c\right)^{2} - 8 \, b\right)} \sin\left(d x + c\right)}{13860 \, d}"," ",0,"-1/13860*(1386*a*cos(d*x + c)^10 - 3465*a*cos(d*x + c)^8 + 2310*a*cos(d*x + c)^6 + 20*(63*b*cos(d*x + c)^10 - 161*b*cos(d*x + c)^8 + 113*b*cos(d*x + c)^6 - 3*b*cos(d*x + c)^4 - 4*b*cos(d*x + c)^2 - 8*b)*sin(d*x + c))/d","A",0
1199,1,95,0,0.907694," ","integrate(cos(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{126 \, b \cos\left(d x + c\right)^{10} - 315 \, b \cos\left(d x + c\right)^{8} + 210 \, b \cos\left(d x + c\right)^{6} - 4 \, {\left(35 \, a \cos\left(d x + c\right)^{8} - 50 \, a \cos\left(d x + c\right)^{6} + 3 \, a \cos\left(d x + c\right)^{4} + 4 \, a \cos\left(d x + c\right)^{2} + 8 \, a\right)} \sin\left(d x + c\right)}{1260 \, d}"," ",0,"-1/1260*(126*b*cos(d*x + c)^10 - 315*b*cos(d*x + c)^8 + 210*b*cos(d*x + c)^6 - 4*(35*a*cos(d*x + c)^8 - 50*a*cos(d*x + c)^6 + 3*a*cos(d*x + c)^4 + 4*a*cos(d*x + c)^2 + 8*a)*sin(d*x + c))/d","A",0
1200,1,84,0,1.572376," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{315 \, a \cos\left(d x + c\right)^{8} - 420 \, a \cos\left(d x + c\right)^{6} + 8 \, {\left(35 \, b \cos\left(d x + c\right)^{8} - 50 \, b \cos\left(d x + c\right)^{6} + 3 \, b \cos\left(d x + c\right)^{4} + 4 \, b \cos\left(d x + c\right)^{2} + 8 \, b\right)} \sin\left(d x + c\right)}{2520 \, d}"," ",0,"1/2520*(315*a*cos(d*x + c)^8 - 420*a*cos(d*x + c)^6 + 8*(35*b*cos(d*x + c)^8 - 50*b*cos(d*x + c)^6 + 3*b*cos(d*x + c)^4 + 4*b*cos(d*x + c)^2 + 8*b)*sin(d*x + c))/d","A",0
1201,1,73,0,1.453443," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, b \cos\left(d x + c\right)^{8} - 140 \, b \cos\left(d x + c\right)^{6} - 8 \, {\left(15 \, a \cos\left(d x + c\right)^{6} - 3 \, a \cos\left(d x + c\right)^{4} - 4 \, a \cos\left(d x + c\right)^{2} - 8 \, a\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*b*cos(d*x + c)^8 - 140*b*cos(d*x + c)^6 - 8*(15*a*cos(d*x + c)^6 - 3*a*cos(d*x + c)^4 - 4*a*cos(d*x + c)^2 - 8*a)*sin(d*x + c))/d","A",0
1202,1,62,0,1.297307," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{35 \, a \cos\left(d x + c\right)^{6} + 2 \, {\left(15 \, b \cos\left(d x + c\right)^{6} - 3 \, b \cos\left(d x + c\right)^{4} - 4 \, b \cos\left(d x + c\right)^{2} - 8 \, b\right)} \sin\left(d x + c\right)}{210 \, d}"," ",0,"-1/210*(35*a*cos(d*x + c)^6 + 2*(15*b*cos(d*x + c)^6 - 3*b*cos(d*x + c)^4 - 4*b*cos(d*x + c)^2 - 8*b)*sin(d*x + c))/d","A",0
1203,1,74,0,1.456857," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, a \cos\left(d x + c\right)^{4} + 30 \, a \cos\left(d x + c\right)^{2} + 60 \, a \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, {\left(3 \, b \cos\left(d x + c\right)^{4} + 4 \, b \cos\left(d x + c\right)^{2} + 8 \, b\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(15*a*cos(d*x + c)^4 + 30*a*cos(d*x + c)^2 + 60*a*log(1/2*sin(d*x + c)) + 4*(3*b*cos(d*x + c)^4 + 4*b*cos(d*x + c)^2 + 8*b)*sin(d*x + c))/d","A",0
1204,1,91,0,1.261550," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{32 \, a \cos\left(d x + c\right)^{4} + 128 \, a \cos\left(d x + c\right)^{2} + 96 \, b \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 3 \, {\left(8 \, b \cos\left(d x + c\right)^{4} + 16 \, b \cos\left(d x + c\right)^{2} - 11 \, b\right)} \sin\left(d x + c\right) - 256 \, a}{96 \, d \sin\left(d x + c\right)}"," ",0,"1/96*(32*a*cos(d*x + c)^4 + 128*a*cos(d*x + c)^2 + 96*b*log(1/2*sin(d*x + c))*sin(d*x + c) + 3*(8*b*cos(d*x + c)^4 + 16*b*cos(d*x + c)^2 - 11*b)*sin(d*x + c) - 256*a)/(d*sin(d*x + c))","A",0
1205,1,102,0,1.428828," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{6 \, a \cos\left(d x + c\right)^{4} - 9 \, a \cos\left(d x + c\right)^{2} + 24 \, {\left(a \cos\left(d x + c\right)^{2} - a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 4 \, {\left(b \cos\left(d x + c\right)^{4} + 4 \, b \cos\left(d x + c\right)^{2} - 8 \, b\right)} \sin\left(d x + c\right) - 3 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/12*(6*a*cos(d*x + c)^4 - 9*a*cos(d*x + c)^2 + 24*(a*cos(d*x + c)^2 - a)*log(1/2*sin(d*x + c)) + 4*(b*cos(d*x + c)^4 + 4*b*cos(d*x + c)^2 - 8*b)*sin(d*x + c) - 3*a)/(d*cos(d*x + c)^2 - d)","A",0
1206,1,117,0,1.167286," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, a \cos\left(d x + c\right)^{4} - 48 \, a \cos\left(d x + c\right)^{2} + 24 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 3 \, {\left(2 \, b \cos\left(d x + c\right)^{4} - 3 \, b \cos\left(d x + c\right)^{2} - b\right)} \sin\left(d x + c\right) + 32 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(12*a*cos(d*x + c)^4 - 48*a*cos(d*x + c)^2 + 24*(b*cos(d*x + c)^2 - b)*log(1/2*sin(d*x + c))*sin(d*x + c) + 3*(2*b*cos(d*x + c)^4 - 3*b*cos(d*x + c)^2 - b)*sin(d*x + c) + 32*a)/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1207,1,110,0,1.286881," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{12 \, a \cos\left(d x + c\right)^{2} - 12 \, {\left(a \cos\left(d x + c\right)^{4} - 2 \, a \cos\left(d x + c\right)^{2} + a\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, {\left(3 \, b \cos\left(d x + c\right)^{4} - 12 \, b \cos\left(d x + c\right)^{2} + 8 \, b\right)} \sin\left(d x + c\right) - 9 \, a}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/12*(12*a*cos(d*x + c)^2 - 12*(a*cos(d*x + c)^4 - 2*a*cos(d*x + c)^2 + a)*log(1/2*sin(d*x + c)) - 4*(3*b*cos(d*x + c)^4 - 12*b*cos(d*x + c)^2 + 8*b)*sin(d*x + c) - 9*a)/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
1208,1,124,0,1.420974," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{60 \, a \cos\left(d x + c\right)^{4} - 80 \, a \cos\left(d x + c\right)^{2} - 60 \, {\left(b \cos\left(d x + c\right)^{4} - 2 \, b \cos\left(d x + c\right)^{2} + b\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 15 \, {\left(4 \, b \cos\left(d x + c\right)^{2} - 3 \, b\right)} \sin\left(d x + c\right) + 32 \, a}{60 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(60*a*cos(d*x + c)^4 - 80*a*cos(d*x + c)^2 - 60*(b*cos(d*x + c)^4 - 2*b*cos(d*x + c)^2 + b)*log(1/2*sin(d*x + c))*sin(d*x + c) + 15*(4*b*cos(d*x + c)^2 - 3*b)*sin(d*x + c) + 32*a)/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
1209,1,100,0,1.334718," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, a \cos\left(d x + c\right)^{4} - 15 \, a \cos\left(d x + c\right)^{2} + 2 \, {\left(15 \, b \cos\left(d x + c\right)^{4} - 20 \, b \cos\left(d x + c\right)^{2} + 8 \, b\right)} \sin\left(d x + c\right) + 5 \, a}{30 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/30*(15*a*cos(d*x + c)^4 - 15*a*cos(d*x + c)^2 + 2*(15*b*cos(d*x + c)^4 - 20*b*cos(d*x + c)^2 + 8*b)*sin(d*x + c) + 5*a)/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
1210,1,106,0,1.136981," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{70 \, a \cos\left(d x + c\right)^{4} - 56 \, a \cos\left(d x + c\right)^{2} + 35 \, {\left(3 \, b \cos\left(d x + c\right)^{4} - 3 \, b \cos\left(d x + c\right)^{2} + b\right)} \sin\left(d x + c\right) + 16 \, a}{210 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/210*(70*a*cos(d*x + c)^4 - 56*a*cos(d*x + c)^2 + 35*(3*b*cos(d*x + c)^4 - 3*b*cos(d*x + c)^2 + b)*sin(d*x + c) + 16*a)/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1211,1,109,0,0.699269," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{210 \, a \cos\left(d x + c\right)^{4} - 140 \, a \cos\left(d x + c\right)^{2} + 8 \, {\left(35 \, b \cos\left(d x + c\right)^{4} - 28 \, b \cos\left(d x + c\right)^{2} + 8 \, b\right)} \sin\left(d x + c\right) + 35 \, a}{840 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/840*(210*a*cos(d*x + c)^4 - 140*a*cos(d*x + c)^2 + 8*(35*b*cos(d*x + c)^4 - 28*b*cos(d*x + c)^2 + 8*b)*sin(d*x + c) + 35*a)/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
1212,1,115,0,1.192058," ","integrate(cos(d*x+c)^5*csc(d*x+c)^10*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{504 \, a \cos\left(d x + c\right)^{4} - 288 \, a \cos\left(d x + c\right)^{2} + 105 \, {\left(6 \, b \cos\left(d x + c\right)^{4} - 4 \, b \cos\left(d x + c\right)^{2} + b\right)} \sin\left(d x + c\right) + 64 \, a}{2520 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/2520*(504*a*cos(d*x + c)^4 - 288*a*cos(d*x + c)^2 + 105*(6*b*cos(d*x + c)^4 - 4*b*cos(d*x + c)^2 + b)*sin(d*x + c) + 64*a)/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
1213,1,122,0,1.447387," ","integrate(cos(d*x+c)^5*csc(d*x+c)^11*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{210 \, a \cos\left(d x + c\right)^{4} - 105 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(63 \, b \cos\left(d x + c\right)^{4} - 36 \, b \cos\left(d x + c\right)^{2} + 8 \, b\right)} \sin\left(d x + c\right) + 21 \, a}{1260 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/1260*(210*a*cos(d*x + c)^4 - 105*a*cos(d*x + c)^2 + 4*(63*b*cos(d*x + c)^4 - 36*b*cos(d*x + c)^2 + 8*b)*sin(d*x + c) + 21*a)/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","A",0
1214,1,128,0,1.374438," ","integrate(cos(d*x+c)^5*csc(d*x+c)^12*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{1980 \, a \cos\left(d x + c\right)^{4} - 880 \, a \cos\left(d x + c\right)^{2} + 231 \, {\left(10 \, b \cos\left(d x + c\right)^{4} - 5 \, b \cos\left(d x + c\right)^{2} + b\right)} \sin\left(d x + c\right) + 160 \, a}{13860 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/13860*(1980*a*cos(d*x + c)^4 - 880*a*cos(d*x + c)^2 + 231*(10*b*cos(d*x + c)^4 - 5*b*cos(d*x + c)^2 + b)*sin(d*x + c) + 160*a)/((d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1215,1,121,0,1.383416," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{315 \, a b \cos\left(d x + c\right)^{8} - 420 \, a b \cos\left(d x + c\right)^{6} + 4 \, {\left(35 \, b^{2} \cos\left(d x + c\right)^{8} - 5 \, {\left(9 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(3 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} + 24 \, a^{2} + 8 \, b^{2}\right)} \sin\left(d x + c\right)}{1260 \, d}"," ",0,"1/1260*(315*a*b*cos(d*x + c)^8 - 420*a*b*cos(d*x + c)^6 + 4*(35*b^2*cos(d*x + c)^8 - 5*(9*a^2 + 10*b^2)*cos(d*x + c)^6 + 3*(3*a^2 + b^2)*cos(d*x + c)^4 + 4*(3*a^2 + b^2)*cos(d*x + c)^2 + 24*a^2 + 8*b^2)*sin(d*x + c))/d","A",0
1216,1,85,0,1.428940," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{105 \, b^{2} \cos\left(d x + c\right)^{8} - 140 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{6} - 16 \, {\left(15 \, a b \cos\left(d x + c\right)^{6} - 3 \, a b \cos\left(d x + c\right)^{4} - 4 \, a b \cos\left(d x + c\right)^{2} - 8 \, a b\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*b^2*cos(d*x + c)^8 - 140*(a^2 + b^2)*cos(d*x + c)^6 - 16*(15*a*b*cos(d*x + c)^6 - 3*a*b*cos(d*x + c)^4 - 4*a*b*cos(d*x + c)^2 - 8*a*b)*sin(d*x + c))/d","A",0
1217,1,96,0,1.287670," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{10 \, b^{2} \cos\left(d x + c\right)^{6} - 15 \, a^{2} \cos\left(d x + c\right)^{4} - 30 \, a^{2} \cos\left(d x + c\right)^{2} - 60 \, a^{2} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 8 \, {\left(3 \, a b \cos\left(d x + c\right)^{4} + 4 \, a b \cos\left(d x + c\right)^{2} + 8 \, a b\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(10*b^2*cos(d*x + c)^6 - 15*a^2*cos(d*x + c)^4 - 30*a^2*cos(d*x + c)^2 - 60*a^2*log(1/2*sin(d*x + c)) - 8*(3*a*b*cos(d*x + c)^4 + 4*a*b*cos(d*x + c)^2 + 8*a*b)*sin(d*x + c))/d","A",0
1218,1,135,0,1.309090," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{48 \, b^{2} \cos\left(d x + c\right)^{6} - 16 \, {\left(5 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} - 480 \, a b \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 64 \, {\left(5 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} + 640 \, a^{2} - 128 \, b^{2} - 15 \, {\left(8 \, a b \cos\left(d x + c\right)^{4} + 16 \, a b \cos\left(d x + c\right)^{2} - 11 \, a b\right)} \sin\left(d x + c\right)}{240 \, d \sin\left(d x + c\right)}"," ",0,"-1/240*(48*b^2*cos(d*x + c)^6 - 16*(5*a^2 - b^2)*cos(d*x + c)^4 - 480*a*b*log(1/2*sin(d*x + c))*sin(d*x + c) - 64*(5*a^2 - b^2)*cos(d*x + c)^2 + 640*a^2 - 128*b^2 - 15*(8*a*b*cos(d*x + c)^4 + 16*a*b*cos(d*x + c)^2 - 11*a*b)*sin(d*x + c))/(d*sin(d*x + c))","A",0
1219,1,160,0,1.512413," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{24 \, b^{2} \cos\left(d x + c\right)^{6} - 24 \, {\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 9 \, {\left(8 \, a^{2} - 9 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 24 \, a^{2} + 33 \, b^{2} - 96 \, {\left({\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} + b^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 64 \, {\left(a b \cos\left(d x + c\right)^{4} + 4 \, a b \cos\left(d x + c\right)^{2} - 8 \, a b\right)} \sin\left(d x + c\right)}{96 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/96*(24*b^2*cos(d*x + c)^6 - 24*(2*a^2 - b^2)*cos(d*x + c)^4 + 9*(8*a^2 - 9*b^2)*cos(d*x + c)^2 + 24*a^2 + 33*b^2 - 96*((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a^2 + b^2)*log(1/2*sin(d*x + c)) - 64*(a*b*cos(d*x + c)^4 + 4*a*b*cos(d*x + c)^2 - 8*a*b)*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
1220,1,158,0,1.441262," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, b^{2} \cos\left(d x + c\right)^{6} - 6 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{4} + 24 \, {\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 24 \, {\left(a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 16 \, a^{2} + 16 \, b^{2} - 3 \, {\left(2 \, a b \cos\left(d x + c\right)^{4} - 3 \, a b \cos\left(d x + c\right)^{2} - a b\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/6*(2*b^2*cos(d*x + c)^6 - 6*(a^2 - b^2)*cos(d*x + c)^4 + 24*(a^2 - b^2)*cos(d*x + c)^2 - 24*(a*b*cos(d*x + c)^2 - a*b)*log(1/2*sin(d*x + c))*sin(d*x + c) - 16*a^2 + 16*b^2 - 3*(2*a*b*cos(d*x + c)^4 - 3*a*b*cos(d*x + c)^2 - a*b)*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1221,1,177,0,1.265556," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{6 \, b^{2} \cos\left(d x + c\right)^{6} - 15 \, b^{2} \cos\left(d x + c\right)^{4} + 6 \, {\left(2 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} - 9 \, a^{2} + 3 \, b^{2} - 12 \, {\left({\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} - 2 \, b^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 8 \, {\left(3 \, a b \cos\left(d x + c\right)^{4} - 12 \, a b \cos\left(d x + c\right)^{2} + 8 \, a b\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/12*(6*b^2*cos(d*x + c)^6 - 15*b^2*cos(d*x + c)^4 + 6*(2*a^2 + b^2)*cos(d*x + c)^2 - 9*a^2 + 3*b^2 - 12*((a^2 - 2*b^2)*cos(d*x + c)^4 - 2*(a^2 - 2*b^2)*cos(d*x + c)^2 + a^2 - 2*b^2)*log(1/2*sin(d*x + c)) - 8*(3*a*b*cos(d*x + c)^4 - 12*a*b*cos(d*x + c)^2 + 8*a*b)*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
1222,1,166,0,1.495348," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{30 \, b^{2} \cos\left(d x + c\right)^{6} + 30 \, {\left(a^{2} - 5 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 40 \, {\left(a^{2} - 5 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 60 \, {\left(a b \cos\left(d x + c\right)^{4} - 2 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 16 \, a^{2} - 80 \, b^{2} + 15 \, {\left(4 \, a b \cos\left(d x + c\right)^{2} - 3 \, a b\right)} \sin\left(d x + c\right)}{30 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/30*(30*b^2*cos(d*x + c)^6 + 30*(a^2 - 5*b^2)*cos(d*x + c)^4 - 40*(a^2 - 5*b^2)*cos(d*x + c)^2 - 60*(a*b*cos(d*x + c)^4 - 2*a*b*cos(d*x + c)^2 + a*b)*log(1/2*sin(d*x + c))*sin(d*x + c) + 16*a^2 - 80*b^2 + 15*(4*a*b*cos(d*x + c)^2 - 3*a*b)*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
1223,1,183,0,1.352854," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{30 \, {\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 15 \, {\left(2 \, a^{2} - 7 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 10 \, a^{2} - 45 \, b^{2} + 60 \, {\left(b^{2} \cos\left(d x + c\right)^{6} - 3 \, b^{2} \cos\left(d x + c\right)^{4} + 3 \, b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + 8 \, {\left(15 \, a b \cos\left(d x + c\right)^{4} - 20 \, a b \cos\left(d x + c\right)^{2} + 8 \, a b\right)} \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/60*(30*(a^2 - 2*b^2)*cos(d*x + c)^4 - 15*(2*a^2 - 7*b^2)*cos(d*x + c)^2 + 10*a^2 - 45*b^2 + 60*(b^2*cos(d*x + c)^6 - 3*b^2*cos(d*x + c)^4 + 3*b^2*cos(d*x + c)^2 - b^2)*log(1/2*sin(d*x + c)) + 8*(15*a*b*cos(d*x + c)^4 - 20*a*b*cos(d*x + c)^2 + 8*a*b)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","A",0
1224,1,146,0,1.282222," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{105 \, b^{2} \cos\left(d x + c\right)^{6} - 35 \, {\left(a^{2} + 7 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 28 \, {\left(a^{2} + 7 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 8 \, a^{2} - 56 \, b^{2} - 35 \, {\left(3 \, a b \cos\left(d x + c\right)^{4} - 3 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \sin\left(d x + c\right)}{105 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/105*(105*b^2*cos(d*x + c)^6 - 35*(a^2 + 7*b^2)*cos(d*x + c)^4 + 28*(a^2 + 7*b^2)*cos(d*x + c)^2 - 8*a^2 - 56*b^2 - 35*(3*a*b*cos(d*x + c)^4 - 3*a*b*cos(d*x + c)^2 + a*b)*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1225,1,148,0,1.266547," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{420 \, b^{2} \cos\left(d x + c\right)^{6} - 210 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 140 \, {\left(a^{2} + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 35 \, a^{2} - 140 \, b^{2} - 16 \, {\left(35 \, a b \cos\left(d x + c\right)^{4} - 28 \, a b \cos\left(d x + c\right)^{2} + 8 \, a b\right)} \sin\left(d x + c\right)}{840 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"1/840*(420*b^2*cos(d*x + c)^6 - 210*(a^2 + 4*b^2)*cos(d*x + c)^4 + 140*(a^2 + 4*b^2)*cos(d*x + c)^2 - 35*a^2 - 140*b^2 - 16*(35*a*b*cos(d*x + c)^4 - 28*a*b*cos(d*x + c)^2 + 8*a*b)*sin(d*x + c))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","A",0
1226,1,279,0,1.439778," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{112 \, a b^{6} \cos\left(d x + c\right)^{6} + 480 \, a^{7} - 3240 \, a^{5} b^{2} + 3185 \, a^{3} b^{4} - 487 \, a b^{6} - 8 \, {\left(35 \, a^{3} b^{4} - 8 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(105 \, a^{5} b^{2} - 115 \, a^{3} b^{4} + 16 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 480 \, {\left(7 \, a^{7} - 10 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + {\left(7 \, a^{6} b - 10 \, a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(80 \, b^{7} \cos\left(d x + c\right)^{6} - 168 \, a^{2} b^{5} \cos\left(d x + c\right)^{4} + 2880 \, a^{6} b - 3800 \, a^{4} b^{3} + 1007 \, a^{2} b^{5} - 25 \, b^{7} + 16 \, {\left(35 \, a^{4} b^{3} - 29 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{480 \, {\left(b^{9} d \sin\left(d x + c\right) + a b^{8} d\right)}}"," ",0,"1/480*(112*a*b^6*cos(d*x + c)^6 + 480*a^7 - 3240*a^5*b^2 + 3185*a^3*b^4 - 487*a*b^6 - 8*(35*a^3*b^4 - 8*a*b^6)*cos(d*x + c)^4 + 16*(105*a^5*b^2 - 115*a^3*b^4 + 16*a*b^6)*cos(d*x + c)^2 + 480*(7*a^7 - 10*a^5*b^2 + 3*a^3*b^4 + (7*a^6*b - 10*a^4*b^3 + 3*a^2*b^5)*sin(d*x + c))*log(b*sin(d*x + c) + a) - (80*b^7*cos(d*x + c)^6 - 168*a^2*b^5*cos(d*x + c)^4 + 2880*a^6*b - 3800*a^4*b^3 + 1007*a^2*b^5 - 25*b^7 + 16*(35*a^4*b^3 - 29*a^2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^9*d*sin(d*x + c) + a*b^8*d)","A",0
1227,1,246,0,1.883546," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{48 \, b^{6} \cos\left(d x + c\right)^{6} + 240 \, a^{6} - 1440 \, a^{4} b^{2} + 1275 \, a^{2} b^{4} - 128 \, b^{6} - 8 \, {\left(15 \, a^{2} b^{4} - 2 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(45 \, a^{4} b^{2} - 45 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 480 \, {\left(3 \, a^{6} - 4 \, a^{4} b^{2} + a^{2} b^{4} + {\left(3 \, a^{5} b - 4 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(72 \, a b^{5} \cos\left(d x + c\right)^{4} - 1200 \, a^{5} b + 1440 \, a^{3} b^{3} - 293 \, a b^{5} - 16 \, {\left(15 \, a^{3} b^{3} - 11 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{240 \, {\left(b^{8} d \sin\left(d x + c\right) + a b^{7} d\right)}}"," ",0,"-1/240*(48*b^6*cos(d*x + c)^6 + 240*a^6 - 1440*a^4*b^2 + 1275*a^2*b^4 - 128*b^6 - 8*(15*a^2*b^4 - 2*b^6)*cos(d*x + c)^4 + 16*(45*a^4*b^2 - 45*a^2*b^4 + 4*b^6)*cos(d*x + c)^2 + 480*(3*a^6 - 4*a^4*b^2 + a^2*b^4 + (3*a^5*b - 4*a^3*b^3 + a*b^5)*sin(d*x + c))*log(b*sin(d*x + c) + a) + (72*a*b^5*cos(d*x + c)^4 - 1200*a^5*b + 1440*a^3*b^3 - 293*a*b^5 - 16*(15*a^3*b^3 - 11*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^8*d*sin(d*x + c) + a*b^7*d)","A",0
1228,1,203,0,0.988924," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{40 \, a b^{4} \cos\left(d x + c\right)^{4} - 96 \, a^{5} + 504 \, a^{3} b^{2} - 383 \, a b^{4} - 16 \, {\left(15 \, a^{3} b^{2} - 13 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} - 96 \, {\left(5 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4} + {\left(5 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(24 \, b^{5} \cos\left(d x + c\right)^{4} - 384 \, a^{4} b + 392 \, a^{2} b^{3} - 33 \, b^{5} - 16 \, {\left(5 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{96 \, {\left(b^{7} d \sin\left(d x + c\right) + a b^{6} d\right)}}"," ",0,"-1/96*(40*a*b^4*cos(d*x + c)^4 - 96*a^5 + 504*a^3*b^2 - 383*a*b^4 - 16*(15*a^3*b^2 - 13*a*b^4)*cos(d*x + c)^2 - 96*(5*a^5 - 6*a^3*b^2 + a*b^4 + (5*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c))*log(b*sin(d*x + c) + a) - (24*b^5*cos(d*x + c)^4 - 384*a^4*b + 392*a^2*b^3 - 33*b^5 - 16*(5*a^2*b^3 - 3*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^7*d*sin(d*x + c) + a*b^6*d)","A",0
1229,1,189,0,1.546205," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, a^{3} b^{2} \cos\left(d x + c\right)^{2} + 4 \, a^{5} - 15 \, a^{3} b^{2} + 4 \, a b^{4} + 4 \, {\left(3 \, a^{5} - 2 \, a^{3} b^{2} - a b^{4} + {\left(3 \, a^{4} b - 2 \, a^{2} b^{3} - b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 4 \, {\left(b^{5} \sin\left(d x + c\right) + a b^{4}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(2 \, a^{2} b^{3} \cos\left(d x + c\right)^{2} + 8 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{2} b^{5} d \sin\left(d x + c\right) + a^{3} b^{4} d\right)}}"," ",0,"1/4*(6*a^3*b^2*cos(d*x + c)^2 + 4*a^5 - 15*a^3*b^2 + 4*a*b^4 + 4*(3*a^5 - 2*a^3*b^2 - a*b^4 + (3*a^4*b - 2*a^2*b^3 - b^5)*sin(d*x + c))*log(b*sin(d*x + c) + a) + 4*(b^5*sin(d*x + c) + a*b^4)*log(-1/2*sin(d*x + c)) - (2*a^2*b^3*cos(d*x + c)^2 + 8*a^4*b - a^2*b^3)*sin(d*x + c))/(a^2*b^5*d*sin(d*x + c) + a^3*b^4*d)","A",0
1230,1,214,0,1.020919," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{a^{4} b \cos\left(d x + c\right)^{2} - a^{4} b + a^{2} b^{3} + 2 \, {\left(a^{4} b - b^{5} - {\left(a^{4} b - b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} - a b^{4}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, {\left(b^{5} \cos\left(d x + c\right)^{2} - a b^{4} \sin\left(d x + c\right) - b^{5}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + {\left(a^{3} b^{2} \cos\left(d x + c\right)^{2} + a^{5} - 3 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \sin\left(d x + c\right)}{a^{3} b^{4} d \cos\left(d x + c\right)^{2} - a^{4} b^{3} d \sin\left(d x + c\right) - a^{3} b^{4} d}"," ",0,"(a^4*b*cos(d*x + c)^2 - a^4*b + a^2*b^3 + 2*(a^4*b - b^5 - (a^4*b - b^5)*cos(d*x + c)^2 + (a^5 - a*b^4)*sin(d*x + c))*log(b*sin(d*x + c) + a) - 2*(b^5*cos(d*x + c)^2 - a*b^4*sin(d*x + c) - b^5)*log(1/2*sin(d*x + c)) + (a^3*b^2*cos(d*x + c)^2 + a^5 - 3*a^3*b^2 + 2*a*b^4)*sin(d*x + c))/(a^3*b^4*d*cos(d*x + c)^2 - a^4*b^3*d*sin(d*x + c) - a^3*b^4*d)","A",0
1231,1,335,0,1.180080," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{3 \, a^{2} b^{3} \sin\left(d x + c\right) + 2 \, a^{5} - 5 \, a^{3} b^{2} + 6 \, a b^{4} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + 2 \, a^{3} b^{2} - 3 \, a b^{4} - {\left(a^{5} + 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b + 2 \, a^{2} b^{3} - 3 \, b^{5} - {\left(a^{4} b + 2 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, {\left(2 \, a^{3} b^{2} - 3 \, a b^{4} - {\left(2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{3} - 3 \, b^{5} - {\left(2 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right)}{2 \, {\left(a^{5} b^{2} d \cos\left(d x + c\right)^{2} - a^{5} b^{2} d + {\left(a^{4} b^{3} d \cos\left(d x + c\right)^{2} - a^{4} b^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/2*(3*a^2*b^3*sin(d*x + c) + 2*a^5 - 5*a^3*b^2 + 6*a*b^4 - 2*(a^5 - 2*a^3*b^2 + 3*a*b^4)*cos(d*x + c)^2 + 2*(a^5 + 2*a^3*b^2 - 3*a*b^4 - (a^5 + 2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + (a^4*b + 2*a^2*b^3 - 3*b^5 - (a^4*b + 2*a^2*b^3 - 3*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(b*sin(d*x + c) + a) - 2*(2*a^3*b^2 - 3*a*b^4 - (2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + (2*a^2*b^3 - 3*b^5 - (2*a^2*b^3 - 3*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*sin(d*x + c)))/(a^5*b^2*d*cos(d*x + c)^2 - a^5*b^2*d + (a^4*b^3*d*cos(d*x + c)^2 - a^4*b^3*d)*sin(d*x + c))","B",0
1232,1,401,0,1.413533," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{5 \, a^{4} b - 6 \, a^{2} b^{3} - 6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(a^{2} b^{3} - b^{5} + {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b^{2} - a b^{4} - {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 12 \, {\left(a^{2} b^{3} - b^{5} + {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b^{2} - a b^{4} - {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(3 \, a^{5} - 14 \, a^{3} b^{2} + 12 \, a b^{4} - 3 \, {\left(a^{5} - 4 \, a^{3} b^{2} + 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{5} b^{2} d \cos\left(d x + c\right)^{4} - 2 \, a^{5} b^{2} d \cos\left(d x + c\right)^{2} + a^{5} b^{2} d - {\left(a^{6} b d \cos\left(d x + c\right)^{2} - a^{6} b d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/3*(5*a^4*b - 6*a^2*b^3 - 6*(a^4*b - a^2*b^3)*cos(d*x + c)^2 - 12*(a^2*b^3 - b^5 + (a^2*b^3 - b^5)*cos(d*x + c)^4 - 2*(a^2*b^3 - b^5)*cos(d*x + c)^2 + (a^3*b^2 - a*b^4 - (a^3*b^2 - a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*log(b*sin(d*x + c) + a) + 12*(a^2*b^3 - b^5 + (a^2*b^3 - b^5)*cos(d*x + c)^4 - 2*(a^2*b^3 - b^5)*cos(d*x + c)^2 + (a^3*b^2 - a*b^4 - (a^3*b^2 - a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*sin(d*x + c)) - (3*a^5 - 14*a^3*b^2 + 12*a*b^4 - 3*(a^5 - 4*a^3*b^2 + 4*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/(a^5*b^2*d*cos(d*x + c)^4 - 2*a^5*b^2*d*cos(d*x + c)^2 + a^5*b^2*d - (a^6*b*d*cos(d*x + c)^2 - a^6*b*d)*sin(d*x + c))","B",0
1233,1,542,0,1.641664," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{21 \, a^{5} - 82 \, a^{3} b^{2} + 60 \, a b^{4} + 12 \, {\left(a^{5} - 6 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(18 \, a^{5} - 77 \, a^{3} b^{2} + 60 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(a^{5} - 6 \, a^{3} b^{2} + 5 \, a b^{4} + {\left(a^{5} - 6 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} - 6 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 6 \, a^{2} b^{3} + 5 \, b^{5} + {\left(a^{4} b - 6 \, a^{2} b^{3} + 5 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b - 6 \, a^{2} b^{3} + 5 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 12 \, {\left(a^{5} - 6 \, a^{3} b^{2} + 5 \, a b^{4} + {\left(a^{5} - 6 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} - 6 \, a^{3} b^{2} + 5 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{4} b - 6 \, a^{2} b^{3} + 5 \, b^{5} + {\left(a^{4} b - 6 \, a^{2} b^{3} + 5 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b - 6 \, a^{2} b^{3} + 5 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(31 \, a^{4} b - 30 \, a^{2} b^{3} - 6 \, {\left(6 \, a^{4} b - 5 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{7} d \cos\left(d x + c\right)^{4} - 2 \, a^{7} d \cos\left(d x + c\right)^{2} + a^{7} d + {\left(a^{6} b d \cos\left(d x + c\right)^{4} - 2 \, a^{6} b d \cos\left(d x + c\right)^{2} + a^{6} b d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/12*(21*a^5 - 82*a^3*b^2 + 60*a*b^4 + 12*(a^5 - 6*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^4 - 2*(18*a^5 - 77*a^3*b^2 + 60*a*b^4)*cos(d*x + c)^2 - 12*(a^5 - 6*a^3*b^2 + 5*a*b^4 + (a^5 - 6*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^4 - 2*(a^5 - 6*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^2 + (a^4*b - 6*a^2*b^3 + 5*b^5 + (a^4*b - 6*a^2*b^3 + 5*b^5)*cos(d*x + c)^4 - 2*(a^4*b - 6*a^2*b^3 + 5*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(b*sin(d*x + c) + a) + 12*(a^5 - 6*a^3*b^2 + 5*a*b^4 + (a^5 - 6*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^4 - 2*(a^5 - 6*a^3*b^2 + 5*a*b^4)*cos(d*x + c)^2 + (a^4*b - 6*a^2*b^3 + 5*b^5 + (a^4*b - 6*a^2*b^3 + 5*b^5)*cos(d*x + c)^4 - 2*(a^4*b - 6*a^2*b^3 + 5*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*sin(d*x + c)) - (31*a^4*b - 30*a^2*b^3 - 6*(6*a^4*b - 5*a^2*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(a^7*d*cos(d*x + c)^4 - 2*a^7*d*cos(d*x + c)^2 + a^7*d + (a^6*b*d*cos(d*x + c)^4 - 2*a^6*b*d*cos(d*x + c)^2 + a^6*b*d)*sin(d*x + c))","B",0
1234,1,696,0,1.318928," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, a^{6} - 105 \, a^{4} b^{2} + 90 \, a^{2} b^{4} + 30 \, {\left(a^{6} - 4 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(8 \, a^{6} - 45 \, a^{4} b^{2} + 36 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 60 \, {\left({\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{4} b^{2} + 4 \, a^{2} b^{4} - 3 \, b^{6} - 3 \, {\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{5} b - 4 \, a^{3} b^{3} + 3 \, a b^{5} + {\left(a^{5} b - 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b - 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 60 \, {\left({\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{4} b^{2} + 4 \, a^{2} b^{4} - 3 \, b^{6} - 3 \, {\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{5} b - 4 \, a^{3} b^{3} + 3 \, a b^{5} + {\left(a^{5} b - 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b - 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) + {\left(91 \, a^{5} b - 270 \, a^{3} b^{3} + 180 \, a b^{5} + 60 \, {\left(a^{5} b - 4 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 10 \, {\left(16 \, a^{5} b - 51 \, a^{3} b^{3} + 36 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{30 \, {\left(a^{7} b d \cos\left(d x + c\right)^{6} - 3 \, a^{7} b d \cos\left(d x + c\right)^{4} + 3 \, a^{7} b d \cos\left(d x + c\right)^{2} - a^{7} b d - {\left(a^{8} d \cos\left(d x + c\right)^{4} - 2 \, a^{8} d \cos\left(d x + c\right)^{2} + a^{8} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/30*(16*a^6 - 105*a^4*b^2 + 90*a^2*b^4 + 30*(a^6 - 4*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)^4 - 5*(8*a^6 - 45*a^4*b^2 + 36*a^2*b^4)*cos(d*x + c)^2 + 60*((a^4*b^2 - 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^6 - a^4*b^2 + 4*a^2*b^4 - 3*b^6 - 3*(a^4*b^2 - 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^4 + 3*(a^4*b^2 - 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^2 - (a^5*b - 4*a^3*b^3 + 3*a*b^5 + (a^5*b - 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^4 - 2*(a^5*b - 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(b*sin(d*x + c) + a) - 60*((a^4*b^2 - 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^6 - a^4*b^2 + 4*a^2*b^4 - 3*b^6 - 3*(a^4*b^2 - 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^4 + 3*(a^4*b^2 - 4*a^2*b^4 + 3*b^6)*cos(d*x + c)^2 - (a^5*b - 4*a^3*b^3 + 3*a*b^5 + (a^5*b - 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^4 - 2*(a^5*b - 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*sin(d*x + c)) + (91*a^5*b - 270*a^3*b^3 + 180*a*b^5 + 60*(a^5*b - 4*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^4 - 10*(16*a^5*b - 51*a^3*b^3 + 36*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(a^7*b*d*cos(d*x + c)^6 - 3*a^7*b*d*cos(d*x + c)^4 + 3*a^7*b*d*cos(d*x + c)^2 - a^7*b*d - (a^8*d*cos(d*x + c)^4 - 2*a^8*d*cos(d*x + c)^2 + a^8*d)*sin(d*x + c))","B",0
1235,1,572,0,1.666414," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, {\left(a b n^{6} + 22 \, a b n^{5} + 190 \, a b n^{4} + 820 \, a b n^{3} + 1849 \, a b n^{2} + 2038 \, a b n + 840 \, a b\right)} \cos\left(d x + c\right)^{6} - 16 \, a b n^{4} - 256 \, a b n^{3} - 2 \, {\left(a b n^{6} + 18 \, a b n^{5} + 118 \, a b n^{4} + 348 \, a b n^{3} + 457 \, a b n^{2} + 210 \, a b n\right)} \cos\left(d x + c\right)^{4} - 1376 \, a b n^{2} - 2816 \, a b n - 8 \, {\left(a b n^{5} + 16 \, a b n^{4} + 86 \, a b n^{3} + 176 \, a b n^{2} + 105 \, a b n\right)} \cos\left(d x + c\right)^{2} - 1680 \, a b + {\left({\left(b^{2} n^{6} + 21 \, b^{2} n^{5} + 175 \, b^{2} n^{4} + 735 \, b^{2} n^{3} + 1624 \, b^{2} n^{2} + 1764 \, b^{2} n + 720 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 8 \, {\left(a^{2} + b^{2}\right)} n^{4} - {\left({\left(a^{2} + b^{2}\right)} n^{6} + {\left(23 \, a^{2} + 17 \, b^{2}\right)} n^{5} + 3 \, {\left(69 \, a^{2} + 37 \, b^{2}\right)} n^{4} + 5 \, {\left(185 \, a^{2} + 71 \, b^{2}\right)} n^{3} + 8 \, {\left(268 \, a^{2} + 73 \, b^{2}\right)} n^{2} + 1008 \, a^{2} + 144 \, b^{2} + 36 \, {\left(67 \, a^{2} + 13 \, b^{2}\right)} n\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(19 \, a^{2} + 13 \, b^{2}\right)} n^{3} - 64 \, {\left(16 \, a^{2} + 7 \, b^{2}\right)} n^{2} - 4 \, {\left({\left(a^{2} + b^{2}\right)} n^{5} + 2 \, {\left(10 \, a^{2} + 7 \, b^{2}\right)} n^{4} + 3 \, {\left(49 \, a^{2} + 23 \, b^{2}\right)} n^{3} + 4 \, {\left(121 \, a^{2} + 37 \, b^{2}\right)} n^{2} + 336 \, a^{2} + 48 \, b^{2} + 4 \, {\left(173 \, a^{2} + 35 \, b^{2}\right)} n\right)} \cos\left(d x + c\right)^{2} - 2688 \, a^{2} - 384 \, b^{2} - 32 \, {\left(89 \, a^{2} + 23 \, b^{2}\right)} n\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{d n^{7} + 28 \, d n^{6} + 322 \, d n^{5} + 1960 \, d n^{4} + 6769 \, d n^{3} + 13132 \, d n^{2} + 13068 \, d n + 5040 \, d}"," ",0,"-(2*(a*b*n^6 + 22*a*b*n^5 + 190*a*b*n^4 + 820*a*b*n^3 + 1849*a*b*n^2 + 2038*a*b*n + 840*a*b)*cos(d*x + c)^6 - 16*a*b*n^4 - 256*a*b*n^3 - 2*(a*b*n^6 + 18*a*b*n^5 + 118*a*b*n^4 + 348*a*b*n^3 + 457*a*b*n^2 + 210*a*b*n)*cos(d*x + c)^4 - 1376*a*b*n^2 - 2816*a*b*n - 8*(a*b*n^5 + 16*a*b*n^4 + 86*a*b*n^3 + 176*a*b*n^2 + 105*a*b*n)*cos(d*x + c)^2 - 1680*a*b + ((b^2*n^6 + 21*b^2*n^5 + 175*b^2*n^4 + 735*b^2*n^3 + 1624*b^2*n^2 + 1764*b^2*n + 720*b^2)*cos(d*x + c)^6 - 8*(a^2 + b^2)*n^4 - ((a^2 + b^2)*n^6 + (23*a^2 + 17*b^2)*n^5 + 3*(69*a^2 + 37*b^2)*n^4 + 5*(185*a^2 + 71*b^2)*n^3 + 8*(268*a^2 + 73*b^2)*n^2 + 1008*a^2 + 144*b^2 + 36*(67*a^2 + 13*b^2)*n)*cos(d*x + c)^4 - 8*(19*a^2 + 13*b^2)*n^3 - 64*(16*a^2 + 7*b^2)*n^2 - 4*((a^2 + b^2)*n^5 + 2*(10*a^2 + 7*b^2)*n^4 + 3*(49*a^2 + 23*b^2)*n^3 + 4*(121*a^2 + 37*b^2)*n^2 + 336*a^2 + 48*b^2 + 4*(173*a^2 + 35*b^2)*n)*cos(d*x + c)^2 - 2688*a^2 - 384*b^2 - 32*(89*a^2 + 23*b^2)*n)*sin(d*x + c))*sin(d*x + c)^n/(d*n^7 + 28*d*n^6 + 322*d*n^5 + 1960*d*n^4 + 6769*d*n^3 + 13132*d*n^2 + 13068*d*n + 5040*d)","B",0
1236,1,282,0,1.246164," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left({\left(b n^{5} + 15 \, b n^{4} + 85 \, b n^{3} + 225 \, b n^{2} + 274 \, b n + 120 \, b\right)} \cos\left(d x + c\right)^{6} - {\left(b n^{5} + 11 \, b n^{4} + 41 \, b n^{3} + 61 \, b n^{2} + 30 \, b n\right)} \cos\left(d x + c\right)^{4} - 8 \, b n^{3} - 72 \, b n^{2} - 4 \, {\left(b n^{4} + 9 \, b n^{3} + 23 \, b n^{2} + 15 \, b n\right)} \cos\left(d x + c\right)^{2} - 184 \, b n - {\left({\left(a n^{5} + 16 \, a n^{4} + 95 \, a n^{3} + 260 \, a n^{2} + 324 \, a n + 144 \, a\right)} \cos\left(d x + c\right)^{4} + 8 \, a n^{3} + 96 \, a n^{2} + 4 \, {\left(a n^{4} + 13 \, a n^{3} + 56 \, a n^{2} + 92 \, a n + 48 \, a\right)} \cos\left(d x + c\right)^{2} + 352 \, a n + 384 \, a\right)} \sin\left(d x + c\right) - 120 \, b\right)} \sin\left(d x + c\right)^{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}"," ",0,"-((b*n^5 + 15*b*n^4 + 85*b*n^3 + 225*b*n^2 + 274*b*n + 120*b)*cos(d*x + c)^6 - (b*n^5 + 11*b*n^4 + 41*b*n^3 + 61*b*n^2 + 30*b*n)*cos(d*x + c)^4 - 8*b*n^3 - 72*b*n^2 - 4*(b*n^4 + 9*b*n^3 + 23*b*n^2 + 15*b*n)*cos(d*x + c)^2 - 184*b*n - ((a*n^5 + 16*a*n^4 + 95*a*n^3 + 260*a*n^2 + 324*a*n + 144*a)*cos(d*x + c)^4 + 8*a*n^3 + 96*a*n^2 + 4*(a*n^4 + 13*a*n^3 + 56*a*n^2 + 92*a*n + 48*a)*cos(d*x + c)^2 + 352*a*n + 384*a)*sin(d*x + c) - 120*b)*sin(d*x + c)^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)","B",0
1237,0,0,0,1.528545," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sin(d*x + c)^n*cos(d*x + c)^5/(b*sin(d*x + c) + a), x)","F",0
1238,0,0,0,1.282776," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-sin(d*x + c)^n*cos(d*x + c)^5/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2), x)","F",0
1239,1,161,0,1.528221," ","integrate(cos(d*x+c)^6*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{354816 \, b^{2} \cos\left(d x + c\right)^{13} - 419328 \, {\left(a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{11} + 512512 \, {\left(2 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{9} - 658944 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{7} + 45045 \, a b d x - 3003 \, {\left(256 \, a b \cos\left(d x + c\right)^{11} - 640 \, a b \cos\left(d x + c\right)^{9} + 432 \, a b \cos\left(d x + c\right)^{7} - 8 \, a b \cos\left(d x + c\right)^{5} - 10 \, a b \cos\left(d x + c\right)^{3} - 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4612608 \, d}"," ",0,"1/4612608*(354816*b^2*cos(d*x + c)^13 - 419328*(a^2 + 3*b^2)*cos(d*x + c)^11 + 512512*(2*a^2 + 3*b^2)*cos(d*x + c)^9 - 658944*(a^2 + b^2)*cos(d*x + c)^7 + 45045*a*b*d*x - 3003*(256*a*b*cos(d*x + c)^11 - 640*a*b*cos(d*x + c)^9 + 432*a*b*cos(d*x + c)^7 - 8*a*b*cos(d*x + c)^5 - 10*a*b*cos(d*x + c)^3 - 15*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1240,1,182,0,1.003711," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{645120 \, a b \cos\left(d x + c\right)^{11} - 1576960 \, a b \cos\left(d x + c\right)^{9} + 1013760 \, a b \cos\left(d x + c\right)^{7} - 3465 \, {\left(12 \, a^{2} + 5 \, b^{2}\right)} d x + 231 \, {\left(1280 \, b^{2} \cos\left(d x + c\right)^{11} - 128 \, {\left(12 \, a^{2} + 25 \, b^{2}\right)} \cos\left(d x + c\right)^{9} + 48 \, {\left(44 \, a^{2} + 45 \, b^{2}\right)} \cos\left(d x + c\right)^{7} - 8 \, {\left(12 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(12 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(12 \, a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3548160 \, d}"," ",0,"-1/3548160*(645120*a*b*cos(d*x + c)^11 - 1576960*a*b*cos(d*x + c)^9 + 1013760*a*b*cos(d*x + c)^7 - 3465*(12*a^2 + 5*b^2)*d*x + 231*(1280*b^2*cos(d*x + c)^11 - 128*(12*a^2 + 25*b^2)*cos(d*x + c)^9 + 48*(44*a^2 + 45*b^2)*cos(d*x + c)^7 - 8*(12*a^2 + 5*b^2)*cos(d*x + c)^5 - 10*(12*a^2 + 5*b^2)*cos(d*x + c)^3 - 15*(12*a^2 + 5*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
1241,1,128,0,1.480157," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{40320 \, b^{2} \cos\left(d x + c\right)^{11} - 49280 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{9} + 63360 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{7} - 10395 \, a b d x - 693 \, {\left(128 \, a b \cos\left(d x + c\right)^{9} - 176 \, a b \cos\left(d x + c\right)^{7} + 8 \, a b \cos\left(d x + c\right)^{5} + 10 \, a b \cos\left(d x + c\right)^{3} + 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{443520 \, d}"," ",0,"-1/443520*(40320*b^2*cos(d*x + c)^11 - 49280*(a^2 + 2*b^2)*cos(d*x + c)^9 + 63360*(a^2 + b^2)*cos(d*x + c)^7 - 10395*a*b*d*x - 693*(128*a*b*cos(d*x + c)^9 - 176*a*b*cos(d*x + c)^7 + 8*a*b*cos(d*x + c)^5 + 10*a*b*cos(d*x + c)^3 + 15*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1242,1,149,0,1.427049," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{17920 \, a b \cos\left(d x + c\right)^{9} - 23040 \, a b \cos\left(d x + c\right)^{7} + 315 \, {\left(10 \, a^{2} + 3 \, b^{2}\right)} d x + 21 \, {\left(384 \, b^{2} \cos\left(d x + c\right)^{9} - 48 \, {\left(10 \, a^{2} + 11 \, b^{2}\right)} \cos\left(d x + c\right)^{7} + 8 \, {\left(10 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{5} + 10 \, {\left(10 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(10 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(17920*a*b*cos(d*x + c)^9 - 23040*a*b*cos(d*x + c)^7 + 315*(10*a^2 + 3*b^2)*d*x + 21*(384*b^2*cos(d*x + c)^9 - 48*(10*a^2 + 11*b^2)*cos(d*x + c)^7 + 8*(10*a^2 + 3*b^2)*cos(d*x + c)^5 + 10*(10*a^2 + 3*b^2)*cos(d*x + c)^3 + 15*(10*a^2 + 3*b^2)*cos(d*x + c))*sin(d*x + c))/d","A",0
1243,1,97,0,1.515358," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{448 \, b^{2} \cos\left(d x + c\right)^{9} - 576 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{7} + 315 \, a b d x - 21 \, {\left(48 \, a b \cos\left(d x + c\right)^{7} - 8 \, a b \cos\left(d x + c\right)^{5} - 10 \, a b \cos\left(d x + c\right)^{3} - 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4032 \, d}"," ",0,"1/4032*(448*b^2*cos(d*x + c)^9 - 576*(a^2 + b^2)*cos(d*x + c)^7 + 315*a*b*d*x - 21*(48*a*b*cos(d*x + c)^7 - 8*a*b*cos(d*x + c)^5 - 10*a*b*cos(d*x + c)^3 - 15*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1244,1,137,0,1.455470," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{120 \, b^{2} \cos\left(d x + c\right)^{7} - 168 \, a^{2} \cos\left(d x + c\right)^{5} - 280 \, a^{2} \cos\left(d x + c\right)^{3} - 525 \, a b d x - 840 \, a^{2} \cos\left(d x + c\right) + 420 \, a^{2} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 420 \, a^{2} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 35 \, {\left(8 \, a b \cos\left(d x + c\right)^{5} + 10 \, a b \cos\left(d x + c\right)^{3} + 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"-1/840*(120*b^2*cos(d*x + c)^7 - 168*a^2*cos(d*x + c)^5 - 280*a^2*cos(d*x + c)^3 - 525*a*b*d*x - 840*a^2*cos(d*x + c) + 420*a^2*log(1/2*cos(d*x + c) + 1/2) - 420*a^2*log(-1/2*cos(d*x + c) + 1/2) - 35*(8*a*b*cos(d*x + c)^5 + 10*a*b*cos(d*x + c)^3 + 15*a*b*cos(d*x + c))*sin(d*x + c))/d","A",0
1245,1,188,0,1.356273," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{40 \, b^{2} \cos\left(d x + c\right)^{7} - 10 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{5} - 25 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{3} + 240 \, a b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 240 \, a b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 75 \, {\left(6 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right) - {\left(96 \, a b \cos\left(d x + c\right)^{5} + 160 \, a b \cos\left(d x + c\right)^{3} - 75 \, {\left(6 \, a^{2} - b^{2}\right)} d x + 480 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d \sin\left(d x + c\right)}"," ",0,"-1/240*(40*b^2*cos(d*x + c)^7 - 10*(6*a^2 - b^2)*cos(d*x + c)^5 - 25*(6*a^2 - b^2)*cos(d*x + c)^3 + 240*a*b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 240*a*b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 75*(6*a^2 - b^2)*cos(d*x + c) - (96*a*b*cos(d*x + c)^5 + 160*a*b*cos(d*x + c)^3 - 75*(6*a^2 - b^2)*d*x + 480*a*b*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
1246,1,244,0,1.332858," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{12 \, b^{2} \cos\left(d x + c\right)^{7} - 225 \, a b d x \cos\left(d x + c\right)^{2} - 4 \, {\left(5 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{5} + 225 \, a b d x - 20 \, {\left(5 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 30 \, {\left(5 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(5 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 5 \, a^{2} + 2 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(5 \, a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 5 \, a^{2} + 2 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(2 \, a b \cos\left(d x + c\right)^{5} + 5 \, a b \cos\left(d x + c\right)^{3} - 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"1/60*(12*b^2*cos(d*x + c)^7 - 225*a*b*d*x*cos(d*x + c)^2 - 4*(5*a^2 - 2*b^2)*cos(d*x + c)^5 + 225*a*b*d*x - 20*(5*a^2 - 2*b^2)*cos(d*x + c)^3 + 30*(5*a^2 - 2*b^2)*cos(d*x + c) + 15*((5*a^2 - 2*b^2)*cos(d*x + c)^2 - 5*a^2 + 2*b^2)*log(1/2*cos(d*x + c) + 1/2) - 15*((5*a^2 - 2*b^2)*cos(d*x + c)^2 - 5*a^2 + 2*b^2)*log(-1/2*cos(d*x + c) + 1/2) - 15*(2*a*b*cos(d*x + c)^5 + 5*a*b*cos(d*x + c)^3 - 15*a*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^2 - d)","A",0
1247,1,252,0,1.488907," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{6 \, b^{2} \cos\left(d x + c\right)^{7} - 3 \, {\left(4 \, a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{5} + 20 \, {\left(4 \, a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 60 \, {\left(a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 60 \, {\left(a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(4 \, a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right) - {\left(16 \, a b \cos\left(d x + c\right)^{5} - 15 \, {\left(4 \, a^{2} - 3 \, b^{2}\right)} d x \cos\left(d x + c\right)^{2} + 80 \, a b \cos\left(d x + c\right)^{3} + 15 \, {\left(4 \, a^{2} - 3 \, b^{2}\right)} d x - 120 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/24*(6*b^2*cos(d*x + c)^7 - 3*(4*a^2 - 3*b^2)*cos(d*x + c)^5 + 20*(4*a^2 - 3*b^2)*cos(d*x + c)^3 + 60*(a*b*cos(d*x + c)^2 - a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 60*(a*b*cos(d*x + c)^2 - a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(4*a^2 - 3*b^2)*cos(d*x + c) - (16*a*b*cos(d*x + c)^5 - 15*(4*a^2 - 3*b^2)*d*x*cos(d*x + c)^2 + 80*a*b*cos(d*x + c)^3 + 15*(4*a^2 - 3*b^2)*d*x - 120*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","A",0
1248,1,309,0,0.881706," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{16 \, b^{2} \cos\left(d x + c\right)^{7} - 240 \, a b d x \cos\left(d x + c\right)^{4} + 480 \, a b d x \cos\left(d x + c\right)^{2} - 16 \, {\left(3 \, a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 240 \, a b d x + 50 \, {\left(3 \, a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(3 \, a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(3 \, a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, a^{2} - 4 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(3 \, a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, a^{2} - 4 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(3 \, a b \cos\left(d x + c\right)^{5} - 20 \, a b \cos\left(d x + c\right)^{3} + 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/48*(16*b^2*cos(d*x + c)^7 - 240*a*b*d*x*cos(d*x + c)^4 + 480*a*b*d*x*cos(d*x + c)^2 - 16*(3*a^2 - 4*b^2)*cos(d*x + c)^5 - 240*a*b*d*x + 50*(3*a^2 - 4*b^2)*cos(d*x + c)^3 - 30*(3*a^2 - 4*b^2)*cos(d*x + c) + 15*((3*a^2 - 4*b^2)*cos(d*x + c)^4 - 2*(3*a^2 - 4*b^2)*cos(d*x + c)^2 + 3*a^2 - 4*b^2)*log(1/2*cos(d*x + c) + 1/2) - 15*((3*a^2 - 4*b^2)*cos(d*x + c)^4 - 2*(3*a^2 - 4*b^2)*cos(d*x + c)^2 + 3*a^2 - 4*b^2)*log(-1/2*cos(d*x + c) + 1/2) - 16*(3*a*b*cos(d*x + c)^5 - 20*a*b*cos(d*x + c)^3 + 15*a*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","A",0
1249,1,306,0,1.442784," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{60 \, b^{2} \cos\left(d x + c\right)^{7} + 92 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 140 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 225 \, {\left(a b \cos\left(d x + c\right)^{4} - 2 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 225 \, {\left(a b \cos\left(d x + c\right)^{4} - 2 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 60 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} \cos\left(d x + c\right) + 30 \, {\left(2 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} d x \cos\left(d x + c\right)^{4} - 8 \, a b \cos\left(d x + c\right)^{5} - 4 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} d x \cos\left(d x + c\right)^{2} + 25 \, a b \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{2} - 5 \, b^{2}\right)} d x - 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"-1/120*(60*b^2*cos(d*x + c)^7 + 92*(2*a^2 - 5*b^2)*cos(d*x + c)^5 - 140*(2*a^2 - 5*b^2)*cos(d*x + c)^3 + 225*(a*b*cos(d*x + c)^4 - 2*a*b*cos(d*x + c)^2 + a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 225*(a*b*cos(d*x + c)^4 - 2*a*b*cos(d*x + c)^2 + a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 60*(2*a^2 - 5*b^2)*cos(d*x + c) + 30*(2*(2*a^2 - 5*b^2)*d*x*cos(d*x + c)^4 - 8*a*b*cos(d*x + c)^5 - 4*(2*a^2 - 5*b^2)*d*x*cos(d*x + c)^2 + 25*a*b*cos(d*x + c)^3 + 2*(2*a^2 - 5*b^2)*d*x - 15*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","A",0
1250,1,360,0,1.569469," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{960 \, a b d x \cos\left(d x + c\right)^{6} - 480 \, b^{2} \cos\left(d x + c\right)^{7} - 2880 \, a b d x \cos\left(d x + c\right)^{4} + 2880 \, a b d x \cos\left(d x + c\right)^{2} - 330 \, {\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 960 \, a b d x + 400 \, {\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - 150 \, {\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right) - 75 \, {\left({\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + 6 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 75 \, {\left({\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{2} - 6 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + 6 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 64 \, {\left(23 \, a b \cos\left(d x + c\right)^{5} - 35 \, a b \cos\left(d x + c\right)^{3} + 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/480*(960*a*b*d*x*cos(d*x + c)^6 - 480*b^2*cos(d*x + c)^7 - 2880*a*b*d*x*cos(d*x + c)^4 + 2880*a*b*d*x*cos(d*x + c)^2 - 330*(a^2 - 6*b^2)*cos(d*x + c)^5 - 960*a*b*d*x + 400*(a^2 - 6*b^2)*cos(d*x + c)^3 - 150*(a^2 - 6*b^2)*cos(d*x + c) - 75*((a^2 - 6*b^2)*cos(d*x + c)^6 - 3*(a^2 - 6*b^2)*cos(d*x + c)^4 + 3*(a^2 - 6*b^2)*cos(d*x + c)^2 - a^2 + 6*b^2)*log(1/2*cos(d*x + c) + 1/2) + 75*((a^2 - 6*b^2)*cos(d*x + c)^6 - 3*(a^2 - 6*b^2)*cos(d*x + c)^4 + 3*(a^2 - 6*b^2)*cos(d*x + c)^2 - a^2 + 6*b^2)*log(-1/2*cos(d*x + c) + 1/2) - 64*(23*a*b*cos(d*x + c)^5 - 35*a*b*cos(d*x + c)^3 + 15*a*b*cos(d*x + c))*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
1251,1,320,0,1.410670," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, {\left(15 \, a^{2} - 161 \, b^{2}\right)} \cos\left(d x + c\right)^{7} + 6496 \, b^{2} \cos\left(d x + c\right)^{5} - 5600 \, b^{2} \cos\left(d x + c\right)^{3} + 1680 \, b^{2} \cos\left(d x + c\right) + 525 \, {\left(a b \cos\left(d x + c\right)^{6} - 3 \, a b \cos\left(d x + c\right)^{4} + 3 \, a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 525 \, {\left(a b \cos\left(d x + c\right)^{6} - 3 \, a b \cos\left(d x + c\right)^{4} + 3 \, a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 70 \, {\left(24 \, b^{2} d x \cos\left(d x + c\right)^{6} - 72 \, b^{2} d x \cos\left(d x + c\right)^{4} - 33 \, a b \cos\left(d x + c\right)^{5} + 72 \, b^{2} d x \cos\left(d x + c\right)^{2} + 40 \, a b \cos\left(d x + c\right)^{3} - 24 \, b^{2} d x - 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/1680*(16*(15*a^2 - 161*b^2)*cos(d*x + c)^7 + 6496*b^2*cos(d*x + c)^5 - 5600*b^2*cos(d*x + c)^3 + 1680*b^2*cos(d*x + c) + 525*(a*b*cos(d*x + c)^6 - 3*a*b*cos(d*x + c)^4 + 3*a*b*cos(d*x + c)^2 - a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 525*(a*b*cos(d*x + c)^6 - 3*a*b*cos(d*x + c)^4 + 3*a*b*cos(d*x + c)^2 - a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 70*(24*b^2*d*x*cos(d*x + c)^6 - 72*b^2*d*x*cos(d*x + c)^4 - 33*a*b*cos(d*x + c)^5 + 72*b^2*d*x*cos(d*x + c)^2 + 40*a*b*cos(d*x + c)^3 - 24*b^2*d*x - 15*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
1252,1,338,0,1.407211," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{1536 \, a b \cos\left(d x + c\right)^{7} \sin\left(d x + c\right) + 42 \, {\left(5 \, a^{2} - 88 \, b^{2}\right)} \cos\left(d x + c\right)^{7} + 1022 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{5} - 770 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{3} + 210 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right) - 105 \, {\left({\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{8} - 4 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} + 8 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left({\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{8} - 4 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{2} + 8 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + a^{2} + 8 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{5376 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/5376*(1536*a*b*cos(d*x + c)^7*sin(d*x + c) + 42*(5*a^2 - 88*b^2)*cos(d*x + c)^7 + 1022*(a^2 + 8*b^2)*cos(d*x + c)^5 - 770*(a^2 + 8*b^2)*cos(d*x + c)^3 + 210*(a^2 + 8*b^2)*cos(d*x + c) - 105*((a^2 + 8*b^2)*cos(d*x + c)^8 - 4*(a^2 + 8*b^2)*cos(d*x + c)^6 + 6*(a^2 + 8*b^2)*cos(d*x + c)^4 - 4*(a^2 + 8*b^2)*cos(d*x + c)^2 + a^2 + 8*b^2)*log(1/2*cos(d*x + c) + 1/2) + 105*((a^2 + 8*b^2)*cos(d*x + c)^8 - 4*(a^2 + 8*b^2)*cos(d*x + c)^6 + 6*(a^2 + 8*b^2)*cos(d*x + c)^4 - 4*(a^2 + 8*b^2)*cos(d*x + c)^2 + a^2 + 8*b^2)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)","B",0
1253,1,291,0,1.515625," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{128 \, {\left(2 \, a^{2} + 9 \, b^{2}\right)} \cos\left(d x + c\right)^{9} - 1152 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{7} + 315 \, {\left(a b \cos\left(d x + c\right)^{8} - 4 \, a b \cos\left(d x + c\right)^{6} + 6 \, a b \cos\left(d x + c\right)^{4} - 4 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 315 \, {\left(a b \cos\left(d x + c\right)^{8} - 4 \, a b \cos\left(d x + c\right)^{6} + 6 \, a b \cos\left(d x + c\right)^{4} - 4 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 42 \, {\left(15 \, a b \cos\left(d x + c\right)^{7} + 73 \, a b \cos\left(d x + c\right)^{5} - 55 \, a b \cos\left(d x + c\right)^{3} + 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8064 \, {\left(d \cos\left(d x + c\right)^{8} - 4 \, d \cos\left(d x + c\right)^{6} + 6 \, d \cos\left(d x + c\right)^{4} - 4 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/8064*(128*(2*a^2 + 9*b^2)*cos(d*x + c)^9 - 1152*(a^2 + b^2)*cos(d*x + c)^7 + 315*(a*b*cos(d*x + c)^8 - 4*a*b*cos(d*x + c)^6 + 6*a*b*cos(d*x + c)^4 - 4*a*b*cos(d*x + c)^2 + a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 315*(a*b*cos(d*x + c)^8 - 4*a*b*cos(d*x + c)^6 + 6*a*b*cos(d*x + c)^4 - 4*a*b*cos(d*x + c)^2 + a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 42*(15*a*b*cos(d*x + c)^7 + 73*a*b*cos(d*x + c)^5 - 55*a*b*cos(d*x + c)^3 + 15*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^8 - 4*d*cos(d*x + c)^6 + 6*d*cos(d*x + c)^4 - 4*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
1254,1,455,0,1.554459," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{630 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{9} - 420 \, {\left(21 \, a^{2} - 58 \, b^{2}\right)} \cos\left(d x + c\right)^{7} - 5376 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{5} + 2940 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - 630 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right) - 315 \, {\left({\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{10} - 5 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{8} + 10 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 10 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, a^{2} - 10 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 315 \, {\left({\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{10} - 5 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{8} + 10 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - 10 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, a^{2} - 10 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5120 \, {\left(2 \, a b \cos\left(d x + c\right)^{9} - 9 \, a b \cos\left(d x + c\right)^{7}\right)} \sin\left(d x + c\right)}{161280 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/161280*(630*(3*a^2 + 10*b^2)*cos(d*x + c)^9 - 420*(21*a^2 - 58*b^2)*cos(d*x + c)^7 - 5376*(3*a^2 + 10*b^2)*cos(d*x + c)^5 + 2940*(3*a^2 + 10*b^2)*cos(d*x + c)^3 - 630*(3*a^2 + 10*b^2)*cos(d*x + c) - 315*((3*a^2 + 10*b^2)*cos(d*x + c)^10 - 5*(3*a^2 + 10*b^2)*cos(d*x + c)^8 + 10*(3*a^2 + 10*b^2)*cos(d*x + c)^6 - 10*(3*a^2 + 10*b^2)*cos(d*x + c)^4 + 5*(3*a^2 + 10*b^2)*cos(d*x + c)^2 - 3*a^2 - 10*b^2)*log(1/2*cos(d*x + c) + 1/2) + 315*((3*a^2 + 10*b^2)*cos(d*x + c)^10 - 5*(3*a^2 + 10*b^2)*cos(d*x + c)^8 + 10*(3*a^2 + 10*b^2)*cos(d*x + c)^6 - 10*(3*a^2 + 10*b^2)*cos(d*x + c)^4 + 5*(3*a^2 + 10*b^2)*cos(d*x + c)^2 - 3*a^2 - 10*b^2)*log(-1/2*cos(d*x + c) + 1/2) + 5120*(2*a*b*cos(d*x + c)^9 - 9*a*b*cos(d*x + c)^7)*sin(d*x + c))/(d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)","B",0
1255,1,363,0,1.526294," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2560 \, {\left(4 \, a^{2} + 11 \, b^{2}\right)} \cos\left(d x + c\right)^{11} - 14080 \, {\left(4 \, a^{2} + 11 \, b^{2}\right)} \cos\left(d x + c\right)^{9} + 126720 \, {\left(a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{7} + 10395 \, {\left(a b \cos\left(d x + c\right)^{10} - 5 \, a b \cos\left(d x + c\right)^{8} + 10 \, a b \cos\left(d x + c\right)^{6} - 10 \, a b \cos\left(d x + c\right)^{4} + 5 \, a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 10395 \, {\left(a b \cos\left(d x + c\right)^{10} - 5 \, a b \cos\left(d x + c\right)^{8} + 10 \, a b \cos\left(d x + c\right)^{6} - 10 \, a b \cos\left(d x + c\right)^{4} + 5 \, a b \cos\left(d x + c\right)^{2} - a b\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 1386 \, {\left(15 \, a b \cos\left(d x + c\right)^{9} - 70 \, a b \cos\left(d x + c\right)^{7} - 128 \, a b \cos\left(d x + c\right)^{5} + 70 \, a b \cos\left(d x + c\right)^{3} - 15 \, a b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{887040 \, {\left(d \cos\left(d x + c\right)^{10} - 5 \, d \cos\left(d x + c\right)^{8} + 10 \, d \cos\left(d x + c\right)^{6} - 10 \, d \cos\left(d x + c\right)^{4} + 5 \, d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"1/887040*(2560*(4*a^2 + 11*b^2)*cos(d*x + c)^11 - 14080*(4*a^2 + 11*b^2)*cos(d*x + c)^9 + 126720*(a^2 + b^2)*cos(d*x + c)^7 + 10395*(a*b*cos(d*x + c)^10 - 5*a*b*cos(d*x + c)^8 + 10*a*b*cos(d*x + c)^6 - 10*a*b*cos(d*x + c)^4 + 5*a*b*cos(d*x + c)^2 - a*b)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 10395*(a*b*cos(d*x + c)^10 - 5*a*b*cos(d*x + c)^8 + 10*a*b*cos(d*x + c)^6 - 10*a*b*cos(d*x + c)^4 + 5*a*b*cos(d*x + c)^2 - a*b)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 1386*(15*a*b*cos(d*x + c)^9 - 70*a*b*cos(d*x + c)^7 - 128*a*b*cos(d*x + c)^5 + 70*a*b*cos(d*x + c)^3 - 15*a*b*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^10 - 5*d*cos(d*x + c)^8 + 10*d*cos(d*x + c)^6 - 10*d*cos(d*x + c)^4 + 5*d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
1256,1,871,0,1.830113," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{160 \, a b^{7} \cos\left(d x + c\right)^{7} - 14 \, {\left(24 \, a^{3} b^{5} - 5 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} + 35 \, {\left(32 \, a^{5} b^{3} - 36 \, a^{3} b^{5} + 5 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 105 \, {\left(64 \, a^{8} - 120 \, a^{6} b^{2} + 60 \, a^{4} b^{4} - 5 \, a^{2} b^{6}\right)} d x + 420 \, {\left(8 \, a^{7} - 11 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + {\left(8 \, a^{6} b - 11 \, a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 105 \, {\left(64 \, a^{7} b - 120 \, a^{5} b^{3} + 60 \, a^{3} b^{5} - 5 \, a b^{7}\right)} \cos\left(d x + c\right) - {\left(120 \, b^{8} \cos\left(d x + c\right)^{7} - 224 \, a^{2} b^{6} \cos\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{4} b^{4} - 7 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(64 \, a^{7} b - 120 \, a^{5} b^{3} + 60 \, a^{3} b^{5} - 5 \, a b^{7}\right)} d x - 105 \, {\left(32 \, a^{6} b^{2} - 52 \, a^{4} b^{4} + 19 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, {\left(b^{10} d \sin\left(d x + c\right) + a b^{9} d\right)}}, \frac{160 \, a b^{7} \cos\left(d x + c\right)^{7} - 14 \, {\left(24 \, a^{3} b^{5} - 5 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} + 35 \, {\left(32 \, a^{5} b^{3} - 36 \, a^{3} b^{5} + 5 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 105 \, {\left(64 \, a^{8} - 120 \, a^{6} b^{2} + 60 \, a^{4} b^{4} - 5 \, a^{2} b^{6}\right)} d x + 840 \, {\left(8 \, a^{7} - 11 \, a^{5} b^{2} + 3 \, a^{3} b^{4} + {\left(8 \, a^{6} b - 11 \, a^{4} b^{3} + 3 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 105 \, {\left(64 \, a^{7} b - 120 \, a^{5} b^{3} + 60 \, a^{3} b^{5} - 5 \, a b^{7}\right)} \cos\left(d x + c\right) - {\left(120 \, b^{8} \cos\left(d x + c\right)^{7} - 224 \, a^{2} b^{6} \cos\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{4} b^{4} - 7 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(64 \, a^{7} b - 120 \, a^{5} b^{3} + 60 \, a^{3} b^{5} - 5 \, a b^{7}\right)} d x - 105 \, {\left(32 \, a^{6} b^{2} - 52 \, a^{4} b^{4} + 19 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, {\left(b^{10} d \sin\left(d x + c\right) + a b^{9} d\right)}}\right]"," ",0,"[1/840*(160*a*b^7*cos(d*x + c)^7 - 14*(24*a^3*b^5 - 5*a*b^7)*cos(d*x + c)^5 + 35*(32*a^5*b^3 - 36*a^3*b^5 + 5*a*b^7)*cos(d*x + c)^3 + 105*(64*a^8 - 120*a^6*b^2 + 60*a^4*b^4 - 5*a^2*b^6)*d*x + 420*(8*a^7 - 11*a^5*b^2 + 3*a^3*b^4 + (8*a^6*b - 11*a^4*b^3 + 3*a^2*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 105*(64*a^7*b - 120*a^5*b^3 + 60*a^3*b^5 - 5*a*b^7)*cos(d*x + c) - (120*b^8*cos(d*x + c)^7 - 224*a^2*b^6*cos(d*x + c)^5 + 70*(8*a^4*b^4 - 7*a^2*b^6)*cos(d*x + c)^3 - 105*(64*a^7*b - 120*a^5*b^3 + 60*a^3*b^5 - 5*a*b^7)*d*x - 105*(32*a^6*b^2 - 52*a^4*b^4 + 19*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/(b^10*d*sin(d*x + c) + a*b^9*d), 1/840*(160*a*b^7*cos(d*x + c)^7 - 14*(24*a^3*b^5 - 5*a*b^7)*cos(d*x + c)^5 + 35*(32*a^5*b^3 - 36*a^3*b^5 + 5*a*b^7)*cos(d*x + c)^3 + 105*(64*a^8 - 120*a^6*b^2 + 60*a^4*b^4 - 5*a^2*b^6)*d*x + 840*(8*a^7 - 11*a^5*b^2 + 3*a^3*b^4 + (8*a^6*b - 11*a^4*b^3 + 3*a^2*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 105*(64*a^7*b - 120*a^5*b^3 + 60*a^3*b^5 - 5*a*b^7)*cos(d*x + c) - (120*b^8*cos(d*x + c)^7 - 224*a^2*b^6*cos(d*x + c)^5 + 70*(8*a^4*b^4 - 7*a^2*b^6)*cos(d*x + c)^3 - 105*(64*a^7*b - 120*a^5*b^3 + 60*a^3*b^5 - 5*a*b^7)*d*x - 105*(32*a^6*b^2 - 52*a^4*b^4 + 19*a^2*b^6)*cos(d*x + c))*sin(d*x + c))/(b^10*d*sin(d*x + c) + a*b^9*d)]","A",0
1257,1,814,0,1.581863," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{40 \, b^{7} \cos\left(d x + c\right)^{7} - 2 \, {\left(42 \, a^{2} b^{5} - 5 \, b^{7}\right)} \cos\left(d x + c\right)^{5} + 5 \, {\left(56 \, a^{4} b^{3} - 58 \, a^{2} b^{5} + 5 \, b^{7}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(112 \, a^{7} - 200 \, a^{5} b^{2} + 90 \, a^{3} b^{4} - 5 \, a b^{6}\right)} d x - 120 \, {\left(7 \, a^{6} - 9 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + {\left(7 \, a^{5} b - 9 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 15 \, {\left(112 \, a^{6} b - 200 \, a^{4} b^{3} + 90 \, a^{2} b^{5} - 5 \, b^{7}\right)} \cos\left(d x + c\right) + {\left(56 \, a b^{6} \cos\left(d x + c\right)^{5} - 10 \, {\left(14 \, a^{3} b^{4} - 11 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(112 \, a^{6} b - 200 \, a^{4} b^{3} + 90 \, a^{2} b^{5} - 5 \, b^{7}\right)} d x + 15 \, {\left(56 \, a^{5} b^{2} - 86 \, a^{3} b^{4} + 27 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(b^{9} d \sin\left(d x + c\right) + a b^{8} d\right)}}, -\frac{40 \, b^{7} \cos\left(d x + c\right)^{7} - 2 \, {\left(42 \, a^{2} b^{5} - 5 \, b^{7}\right)} \cos\left(d x + c\right)^{5} + 5 \, {\left(56 \, a^{4} b^{3} - 58 \, a^{2} b^{5} + 5 \, b^{7}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(112 \, a^{7} - 200 \, a^{5} b^{2} + 90 \, a^{3} b^{4} - 5 \, a b^{6}\right)} d x + 240 \, {\left(7 \, a^{6} - 9 \, a^{4} b^{2} + 2 \, a^{2} b^{4} + {\left(7 \, a^{5} b - 9 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 15 \, {\left(112 \, a^{6} b - 200 \, a^{4} b^{3} + 90 \, a^{2} b^{5} - 5 \, b^{7}\right)} \cos\left(d x + c\right) + {\left(56 \, a b^{6} \cos\left(d x + c\right)^{5} - 10 \, {\left(14 \, a^{3} b^{4} - 11 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(112 \, a^{6} b - 200 \, a^{4} b^{3} + 90 \, a^{2} b^{5} - 5 \, b^{7}\right)} d x + 15 \, {\left(56 \, a^{5} b^{2} - 86 \, a^{3} b^{4} + 27 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(b^{9} d \sin\left(d x + c\right) + a b^{8} d\right)}}\right]"," ",0,"[-1/240*(40*b^7*cos(d*x + c)^7 - 2*(42*a^2*b^5 - 5*b^7)*cos(d*x + c)^5 + 5*(56*a^4*b^3 - 58*a^2*b^5 + 5*b^7)*cos(d*x + c)^3 + 15*(112*a^7 - 200*a^5*b^2 + 90*a^3*b^4 - 5*a*b^6)*d*x - 120*(7*a^6 - 9*a^4*b^2 + 2*a^2*b^4 + (7*a^5*b - 9*a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 15*(112*a^6*b - 200*a^4*b^3 + 90*a^2*b^5 - 5*b^7)*cos(d*x + c) + (56*a*b^6*cos(d*x + c)^5 - 10*(14*a^3*b^4 - 11*a*b^6)*cos(d*x + c)^3 + 15*(112*a^6*b - 200*a^4*b^3 + 90*a^2*b^5 - 5*b^7)*d*x + 15*(56*a^5*b^2 - 86*a^3*b^4 + 27*a*b^6)*cos(d*x + c))*sin(d*x + c))/(b^9*d*sin(d*x + c) + a*b^8*d), -1/240*(40*b^7*cos(d*x + c)^7 - 2*(42*a^2*b^5 - 5*b^7)*cos(d*x + c)^5 + 5*(56*a^4*b^3 - 58*a^2*b^5 + 5*b^7)*cos(d*x + c)^3 + 15*(112*a^7 - 200*a^5*b^2 + 90*a^3*b^4 - 5*a*b^6)*d*x + 240*(7*a^6 - 9*a^4*b^2 + 2*a^2*b^4 + (7*a^5*b - 9*a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 15*(112*a^6*b - 200*a^4*b^3 + 90*a^2*b^5 - 5*b^7)*cos(d*x + c) + (56*a*b^6*cos(d*x + c)^5 - 10*(14*a^3*b^4 - 11*a*b^6)*cos(d*x + c)^3 + 15*(112*a^6*b - 200*a^4*b^3 + 90*a^2*b^5 - 5*b^7)*d*x + 15*(56*a^5*b^2 - 86*a^3*b^4 + 27*a*b^6)*cos(d*x + c))*sin(d*x + c))/(b^9*d*sin(d*x + c) + a*b^8*d)]","A",0
1258,1,697,0,1.772461," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{18 \, a b^{5} \cos\left(d x + c\right)^{5} - 5 \, {\left(12 \, a^{3} b^{3} - 11 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(24 \, a^{6} - 40 \, a^{4} b^{2} + 15 \, a^{2} b^{4}\right)} d x - 30 \, {\left(6 \, a^{5} - 7 \, a^{3} b^{2} + a b^{4} + {\left(6 \, a^{4} b - 7 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 15 \, {\left(24 \, a^{5} b - 40 \, a^{3} b^{3} + 15 \, a b^{5}\right)} \cos\left(d x + c\right) - {\left(12 \, b^{6} \cos\left(d x + c\right)^{5} - 10 \, {\left(3 \, a^{2} b^{4} - 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(24 \, a^{5} b - 40 \, a^{3} b^{3} + 15 \, a b^{5}\right)} d x + 15 \, {\left(12 \, a^{4} b^{2} - 17 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, {\left(b^{8} d \sin\left(d x + c\right) + a b^{7} d\right)}}, -\frac{18 \, a b^{5} \cos\left(d x + c\right)^{5} - 5 \, {\left(12 \, a^{3} b^{3} - 11 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(24 \, a^{6} - 40 \, a^{4} b^{2} + 15 \, a^{2} b^{4}\right)} d x - 60 \, {\left(6 \, a^{5} - 7 \, a^{3} b^{2} + a b^{4} + {\left(6 \, a^{4} b - 7 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 15 \, {\left(24 \, a^{5} b - 40 \, a^{3} b^{3} + 15 \, a b^{5}\right)} \cos\left(d x + c\right) - {\left(12 \, b^{6} \cos\left(d x + c\right)^{5} - 10 \, {\left(3 \, a^{2} b^{4} - 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(24 \, a^{5} b - 40 \, a^{3} b^{3} + 15 \, a b^{5}\right)} d x + 15 \, {\left(12 \, a^{4} b^{2} - 17 \, a^{2} b^{4} + 4 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, {\left(b^{8} d \sin\left(d x + c\right) + a b^{7} d\right)}}\right]"," ",0,"[-1/60*(18*a*b^5*cos(d*x + c)^5 - 5*(12*a^3*b^3 - 11*a*b^5)*cos(d*x + c)^3 - 15*(24*a^6 - 40*a^4*b^2 + 15*a^2*b^4)*d*x - 30*(6*a^5 - 7*a^3*b^2 + a*b^4 + (6*a^4*b - 7*a^2*b^3 + b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 15*(24*a^5*b - 40*a^3*b^3 + 15*a*b^5)*cos(d*x + c) - (12*b^6*cos(d*x + c)^5 - 10*(3*a^2*b^4 - 2*b^6)*cos(d*x + c)^3 + 15*(24*a^5*b - 40*a^3*b^3 + 15*a*b^5)*d*x + 15*(12*a^4*b^2 - 17*a^2*b^4 + 4*b^6)*cos(d*x + c))*sin(d*x + c))/(b^8*d*sin(d*x + c) + a*b^7*d), -1/60*(18*a*b^5*cos(d*x + c)^5 - 5*(12*a^3*b^3 - 11*a*b^5)*cos(d*x + c)^3 - 15*(24*a^6 - 40*a^4*b^2 + 15*a^2*b^4)*d*x - 60*(6*a^5 - 7*a^3*b^2 + a*b^4 + (6*a^4*b - 7*a^2*b^3 + b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 15*(24*a^5*b - 40*a^3*b^3 + 15*a*b^5)*cos(d*x + c) - (12*b^6*cos(d*x + c)^5 - 10*(3*a^2*b^4 - 2*b^6)*cos(d*x + c)^3 + 15*(24*a^5*b - 40*a^3*b^3 + 15*a*b^5)*d*x + 15*(12*a^4*b^2 - 17*a^2*b^4 + 4*b^6)*cos(d*x + c))*sin(d*x + c))/(b^8*d*sin(d*x + c) + a*b^7*d)]","A",0
1259,1,698,0,2.679937," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{3} b^{3} \cos\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{6} - 5 \, a^{4} b^{2}\right)} d x - 3 \, {\left(4 \, a^{5} - 3 \, a^{3} b^{2} - a b^{4} + {\left(4 \, a^{4} b - 3 \, a^{2} b^{3} - b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 6 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - 3 \, {\left(b^{6} \sin\left(d x + c\right) + a b^{5}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(b^{6} \sin\left(d x + c\right) + a b^{5}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{2} b^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3}\right)} d x - 6 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{6} d \sin\left(d x + c\right) + a^{3} b^{5} d\right)}}, \frac{4 \, a^{3} b^{3} \cos\left(d x + c\right)^{3} + 6 \, {\left(4 \, a^{6} - 5 \, a^{4} b^{2}\right)} d x + 6 \, {\left(4 \, a^{5} - 3 \, a^{3} b^{2} - a b^{4} + {\left(4 \, a^{4} b - 3 \, a^{2} b^{3} - b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 6 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - 3 \, {\left(b^{6} \sin\left(d x + c\right) + a b^{5}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(b^{6} \sin\left(d x + c\right) + a b^{5}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{2} b^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3}\right)} d x - 6 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{2} b^{6} d \sin\left(d x + c\right) + a^{3} b^{5} d\right)}}\right]"," ",0,"[1/6*(4*a^3*b^3*cos(d*x + c)^3 + 6*(4*a^6 - 5*a^4*b^2)*d*x - 3*(4*a^5 - 3*a^3*b^2 - a*b^4 + (4*a^4*b - 3*a^2*b^3 - b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 6*(4*a^5*b - 5*a^3*b^3 + a*b^5)*cos(d*x + c) - 3*(b^6*sin(d*x + c) + a*b^5)*log(1/2*cos(d*x + c) + 1/2) + 3*(b^6*sin(d*x + c) + a*b^5)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^2*b^4*cos(d*x + c)^3 - 3*(4*a^5*b - 5*a^3*b^3)*d*x - 6*(a^4*b^2 - a^2*b^4)*cos(d*x + c))*sin(d*x + c))/(a^2*b^6*d*sin(d*x + c) + a^3*b^5*d), 1/6*(4*a^3*b^3*cos(d*x + c)^3 + 6*(4*a^6 - 5*a^4*b^2)*d*x + 6*(4*a^5 - 3*a^3*b^2 - a*b^4 + (4*a^4*b - 3*a^2*b^3 - b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 6*(4*a^5*b - 5*a^3*b^3 + a*b^5)*cos(d*x + c) - 3*(b^6*sin(d*x + c) + a*b^5)*log(1/2*cos(d*x + c) + 1/2) + 3*(b^6*sin(d*x + c) + a*b^5)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^2*b^4*cos(d*x + c)^3 - 3*(4*a^5*b - 5*a^3*b^3)*d*x - 6*(a^4*b^2 - a^2*b^4)*cos(d*x + c))*sin(d*x + c))/(a^2*b^6*d*sin(d*x + c) + a^3*b^5*d)]","A",0
1260,1,901,0,2.561037," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{3 \, a^{4} b^{2} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{5} b - 5 \, a^{3} b^{3}\right)} d x \cos\left(d x + c\right)^{2} - {\left(6 \, a^{5} b - 5 \, a^{3} b^{3}\right)} d x - {\left(3 \, a^{4} b - a^{2} b^{3} - 2 \, b^{5} - {\left(3 \, a^{4} b - a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{5} - a^{3} b^{2} - 2 \, a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - {\left(3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) - 2 \, {\left(b^{6} \cos\left(d x + c\right)^{2} - a b^{5} \sin\left(d x + c\right) - b^{6}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(b^{6} \cos\left(d x + c\right)^{2} - a b^{5} \sin\left(d x + c\right) - b^{6}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{3} b^{3} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{6} - 5 \, a^{4} b^{2}\right)} d x + {\left(6 \, a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{3} b^{5} d \cos\left(d x + c\right)^{2} - a^{4} b^{4} d \sin\left(d x + c\right) - a^{3} b^{5} d\right)}}, -\frac{3 \, a^{4} b^{2} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{5} b - 5 \, a^{3} b^{3}\right)} d x \cos\left(d x + c\right)^{2} - {\left(6 \, a^{5} b - 5 \, a^{3} b^{3}\right)} d x - 2 \, {\left(3 \, a^{4} b - a^{2} b^{3} - 2 \, b^{5} - {\left(3 \, a^{4} b - a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{5} - a^{3} b^{2} - 2 \, a b^{4}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) - 2 \, {\left(b^{6} \cos\left(d x + c\right)^{2} - a b^{5} \sin\left(d x + c\right) - b^{6}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(b^{6} \cos\left(d x + c\right)^{2} - a b^{5} \sin\left(d x + c\right) - b^{6}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{3} b^{3} \cos\left(d x + c\right)^{3} + {\left(6 \, a^{6} - 5 \, a^{4} b^{2}\right)} d x + {\left(6 \, a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{3} b^{5} d \cos\left(d x + c\right)^{2} - a^{4} b^{4} d \sin\left(d x + c\right) - a^{3} b^{5} d\right)}}\right]"," ",0,"[-1/2*(3*a^4*b^2*cos(d*x + c)^3 + (6*a^5*b - 5*a^3*b^3)*d*x*cos(d*x + c)^2 - (6*a^5*b - 5*a^3*b^3)*d*x - (3*a^4*b - a^2*b^3 - 2*b^5 - (3*a^4*b - a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + (3*a^5 - a^3*b^2 - 2*a*b^4)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - (3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c) - 2*(b^6*cos(d*x + c)^2 - a*b^5*sin(d*x + c) - b^6)*log(1/2*cos(d*x + c) + 1/2) + 2*(b^6*cos(d*x + c)^2 - a*b^5*sin(d*x + c) - b^6)*log(-1/2*cos(d*x + c) + 1/2) - (a^3*b^3*cos(d*x + c)^3 + (6*a^6 - 5*a^4*b^2)*d*x + (6*a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^3*b^5*d*cos(d*x + c)^2 - a^4*b^4*d*sin(d*x + c) - a^3*b^5*d), -1/2*(3*a^4*b^2*cos(d*x + c)^3 + (6*a^5*b - 5*a^3*b^3)*d*x*cos(d*x + c)^2 - (6*a^5*b - 5*a^3*b^3)*d*x - 2*(3*a^4*b - a^2*b^3 - 2*b^5 - (3*a^4*b - a^2*b^3 - 2*b^5)*cos(d*x + c)^2 + (3*a^5 - a^3*b^2 - 2*a*b^4)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c) - 2*(b^6*cos(d*x + c)^2 - a*b^5*sin(d*x + c) - b^6)*log(1/2*cos(d*x + c) + 1/2) + 2*(b^6*cos(d*x + c)^2 - a*b^5*sin(d*x + c) - b^6)*log(-1/2*cos(d*x + c) + 1/2) - (a^3*b^3*cos(d*x + c)^3 + (6*a^6 - 5*a^4*b^2)*d*x + (6*a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^3*b^5*d*cos(d*x + c)^2 - a^4*b^4*d*sin(d*x + c) - a^3*b^5*d)]","A",0
1261,1,1210,0,2.943280," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{8 \, a^{6} d x \cos\left(d x + c\right)^{2} - 8 \, a^{6} d x + 4 \, {\left(2 \, a^{5} b - 2 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4} - {\left(2 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3} - 3 \, b^{5} - {\left(2 \, a^{4} b + a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right) - {\left(5 \, a^{3} b^{3} - 6 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{2} b^{4} - 6 \, b^{6} - {\left(5 \, a^{2} b^{4} - 6 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(5 \, a^{3} b^{3} - 6 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{2} b^{4} - 6 \, b^{6} - {\left(5 \, a^{2} b^{4} - 6 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(4 \, a^{5} b d x \cos\left(d x + c\right)^{2} + 2 \, a^{4} b^{2} \cos\left(d x + c\right)^{3} - 4 \, a^{5} b d x - {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} b^{3} d \cos\left(d x + c\right)^{2} - a^{5} b^{3} d + {\left(a^{4} b^{4} d \cos\left(d x + c\right)^{2} - a^{4} b^{4} d\right)} \sin\left(d x + c\right)\right)}}, \frac{8 \, a^{6} d x \cos\left(d x + c\right)^{2} - 8 \, a^{6} d x + 4 \, {\left(2 \, a^{5} b - 2 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4} - {\left(2 \, a^{5} + a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{4} b + a^{2} b^{3} - 3 \, b^{5} - {\left(2 \, a^{4} b + a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 2 \, {\left(4 \, a^{5} b - 5 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right) - {\left(5 \, a^{3} b^{3} - 6 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{2} b^{4} - 6 \, b^{6} - {\left(5 \, a^{2} b^{4} - 6 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(5 \, a^{3} b^{3} - 6 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{2} b^{4} - 6 \, b^{6} - {\left(5 \, a^{2} b^{4} - 6 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(4 \, a^{5} b d x \cos\left(d x + c\right)^{2} + 2 \, a^{4} b^{2} \cos\left(d x + c\right)^{3} - 4 \, a^{5} b d x - {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} b^{3} d \cos\left(d x + c\right)^{2} - a^{5} b^{3} d + {\left(a^{4} b^{4} d \cos\left(d x + c\right)^{2} - a^{4} b^{4} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(8*a^6*d*x*cos(d*x + c)^2 - 8*a^6*d*x + 4*(2*a^5*b - 2*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3 + 2*(2*a^5 + a^3*b^2 - 3*a*b^4 - (2*a^5 + a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + (2*a^4*b + a^2*b^3 - 3*b^5 - (2*a^4*b + a^2*b^3 - 3*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(4*a^5*b - 5*a^3*b^3 + 6*a*b^5)*cos(d*x + c) - (5*a^3*b^3 - 6*a*b^5 - (5*a^3*b^3 - 6*a*b^5)*cos(d*x + c)^2 + (5*a^2*b^4 - 6*b^6 - (5*a^2*b^4 - 6*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (5*a^3*b^3 - 6*a*b^5 - (5*a^3*b^3 - 6*a*b^5)*cos(d*x + c)^2 + (5*a^2*b^4 - 6*b^6 - (5*a^2*b^4 - 6*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(4*a^5*b*d*x*cos(d*x + c)^2 + 2*a^4*b^2*cos(d*x + c)^3 - 4*a^5*b*d*x - (2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/(a^5*b^3*d*cos(d*x + c)^2 - a^5*b^3*d + (a^4*b^4*d*cos(d*x + c)^2 - a^4*b^4*d)*sin(d*x + c)), 1/4*(8*a^6*d*x*cos(d*x + c)^2 - 8*a^6*d*x + 4*(2*a^5*b - 2*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3 - 4*(2*a^5 + a^3*b^2 - 3*a*b^4 - (2*a^5 + a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2 + (2*a^4*b + a^2*b^3 - 3*b^5 - (2*a^4*b + a^2*b^3 - 3*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 2*(4*a^5*b - 5*a^3*b^3 + 6*a*b^5)*cos(d*x + c) - (5*a^3*b^3 - 6*a*b^5 - (5*a^3*b^3 - 6*a*b^5)*cos(d*x + c)^2 + (5*a^2*b^4 - 6*b^6 - (5*a^2*b^4 - 6*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (5*a^3*b^3 - 6*a*b^5 - (5*a^3*b^3 - 6*a*b^5)*cos(d*x + c)^2 + (5*a^2*b^4 - 6*b^6 - (5*a^2*b^4 - 6*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(4*a^5*b*d*x*cos(d*x + c)^2 + 2*a^4*b^2*cos(d*x + c)^3 - 4*a^5*b*d*x - (2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c))*sin(d*x + c))/(a^5*b^3*d*cos(d*x + c)^2 - a^5*b^3*d + (a^4*b^4*d*cos(d*x + c)^2 - a^4*b^4*d)*sin(d*x + c))]","B",0
1262,1,1437,0,2.470958," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, a^{5} b d x \cos\left(d x + c\right)^{4} - 12 \, a^{5} b d x \cos\left(d x + c\right)^{2} + 6 \, a^{5} b d x + 2 \, {\left(7 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b + 3 \, a^{2} b^{3} - 4 \, b^{5} + {\left(a^{4} b + 3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{3} b^{2} - 4 \, a b^{4} - {\left(a^{5} + 3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 12 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6} + {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{3} b^{3} - 4 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6} + {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{3} b^{3} - 4 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(3 \, a^{6} d x \cos\left(d x + c\right)^{2} - 3 \, a^{6} d x + {\left(3 \, a^{5} b - 13 \, a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{5} b^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{5} b^{3} d \cos\left(d x + c\right)^{2} + a^{5} b^{3} d - {\left(a^{6} b^{2} d \cos\left(d x + c\right)^{2} - a^{6} b^{2} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{6 \, a^{5} b d x \cos\left(d x + c\right)^{4} - 12 \, a^{5} b d x \cos\left(d x + c\right)^{2} + 6 \, a^{5} b d x + 2 \, {\left(7 \, a^{4} b^{2} - 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left(a^{4} b + 3 \, a^{2} b^{3} - 4 \, b^{5} + {\left(a^{4} b + 3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{3} b^{2} - 4 \, a b^{4} - {\left(a^{5} + 3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 12 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right) + 3 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6} + {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{3} b^{3} - 4 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6} + {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{2} b^{4} - 4 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{3} b^{3} - 4 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(3 \, a^{6} d x \cos\left(d x + c\right)^{2} - 3 \, a^{6} d x + {\left(3 \, a^{5} b - 13 \, a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{5} b - 5 \, a^{3} b^{3} + 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{5} b^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{5} b^{3} d \cos\left(d x + c\right)^{2} + a^{5} b^{3} d - {\left(a^{6} b^{2} d \cos\left(d x + c\right)^{2} - a^{6} b^{2} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/6*(6*a^5*b*d*x*cos(d*x + c)^4 - 12*a^5*b*d*x*cos(d*x + c)^2 + 6*a^5*b*d*x + 2*(7*a^4*b^2 - 6*a^2*b^4)*cos(d*x + c)^3 + 3*(a^4*b + 3*a^2*b^3 - 4*b^5 + (a^4*b + 3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - 2*(a^4*b + 3*a^2*b^3 - 4*b^5)*cos(d*x + c)^2 + (a^5 + 3*a^3*b^2 - 4*a*b^4 - (a^5 + 3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 12*(a^4*b^2 - a^2*b^4)*cos(d*x + c) + 3*(5*a^2*b^4 - 4*b^6 + (5*a^2*b^4 - 4*b^6)*cos(d*x + c)^4 - 2*(5*a^2*b^4 - 4*b^6)*cos(d*x + c)^2 + (5*a^3*b^3 - 4*a*b^5 - (5*a^3*b^3 - 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(5*a^2*b^4 - 4*b^6 + (5*a^2*b^4 - 4*b^6)*cos(d*x + c)^4 - 2*(5*a^2*b^4 - 4*b^6)*cos(d*x + c)^2 + (5*a^3*b^3 - 4*a*b^5 - (5*a^3*b^3 - 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(3*a^6*d*x*cos(d*x + c)^2 - 3*a^6*d*x + (3*a^5*b - 13*a^3*b^3 + 12*a*b^5)*cos(d*x + c)^3 - 3*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^5*b^3*d*cos(d*x + c)^4 - 2*a^5*b^3*d*cos(d*x + c)^2 + a^5*b^3*d - (a^6*b^2*d*cos(d*x + c)^2 - a^6*b^2*d)*sin(d*x + c)), -1/6*(6*a^5*b*d*x*cos(d*x + c)^4 - 12*a^5*b*d*x*cos(d*x + c)^2 + 6*a^5*b*d*x + 2*(7*a^4*b^2 - 6*a^2*b^4)*cos(d*x + c)^3 + 6*(a^4*b + 3*a^2*b^3 - 4*b^5 + (a^4*b + 3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - 2*(a^4*b + 3*a^2*b^3 - 4*b^5)*cos(d*x + c)^2 + (a^5 + 3*a^3*b^2 - 4*a*b^4 - (a^5 + 3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 12*(a^4*b^2 - a^2*b^4)*cos(d*x + c) + 3*(5*a^2*b^4 - 4*b^6 + (5*a^2*b^4 - 4*b^6)*cos(d*x + c)^4 - 2*(5*a^2*b^4 - 4*b^6)*cos(d*x + c)^2 + (5*a^3*b^3 - 4*a*b^5 - (5*a^3*b^3 - 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(5*a^2*b^4 - 4*b^6 + (5*a^2*b^4 - 4*b^6)*cos(d*x + c)^4 - 2*(5*a^2*b^4 - 4*b^6)*cos(d*x + c)^2 + (5*a^3*b^3 - 4*a*b^5 - (5*a^3*b^3 - 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(3*a^6*d*x*cos(d*x + c)^2 - 3*a^6*d*x + (3*a^5*b - 13*a^3*b^3 + 12*a*b^5)*cos(d*x + c)^3 - 3*(a^5*b - 5*a^3*b^3 + 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^5*b^3*d*cos(d*x + c)^4 - 2*a^5*b^3*d*cos(d*x + c)^2 + a^5*b^3*d - (a^6*b^2*d*cos(d*x + c)^2 - a^6*b^2*d)*sin(d*x + c))]","B",0
1263,1,1576,0,1.778280," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(3 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(15 \, a^{5} - 68 \, a^{3} b^{2} + 48 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 120 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{4} + a^{3} b - a b^{3} - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{2} b^{2} - b^{4} - 2 \, {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 30 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right) - 15 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4} + {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4} + {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 10 \, {\left({\left(17 \, a^{4} b - 12 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{7} d \cos\left(d x + c\right)^{4} - 2 \, a^{7} d \cos\left(d x + c\right)^{2} + a^{7} d + {\left(a^{6} b d \cos\left(d x + c\right)^{4} - 2 \, a^{6} b d \cos\left(d x + c\right)^{2} + a^{6} b d\right)} \sin\left(d x + c\right)\right)}}, \frac{16 \, {\left(3 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(15 \, a^{5} - 68 \, a^{3} b^{2} + 48 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 240 \, {\left({\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{4} + a^{3} b - a b^{3} - 2 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{2} b^{2} - b^{4} - 2 \, {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 30 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right) - 15 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4} + {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4} + {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 12 \, a^{3} b^{2} + 8 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 10 \, {\left({\left(17 \, a^{4} b - 12 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{7} d \cos\left(d x + c\right)^{4} - 2 \, a^{7} d \cos\left(d x + c\right)^{2} + a^{7} d + {\left(a^{6} b d \cos\left(d x + c\right)^{4} - 2 \, a^{6} b d \cos\left(d x + c\right)^{2} + a^{6} b d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/48*(16*(3*a^5 - 20*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 - 10*(15*a^5 - 68*a^3*b^2 + 48*a*b^4)*cos(d*x + c)^3 - 120*((a^3*b - a*b^3)*cos(d*x + c)^4 + a^3*b - a*b^3 - 2*(a^3*b - a*b^3)*cos(d*x + c)^2 + ((a^2*b^2 - b^4)*cos(d*x + c)^4 + a^2*b^2 - b^4 - 2*(a^2*b^2 - b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 30*(3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c) - 15*(3*a^5 - 12*a^3*b^2 + 8*a*b^4 + (3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - 12*a^2*b^3 + 8*b^5 + (3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 15*(3*a^5 - 12*a^3*b^2 + 8*a*b^4 + (3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - 12*a^2*b^3 + 8*b^5 + (3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 10*((17*a^4*b - 12*a^2*b^3)*cos(d*x + c)^3 - 3*(5*a^4*b - 4*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(a^7*d*cos(d*x + c)^4 - 2*a^7*d*cos(d*x + c)^2 + a^7*d + (a^6*b*d*cos(d*x + c)^4 - 2*a^6*b*d*cos(d*x + c)^2 + a^6*b*d)*sin(d*x + c)), 1/48*(16*(3*a^5 - 20*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 - 10*(15*a^5 - 68*a^3*b^2 + 48*a*b^4)*cos(d*x + c)^3 + 240*((a^3*b - a*b^3)*cos(d*x + c)^4 + a^3*b - a*b^3 - 2*(a^3*b - a*b^3)*cos(d*x + c)^2 + ((a^2*b^2 - b^4)*cos(d*x + c)^4 + a^2*b^2 - b^4 - 2*(a^2*b^2 - b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 30*(3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c) - 15*(3*a^5 - 12*a^3*b^2 + 8*a*b^4 + (3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - 12*a^2*b^3 + 8*b^5 + (3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 15*(3*a^5 - 12*a^3*b^2 + 8*a*b^4 + (3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c)^4 - 2*(3*a^5 - 12*a^3*b^2 + 8*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - 12*a^2*b^3 + 8*b^5 + (3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 10*((17*a^4*b - 12*a^2*b^3)*cos(d*x + c)^3 - 3*(5*a^4*b - 4*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(a^7*d*cos(d*x + c)^4 - 2*a^7*d*cos(d*x + c)^2 + a^7*d + (a^6*b*d*cos(d*x + c)^4 - 2*a^6*b*d*cos(d*x + c)^2 + a^6*b*d)*sin(d*x + c))]","B",0
1264,1,2011,0,2.693212," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(92 \, a^{6} - 285 \, a^{4} b^{2} + 180 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{5} - 40 \, {\left(7 \, a^{6} - 27 \, a^{4} b^{2} + 18 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 60 \, {\left({\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{6} - a^{4} b + 7 \, a^{2} b^{3} - 6 \, b^{5} - 3 \, {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4} + {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 30 \, {\left(4 \, a^{6} - 17 \, a^{4} b^{2} + 12 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 15 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 24 \, b^{6} - 3 \, {\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5} + {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 15 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 24 \, b^{6} - 3 \, {\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5} + {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(4 \, {\left(38 \, a^{5} b - 135 \, a^{3} b^{3} + 90 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 5 \, {\left(79 \, a^{5} b - 228 \, a^{3} b^{3} + 144 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(a^{7} b d \cos\left(d x + c\right)^{6} - 3 \, a^{7} b d \cos\left(d x + c\right)^{4} + 3 \, a^{7} b d \cos\left(d x + c\right)^{2} - a^{7} b d - {\left(a^{8} d \cos\left(d x + c\right)^{4} - 2 \, a^{8} d \cos\left(d x + c\right)^{2} + a^{8} d\right)} \sin\left(d x + c\right)\right)}}, \frac{2 \, {\left(92 \, a^{6} - 285 \, a^{4} b^{2} + 180 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{5} - 40 \, {\left(7 \, a^{6} - 27 \, a^{4} b^{2} + 18 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 120 \, {\left({\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{6} - a^{4} b + 7 \, a^{2} b^{3} - 6 \, b^{5} - 3 \, {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b - 7 \, a^{2} b^{3} + 6 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4} + {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} - 7 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 30 \, {\left(4 \, a^{6} - 17 \, a^{4} b^{2} + 12 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 15 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 24 \, b^{6} - 3 \, {\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5} + {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 15 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 24 \, b^{6} - 3 \, {\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(15 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5} + {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(4 \, {\left(38 \, a^{5} b - 135 \, a^{3} b^{3} + 90 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 5 \, {\left(79 \, a^{5} b - 228 \, a^{3} b^{3} + 144 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(15 \, a^{5} b - 40 \, a^{3} b^{3} + 24 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(a^{7} b d \cos\left(d x + c\right)^{6} - 3 \, a^{7} b d \cos\left(d x + c\right)^{4} + 3 \, a^{7} b d \cos\left(d x + c\right)^{2} - a^{7} b d - {\left(a^{8} d \cos\left(d x + c\right)^{4} - 2 \, a^{8} d \cos\left(d x + c\right)^{2} + a^{8} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/120*(2*(92*a^6 - 285*a^4*b^2 + 180*a^2*b^4)*cos(d*x + c)^5 - 40*(7*a^6 - 27*a^4*b^2 + 18*a^2*b^4)*cos(d*x + c)^3 + 60*((a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^6 - a^4*b + 7*a^2*b^3 - 6*b^5 - 3*(a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^4 + 3*(a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^2 - (a^5 - 7*a^3*b^2 + 6*a*b^4 + (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^4 - 2*(a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 30*(4*a^6 - 17*a^4*b^2 + 12*a^2*b^4)*cos(d*x + c) + 15*((15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^6 - 15*a^4*b^2 + 40*a^2*b^4 - 24*b^6 - 3*(15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^4 + 3*(15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 - (15*a^5*b - 40*a^3*b^3 + 24*a*b^5 + (15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c)^4 - 2*(15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 15*((15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^6 - 15*a^4*b^2 + 40*a^2*b^4 - 24*b^6 - 3*(15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^4 + 3*(15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 - (15*a^5*b - 40*a^3*b^3 + 24*a*b^5 + (15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c)^4 - 2*(15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(4*(38*a^5*b - 135*a^3*b^3 + 90*a*b^5)*cos(d*x + c)^5 - 5*(79*a^5*b - 228*a^3*b^3 + 144*a*b^5)*cos(d*x + c)^3 + 15*(15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^7*b*d*cos(d*x + c)^6 - 3*a^7*b*d*cos(d*x + c)^4 + 3*a^7*b*d*cos(d*x + c)^2 - a^7*b*d - (a^8*d*cos(d*x + c)^4 - 2*a^8*d*cos(d*x + c)^2 + a^8*d)*sin(d*x + c)), 1/120*(2*(92*a^6 - 285*a^4*b^2 + 180*a^2*b^4)*cos(d*x + c)^5 - 40*(7*a^6 - 27*a^4*b^2 + 18*a^2*b^4)*cos(d*x + c)^3 + 120*((a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^6 - a^4*b + 7*a^2*b^3 - 6*b^5 - 3*(a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^4 + 3*(a^4*b - 7*a^2*b^3 + 6*b^5)*cos(d*x + c)^2 - (a^5 - 7*a^3*b^2 + 6*a*b^4 + (a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^4 - 2*(a^5 - 7*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 30*(4*a^6 - 17*a^4*b^2 + 12*a^2*b^4)*cos(d*x + c) + 15*((15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^6 - 15*a^4*b^2 + 40*a^2*b^4 - 24*b^6 - 3*(15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^4 + 3*(15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 - (15*a^5*b - 40*a^3*b^3 + 24*a*b^5 + (15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c)^4 - 2*(15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 15*((15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^6 - 15*a^4*b^2 + 40*a^2*b^4 - 24*b^6 - 3*(15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^4 + 3*(15*a^4*b^2 - 40*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 - (15*a^5*b - 40*a^3*b^3 + 24*a*b^5 + (15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c)^4 - 2*(15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(4*(38*a^5*b - 135*a^3*b^3 + 90*a*b^5)*cos(d*x + c)^5 - 5*(79*a^5*b - 228*a^3*b^3 + 144*a*b^5)*cos(d*x + c)^3 + 15*(15*a^5*b - 40*a^3*b^3 + 24*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^7*b*d*cos(d*x + c)^6 - 3*a^7*b*d*cos(d*x + c)^4 + 3*a^7*b*d*cos(d*x + c)^2 - a^7*b*d - (a^8*d*cos(d*x + c)^4 - 2*a^8*d*cos(d*x + c)^2 + a^8*d)*sin(d*x + c))]","B",0
1265,1,2588,0,3.935300," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{32 \, {\left(61 \, a^{5} b^{2} - 170 \, a^{3} b^{4} + 105 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} + 2 \, {\left(165 \, a^{7} - 3386 \, a^{5} b^{2} + 8440 \, a^{3} b^{4} - 5040 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 80 \, {\left(5 \, a^{7} - 94 \, a^{5} b^{2} + 218 \, a^{3} b^{4} - 126 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 240 \, {\left({\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{6} - 2 \, a^{5} b + 9 \, a^{3} b^{3} - 7 \, a b^{5} - 3 \, {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 7 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 2 \, a^{4} b^{2} + 9 \, a^{2} b^{4} - 7 \, b^{6} - 3 \, {\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 7 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 7 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 30 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right) - 15 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6} - {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7} - {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6} - {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7} - {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(571 \, a^{6} b - 1430 \, a^{4} b^{3} + 840 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{5} - 40 \, {\left(23 \, a^{6} b - 68 \, a^{4} b^{3} + 42 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(27 \, a^{6} b - 86 \, a^{4} b^{3} + 56 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(a^{9} d \cos\left(d x + c\right)^{6} - 3 \, a^{9} d \cos\left(d x + c\right)^{4} + 3 \, a^{9} d \cos\left(d x + c\right)^{2} - a^{9} d + {\left(a^{8} b d \cos\left(d x + c\right)^{6} - 3 \, a^{8} b d \cos\left(d x + c\right)^{4} + 3 \, a^{8} b d \cos\left(d x + c\right)^{2} - a^{8} b d\right)} \sin\left(d x + c\right)\right)}}, \frac{32 \, {\left(61 \, a^{5} b^{2} - 170 \, a^{3} b^{4} + 105 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} + 2 \, {\left(165 \, a^{7} - 3386 \, a^{5} b^{2} + 8440 \, a^{3} b^{4} - 5040 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 80 \, {\left(5 \, a^{7} - 94 \, a^{5} b^{2} + 218 \, a^{3} b^{4} - 126 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 480 \, {\left({\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{6} - 2 \, a^{5} b + 9 \, a^{3} b^{3} - 7 \, a b^{5} - 3 \, {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, a^{5} b - 9 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 7 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 2 \, a^{4} b^{2} + 9 \, a^{2} b^{4} - 7 \, b^{6} - 3 \, {\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 7 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, a^{4} b^{2} - 9 \, a^{2} b^{4} + 7 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 30 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right) - 15 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6} - {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7} - {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6} - {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{7} - 90 \, a^{5} b^{2} + 200 \, a^{3} b^{4} - 112 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7} - {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{6} b - 90 \, a^{4} b^{3} + 200 \, a^{2} b^{5} - 112 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(571 \, a^{6} b - 1430 \, a^{4} b^{3} + 840 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{5} - 40 \, {\left(23 \, a^{6} b - 68 \, a^{4} b^{3} + 42 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(27 \, a^{6} b - 86 \, a^{4} b^{3} + 56 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(a^{9} d \cos\left(d x + c\right)^{6} - 3 \, a^{9} d \cos\left(d x + c\right)^{4} + 3 \, a^{9} d \cos\left(d x + c\right)^{2} - a^{9} d + {\left(a^{8} b d \cos\left(d x + c\right)^{6} - 3 \, a^{8} b d \cos\left(d x + c\right)^{4} + 3 \, a^{8} b d \cos\left(d x + c\right)^{2} - a^{8} b d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/480*(32*(61*a^5*b^2 - 170*a^3*b^4 + 105*a*b^6)*cos(d*x + c)^7 + 2*(165*a^7 - 3386*a^5*b^2 + 8440*a^3*b^4 - 5040*a*b^6)*cos(d*x + c)^5 - 80*(5*a^7 - 94*a^5*b^2 + 218*a^3*b^4 - 126*a*b^6)*cos(d*x + c)^3 + 240*((2*a^5*b - 9*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^6 - 2*a^5*b + 9*a^3*b^3 - 7*a*b^5 - 3*(2*a^5*b - 9*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^4 + 3*(2*a^5*b - 9*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^2 + ((2*a^4*b^2 - 9*a^2*b^4 + 7*b^6)*cos(d*x + c)^6 - 2*a^4*b^2 + 9*a^2*b^4 - 7*b^6 - 3*(2*a^4*b^2 - 9*a^2*b^4 + 7*b^6)*cos(d*x + c)^4 + 3*(2*a^4*b^2 - 9*a^2*b^4 + 7*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 30*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c) - 15*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6 - (5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^6 + 3*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^4 - 3*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^2 + (5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7 - (5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^6 + 3*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^4 - 3*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 15*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6 - (5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^6 + 3*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^4 - 3*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^2 + (5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7 - (5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^6 + 3*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^4 - 3*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*((571*a^6*b - 1430*a^4*b^3 + 840*a^2*b^5)*cos(d*x + c)^5 - 40*(23*a^6*b - 68*a^4*b^3 + 42*a^2*b^5)*cos(d*x + c)^3 + 15*(27*a^6*b - 86*a^4*b^3 + 56*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(a^9*d*cos(d*x + c)^6 - 3*a^9*d*cos(d*x + c)^4 + 3*a^9*d*cos(d*x + c)^2 - a^9*d + (a^8*b*d*cos(d*x + c)^6 - 3*a^8*b*d*cos(d*x + c)^4 + 3*a^8*b*d*cos(d*x + c)^2 - a^8*b*d)*sin(d*x + c)), 1/480*(32*(61*a^5*b^2 - 170*a^3*b^4 + 105*a*b^6)*cos(d*x + c)^7 + 2*(165*a^7 - 3386*a^5*b^2 + 8440*a^3*b^4 - 5040*a*b^6)*cos(d*x + c)^5 - 80*(5*a^7 - 94*a^5*b^2 + 218*a^3*b^4 - 126*a*b^6)*cos(d*x + c)^3 - 480*((2*a^5*b - 9*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^6 - 2*a^5*b + 9*a^3*b^3 - 7*a*b^5 - 3*(2*a^5*b - 9*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^4 + 3*(2*a^5*b - 9*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^2 + ((2*a^4*b^2 - 9*a^2*b^4 + 7*b^6)*cos(d*x + c)^6 - 2*a^4*b^2 + 9*a^2*b^4 - 7*b^6 - 3*(2*a^4*b^2 - 9*a^2*b^4 + 7*b^6)*cos(d*x + c)^4 + 3*(2*a^4*b^2 - 9*a^2*b^4 + 7*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 30*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c) - 15*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6 - (5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^6 + 3*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^4 - 3*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^2 + (5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7 - (5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^6 + 3*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^4 - 3*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 15*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6 - (5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^6 + 3*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^4 - 3*(5*a^7 - 90*a^5*b^2 + 200*a^3*b^4 - 112*a*b^6)*cos(d*x + c)^2 + (5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7 - (5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^6 + 3*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^4 - 3*(5*a^6*b - 90*a^4*b^3 + 200*a^2*b^5 - 112*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*((571*a^6*b - 1430*a^4*b^3 + 840*a^2*b^5)*cos(d*x + c)^5 - 40*(23*a^6*b - 68*a^4*b^3 + 42*a^2*b^5)*cos(d*x + c)^3 + 15*(27*a^6*b - 86*a^4*b^3 + 56*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(a^9*d*cos(d*x + c)^6 - 3*a^9*d*cos(d*x + c)^4 + 3*a^9*d*cos(d*x + c)^2 - a^9*d + (a^8*b*d*cos(d*x + c)^6 - 3*a^8*b*d*cos(d*x + c)^4 + 3*a^8*b*d*cos(d*x + c)^2 - a^8*b*d)*sin(d*x + c))]","B",0
1266,1,1128,0,1.850838," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{64 \, a b^{7} \cos\left(d x + c\right)^{7} - 4 \, {\left(56 \, a^{3} b^{5} - 19 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} + 15 \, {\left(448 \, a^{6} b^{2} - 600 \, a^{4} b^{4} + 180 \, a^{2} b^{6} - 5 \, b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 10 \, {\left(224 \, a^{5} b^{3} - 244 \, a^{3} b^{5} + 43 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(448 \, a^{8} - 152 \, a^{6} b^{2} - 420 \, a^{4} b^{4} + 175 \, a^{2} b^{6} - 5 \, b^{8}\right)} d x + 60 \, {\left(56 \, a^{7} + 9 \, a^{5} b^{2} - 41 \, a^{3} b^{4} + 6 \, a b^{6} - {\left(56 \, a^{5} b^{2} - 47 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(56 \, a^{6} b - 47 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 30 \, {\left(224 \, a^{7} b - 188 \, a^{5} b^{3} - 32 \, a^{3} b^{5} + 19 \, a b^{7}\right)} \cos\left(d x + c\right) - {\left(40 \, b^{8} \cos\left(d x + c\right)^{7} - 2 \, {\left(56 \, a^{2} b^{6} - 5 \, b^{8}\right)} \cos\left(d x + c\right)^{5} + 5 \, {\left(112 \, a^{4} b^{4} - 94 \, a^{2} b^{6} + 5 \, b^{8}\right)} \cos\left(d x + c\right)^{3} + 30 \, {\left(448 \, a^{7} b - 600 \, a^{5} b^{3} + 180 \, a^{3} b^{5} - 5 \, a b^{7}\right)} d x + 15 \, {\left(672 \, a^{6} b^{2} - 844 \, a^{4} b^{4} + 223 \, a^{2} b^{6} - 5 \, b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(b^{11} d \cos\left(d x + c\right)^{2} - 2 \, a b^{10} d \sin\left(d x + c\right) - {\left(a^{2} b^{9} + b^{11}\right)} d\right)}}, -\frac{64 \, a b^{7} \cos\left(d x + c\right)^{7} - 4 \, {\left(56 \, a^{3} b^{5} - 19 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} + 15 \, {\left(448 \, a^{6} b^{2} - 600 \, a^{4} b^{4} + 180 \, a^{2} b^{6} - 5 \, b^{8}\right)} d x \cos\left(d x + c\right)^{2} + 10 \, {\left(224 \, a^{5} b^{3} - 244 \, a^{3} b^{5} + 43 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(448 \, a^{8} - 152 \, a^{6} b^{2} - 420 \, a^{4} b^{4} + 175 \, a^{2} b^{6} - 5 \, b^{8}\right)} d x - 120 \, {\left(56 \, a^{7} + 9 \, a^{5} b^{2} - 41 \, a^{3} b^{4} + 6 \, a b^{6} - {\left(56 \, a^{5} b^{2} - 47 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(56 \, a^{6} b - 47 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 30 \, {\left(224 \, a^{7} b - 188 \, a^{5} b^{3} - 32 \, a^{3} b^{5} + 19 \, a b^{7}\right)} \cos\left(d x + c\right) - {\left(40 \, b^{8} \cos\left(d x + c\right)^{7} - 2 \, {\left(56 \, a^{2} b^{6} - 5 \, b^{8}\right)} \cos\left(d x + c\right)^{5} + 5 \, {\left(112 \, a^{4} b^{4} - 94 \, a^{2} b^{6} + 5 \, b^{8}\right)} \cos\left(d x + c\right)^{3} + 30 \, {\left(448 \, a^{7} b - 600 \, a^{5} b^{3} + 180 \, a^{3} b^{5} - 5 \, a b^{7}\right)} d x + 15 \, {\left(672 \, a^{6} b^{2} - 844 \, a^{4} b^{4} + 223 \, a^{2} b^{6} - 5 \, b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(b^{11} d \cos\left(d x + c\right)^{2} - 2 \, a b^{10} d \sin\left(d x + c\right) - {\left(a^{2} b^{9} + b^{11}\right)} d\right)}}\right]"," ",0,"[-1/240*(64*a*b^7*cos(d*x + c)^7 - 4*(56*a^3*b^5 - 19*a*b^7)*cos(d*x + c)^5 + 15*(448*a^6*b^2 - 600*a^4*b^4 + 180*a^2*b^6 - 5*b^8)*d*x*cos(d*x + c)^2 + 10*(224*a^5*b^3 - 244*a^3*b^5 + 43*a*b^7)*cos(d*x + c)^3 - 15*(448*a^8 - 152*a^6*b^2 - 420*a^4*b^4 + 175*a^2*b^6 - 5*b^8)*d*x + 60*(56*a^7 + 9*a^5*b^2 - 41*a^3*b^4 + 6*a*b^6 - (56*a^5*b^2 - 47*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + 2*(56*a^6*b - 47*a^4*b^3 + 6*a^2*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 30*(224*a^7*b - 188*a^5*b^3 - 32*a^3*b^5 + 19*a*b^7)*cos(d*x + c) - (40*b^8*cos(d*x + c)^7 - 2*(56*a^2*b^6 - 5*b^8)*cos(d*x + c)^5 + 5*(112*a^4*b^4 - 94*a^2*b^6 + 5*b^8)*cos(d*x + c)^3 + 30*(448*a^7*b - 600*a^5*b^3 + 180*a^3*b^5 - 5*a*b^7)*d*x + 15*(672*a^6*b^2 - 844*a^4*b^4 + 223*a^2*b^6 - 5*b^8)*cos(d*x + c))*sin(d*x + c))/(b^11*d*cos(d*x + c)^2 - 2*a*b^10*d*sin(d*x + c) - (a^2*b^9 + b^11)*d), -1/240*(64*a*b^7*cos(d*x + c)^7 - 4*(56*a^3*b^5 - 19*a*b^7)*cos(d*x + c)^5 + 15*(448*a^6*b^2 - 600*a^4*b^4 + 180*a^2*b^6 - 5*b^8)*d*x*cos(d*x + c)^2 + 10*(224*a^5*b^3 - 244*a^3*b^5 + 43*a*b^7)*cos(d*x + c)^3 - 15*(448*a^8 - 152*a^6*b^2 - 420*a^4*b^4 + 175*a^2*b^6 - 5*b^8)*d*x - 120*(56*a^7 + 9*a^5*b^2 - 41*a^3*b^4 + 6*a*b^6 - (56*a^5*b^2 - 47*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2 + 2*(56*a^6*b - 47*a^4*b^3 + 6*a^2*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 30*(224*a^7*b - 188*a^5*b^3 - 32*a^3*b^5 + 19*a*b^7)*cos(d*x + c) - (40*b^8*cos(d*x + c)^7 - 2*(56*a^2*b^6 - 5*b^8)*cos(d*x + c)^5 + 5*(112*a^4*b^4 - 94*a^2*b^6 + 5*b^8)*cos(d*x + c)^3 + 30*(448*a^7*b - 600*a^5*b^3 + 180*a^3*b^5 - 5*a*b^7)*d*x + 15*(672*a^6*b^2 - 844*a^4*b^4 + 223*a^2*b^6 - 5*b^8)*cos(d*x + c))*sin(d*x + c))/(b^11*d*cos(d*x + c)^2 - 2*a*b^10*d*sin(d*x + c) - (a^2*b^9 + b^11)*d)]","A",0
1267,1,995,0,1.455088," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{24 \, b^{7} \cos\left(d x + c\right)^{7} - 4 \, {\left(21 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{5} + 15 \, {\left(168 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 45 \, a b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 10 \, {\left(84 \, a^{4} b^{3} - 79 \, a^{2} b^{5} + 8 \, b^{7}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(168 \, a^{7} - 32 \, a^{5} b^{2} - 155 \, a^{3} b^{4} + 45 \, a b^{6}\right)} d x - 30 \, {\left(42 \, a^{6} + 13 \, a^{4} b^{2} - 27 \, a^{2} b^{4} + 2 \, b^{6} - {\left(42 \, a^{4} b^{2} - 29 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(42 \, a^{5} b - 29 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 30 \, {\left(84 \, a^{6} b - 58 \, a^{4} b^{3} - 17 \, a^{2} b^{5} + 4 \, b^{7}\right)} \cos\left(d x + c\right) + {\left(42 \, a b^{6} \cos\left(d x + c\right)^{5} - 5 \, {\left(42 \, a^{3} b^{4} - 29 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(168 \, a^{6} b - 200 \, a^{4} b^{3} + 45 \, a^{2} b^{5}\right)} d x - 15 \, {\left(252 \, a^{5} b^{2} - 279 \, a^{3} b^{4} + 53 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(b^{10} d \cos\left(d x + c\right)^{2} - 2 \, a b^{9} d \sin\left(d x + c\right) - {\left(a^{2} b^{8} + b^{10}\right)} d\right)}}, \frac{24 \, b^{7} \cos\left(d x + c\right)^{7} - 4 \, {\left(21 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{5} + 15 \, {\left(168 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 45 \, a b^{6}\right)} d x \cos\left(d x + c\right)^{2} + 10 \, {\left(84 \, a^{4} b^{3} - 79 \, a^{2} b^{5} + 8 \, b^{7}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(168 \, a^{7} - 32 \, a^{5} b^{2} - 155 \, a^{3} b^{4} + 45 \, a b^{6}\right)} d x - 60 \, {\left(42 \, a^{6} + 13 \, a^{4} b^{2} - 27 \, a^{2} b^{4} + 2 \, b^{6} - {\left(42 \, a^{4} b^{2} - 29 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(42 \, a^{5} b - 29 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 30 \, {\left(84 \, a^{6} b - 58 \, a^{4} b^{3} - 17 \, a^{2} b^{5} + 4 \, b^{7}\right)} \cos\left(d x + c\right) + {\left(42 \, a b^{6} \cos\left(d x + c\right)^{5} - 5 \, {\left(42 \, a^{3} b^{4} - 29 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(168 \, a^{6} b - 200 \, a^{4} b^{3} + 45 \, a^{2} b^{5}\right)} d x - 15 \, {\left(252 \, a^{5} b^{2} - 279 \, a^{3} b^{4} + 53 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(b^{10} d \cos\left(d x + c\right)^{2} - 2 \, a b^{9} d \sin\left(d x + c\right) - {\left(a^{2} b^{8} + b^{10}\right)} d\right)}}\right]"," ",0,"[1/120*(24*b^7*cos(d*x + c)^7 - 4*(21*a^2*b^5 - 4*b^7)*cos(d*x + c)^5 + 15*(168*a^5*b^2 - 200*a^3*b^4 + 45*a*b^6)*d*x*cos(d*x + c)^2 + 10*(84*a^4*b^3 - 79*a^2*b^5 + 8*b^7)*cos(d*x + c)^3 - 15*(168*a^7 - 32*a^5*b^2 - 155*a^3*b^4 + 45*a*b^6)*d*x - 30*(42*a^6 + 13*a^4*b^2 - 27*a^2*b^4 + 2*b^6 - (42*a^4*b^2 - 29*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(42*a^5*b - 29*a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 30*(84*a^6*b - 58*a^4*b^3 - 17*a^2*b^5 + 4*b^7)*cos(d*x + c) + (42*a*b^6*cos(d*x + c)^5 - 5*(42*a^3*b^4 - 29*a*b^6)*cos(d*x + c)^3 - 30*(168*a^6*b - 200*a^4*b^3 + 45*a^2*b^5)*d*x - 15*(252*a^5*b^2 - 279*a^3*b^4 + 53*a*b^6)*cos(d*x + c))*sin(d*x + c))/(b^10*d*cos(d*x + c)^2 - 2*a*b^9*d*sin(d*x + c) - (a^2*b^8 + b^10)*d), 1/120*(24*b^7*cos(d*x + c)^7 - 4*(21*a^2*b^5 - 4*b^7)*cos(d*x + c)^5 + 15*(168*a^5*b^2 - 200*a^3*b^4 + 45*a*b^6)*d*x*cos(d*x + c)^2 + 10*(84*a^4*b^3 - 79*a^2*b^5 + 8*b^7)*cos(d*x + c)^3 - 15*(168*a^7 - 32*a^5*b^2 - 155*a^3*b^4 + 45*a*b^6)*d*x - 60*(42*a^6 + 13*a^4*b^2 - 27*a^2*b^4 + 2*b^6 - (42*a^4*b^2 - 29*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(42*a^5*b - 29*a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 30*(84*a^6*b - 58*a^4*b^3 - 17*a^2*b^5 + 4*b^7)*cos(d*x + c) + (42*a*b^6*cos(d*x + c)^5 - 5*(42*a^3*b^4 - 29*a*b^6)*cos(d*x + c)^3 - 30*(168*a^6*b - 200*a^4*b^3 + 45*a^2*b^5)*d*x - 15*(252*a^5*b^2 - 279*a^3*b^4 + 53*a*b^6)*cos(d*x + c))*sin(d*x + c))/(b^10*d*cos(d*x + c)^2 - 2*a*b^9*d*sin(d*x + c) - (a^2*b^8 + b^10)*d)]","A",0
1268,1,837,0,1.758581," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, a b^{5} \cos\left(d x + c\right)^{5} - 15 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} d x \cos\left(d x + c\right)^{2} - 10 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{6} - 7 \, a^{2} b^{4} + b^{6}\right)} d x + 30 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 30 \, {\left(4 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right) - {\left(2 \, b^{6} \cos\left(d x + c\right)^{5} - 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(8 \, a^{5} b - 8 \, a^{3} b^{3} + a b^{5}\right)} d x - 15 \, {\left(12 \, a^{4} b^{2} - 11 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left(b^{9} d \cos\left(d x + c\right)^{2} - 2 \, a b^{8} d \sin\left(d x + c\right) - {\left(a^{2} b^{7} + b^{9}\right)} d\right)}}, \frac{4 \, a b^{5} \cos\left(d x + c\right)^{5} - 15 \, {\left(8 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + b^{6}\right)} d x \cos\left(d x + c\right)^{2} - 10 \, {\left(4 \, a^{3} b^{3} - 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{6} - 7 \, a^{2} b^{4} + b^{6}\right)} d x + 60 \, {\left(2 \, a^{5} + a^{3} b^{2} - a b^{4} - {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 30 \, {\left(4 \, a^{5} b - 2 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right) - {\left(2 \, b^{6} \cos\left(d x + c\right)^{5} - 5 \, {\left(2 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(8 \, a^{5} b - 8 \, a^{3} b^{3} + a b^{5}\right)} d x - 15 \, {\left(12 \, a^{4} b^{2} - 11 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{8 \, {\left(b^{9} d \cos\left(d x + c\right)^{2} - 2 \, a b^{8} d \sin\left(d x + c\right) - {\left(a^{2} b^{7} + b^{9}\right)} d\right)}}\right]"," ",0,"[1/8*(4*a*b^5*cos(d*x + c)^5 - 15*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*d*x*cos(d*x + c)^2 - 10*(4*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^3 + 15*(8*a^6 - 7*a^2*b^4 + b^6)*d*x + 30*(2*a^5 + a^3*b^2 - a*b^4 - (2*a^3*b^2 - a*b^4)*cos(d*x + c)^2 + 2*(2*a^4*b - a^2*b^3)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 30*(4*a^5*b - 2*a^3*b^3 - a*b^5)*cos(d*x + c) - (2*b^6*cos(d*x + c)^5 - 5*(2*a^2*b^4 - b^6)*cos(d*x + c)^3 - 30*(8*a^5*b - 8*a^3*b^3 + a*b^5)*d*x - 15*(12*a^4*b^2 - 11*a^2*b^4 + b^6)*cos(d*x + c))*sin(d*x + c))/(b^9*d*cos(d*x + c)^2 - 2*a*b^8*d*sin(d*x + c) - (a^2*b^7 + b^9)*d), 1/8*(4*a*b^5*cos(d*x + c)^5 - 15*(8*a^4*b^2 - 8*a^2*b^4 + b^6)*d*x*cos(d*x + c)^2 - 10*(4*a^3*b^3 - 3*a*b^5)*cos(d*x + c)^3 + 15*(8*a^6 - 7*a^2*b^4 + b^6)*d*x + 60*(2*a^5 + a^3*b^2 - a*b^4 - (2*a^3*b^2 - a*b^4)*cos(d*x + c)^2 + 2*(2*a^4*b - a^2*b^3)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 30*(4*a^5*b - 2*a^3*b^3 - a*b^5)*cos(d*x + c) - (2*b^6*cos(d*x + c)^5 - 5*(2*a^2*b^4 - b^6)*cos(d*x + c)^3 - 30*(8*a^5*b - 8*a^3*b^3 + a*b^5)*d*x - 15*(12*a^4*b^2 - 11*a^2*b^4 + b^6)*cos(d*x + c))*sin(d*x + c))/(b^9*d*cos(d*x + c)^2 - 2*a*b^8*d*sin(d*x + c) - (a^2*b^7 + b^9)*d)]","A",0
1269,1,1007,0,2.535085," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{8 \, a^{4} b^{3} \cos\left(d x + c\right)^{3} + 2 \, {\left(12 \, a^{5} b^{2} - 5 \, a^{3} b^{4}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(12 \, a^{7} + 7 \, a^{5} b^{2} - 5 \, a^{3} b^{4}\right)} d x + {\left(12 \, a^{6} + 13 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 2 \, b^{6} - {\left(12 \, a^{4} b^{2} + a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{5} b + a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(12 \, a^{6} b + a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right) + 2 \, {\left(b^{7} \cos\left(d x + c\right)^{2} - 2 \, a b^{6} \sin\left(d x + c\right) - a^{2} b^{5} - b^{7}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(b^{7} \cos\left(d x + c\right)^{2} - 2 \, a b^{6} \sin\left(d x + c\right) - a^{2} b^{5} - b^{7}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{3} b^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(12 \, a^{6} b - 5 \, a^{4} b^{3}\right)} d x + 2 \, {\left(9 \, a^{5} b^{2} - 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{3} b^{7} d \cos\left(d x + c\right)^{2} - 2 \, a^{4} b^{6} d \sin\left(d x + c\right) - {\left(a^{5} b^{5} + a^{3} b^{7}\right)} d\right)}}, -\frac{4 \, a^{4} b^{3} \cos\left(d x + c\right)^{3} + {\left(12 \, a^{5} b^{2} - 5 \, a^{3} b^{4}\right)} d x \cos\left(d x + c\right)^{2} - {\left(12 \, a^{7} + 7 \, a^{5} b^{2} - 5 \, a^{3} b^{4}\right)} d x - {\left(12 \, a^{6} + 13 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 2 \, b^{6} - {\left(12 \, a^{4} b^{2} + a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(12 \, a^{5} b + a^{3} b^{3} + 2 \, a b^{5}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(12 \, a^{6} b + a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right) + {\left(b^{7} \cos\left(d x + c\right)^{2} - 2 \, a b^{6} \sin\left(d x + c\right) - a^{2} b^{5} - b^{7}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(b^{7} \cos\left(d x + c\right)^{2} - 2 \, a b^{6} \sin\left(d x + c\right) - a^{2} b^{5} - b^{7}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{3} b^{4} \cos\left(d x + c\right)^{3} + 2 \, {\left(12 \, a^{6} b - 5 \, a^{4} b^{3}\right)} d x + 2 \, {\left(9 \, a^{5} b^{2} - 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{3} b^{7} d \cos\left(d x + c\right)^{2} - 2 \, a^{4} b^{6} d \sin\left(d x + c\right) - {\left(a^{5} b^{5} + a^{3} b^{7}\right)} d\right)}}\right]"," ",0,"[-1/4*(8*a^4*b^3*cos(d*x + c)^3 + 2*(12*a^5*b^2 - 5*a^3*b^4)*d*x*cos(d*x + c)^2 - 2*(12*a^7 + 7*a^5*b^2 - 5*a^3*b^4)*d*x + (12*a^6 + 13*a^4*b^2 + 3*a^2*b^4 + 2*b^6 - (12*a^4*b^2 + a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(12*a^5*b + a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(12*a^6*b + a^4*b^3 - 3*a^2*b^5)*cos(d*x + c) + 2*(b^7*cos(d*x + c)^2 - 2*a*b^6*sin(d*x + c) - a^2*b^5 - b^7)*log(1/2*cos(d*x + c) + 1/2) - 2*(b^7*cos(d*x + c)^2 - 2*a*b^6*sin(d*x + c) - a^2*b^5 - b^7)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^3*b^4*cos(d*x + c)^3 + 2*(12*a^6*b - 5*a^4*b^3)*d*x + 2*(9*a^5*b^2 - 3*a^3*b^4 - a*b^6)*cos(d*x + c))*sin(d*x + c))/(a^3*b^7*d*cos(d*x + c)^2 - 2*a^4*b^6*d*sin(d*x + c) - (a^5*b^5 + a^3*b^7)*d), -1/2*(4*a^4*b^3*cos(d*x + c)^3 + (12*a^5*b^2 - 5*a^3*b^4)*d*x*cos(d*x + c)^2 - (12*a^7 + 7*a^5*b^2 - 5*a^3*b^4)*d*x - (12*a^6 + 13*a^4*b^2 + 3*a^2*b^4 + 2*b^6 - (12*a^4*b^2 + a^2*b^4 + 2*b^6)*cos(d*x + c)^2 + 2*(12*a^5*b + a^3*b^3 + 2*a*b^5)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (12*a^6*b + a^4*b^3 - 3*a^2*b^5)*cos(d*x + c) + (b^7*cos(d*x + c)^2 - 2*a*b^6*sin(d*x + c) - a^2*b^5 - b^7)*log(1/2*cos(d*x + c) + 1/2) - (b^7*cos(d*x + c)^2 - 2*a*b^6*sin(d*x + c) - a^2*b^5 - b^7)*log(-1/2*cos(d*x + c) + 1/2) - (a^3*b^4*cos(d*x + c)^3 + 2*(12*a^6*b - 5*a^4*b^3)*d*x + 2*(9*a^5*b^2 - 3*a^3*b^4 - a*b^6)*cos(d*x + c))*sin(d*x + c))/(a^3*b^7*d*cos(d*x + c)^2 - 2*a^4*b^6*d*sin(d*x + c) - (a^5*b^5 + a^3*b^7)*d)]","A",0
1270,1,1171,0,2.191841," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{24 \, a^{6} b d x \cos\left(d x + c\right)^{2} - 24 \, a^{6} b d x + 2 \, {\left(9 \, a^{5} b^{2} - a^{3} b^{4} - 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{5} b + 2 \, a^{3} b^{3} + 4 \, a b^{5} - 2 \, {\left(2 \, a^{5} b + a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 2 \, b^{6} - {\left(2 \, a^{4} b^{2} + a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(3 \, a^{5} b^{2} - a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right) + 6 \, {\left(2 \, a b^{6} \cos\left(d x + c\right)^{2} - 2 \, a b^{6} + {\left(b^{7} \cos\left(d x + c\right)^{2} - a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 6 \, {\left(2 \, a b^{6} \cos\left(d x + c\right)^{2} - 2 \, a b^{6} + {\left(b^{7} \cos\left(d x + c\right)^{2} - a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(6 \, a^{5} b^{2} d x \cos\left(d x + c\right)^{2} + 2 \, a^{4} b^{3} \cos\left(d x + c\right)^{3} - 6 \, {\left(a^{7} + a^{5} b^{2}\right)} d x - 3 \, {\left(2 \, a^{6} b + a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(2 \, a^{5} b^{5} d \cos\left(d x + c\right)^{2} - 2 \, a^{5} b^{5} d + {\left(a^{4} b^{6} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b^{4} + a^{4} b^{6}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{12 \, a^{6} b d x \cos\left(d x + c\right)^{2} - 12 \, a^{6} b d x + {\left(9 \, a^{5} b^{2} - a^{3} b^{4} - 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{5} b + 2 \, a^{3} b^{3} + 4 \, a b^{5} - 2 \, {\left(2 \, a^{5} b + a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} + 2 \, b^{6} - {\left(2 \, a^{4} b^{2} + a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left(3 \, a^{5} b^{2} - a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right) + 3 \, {\left(2 \, a b^{6} \cos\left(d x + c\right)^{2} - 2 \, a b^{6} + {\left(b^{7} \cos\left(d x + c\right)^{2} - a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(2 \, a b^{6} \cos\left(d x + c\right)^{2} - 2 \, a b^{6} + {\left(b^{7} \cos\left(d x + c\right)^{2} - a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(6 \, a^{5} b^{2} d x \cos\left(d x + c\right)^{2} + 2 \, a^{4} b^{3} \cos\left(d x + c\right)^{3} - 6 \, {\left(a^{7} + a^{5} b^{2}\right)} d x - 3 \, {\left(2 \, a^{6} b + a^{4} b^{3} - 3 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left(2 \, a^{5} b^{5} d \cos\left(d x + c\right)^{2} - 2 \, a^{5} b^{5} d + {\left(a^{4} b^{6} d \cos\left(d x + c\right)^{2} - {\left(a^{6} b^{4} + a^{4} b^{6}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(24*a^6*b*d*x*cos(d*x + c)^2 - 24*a^6*b*d*x + 2*(9*a^5*b^2 - a^3*b^4 - 6*a*b^6)*cos(d*x + c)^3 - 3*(4*a^5*b + 2*a^3*b^3 + 4*a*b^5 - 2*(2*a^5*b + a^3*b^3 + 2*a*b^5)*cos(d*x + c)^2 + (2*a^6 + 3*a^4*b^2 + 3*a^2*b^4 + 2*b^6 - (2*a^4*b^2 + a^2*b^4 + 2*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(3*a^5*b^2 - a^3*b^4 - 2*a*b^6)*cos(d*x + c) + 6*(2*a*b^6*cos(d*x + c)^2 - 2*a*b^6 + (b^7*cos(d*x + c)^2 - a^2*b^5 - b^7)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 6*(2*a*b^6*cos(d*x + c)^2 - 2*a*b^6 + (b^7*cos(d*x + c)^2 - a^2*b^5 - b^7)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 2*(6*a^5*b^2*d*x*cos(d*x + c)^2 + 2*a^4*b^3*cos(d*x + c)^3 - 6*(a^7 + a^5*b^2)*d*x - 3*(2*a^6*b + a^4*b^3 - 3*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(2*a^5*b^5*d*cos(d*x + c)^2 - 2*a^5*b^5*d + (a^4*b^6*d*cos(d*x + c)^2 - (a^6*b^4 + a^4*b^6)*d)*sin(d*x + c)), 1/2*(12*a^6*b*d*x*cos(d*x + c)^2 - 12*a^6*b*d*x + (9*a^5*b^2 - a^3*b^4 - 6*a*b^6)*cos(d*x + c)^3 - 3*(4*a^5*b + 2*a^3*b^3 + 4*a*b^5 - 2*(2*a^5*b + a^3*b^3 + 2*a*b^5)*cos(d*x + c)^2 + (2*a^6 + 3*a^4*b^2 + 3*a^2*b^4 + 2*b^6 - (2*a^4*b^2 + a^2*b^4 + 2*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*(3*a^5*b^2 - a^3*b^4 - 2*a*b^6)*cos(d*x + c) + 3*(2*a*b^6*cos(d*x + c)^2 - 2*a*b^6 + (b^7*cos(d*x + c)^2 - a^2*b^5 - b^7)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*(2*a*b^6*cos(d*x + c)^2 - 2*a*b^6 + (b^7*cos(d*x + c)^2 - a^2*b^5 - b^7)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + (6*a^5*b^2*d*x*cos(d*x + c)^2 + 2*a^4*b^3*cos(d*x + c)^3 - 6*(a^7 + a^5*b^2)*d*x - 3*(2*a^6*b + a^4*b^3 - 3*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(2*a^5*b^5*d*cos(d*x + c)^2 - 2*a^5*b^5*d + (a^4*b^6*d*cos(d*x + c)^2 - (a^6*b^4 + a^4*b^6)*d)*sin(d*x + c))]","A",0
1271,1,1658,0,2.870425," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{5} b^{2} d x \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{7} + 2 \, a^{5} b^{2}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{6} b + 5 \, a^{4} b^{3} - 18 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{7} + a^{5} b^{2}\right)} d x - {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + 13 \, a^{2} b^{4} + 12 \, b^{6} + {\left(2 \, a^{4} b^{2} + a^{2} b^{4} + 12 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{6} + 5 \, a^{4} b^{2} + 14 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{5} b + a^{3} b^{3} + 12 \, a b^{5} - {\left(2 \, a^{5} b + a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 4 \, {\left(a^{6} b + 3 \, a^{4} b^{3} - 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right) - {\left(5 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 12 \, b^{7} + {\left(5 \, a^{2} b^{5} - 12 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - 24 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{4} - 12 \, a b^{6} - {\left(5 \, a^{3} b^{4} - 12 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(5 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 12 \, b^{7} + {\left(5 \, a^{2} b^{5} - 12 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - 24 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{4} - 12 \, a b^{6} - {\left(5 \, a^{3} b^{4} - 12 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(4 \, a^{6} b d x \cos\left(d x + c\right)^{2} - 4 \, a^{6} b d x + 3 \, {\left(a^{5} b^{2} + a^{3} b^{4} - 4 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{5} b^{2} - a^{3} b^{4} - 12 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} b^{5} d \cos\left(d x + c\right)^{4} - {\left(a^{7} b^{3} + 2 \, a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{7} b^{3} + a^{5} b^{5}\right)} d - 2 \, {\left(a^{6} b^{4} d \cos\left(d x + c\right)^{2} - a^{6} b^{4} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{4 \, a^{5} b^{2} d x \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{7} + 2 \, a^{5} b^{2}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{6} b + 5 \, a^{4} b^{3} - 18 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 4 \, {\left(a^{7} + a^{5} b^{2}\right)} d x + 2 \, {\left(2 \, a^{6} + 3 \, a^{4} b^{2} + 13 \, a^{2} b^{4} + 12 \, b^{6} + {\left(2 \, a^{4} b^{2} + a^{2} b^{4} + 12 \, b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{6} + 5 \, a^{4} b^{2} + 14 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{5} b + a^{3} b^{3} + 12 \, a b^{5} - {\left(2 \, a^{5} b + a^{3} b^{3} + 12 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 4 \, {\left(a^{6} b + 3 \, a^{4} b^{3} - 9 \, a^{2} b^{5}\right)} \cos\left(d x + c\right) - {\left(5 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 12 \, b^{7} + {\left(5 \, a^{2} b^{5} - 12 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - 24 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{4} - 12 \, a b^{6} - {\left(5 \, a^{3} b^{4} - 12 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(5 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 12 \, b^{7} + {\left(5 \, a^{2} b^{5} - 12 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(5 \, a^{4} b^{3} - 2 \, a^{2} b^{5} - 24 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} b^{4} - 12 \, a b^{6} - {\left(5 \, a^{3} b^{4} - 12 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(4 \, a^{6} b d x \cos\left(d x + c\right)^{2} - 4 \, a^{6} b d x + 3 \, {\left(a^{5} b^{2} + a^{3} b^{4} - 4 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{5} b^{2} - a^{3} b^{4} - 12 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} b^{5} d \cos\left(d x + c\right)^{4} - {\left(a^{7} b^{3} + 2 \, a^{5} b^{5}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{7} b^{3} + a^{5} b^{5}\right)} d - 2 \, {\left(a^{6} b^{4} d \cos\left(d x + c\right)^{2} - a^{6} b^{4} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^5*b^2*d*x*cos(d*x + c)^4 - 4*(a^7 + 2*a^5*b^2)*d*x*cos(d*x + c)^2 - 2*(2*a^6*b + 5*a^4*b^3 - 18*a^2*b^5)*cos(d*x + c)^3 + 4*(a^7 + a^5*b^2)*d*x - (2*a^6 + 3*a^4*b^2 + 13*a^2*b^4 + 12*b^6 + (2*a^4*b^2 + a^2*b^4 + 12*b^6)*cos(d*x + c)^4 - (2*a^6 + 5*a^4*b^2 + 14*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 + 2*(2*a^5*b + a^3*b^3 + 12*a*b^5 - (2*a^5*b + a^3*b^3 + 12*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 4*(a^6*b + 3*a^4*b^3 - 9*a^2*b^5)*cos(d*x + c) - (5*a^4*b^3 - 7*a^2*b^5 - 12*b^7 + (5*a^2*b^5 - 12*b^7)*cos(d*x + c)^4 - (5*a^4*b^3 - 2*a^2*b^5 - 24*b^7)*cos(d*x + c)^2 + 2*(5*a^3*b^4 - 12*a*b^6 - (5*a^3*b^4 - 12*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (5*a^4*b^3 - 7*a^2*b^5 - 12*b^7 + (5*a^2*b^5 - 12*b^7)*cos(d*x + c)^4 - (5*a^4*b^3 - 2*a^2*b^5 - 24*b^7)*cos(d*x + c)^2 + 2*(5*a^3*b^4 - 12*a*b^6 - (5*a^3*b^4 - 12*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(4*a^6*b*d*x*cos(d*x + c)^2 - 4*a^6*b*d*x + 3*(a^5*b^2 + a^3*b^4 - 4*a*b^6)*cos(d*x + c)^3 - (3*a^5*b^2 - a^3*b^4 - 12*a*b^6)*cos(d*x + c))*sin(d*x + c))/(a^5*b^5*d*cos(d*x + c)^4 - (a^7*b^3 + 2*a^5*b^5)*d*cos(d*x + c)^2 + (a^7*b^3 + a^5*b^5)*d - 2*(a^6*b^4*d*cos(d*x + c)^2 - a^6*b^4*d)*sin(d*x + c)), -1/4*(4*a^5*b^2*d*x*cos(d*x + c)^4 - 4*(a^7 + 2*a^5*b^2)*d*x*cos(d*x + c)^2 - 2*(2*a^6*b + 5*a^4*b^3 - 18*a^2*b^5)*cos(d*x + c)^3 + 4*(a^7 + a^5*b^2)*d*x + 2*(2*a^6 + 3*a^4*b^2 + 13*a^2*b^4 + 12*b^6 + (2*a^4*b^2 + a^2*b^4 + 12*b^6)*cos(d*x + c)^4 - (2*a^6 + 5*a^4*b^2 + 14*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 + 2*(2*a^5*b + a^3*b^3 + 12*a*b^5 - (2*a^5*b + a^3*b^3 + 12*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 4*(a^6*b + 3*a^4*b^3 - 9*a^2*b^5)*cos(d*x + c) - (5*a^4*b^3 - 7*a^2*b^5 - 12*b^7 + (5*a^2*b^5 - 12*b^7)*cos(d*x + c)^4 - (5*a^4*b^3 - 2*a^2*b^5 - 24*b^7)*cos(d*x + c)^2 + 2*(5*a^3*b^4 - 12*a*b^6 - (5*a^3*b^4 - 12*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + (5*a^4*b^3 - 7*a^2*b^5 - 12*b^7 + (5*a^2*b^5 - 12*b^7)*cos(d*x + c)^4 - (5*a^4*b^3 - 2*a^2*b^5 - 24*b^7)*cos(d*x + c)^2 + 2*(5*a^3*b^4 - 12*a*b^6 - (5*a^3*b^4 - 12*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(4*a^6*b*d*x*cos(d*x + c)^2 - 4*a^6*b*d*x + 3*(a^5*b^2 + a^3*b^4 - 4*a*b^6)*cos(d*x + c)^3 - (3*a^5*b^2 - a^3*b^4 - 12*a*b^6)*cos(d*x + c))*sin(d*x + c))/(a^5*b^5*d*cos(d*x + c)^4 - (a^7*b^3 + 2*a^5*b^5)*d*cos(d*x + c)^2 + (a^7*b^3 + a^5*b^5)*d - 2*(a^6*b^4*d*cos(d*x + c)^2 - a^6*b^4*d)*sin(d*x + c))]","B",0
1272,1,1553,0,1.811595," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, a^{5} + 35 \, a^{3} b^{2} - 60 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} - 20 \, {\left(2 \, a^{5} + 5 \, a^{3} b^{2} - 12 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(2 \, {\left(a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{4} + 2 \, a^{3} b - 8 \, a b^{3} - 4 \, {\left(a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} - 3 \, a^{2} b^{2} - 4 \, b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 30 \, {\left(a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right) - 15 \, {\left(6 \, a^{3} b^{2} - 8 \, a b^{4} + 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - a^{2} b^{3} - 4 \, b^{5} + {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(6 \, a^{3} b^{2} - 8 \, a b^{4} + 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - a^{2} b^{3} - 4 \, b^{5} + {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 10 \, {\left({\left(11 \, a^{4} b - 18 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(2 \, a^{7} b d \cos\left(d x + c\right)^{4} - 4 \, a^{7} b d \cos\left(d x + c\right)^{2} + 2 \, a^{7} b d + {\left(a^{6} b^{2} d \cos\left(d x + c\right)^{4} - {\left(a^{8} + 2 \, a^{6} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} + a^{6} b^{2}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{2 \, {\left(3 \, a^{5} + 35 \, a^{3} b^{2} - 60 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} - 20 \, {\left(2 \, a^{5} + 5 \, a^{3} b^{2} - 12 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 30 \, {\left(2 \, {\left(a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{4} + 2 \, a^{3} b - 8 \, a b^{3} - 4 \, {\left(a^{3} b - 4 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{2} b^{2} - 4 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} - 3 \, a^{2} b^{2} - 4 \, b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 30 \, {\left(a^{5} + a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right) - 15 \, {\left(6 \, a^{3} b^{2} - 8 \, a b^{4} + 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - a^{2} b^{3} - 4 \, b^{5} + {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(6 \, a^{3} b^{2} - 8 \, a b^{4} + 2 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{3} b^{2} - 4 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} + {\left(3 \, a^{4} b - a^{2} b^{3} - 4 \, b^{5} + {\left(3 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - {\left(3 \, a^{4} b + 2 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 10 \, {\left({\left(11 \, a^{4} b - 18 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(2 \, a^{7} b d \cos\left(d x + c\right)^{4} - 4 \, a^{7} b d \cos\left(d x + c\right)^{2} + 2 \, a^{7} b d + {\left(a^{6} b^{2} d \cos\left(d x + c\right)^{4} - {\left(a^{8} + 2 \, a^{6} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{8} + a^{6} b^{2}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(2*(3*a^5 + 35*a^3*b^2 - 60*a*b^4)*cos(d*x + c)^5 - 20*(2*a^5 + 5*a^3*b^2 - 12*a*b^4)*cos(d*x + c)^3 - 15*(2*(a^3*b - 4*a*b^3)*cos(d*x + c)^4 + 2*a^3*b - 8*a*b^3 - 4*(a^3*b - 4*a*b^3)*cos(d*x + c)^2 + ((a^2*b^2 - 4*b^4)*cos(d*x + c)^4 + a^4 - 3*a^2*b^2 - 4*b^4 - (a^4 - 2*a^2*b^2 - 8*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 30*(a^5 + a^3*b^2 - 4*a*b^4)*cos(d*x + c) - 15*(6*a^3*b^2 - 8*a*b^4 + 2*(3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^4 - 4*(3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - a^2*b^3 - 4*b^5 + (3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - (3*a^4*b + 2*a^2*b^3 - 8*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 15*(6*a^3*b^2 - 8*a*b^4 + 2*(3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^4 - 4*(3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - a^2*b^3 - 4*b^5 + (3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - (3*a^4*b + 2*a^2*b^3 - 8*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 10*((11*a^4*b - 18*a^2*b^3)*cos(d*x + c)^3 - 6*(2*a^4*b - 3*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(2*a^7*b*d*cos(d*x + c)^4 - 4*a^7*b*d*cos(d*x + c)^2 + 2*a^7*b*d + (a^6*b^2*d*cos(d*x + c)^4 - (a^8 + 2*a^6*b^2)*d*cos(d*x + c)^2 + (a^8 + a^6*b^2)*d)*sin(d*x + c)), 1/12*(2*(3*a^5 + 35*a^3*b^2 - 60*a*b^4)*cos(d*x + c)^5 - 20*(2*a^5 + 5*a^3*b^2 - 12*a*b^4)*cos(d*x + c)^3 - 30*(2*(a^3*b - 4*a*b^3)*cos(d*x + c)^4 + 2*a^3*b - 8*a*b^3 - 4*(a^3*b - 4*a*b^3)*cos(d*x + c)^2 + ((a^2*b^2 - 4*b^4)*cos(d*x + c)^4 + a^4 - 3*a^2*b^2 - 4*b^4 - (a^4 - 2*a^2*b^2 - 8*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 30*(a^5 + a^3*b^2 - 4*a*b^4)*cos(d*x + c) - 15*(6*a^3*b^2 - 8*a*b^4 + 2*(3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^4 - 4*(3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - a^2*b^3 - 4*b^5 + (3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - (3*a^4*b + 2*a^2*b^3 - 8*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 15*(6*a^3*b^2 - 8*a*b^4 + 2*(3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^4 - 4*(3*a^3*b^2 - 4*a*b^4)*cos(d*x + c)^2 + (3*a^4*b - a^2*b^3 - 4*b^5 + (3*a^2*b^3 - 4*b^5)*cos(d*x + c)^4 - (3*a^4*b + 2*a^2*b^3 - 8*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 10*((11*a^4*b - 18*a^2*b^3)*cos(d*x + c)^3 - 6*(2*a^4*b - 3*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(2*a^7*b*d*cos(d*x + c)^4 - 4*a^7*b*d*cos(d*x + c)^2 + 2*a^7*b*d + (a^6*b^2*d*cos(d*x + c)^4 - (a^8 + 2*a^6*b^2)*d*cos(d*x + c)^2 + (a^8 + a^6*b^2)*d)*sin(d*x + c))]","B",0
1273,1,2022,0,2.329262," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(8 \, a^{6} - 155 \, a^{4} b^{2} + 180 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(5 \, a^{6} - 64 \, a^{4} b^{2} + 72 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 60 \, {\left({\left(a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{6} - a^{4} b + a^{2} b^{3} + 2 \, b^{5} - {\left(a^{4} b + a^{2} b^{3} - 6 \, b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, a^{4} b - a^{2} b^{3} - 6 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{2} - 2 \, a b^{4} + {\left(a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 30 \, {\left(a^{6} - 11 \, a^{4} b^{2} + 12 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(a^{4} b^{2} - 8 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{6} + 7 \, a^{4} b^{2} - 8 \, b^{6} - {\left(a^{6} - 5 \, a^{4} b^{2} - 16 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, a^{6} - 13 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5} + {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(a^{4} b^{2} - 8 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{6} + 7 \, a^{4} b^{2} - 8 \, b^{6} - {\left(a^{6} - 5 \, a^{4} b^{2} - 16 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, a^{6} - 13 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5} + {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(2 \, {\left(a^{5} b - 25 \, a^{3} b^{3} + 30 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{5} b + 16 \, a^{3} b^{3} - 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(a^{5} b + 2 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{7} b^{2} d \cos\left(d x + c\right)^{6} - {\left(a^{9} + 3 \, a^{7} b^{2}\right)} d \cos\left(d x + c\right)^{4} + {\left(2 \, a^{9} + 3 \, a^{7} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{9} + a^{7} b^{2}\right)} d - 2 \, {\left(a^{8} b d \cos\left(d x + c\right)^{4} - 2 \, a^{8} b d \cos\left(d x + c\right)^{2} + a^{8} b d\right)} \sin\left(d x + c\right)\right)}}, -\frac{2 \, {\left(8 \, a^{6} - 155 \, a^{4} b^{2} + 180 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{5} - 10 \, {\left(5 \, a^{6} - 64 \, a^{4} b^{2} + 72 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 120 \, {\left({\left(a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{6} - a^{4} b + a^{2} b^{3} + 2 \, b^{5} - {\left(a^{4} b + a^{2} b^{3} - 6 \, b^{5}\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, a^{4} b - a^{2} b^{3} - 6 \, b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{3} b^{2} - 2 \, a b^{4} + {\left(a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 30 \, {\left(a^{6} - 11 \, a^{4} b^{2} + 12 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(a^{4} b^{2} - 8 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{6} + 7 \, a^{4} b^{2} - 8 \, b^{6} - {\left(a^{6} - 5 \, a^{4} b^{2} - 16 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, a^{6} - 13 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5} + {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(a^{4} b^{2} - 8 \, a^{2} b^{4} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{6} + 7 \, a^{4} b^{2} - 8 \, b^{6} - {\left(a^{6} - 5 \, a^{4} b^{2} - 16 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(2 \, a^{6} - 13 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + 24 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5} + {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{5} b - 8 \, a^{3} b^{3} + 8 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(2 \, {\left(a^{5} b - 25 \, a^{3} b^{3} + 30 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{5} b + 16 \, a^{3} b^{3} - 24 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 15 \, {\left(a^{5} b + 2 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{7} b^{2} d \cos\left(d x + c\right)^{6} - {\left(a^{9} + 3 \, a^{7} b^{2}\right)} d \cos\left(d x + c\right)^{4} + {\left(2 \, a^{9} + 3 \, a^{7} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{9} + a^{7} b^{2}\right)} d - 2 \, {\left(a^{8} b d \cos\left(d x + c\right)^{4} - 2 \, a^{8} b d \cos\left(d x + c\right)^{2} + a^{8} b d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(2*(8*a^6 - 155*a^4*b^2 + 180*a^2*b^4)*cos(d*x + c)^5 - 10*(5*a^6 - 64*a^4*b^2 + 72*a^2*b^4)*cos(d*x + c)^3 + 60*((a^2*b^3 - 2*b^5)*cos(d*x + c)^6 - a^4*b + a^2*b^3 + 2*b^5 - (a^4*b + a^2*b^3 - 6*b^5)*cos(d*x + c)^4 + (2*a^4*b - a^2*b^3 - 6*b^5)*cos(d*x + c)^2 - 2*(a^3*b^2 - 2*a*b^4 + (a^3*b^2 - 2*a*b^4)*cos(d*x + c)^4 - 2*(a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 30*(a^6 - 11*a^4*b^2 + 12*a^2*b^4)*cos(d*x + c) + 15*((a^4*b^2 - 8*a^2*b^4 + 8*b^6)*cos(d*x + c)^6 - a^6 + 7*a^4*b^2 - 8*b^6 - (a^6 - 5*a^4*b^2 - 16*a^2*b^4 + 24*b^6)*cos(d*x + c)^4 + (2*a^6 - 13*a^4*b^2 - 8*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 - 2*(a^5*b - 8*a^3*b^3 + 8*a*b^5 + (a^5*b - 8*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^4 - 2*(a^5*b - 8*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 15*((a^4*b^2 - 8*a^2*b^4 + 8*b^6)*cos(d*x + c)^6 - a^6 + 7*a^4*b^2 - 8*b^6 - (a^6 - 5*a^4*b^2 - 16*a^2*b^4 + 24*b^6)*cos(d*x + c)^4 + (2*a^6 - 13*a^4*b^2 - 8*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 - 2*(a^5*b - 8*a^3*b^3 + 8*a*b^5 + (a^5*b - 8*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^4 - 2*(a^5*b - 8*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(2*(a^5*b - 25*a^3*b^3 + 30*a*b^5)*cos(d*x + c)^5 + 5*(3*a^5*b + 16*a^3*b^3 - 24*a*b^5)*cos(d*x + c)^3 - 15*(a^5*b + 2*a^3*b^3 - 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^7*b^2*d*cos(d*x + c)^6 - (a^9 + 3*a^7*b^2)*d*cos(d*x + c)^4 + (2*a^9 + 3*a^7*b^2)*d*cos(d*x + c)^2 - (a^9 + a^7*b^2)*d - 2*(a^8*b*d*cos(d*x + c)^4 - 2*a^8*b*d*cos(d*x + c)^2 + a^8*b*d)*sin(d*x + c)), -1/16*(2*(8*a^6 - 155*a^4*b^2 + 180*a^2*b^4)*cos(d*x + c)^5 - 10*(5*a^6 - 64*a^4*b^2 + 72*a^2*b^4)*cos(d*x + c)^3 - 120*((a^2*b^3 - 2*b^5)*cos(d*x + c)^6 - a^4*b + a^2*b^3 + 2*b^5 - (a^4*b + a^2*b^3 - 6*b^5)*cos(d*x + c)^4 + (2*a^4*b - a^2*b^3 - 6*b^5)*cos(d*x + c)^2 - 2*(a^3*b^2 - 2*a*b^4 + (a^3*b^2 - 2*a*b^4)*cos(d*x + c)^4 - 2*(a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 30*(a^6 - 11*a^4*b^2 + 12*a^2*b^4)*cos(d*x + c) + 15*((a^4*b^2 - 8*a^2*b^4 + 8*b^6)*cos(d*x + c)^6 - a^6 + 7*a^4*b^2 - 8*b^6 - (a^6 - 5*a^4*b^2 - 16*a^2*b^4 + 24*b^6)*cos(d*x + c)^4 + (2*a^6 - 13*a^4*b^2 - 8*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 - 2*(a^5*b - 8*a^3*b^3 + 8*a*b^5 + (a^5*b - 8*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^4 - 2*(a^5*b - 8*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 15*((a^4*b^2 - 8*a^2*b^4 + 8*b^6)*cos(d*x + c)^6 - a^6 + 7*a^4*b^2 - 8*b^6 - (a^6 - 5*a^4*b^2 - 16*a^2*b^4 + 24*b^6)*cos(d*x + c)^4 + (2*a^6 - 13*a^4*b^2 - 8*a^2*b^4 + 24*b^6)*cos(d*x + c)^2 - 2*(a^5*b - 8*a^3*b^3 + 8*a*b^5 + (a^5*b - 8*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^4 - 2*(a^5*b - 8*a^3*b^3 + 8*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(2*(a^5*b - 25*a^3*b^3 + 30*a*b^5)*cos(d*x + c)^5 + 5*(3*a^5*b + 16*a^3*b^3 - 24*a*b^5)*cos(d*x + c)^3 - 15*(a^5*b + 2*a^3*b^3 - 4*a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^7*b^2*d*cos(d*x + c)^6 - (a^9 + 3*a^7*b^2)*d*cos(d*x + c)^4 + (2*a^9 + 3*a^7*b^2)*d*cos(d*x + c)^2 - (a^9 + a^7*b^2)*d - 2*(a^8*b*d*cos(d*x + c)^4 - 2*a^8*b*d*cos(d*x + c)^2 + a^8*b*d)*sin(d*x + c))]","B",0
1274,1,2571,0,2.676487," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{8 \, {\left(91 \, a^{5} b^{2} - 645 \, a^{3} b^{4} + 630 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} - 4 \, {\left(92 \, a^{7} + 67 \, a^{5} b^{2} - 3450 \, a^{3} b^{4} + 3780 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 40 \, {\left(14 \, a^{7} - 37 \, a^{5} b^{2} - 303 \, a^{3} b^{4} + 378 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 60 \, {\left(2 \, {\left(2 \, a^{5} b - 29 \, a^{3} b^{3} + 42 \, a b^{5}\right)} \cos\left(d x + c\right)^{6} - 4 \, a^{5} b + 58 \, a^{3} b^{3} - 84 \, a b^{5} - 6 \, {\left(2 \, a^{5} b - 29 \, a^{3} b^{3} + 42 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(2 \, a^{5} b - 29 \, a^{3} b^{3} + 42 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, a^{4} b^{2} - 29 \, a^{2} b^{4} + 42 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 2 \, a^{6} + 27 \, a^{4} b^{2} - 13 \, a^{2} b^{4} - 42 \, b^{6} - {\left(2 \, a^{6} - 23 \, a^{4} b^{2} - 45 \, a^{2} b^{4} + 126 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{6} - 52 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 126 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 60 \, {\left(4 \, a^{7} - 17 \, a^{5} b^{2} - 58 \, a^{3} b^{4} + 84 \, a b^{6}\right)} \cos\left(d x + c\right) + 15 \, {\left(90 \, a^{5} b^{2} - 400 \, a^{3} b^{4} + 336 \, a b^{6} - 2 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 6 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(45 \, a^{6} b - 155 \, a^{4} b^{3} - 32 \, a^{2} b^{5} + 168 \, b^{7} - {\left(45 \, a^{4} b^{3} - 200 \, a^{2} b^{5} + 168 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + {\left(45 \, a^{6} b - 65 \, a^{4} b^{3} - 432 \, a^{2} b^{5} + 504 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(90 \, a^{6} b - 265 \, a^{4} b^{3} - 264 \, a^{2} b^{5} + 504 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(90 \, a^{5} b^{2} - 400 \, a^{3} b^{4} + 336 \, a b^{6} - 2 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 6 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(45 \, a^{6} b - 155 \, a^{4} b^{3} - 32 \, a^{2} b^{5} + 168 \, b^{7} - {\left(45 \, a^{4} b^{3} - 200 \, a^{2} b^{5} + 168 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + {\left(45 \, a^{6} b - 65 \, a^{4} b^{3} - 432 \, a^{2} b^{5} + 504 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(90 \, a^{6} b - 265 \, a^{4} b^{3} - 264 \, a^{2} b^{5} + 504 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(608 \, a^{6} b - 3975 \, a^{4} b^{3} + 3780 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{5} - 5 \, {\left(289 \, a^{6} b - 1632 \, a^{4} b^{3} + 1512 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(53 \, a^{6} b - 279 \, a^{4} b^{3} + 252 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(2 \, a^{9} b d \cos\left(d x + c\right)^{6} - 6 \, a^{9} b d \cos\left(d x + c\right)^{4} + 6 \, a^{9} b d \cos\left(d x + c\right)^{2} - 2 \, a^{9} b d + {\left(a^{8} b^{2} d \cos\left(d x + c\right)^{6} - {\left(a^{10} + 3 \, a^{8} b^{2}\right)} d \cos\left(d x + c\right)^{4} + {\left(2 \, a^{10} + 3 \, a^{8} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + a^{8} b^{2}\right)} d\right)} \sin\left(d x + c\right)\right)}}, -\frac{8 \, {\left(91 \, a^{5} b^{2} - 645 \, a^{3} b^{4} + 630 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} - 4 \, {\left(92 \, a^{7} + 67 \, a^{5} b^{2} - 3450 \, a^{3} b^{4} + 3780 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} + 40 \, {\left(14 \, a^{7} - 37 \, a^{5} b^{2} - 303 \, a^{3} b^{4} + 378 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} - 120 \, {\left(2 \, {\left(2 \, a^{5} b - 29 \, a^{3} b^{3} + 42 \, a b^{5}\right)} \cos\left(d x + c\right)^{6} - 4 \, a^{5} b + 58 \, a^{3} b^{3} - 84 \, a b^{5} - 6 \, {\left(2 \, a^{5} b - 29 \, a^{3} b^{3} + 42 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} + 6 \, {\left(2 \, a^{5} b - 29 \, a^{3} b^{3} + 42 \, a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, a^{4} b^{2} - 29 \, a^{2} b^{4} + 42 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 2 \, a^{6} + 27 \, a^{4} b^{2} - 13 \, a^{2} b^{4} - 42 \, b^{6} - {\left(2 \, a^{6} - 23 \, a^{4} b^{2} - 45 \, a^{2} b^{4} + 126 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{6} - 52 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + 126 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 60 \, {\left(4 \, a^{7} - 17 \, a^{5} b^{2} - 58 \, a^{3} b^{4} + 84 \, a b^{6}\right)} \cos\left(d x + c\right) + 15 \, {\left(90 \, a^{5} b^{2} - 400 \, a^{3} b^{4} + 336 \, a b^{6} - 2 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 6 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(45 \, a^{6} b - 155 \, a^{4} b^{3} - 32 \, a^{2} b^{5} + 168 \, b^{7} - {\left(45 \, a^{4} b^{3} - 200 \, a^{2} b^{5} + 168 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + {\left(45 \, a^{6} b - 65 \, a^{4} b^{3} - 432 \, a^{2} b^{5} + 504 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(90 \, a^{6} b - 265 \, a^{4} b^{3} - 264 \, a^{2} b^{5} + 504 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left(90 \, a^{5} b^{2} - 400 \, a^{3} b^{4} + 336 \, a b^{6} - 2 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 6 \, {\left(45 \, a^{5} b^{2} - 200 \, a^{3} b^{4} + 168 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left(45 \, a^{6} b - 155 \, a^{4} b^{3} - 32 \, a^{2} b^{5} + 168 \, b^{7} - {\left(45 \, a^{4} b^{3} - 200 \, a^{2} b^{5} + 168 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + {\left(45 \, a^{6} b - 65 \, a^{4} b^{3} - 432 \, a^{2} b^{5} + 504 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(90 \, a^{6} b - 265 \, a^{4} b^{3} - 264 \, a^{2} b^{5} + 504 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(608 \, a^{6} b - 3975 \, a^{4} b^{3} + 3780 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{5} - 5 \, {\left(289 \, a^{6} b - 1632 \, a^{4} b^{3} + 1512 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(53 \, a^{6} b - 279 \, a^{4} b^{3} + 252 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(2 \, a^{9} b d \cos\left(d x + c\right)^{6} - 6 \, a^{9} b d \cos\left(d x + c\right)^{4} + 6 \, a^{9} b d \cos\left(d x + c\right)^{2} - 2 \, a^{9} b d + {\left(a^{8} b^{2} d \cos\left(d x + c\right)^{6} - {\left(a^{10} + 3 \, a^{8} b^{2}\right)} d \cos\left(d x + c\right)^{4} + {\left(2 \, a^{10} + 3 \, a^{8} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{10} + a^{8} b^{2}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/240*(8*(91*a^5*b^2 - 645*a^3*b^4 + 630*a*b^6)*cos(d*x + c)^7 - 4*(92*a^7 + 67*a^5*b^2 - 3450*a^3*b^4 + 3780*a*b^6)*cos(d*x + c)^5 + 40*(14*a^7 - 37*a^5*b^2 - 303*a^3*b^4 + 378*a*b^6)*cos(d*x + c)^3 - 60*(2*(2*a^5*b - 29*a^3*b^3 + 42*a*b^5)*cos(d*x + c)^6 - 4*a^5*b + 58*a^3*b^3 - 84*a*b^5 - 6*(2*a^5*b - 29*a^3*b^3 + 42*a*b^5)*cos(d*x + c)^4 + 6*(2*a^5*b - 29*a^3*b^3 + 42*a*b^5)*cos(d*x + c)^2 + ((2*a^4*b^2 - 29*a^2*b^4 + 42*b^6)*cos(d*x + c)^6 - 2*a^6 + 27*a^4*b^2 - 13*a^2*b^4 - 42*b^6 - (2*a^6 - 23*a^4*b^2 - 45*a^2*b^4 + 126*b^6)*cos(d*x + c)^4 + (4*a^6 - 52*a^4*b^2 - 3*a^2*b^4 + 126*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 60*(4*a^7 - 17*a^5*b^2 - 58*a^3*b^4 + 84*a*b^6)*cos(d*x + c) + 15*(90*a^5*b^2 - 400*a^3*b^4 + 336*a*b^6 - 2*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^6 + 6*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^4 - 6*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^2 + (45*a^6*b - 155*a^4*b^3 - 32*a^2*b^5 + 168*b^7 - (45*a^4*b^3 - 200*a^2*b^5 + 168*b^7)*cos(d*x + c)^6 + (45*a^6*b - 65*a^4*b^3 - 432*a^2*b^5 + 504*b^7)*cos(d*x + c)^4 - (90*a^6*b - 265*a^4*b^3 - 264*a^2*b^5 + 504*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 15*(90*a^5*b^2 - 400*a^3*b^4 + 336*a*b^6 - 2*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^6 + 6*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^4 - 6*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^2 + (45*a^6*b - 155*a^4*b^3 - 32*a^2*b^5 + 168*b^7 - (45*a^4*b^3 - 200*a^2*b^5 + 168*b^7)*cos(d*x + c)^6 + (45*a^6*b - 65*a^4*b^3 - 432*a^2*b^5 + 504*b^7)*cos(d*x + c)^4 - (90*a^6*b - 265*a^4*b^3 - 264*a^2*b^5 + 504*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*((608*a^6*b - 3975*a^4*b^3 + 3780*a^2*b^5)*cos(d*x + c)^5 - 5*(289*a^6*b - 1632*a^4*b^3 + 1512*a^2*b^5)*cos(d*x + c)^3 + 15*(53*a^6*b - 279*a^4*b^3 + 252*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(2*a^9*b*d*cos(d*x + c)^6 - 6*a^9*b*d*cos(d*x + c)^4 + 6*a^9*b*d*cos(d*x + c)^2 - 2*a^9*b*d + (a^8*b^2*d*cos(d*x + c)^6 - (a^10 + 3*a^8*b^2)*d*cos(d*x + c)^4 + (2*a^10 + 3*a^8*b^2)*d*cos(d*x + c)^2 - (a^10 + a^8*b^2)*d)*sin(d*x + c)), -1/240*(8*(91*a^5*b^2 - 645*a^3*b^4 + 630*a*b^6)*cos(d*x + c)^7 - 4*(92*a^7 + 67*a^5*b^2 - 3450*a^3*b^4 + 3780*a*b^6)*cos(d*x + c)^5 + 40*(14*a^7 - 37*a^5*b^2 - 303*a^3*b^4 + 378*a*b^6)*cos(d*x + c)^3 - 120*(2*(2*a^5*b - 29*a^3*b^3 + 42*a*b^5)*cos(d*x + c)^6 - 4*a^5*b + 58*a^3*b^3 - 84*a*b^5 - 6*(2*a^5*b - 29*a^3*b^3 + 42*a*b^5)*cos(d*x + c)^4 + 6*(2*a^5*b - 29*a^3*b^3 + 42*a*b^5)*cos(d*x + c)^2 + ((2*a^4*b^2 - 29*a^2*b^4 + 42*b^6)*cos(d*x + c)^6 - 2*a^6 + 27*a^4*b^2 - 13*a^2*b^4 - 42*b^6 - (2*a^6 - 23*a^4*b^2 - 45*a^2*b^4 + 126*b^6)*cos(d*x + c)^4 + (4*a^6 - 52*a^4*b^2 - 3*a^2*b^4 + 126*b^6)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 60*(4*a^7 - 17*a^5*b^2 - 58*a^3*b^4 + 84*a*b^6)*cos(d*x + c) + 15*(90*a^5*b^2 - 400*a^3*b^4 + 336*a*b^6 - 2*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^6 + 6*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^4 - 6*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^2 + (45*a^6*b - 155*a^4*b^3 - 32*a^2*b^5 + 168*b^7 - (45*a^4*b^3 - 200*a^2*b^5 + 168*b^7)*cos(d*x + c)^6 + (45*a^6*b - 65*a^4*b^3 - 432*a^2*b^5 + 504*b^7)*cos(d*x + c)^4 - (90*a^6*b - 265*a^4*b^3 - 264*a^2*b^5 + 504*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 15*(90*a^5*b^2 - 400*a^3*b^4 + 336*a*b^6 - 2*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^6 + 6*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^4 - 6*(45*a^5*b^2 - 200*a^3*b^4 + 168*a*b^6)*cos(d*x + c)^2 + (45*a^6*b - 155*a^4*b^3 - 32*a^2*b^5 + 168*b^7 - (45*a^4*b^3 - 200*a^2*b^5 + 168*b^7)*cos(d*x + c)^6 + (45*a^6*b - 65*a^4*b^3 - 432*a^2*b^5 + 504*b^7)*cos(d*x + c)^4 - (90*a^6*b - 265*a^4*b^3 - 264*a^2*b^5 + 504*b^7)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*((608*a^6*b - 3975*a^4*b^3 + 3780*a^2*b^5)*cos(d*x + c)^5 - 5*(289*a^6*b - 1632*a^4*b^3 + 1512*a^2*b^5)*cos(d*x + c)^3 + 15*(53*a^6*b - 279*a^4*b^3 + 252*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/(2*a^9*b*d*cos(d*x + c)^6 - 6*a^9*b*d*cos(d*x + c)^4 + 6*a^9*b*d*cos(d*x + c)^2 - 2*a^9*b*d + (a^8*b^2*d*cos(d*x + c)^6 - (a^10 + 3*a^8*b^2)*d*cos(d*x + c)^4 + (2*a^10 + 3*a^8*b^2)*d*cos(d*x + c)^2 - (a^10 + a^8*b^2)*d)*sin(d*x + c))]","B",0
1275,1,3687,0,4.001578," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(10 \, a^{7} b^{2} - 889 \, a^{5} b^{4} + 3255 \, a^{3} b^{6} - 2520 \, a b^{8}\right)} \cos\left(d x + c\right)^{9} - 4 \, {\left(40 \, a^{9} - 1381 \, a^{7} b^{2} - 9492 \, a^{5} b^{4} + 48720 \, a^{3} b^{6} - 40320 \, a b^{8}\right)} \cos\left(d x + c\right)^{7} - 28 \, {\left(563 \, a^{7} b^{2} + 1068 \, a^{5} b^{4} - 9720 \, a^{3} b^{6} + 8640 \, a b^{8}\right)} \cos\left(d x + c\right)^{5} + 140 \, {\left(105 \, a^{7} b^{2} + 20 \, a^{5} b^{4} - 1200 \, a^{3} b^{6} + 1152 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + 840 \, {\left(2 \, {\left(4 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 24 \, a b^{7}\right)} \cos\left(d x + c\right)^{8} + 8 \, a^{5} b^{3} - 46 \, a^{3} b^{5} + 48 \, a b^{7} - 8 \, {\left(4 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 24 \, a b^{7}\right)} \cos\left(d x + c\right)^{6} + 12 \, {\left(4 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 24 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(4 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 24 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} b^{4} - 23 \, a^{2} b^{6} + 24 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 4 \, a^{6} b^{2} - 19 \, a^{4} b^{4} + a^{2} b^{6} + 24 \, b^{8} - {\left(4 \, a^{6} b^{2} - 7 \, a^{4} b^{4} - 68 \, a^{2} b^{6} + 96 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(4 \, a^{6} b^{2} - 15 \, a^{4} b^{4} - 22 \, a^{2} b^{6} + 48 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(12 \, a^{6} b^{2} - 53 \, a^{4} b^{4} - 20 \, a^{2} b^{6} + 96 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 420 \, {\left(11 \, a^{7} b^{2} - 8 \, a^{5} b^{4} - 92 \, a^{3} b^{6} + 96 \, a b^{8}\right)} \cos\left(d x + c\right) - 105 \, {\left(10 \, a^{7} b^{2} - 200 \, a^{5} b^{4} + 560 \, a^{3} b^{6} - 384 \, a b^{8} + 2 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{8} - 8 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{6} + 12 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{8} b - 95 \, a^{6} b^{3} + 180 \, a^{4} b^{5} + 88 \, a^{2} b^{7} - 192 \, b^{9} + {\left(5 \, a^{6} b^{3} - 100 \, a^{4} b^{5} + 280 \, a^{2} b^{7} - 192 \, b^{9}\right)} \cos\left(d x + c\right)^{8} - {\left(5 \, a^{8} b - 80 \, a^{6} b^{3} - 120 \, a^{4} b^{5} + 928 \, a^{2} b^{7} - 768 \, b^{9}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{8} b - 90 \, a^{6} b^{3} + 80 \, a^{4} b^{5} + 368 \, a^{2} b^{7} - 384 \, b^{9}\right)} \cos\left(d x + c\right)^{4} - {\left(15 \, a^{8} b - 280 \, a^{6} b^{3} + 440 \, a^{4} b^{5} + 544 \, a^{2} b^{7} - 768 \, b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(10 \, a^{7} b^{2} - 200 \, a^{5} b^{4} + 560 \, a^{3} b^{6} - 384 \, a b^{8} + 2 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{8} - 8 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{6} + 12 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{8} b - 95 \, a^{6} b^{3} + 180 \, a^{4} b^{5} + 88 \, a^{2} b^{7} - 192 \, b^{9} + {\left(5 \, a^{6} b^{3} - 100 \, a^{4} b^{5} + 280 \, a^{2} b^{7} - 192 \, b^{9}\right)} \cos\left(d x + c\right)^{8} - {\left(5 \, a^{8} b - 80 \, a^{6} b^{3} - 120 \, a^{4} b^{5} + 928 \, a^{2} b^{7} - 768 \, b^{9}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{8} b - 90 \, a^{6} b^{3} + 80 \, a^{4} b^{5} + 368 \, a^{2} b^{7} - 384 \, b^{9}\right)} \cos\left(d x + c\right)^{4} - {\left(15 \, a^{8} b - 280 \, a^{6} b^{3} + 440 \, a^{4} b^{5} + 544 \, a^{2} b^{7} - 768 \, b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(160 \, a^{8} b - 11389 \, a^{6} b^{3} + 39900 \, a^{4} b^{5} - 30240 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{7} - 7 \, {\left(165 \, a^{8} b - 5207 \, a^{6} b^{3} + 17340 \, a^{4} b^{5} - 12960 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{5} + 35 \, {\left(40 \, a^{8} b - 1097 \, a^{6} b^{3} + 3516 \, a^{4} b^{5} - 2592 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(5 \, a^{8} b - 127 \, a^{6} b^{3} + 396 \, a^{4} b^{5} - 288 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1120 \, {\left(2 \, a^{11} b d \cos\left(d x + c\right)^{8} - 8 \, a^{11} b d \cos\left(d x + c\right)^{6} + 12 \, a^{11} b d \cos\left(d x + c\right)^{4} - 8 \, a^{11} b d \cos\left(d x + c\right)^{2} + 2 \, a^{11} b d + {\left(a^{10} b^{2} d \cos\left(d x + c\right)^{8} - {\left(a^{12} + 4 \, a^{10} b^{2}\right)} d \cos\left(d x + c\right)^{6} + 3 \, {\left(a^{12} + 2 \, a^{10} b^{2}\right)} d \cos\left(d x + c\right)^{4} - {\left(3 \, a^{12} + 4 \, a^{10} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} + a^{10} b^{2}\right)} d\right)} \sin\left(d x + c\right)\right)}}, \frac{16 \, {\left(10 \, a^{7} b^{2} - 889 \, a^{5} b^{4} + 3255 \, a^{3} b^{6} - 2520 \, a b^{8}\right)} \cos\left(d x + c\right)^{9} - 4 \, {\left(40 \, a^{9} - 1381 \, a^{7} b^{2} - 9492 \, a^{5} b^{4} + 48720 \, a^{3} b^{6} - 40320 \, a b^{8}\right)} \cos\left(d x + c\right)^{7} - 28 \, {\left(563 \, a^{7} b^{2} + 1068 \, a^{5} b^{4} - 9720 \, a^{3} b^{6} + 8640 \, a b^{8}\right)} \cos\left(d x + c\right)^{5} + 140 \, {\left(105 \, a^{7} b^{2} + 20 \, a^{5} b^{4} - 1200 \, a^{3} b^{6} + 1152 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} + 1680 \, {\left(2 \, {\left(4 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 24 \, a b^{7}\right)} \cos\left(d x + c\right)^{8} + 8 \, a^{5} b^{3} - 46 \, a^{3} b^{5} + 48 \, a b^{7} - 8 \, {\left(4 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 24 \, a b^{7}\right)} \cos\left(d x + c\right)^{6} + 12 \, {\left(4 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 24 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(4 \, a^{5} b^{3} - 23 \, a^{3} b^{5} + 24 \, a b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(4 \, a^{4} b^{4} - 23 \, a^{2} b^{6} + 24 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 4 \, a^{6} b^{2} - 19 \, a^{4} b^{4} + a^{2} b^{6} + 24 \, b^{8} - {\left(4 \, a^{6} b^{2} - 7 \, a^{4} b^{4} - 68 \, a^{2} b^{6} + 96 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(4 \, a^{6} b^{2} - 15 \, a^{4} b^{4} - 22 \, a^{2} b^{6} + 48 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - {\left(12 \, a^{6} b^{2} - 53 \, a^{4} b^{4} - 20 \, a^{2} b^{6} + 96 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 420 \, {\left(11 \, a^{7} b^{2} - 8 \, a^{5} b^{4} - 92 \, a^{3} b^{6} + 96 \, a b^{8}\right)} \cos\left(d x + c\right) - 105 \, {\left(10 \, a^{7} b^{2} - 200 \, a^{5} b^{4} + 560 \, a^{3} b^{6} - 384 \, a b^{8} + 2 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{8} - 8 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{6} + 12 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{8} b - 95 \, a^{6} b^{3} + 180 \, a^{4} b^{5} + 88 \, a^{2} b^{7} - 192 \, b^{9} + {\left(5 \, a^{6} b^{3} - 100 \, a^{4} b^{5} + 280 \, a^{2} b^{7} - 192 \, b^{9}\right)} \cos\left(d x + c\right)^{8} - {\left(5 \, a^{8} b - 80 \, a^{6} b^{3} - 120 \, a^{4} b^{5} + 928 \, a^{2} b^{7} - 768 \, b^{9}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{8} b - 90 \, a^{6} b^{3} + 80 \, a^{4} b^{5} + 368 \, a^{2} b^{7} - 384 \, b^{9}\right)} \cos\left(d x + c\right)^{4} - {\left(15 \, a^{8} b - 280 \, a^{6} b^{3} + 440 \, a^{4} b^{5} + 544 \, a^{2} b^{7} - 768 \, b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left(10 \, a^{7} b^{2} - 200 \, a^{5} b^{4} + 560 \, a^{3} b^{6} - 384 \, a b^{8} + 2 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{8} - 8 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{6} + 12 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(5 \, a^{7} b^{2} - 100 \, a^{5} b^{4} + 280 \, a^{3} b^{6} - 192 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left(5 \, a^{8} b - 95 \, a^{6} b^{3} + 180 \, a^{4} b^{5} + 88 \, a^{2} b^{7} - 192 \, b^{9} + {\left(5 \, a^{6} b^{3} - 100 \, a^{4} b^{5} + 280 \, a^{2} b^{7} - 192 \, b^{9}\right)} \cos\left(d x + c\right)^{8} - {\left(5 \, a^{8} b - 80 \, a^{6} b^{3} - 120 \, a^{4} b^{5} + 928 \, a^{2} b^{7} - 768 \, b^{9}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{8} b - 90 \, a^{6} b^{3} + 80 \, a^{4} b^{5} + 368 \, a^{2} b^{7} - 384 \, b^{9}\right)} \cos\left(d x + c\right)^{4} - {\left(15 \, a^{8} b - 280 \, a^{6} b^{3} + 440 \, a^{4} b^{5} + 544 \, a^{2} b^{7} - 768 \, b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(160 \, a^{8} b - 11389 \, a^{6} b^{3} + 39900 \, a^{4} b^{5} - 30240 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{7} - 7 \, {\left(165 \, a^{8} b - 5207 \, a^{6} b^{3} + 17340 \, a^{4} b^{5} - 12960 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{5} + 35 \, {\left(40 \, a^{8} b - 1097 \, a^{6} b^{3} + 3516 \, a^{4} b^{5} - 2592 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(5 \, a^{8} b - 127 \, a^{6} b^{3} + 396 \, a^{4} b^{5} - 288 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1120 \, {\left(2 \, a^{11} b d \cos\left(d x + c\right)^{8} - 8 \, a^{11} b d \cos\left(d x + c\right)^{6} + 12 \, a^{11} b d \cos\left(d x + c\right)^{4} - 8 \, a^{11} b d \cos\left(d x + c\right)^{2} + 2 \, a^{11} b d + {\left(a^{10} b^{2} d \cos\left(d x + c\right)^{8} - {\left(a^{12} + 4 \, a^{10} b^{2}\right)} d \cos\left(d x + c\right)^{6} + 3 \, {\left(a^{12} + 2 \, a^{10} b^{2}\right)} d \cos\left(d x + c\right)^{4} - {\left(3 \, a^{12} + 4 \, a^{10} b^{2}\right)} d \cos\left(d x + c\right)^{2} + {\left(a^{12} + a^{10} b^{2}\right)} d\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/1120*(16*(10*a^7*b^2 - 889*a^5*b^4 + 3255*a^3*b^6 - 2520*a*b^8)*cos(d*x + c)^9 - 4*(40*a^9 - 1381*a^7*b^2 - 9492*a^5*b^4 + 48720*a^3*b^6 - 40320*a*b^8)*cos(d*x + c)^7 - 28*(563*a^7*b^2 + 1068*a^5*b^4 - 9720*a^3*b^6 + 8640*a*b^8)*cos(d*x + c)^5 + 140*(105*a^7*b^2 + 20*a^5*b^4 - 1200*a^3*b^6 + 1152*a*b^8)*cos(d*x + c)^3 + 840*(2*(4*a^5*b^3 - 23*a^3*b^5 + 24*a*b^7)*cos(d*x + c)^8 + 8*a^5*b^3 - 46*a^3*b^5 + 48*a*b^7 - 8*(4*a^5*b^3 - 23*a^3*b^5 + 24*a*b^7)*cos(d*x + c)^6 + 12*(4*a^5*b^3 - 23*a^3*b^5 + 24*a*b^7)*cos(d*x + c)^4 - 8*(4*a^5*b^3 - 23*a^3*b^5 + 24*a*b^7)*cos(d*x + c)^2 + ((4*a^4*b^4 - 23*a^2*b^6 + 24*b^8)*cos(d*x + c)^8 + 4*a^6*b^2 - 19*a^4*b^4 + a^2*b^6 + 24*b^8 - (4*a^6*b^2 - 7*a^4*b^4 - 68*a^2*b^6 + 96*b^8)*cos(d*x + c)^6 + 3*(4*a^6*b^2 - 15*a^4*b^4 - 22*a^2*b^6 + 48*b^8)*cos(d*x + c)^4 - (12*a^6*b^2 - 53*a^4*b^4 - 20*a^2*b^6 + 96*b^8)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 420*(11*a^7*b^2 - 8*a^5*b^4 - 92*a^3*b^6 + 96*a*b^8)*cos(d*x + c) - 105*(10*a^7*b^2 - 200*a^5*b^4 + 560*a^3*b^6 - 384*a*b^8 + 2*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^8 - 8*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^6 + 12*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^4 - 8*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^2 + (5*a^8*b - 95*a^6*b^3 + 180*a^4*b^5 + 88*a^2*b^7 - 192*b^9 + (5*a^6*b^3 - 100*a^4*b^5 + 280*a^2*b^7 - 192*b^9)*cos(d*x + c)^8 - (5*a^8*b - 80*a^6*b^3 - 120*a^4*b^5 + 928*a^2*b^7 - 768*b^9)*cos(d*x + c)^6 + 3*(5*a^8*b - 90*a^6*b^3 + 80*a^4*b^5 + 368*a^2*b^7 - 384*b^9)*cos(d*x + c)^4 - (15*a^8*b - 280*a^6*b^3 + 440*a^4*b^5 + 544*a^2*b^7 - 768*b^9)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 105*(10*a^7*b^2 - 200*a^5*b^4 + 560*a^3*b^6 - 384*a*b^8 + 2*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^8 - 8*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^6 + 12*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^4 - 8*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^2 + (5*a^8*b - 95*a^6*b^3 + 180*a^4*b^5 + 88*a^2*b^7 - 192*b^9 + (5*a^6*b^3 - 100*a^4*b^5 + 280*a^2*b^7 - 192*b^9)*cos(d*x + c)^8 - (5*a^8*b - 80*a^6*b^3 - 120*a^4*b^5 + 928*a^2*b^7 - 768*b^9)*cos(d*x + c)^6 + 3*(5*a^8*b - 90*a^6*b^3 + 80*a^4*b^5 + 368*a^2*b^7 - 384*b^9)*cos(d*x + c)^4 - (15*a^8*b - 280*a^6*b^3 + 440*a^4*b^5 + 544*a^2*b^7 - 768*b^9)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*((160*a^8*b - 11389*a^6*b^3 + 39900*a^4*b^5 - 30240*a^2*b^7)*cos(d*x + c)^7 - 7*(165*a^8*b - 5207*a^6*b^3 + 17340*a^4*b^5 - 12960*a^2*b^7)*cos(d*x + c)^5 + 35*(40*a^8*b - 1097*a^6*b^3 + 3516*a^4*b^5 - 2592*a^2*b^7)*cos(d*x + c)^3 - 105*(5*a^8*b - 127*a^6*b^3 + 396*a^4*b^5 - 288*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/(2*a^11*b*d*cos(d*x + c)^8 - 8*a^11*b*d*cos(d*x + c)^6 + 12*a^11*b*d*cos(d*x + c)^4 - 8*a^11*b*d*cos(d*x + c)^2 + 2*a^11*b*d + (a^10*b^2*d*cos(d*x + c)^8 - (a^12 + 4*a^10*b^2)*d*cos(d*x + c)^6 + 3*(a^12 + 2*a^10*b^2)*d*cos(d*x + c)^4 - (3*a^12 + 4*a^10*b^2)*d*cos(d*x + c)^2 + (a^12 + a^10*b^2)*d)*sin(d*x + c)), 1/1120*(16*(10*a^7*b^2 - 889*a^5*b^4 + 3255*a^3*b^6 - 2520*a*b^8)*cos(d*x + c)^9 - 4*(40*a^9 - 1381*a^7*b^2 - 9492*a^5*b^4 + 48720*a^3*b^6 - 40320*a*b^8)*cos(d*x + c)^7 - 28*(563*a^7*b^2 + 1068*a^5*b^4 - 9720*a^3*b^6 + 8640*a*b^8)*cos(d*x + c)^5 + 140*(105*a^7*b^2 + 20*a^5*b^4 - 1200*a^3*b^6 + 1152*a*b^8)*cos(d*x + c)^3 + 1680*(2*(4*a^5*b^3 - 23*a^3*b^5 + 24*a*b^7)*cos(d*x + c)^8 + 8*a^5*b^3 - 46*a^3*b^5 + 48*a*b^7 - 8*(4*a^5*b^3 - 23*a^3*b^5 + 24*a*b^7)*cos(d*x + c)^6 + 12*(4*a^5*b^3 - 23*a^3*b^5 + 24*a*b^7)*cos(d*x + c)^4 - 8*(4*a^5*b^3 - 23*a^3*b^5 + 24*a*b^7)*cos(d*x + c)^2 + ((4*a^4*b^4 - 23*a^2*b^6 + 24*b^8)*cos(d*x + c)^8 + 4*a^6*b^2 - 19*a^4*b^4 + a^2*b^6 + 24*b^8 - (4*a^6*b^2 - 7*a^4*b^4 - 68*a^2*b^6 + 96*b^8)*cos(d*x + c)^6 + 3*(4*a^6*b^2 - 15*a^4*b^4 - 22*a^2*b^6 + 48*b^8)*cos(d*x + c)^4 - (12*a^6*b^2 - 53*a^4*b^4 - 20*a^2*b^6 + 96*b^8)*cos(d*x + c)^2)*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 420*(11*a^7*b^2 - 8*a^5*b^4 - 92*a^3*b^6 + 96*a*b^8)*cos(d*x + c) - 105*(10*a^7*b^2 - 200*a^5*b^4 + 560*a^3*b^6 - 384*a*b^8 + 2*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^8 - 8*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^6 + 12*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^4 - 8*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^2 + (5*a^8*b - 95*a^6*b^3 + 180*a^4*b^5 + 88*a^2*b^7 - 192*b^9 + (5*a^6*b^3 - 100*a^4*b^5 + 280*a^2*b^7 - 192*b^9)*cos(d*x + c)^8 - (5*a^8*b - 80*a^6*b^3 - 120*a^4*b^5 + 928*a^2*b^7 - 768*b^9)*cos(d*x + c)^6 + 3*(5*a^8*b - 90*a^6*b^3 + 80*a^4*b^5 + 368*a^2*b^7 - 384*b^9)*cos(d*x + c)^4 - (15*a^8*b - 280*a^6*b^3 + 440*a^4*b^5 + 544*a^2*b^7 - 768*b^9)*cos(d*x + c)^2)*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 105*(10*a^7*b^2 - 200*a^5*b^4 + 560*a^3*b^6 - 384*a*b^8 + 2*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^8 - 8*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^6 + 12*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^4 - 8*(5*a^7*b^2 - 100*a^5*b^4 + 280*a^3*b^6 - 192*a*b^8)*cos(d*x + c)^2 + (5*a^8*b - 95*a^6*b^3 + 180*a^4*b^5 + 88*a^2*b^7 - 192*b^9 + (5*a^6*b^3 - 100*a^4*b^5 + 280*a^2*b^7 - 192*b^9)*cos(d*x + c)^8 - (5*a^8*b - 80*a^6*b^3 - 120*a^4*b^5 + 928*a^2*b^7 - 768*b^9)*cos(d*x + c)^6 + 3*(5*a^8*b - 90*a^6*b^3 + 80*a^4*b^5 + 368*a^2*b^7 - 384*b^9)*cos(d*x + c)^4 - (15*a^8*b - 280*a^6*b^3 + 440*a^4*b^5 + 544*a^2*b^7 - 768*b^9)*cos(d*x + c)^2)*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*((160*a^8*b - 11389*a^6*b^3 + 39900*a^4*b^5 - 30240*a^2*b^7)*cos(d*x + c)^7 - 7*(165*a^8*b - 5207*a^6*b^3 + 17340*a^4*b^5 - 12960*a^2*b^7)*cos(d*x + c)^5 + 35*(40*a^8*b - 1097*a^6*b^3 + 3516*a^4*b^5 - 2592*a^2*b^7)*cos(d*x + c)^3 - 105*(5*a^8*b - 127*a^6*b^3 + 396*a^4*b^5 - 288*a^2*b^7)*cos(d*x + c))*sin(d*x + c))/(2*a^11*b*d*cos(d*x + c)^8 - 8*a^11*b*d*cos(d*x + c)^6 + 12*a^11*b*d*cos(d*x + c)^4 - 8*a^11*b*d*cos(d*x + c)^2 + 2*a^11*b*d + (a^10*b^2*d*cos(d*x + c)^8 - (a^12 + 4*a^10*b^2)*d*cos(d*x + c)^6 + 3*(a^12 + 2*a^10*b^2)*d*cos(d*x + c)^4 - (3*a^12 + 4*a^10*b^2)*d*cos(d*x + c)^2 + (a^12 + a^10*b^2)*d)*sin(d*x + c))]","B",0
1276,0,0,0,1.470666," ","integrate(cos(f*x+e)^6/(a+b*sin(f*x+e))^(13/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right)} \cos\left(f x + e\right)^{6}}{b^{7} d \cos\left(f x + e\right)^{8} - {\left(21 \, a^{2} b^{5} + 4 \, b^{7}\right)} d \cos\left(f x + e\right)^{6} + {\left(35 \, a^{4} b^{3} + 63 \, a^{2} b^{5} + 6 \, b^{7}\right)} d \cos\left(f x + e\right)^{4} - {\left(7 \, a^{6} b + 70 \, a^{4} b^{3} + 63 \, a^{2} b^{5} + 4 \, b^{7}\right)} d \cos\left(f x + e\right)^{2} + {\left(7 \, a^{6} b + 35 \, a^{4} b^{3} + 21 \, a^{2} b^{5} + b^{7}\right)} d - {\left(7 \, a b^{6} d \cos\left(f x + e\right)^{6} - 7 \, {\left(5 \, a^{3} b^{4} + 3 \, a b^{6}\right)} d \cos\left(f x + e\right)^{4} + 7 \, {\left(3 \, a^{5} b^{2} + 10 \, a^{3} b^{4} + 3 \, a b^{6}\right)} d \cos\left(f x + e\right)^{2} - {\left(a^{7} + 21 \, a^{5} b^{2} + 35 \, a^{3} b^{4} + 7 \, a b^{6}\right)} d\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))*cos(f*x + e)^6/(b^7*d*cos(f*x + e)^8 - (21*a^2*b^5 + 4*b^7)*d*cos(f*x + e)^6 + (35*a^4*b^3 + 63*a^2*b^5 + 6*b^7)*d*cos(f*x + e)^4 - (7*a^6*b + 70*a^4*b^3 + 63*a^2*b^5 + 4*b^7)*d*cos(f*x + e)^2 + (7*a^6*b + 35*a^4*b^3 + 21*a^2*b^5 + b^7)*d - (7*a*b^6*d*cos(f*x + e)^6 - 7*(5*a^3*b^4 + 3*a*b^6)*d*cos(f*x + e)^4 + 7*(3*a^5*b^2 + 10*a^3*b^4 + 3*a*b^6)*d*cos(f*x + e)^2 - (a^7 + 21*a^5*b^2 + 35*a^3*b^4 + 7*a*b^6)*d)*sin(f*x + e)), x)","F",0
1277,0,0,0,1.538959," ","integrate((a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \cos\left(f x + e\right)^{2} - 2 \, a b \sin\left(f x + e\right) - a^{2} - b^{2}\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{d \sin\left(f x + e\right)}}{d g^{3} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(b^2*cos(f*x + e)^2 - 2*a*b*sin(f*x + e) - a^2 - b^2)*sqrt(g*cos(f*x + e))*sqrt(d*sin(f*x + e))/(d*g^3*cos(f*x + e)^3*sin(f*x + e)), x)","F",0
1278,0,0,0,1.634565," ","integrate((a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(7/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b^{2} \cos\left(f x + e\right)^{2} - 2 \, a b \sin\left(f x + e\right) - a^{2} - b^{2}\right)} \sqrt{g \cos\left(f x + e\right)} \sqrt{d \sin\left(f x + e\right)}}{d g^{4} \cos\left(f x + e\right)^{4} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(b^2*cos(f*x + e)^2 - 2*a*b*sin(f*x + e) - a^2 - b^2)*sqrt(g*cos(f*x + e))*sqrt(d*sin(f*x + e))/(d*g^4*cos(f*x + e)^4*sin(f*x + e)), x)","F",0
1279,1,71,0,1.365083," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a b^{2} \cos\left(d x + c\right)^{2} - 6 \, a^{3} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{6 \, b^{4} d}"," ",0,"1/6*(3*a*b^2*cos(d*x + c)^2 - 6*a^3*log(b*sin(d*x + c) + a) - 2*(b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sin(d*x + c))/(b^4*d)","A",0
1280,1,47,0,1.470259," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} \log\left(b \sin\left(d x + c\right) + a\right) + 2 \, a b \sin\left(d x + c\right)}{2 \, b^{3} d}"," ",0,"-1/2*(b^2*cos(d*x + c)^2 - 2*a^2*log(b*sin(d*x + c) + a) + 2*a*b*sin(d*x + c))/(b^3*d)","A",0
1281,1,31,0,1.424893," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a \log\left(b \sin\left(d x + c\right) + a\right) - b \sin\left(d x + c\right)}{b^{2} d}"," ",0,"-(a*log(b*sin(d*x + c) + a) - b*sin(d*x + c))/(b^2*d)","A",0
1282,1,31,0,1.312975," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{\log\left(b \sin\left(d x + c\right) + a\right) - \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right)}{a d}"," ",0,"-(log(b*sin(d*x + c) + a) - log(-1/2*sin(d*x + c)))/(a*d)","A",0
1283,1,56,0,0.843692," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{b \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) - b \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - a}{a^{2} d \sin\left(d x + c\right)}"," ",0,"(b*log(b*sin(d*x + c) + a)*sin(d*x + c) - b*log(1/2*sin(d*x + c))*sin(d*x + c) - a)/(a^2*d*sin(d*x + c))","A",0
1284,1,100,0,1.268094," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b \sin\left(d x + c\right) - a^{2} + 2 \, {\left(b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, {\left(b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right)}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}"," ",0,"-1/2*(2*a*b*sin(d*x + c) - a^2 + 2*(b^2*cos(d*x + c)^2 - b^2)*log(b*sin(d*x + c) + a) - 2*(b^2*cos(d*x + c)^2 - b^2)*log(-1/2*sin(d*x + c)))/(a^3*d*cos(d*x + c)^2 - a^3*d)","A",0
1285,1,427,0,1.351237," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{24 \, b^{5} \cos\left(d x + c\right)^{5} + 120 \, a^{4} b \cos\left(d x + c\right) + 60 \, \sqrt{-a^{2} + b^{2}} a^{4} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 40 \, {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{5} - 4 \, a^{3} b^{2} - a b^{4}\right)} d x + 15 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, b^{6} d}, \frac{24 \, b^{5} \cos\left(d x + c\right)^{5} + 120 \, a^{4} b \cos\left(d x + c\right) + 120 \, \sqrt{a^{2} - b^{2}} a^{4} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 40 \, {\left(a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{5} - 4 \, a^{3} b^{2} - a b^{4}\right)} d x + 15 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, b^{6} d}\right]"," ",0,"[1/120*(24*b^5*cos(d*x + c)^5 + 120*a^4*b*cos(d*x + c) + 60*sqrt(-a^2 + b^2)*a^4*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 40*(a^2*b^3 + b^5)*cos(d*x + c)^3 + 15*(8*a^5 - 4*a^3*b^2 - a*b^4)*d*x + 15*(2*a*b^4*cos(d*x + c)^3 - (4*a^3*b^2 + a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^6*d), 1/120*(24*b^5*cos(d*x + c)^5 + 120*a^4*b*cos(d*x + c) + 120*sqrt(a^2 - b^2)*a^4*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 40*(a^2*b^3 + b^5)*cos(d*x + c)^3 + 15*(8*a^5 - 4*a^3*b^2 - a*b^4)*d*x + 15*(2*a*b^4*cos(d*x + c)^3 - (4*a^3*b^2 + a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^6*d)]","A",0
1286,1,380,0,1.407520," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{8 \, a b^{3} \cos\left(d x + c\right)^{3} - 24 \, a^{3} b \cos\left(d x + c\right) + 12 \, \sqrt{-a^{2} + b^{2}} a^{3} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 3 \, {\left(8 \, a^{4} - 4 \, a^{2} b^{2} - b^{4}\right)} d x - 3 \, {\left(2 \, b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, b^{5} d}, \frac{8 \, a b^{3} \cos\left(d x + c\right)^{3} - 24 \, a^{3} b \cos\left(d x + c\right) - 24 \, \sqrt{a^{2} - b^{2}} a^{3} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left(8 \, a^{4} - 4 \, a^{2} b^{2} - b^{4}\right)} d x - 3 \, {\left(2 \, b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, b^{5} d}\right]"," ",0,"[1/24*(8*a*b^3*cos(d*x + c)^3 - 24*a^3*b*cos(d*x + c) + 12*sqrt(-a^2 + b^2)*a^3*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 3*(8*a^4 - 4*a^2*b^2 - b^4)*d*x - 3*(2*b^4*cos(d*x + c)^3 - (4*a^2*b^2 + b^4)*cos(d*x + c))*sin(d*x + c))/(b^5*d), 1/24*(8*a*b^3*cos(d*x + c)^3 - 24*a^3*b*cos(d*x + c) - 24*sqrt(a^2 - b^2)*a^3*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*(8*a^4 - 4*a^2*b^2 - b^4)*d*x - 3*(2*b^4*cos(d*x + c)^3 - (4*a^2*b^2 + b^4)*cos(d*x + c))*sin(d*x + c))/(b^5*d)]","A",0
1287,1,315,0,1.475402," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, a^{2} b \cos\left(d x + c\right) - 3 \, \sqrt{-a^{2} + b^{2}} a^{2} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 3 \, {\left(2 \, a^{3} - a b^{2}\right)} d x}{6 \, b^{4} d}, -\frac{2 \, b^{3} \cos\left(d x + c\right)^{3} + 3 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, a^{2} b \cos\left(d x + c\right) - 6 \, \sqrt{a^{2} - b^{2}} a^{2} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left(2 \, a^{3} - a b^{2}\right)} d x}{6 \, b^{4} d}\right]"," ",0,"[-1/6*(2*b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)*sin(d*x + c) - 6*a^2*b*cos(d*x + c) - 3*sqrt(-a^2 + b^2)*a^2*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 3*(2*a^3 - a*b^2)*d*x)/(b^4*d), -1/6*(2*b^3*cos(d*x + c)^3 + 3*a*b^2*cos(d*x + c)*sin(d*x + c) - 6*a^2*b*cos(d*x + c) - 6*sqrt(a^2 - b^2)*a^2*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*(2*a^3 - a*b^2)*d*x)/(b^4*d)]","A",0
1288,1,275,0,1.421869," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(2 \, a^{2} - b^{2}\right)} d x - 2 \, a b \cos\left(d x + c\right) + \sqrt{-a^{2} + b^{2}} a \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, b^{3} d}, \frac{b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(2 \, a^{2} - b^{2}\right)} d x - 2 \, a b \cos\left(d x + c\right) - 2 \, \sqrt{a^{2} - b^{2}} a \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{2 \, b^{3} d}\right]"," ",0,"[1/2*(b^2*cos(d*x + c)*sin(d*x + c) - (2*a^2 - b^2)*d*x - 2*a*b*cos(d*x + c) + sqrt(-a^2 + b^2)*a*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/(b^3*d), 1/2*(b^2*cos(d*x + c)*sin(d*x + c) - (2*a^2 - b^2)*d*x - 2*a*b*cos(d*x + c) - 2*sqrt(a^2 - b^2)*a*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/(b^3*d)]","A",0
1289,1,262,0,1.399747," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{2 \, a d x + b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, a b d}, -\frac{2 \, a d x + b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{2 \, a b d}\right]"," ",0,"[-1/2*(2*a*d*x + b*log(1/2*cos(d*x + c) + 1/2) - b*log(-1/2*cos(d*x + c) + 1/2) - sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/(a*b*d), -1/2*(2*a*d*x + b*log(1/2*cos(d*x + c) + 1/2) - b*log(-1/2*cos(d*x + c) + 1/2) + 2*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/(a*b*d)]","A",0
1290,1,314,0,1.609682," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right)}{2 \, a^{2} d \sin\left(d x + c\right)}, \frac{b \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - b \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, a \cos\left(d x + c\right)}{2 \, a^{2} d \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 2*a*cos(d*x + c))/(a^2*d*sin(d*x + c)), 1/2*(b*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - b*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - 2*a*cos(d*x + c))/(a^2*d*sin(d*x + c))]","A",0
1291,1,472,0,1.594459," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{4 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} \cos\left(d x + c\right) - 2 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - {\left({\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + 2 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + 2 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}, -\frac{4 \, a b \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} \cos\left(d x + c\right) + 4 \, {\left(b \cos\left(d x + c\right)^{2} - b\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left({\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + 2 \, b^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{2} - 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + 2 \, b^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}\right]"," ",0,"[-1/4*(4*a*b*cos(d*x + c)*sin(d*x + c) - 2*a^2*cos(d*x + c) - 2*(b*cos(d*x + c)^2 - b)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - ((a^2 - 2*b^2)*cos(d*x + c)^2 - a^2 + 2*b^2)*log(1/2*cos(d*x + c) + 1/2) + ((a^2 - 2*b^2)*cos(d*x + c)^2 - a^2 + 2*b^2)*log(-1/2*cos(d*x + c) + 1/2))/(a^3*d*cos(d*x + c)^2 - a^3*d), -1/4*(4*a*b*cos(d*x + c)*sin(d*x + c) - 2*a^2*cos(d*x + c) + 4*(b*cos(d*x + c)^2 - b)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - ((a^2 - 2*b^2)*cos(d*x + c)^2 - a^2 + 2*b^2)*log(1/2*cos(d*x + c) + 1/2) + ((a^2 - 2*b^2)*cos(d*x + c)^2 - a^2 + 2*b^2)*log(-1/2*cos(d*x + c) + 1/2))/(a^3*d*cos(d*x + c)^2 - a^3*d)]","A",0
1292,1,591,0,1.584747," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, a^{2} b \cos\left(d x + c\right) \sin\left(d x + c\right) - 12 \, a b^{2} \cos\left(d x + c\right) - 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 3 \, {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right)}{12 \, {\left(a^{4} d \cos\left(d x + c\right)^{2} - a^{4} d\right)} \sin\left(d x + c\right)}, -\frac{6 \, a^{2} b \cos\left(d x + c\right) \sin\left(d x + c\right) - 12 \, a b^{2} \cos\left(d x + c\right) - 4 \, {\left(a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - 12 \, {\left(b^{2} \cos\left(d x + c\right)^{2} - b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - 3 \, {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(a^{2} b - 2 \, b^{3} - {\left(a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right)}{12 \, {\left(a^{4} d \cos\left(d x + c\right)^{2} - a^{4} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/12*(6*a^2*b*cos(d*x + c)*sin(d*x + c) - 12*a*b^2*cos(d*x + c) - 4*(a^3 - 3*a*b^2)*cos(d*x + c)^3 - 6*(b^2*cos(d*x + c)^2 - b^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 3*(a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c))/((a^4*d*cos(d*x + c)^2 - a^4*d)*sin(d*x + c)), -1/12*(6*a^2*b*cos(d*x + c)*sin(d*x + c) - 12*a*b^2*cos(d*x + c) - 4*(a^3 - 3*a*b^2)*cos(d*x + c)^3 - 12*(b^2*cos(d*x + c)^2 - b^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - 3*(a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(a^2*b - 2*b^3 - (a^2*b - 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c))/((a^4*d*cos(d*x + c)^2 - a^4*d)*sin(d*x + c))]","A",0
1293,1,808,0,2.054320," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(a^{4} - 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} - 24 \, {\left(b^{3} \cos\left(d x + c\right)^{4} - 2 \, b^{3} \cos\left(d x + c\right)^{2} + b^{3}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 6 \, {\left(a^{4} + 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right) - 3 \, {\left({\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4} - 2 \, {\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4} - 2 \, {\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(3 \, a b^{3} \cos\left(d x + c\right) + {\left(a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{5} d \cos\left(d x + c\right)^{4} - 2 \, a^{5} d \cos\left(d x + c\right)^{2} + a^{5} d\right)}}, -\frac{6 \, {\left(a^{4} - 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 48 \, {\left(b^{3} \cos\left(d x + c\right)^{4} - 2 \, b^{3} \cos\left(d x + c\right)^{2} + b^{3}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 6 \, {\left(a^{4} + 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right) - 3 \, {\left({\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4} - 2 \, {\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4} - 2 \, {\left(a^{4} + 4 \, a^{2} b^{2} - 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left(3 \, a b^{3} \cos\left(d x + c\right) + {\left(a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{5} d \cos\left(d x + c\right)^{4} - 2 \, a^{5} d \cos\left(d x + c\right)^{2} + a^{5} d\right)}}\right]"," ",0,"[-1/48*(6*(a^4 - 4*a^2*b^2)*cos(d*x + c)^3 - 24*(b^3*cos(d*x + c)^4 - 2*b^3*cos(d*x + c)^2 + b^3)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 6*(a^4 + 4*a^2*b^2)*cos(d*x + c) - 3*((a^4 + 4*a^2*b^2 - 8*b^4)*cos(d*x + c)^4 + a^4 + 4*a^2*b^2 - 8*b^4 - 2*(a^4 + 4*a^2*b^2 - 8*b^4)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 3*((a^4 + 4*a^2*b^2 - 8*b^4)*cos(d*x + c)^4 + a^4 + 4*a^2*b^2 - 8*b^4 - 2*(a^4 + 4*a^2*b^2 - 8*b^4)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 16*(3*a*b^3*cos(d*x + c) + (a^3*b - 3*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(a^5*d*cos(d*x + c)^4 - 2*a^5*d*cos(d*x + c)^2 + a^5*d), -1/48*(6*(a^4 - 4*a^2*b^2)*cos(d*x + c)^3 + 48*(b^3*cos(d*x + c)^4 - 2*b^3*cos(d*x + c)^2 + b^3)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 6*(a^4 + 4*a^2*b^2)*cos(d*x + c) - 3*((a^4 + 4*a^2*b^2 - 8*b^4)*cos(d*x + c)^4 + a^4 + 4*a^2*b^2 - 8*b^4 - 2*(a^4 + 4*a^2*b^2 - 8*b^4)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 3*((a^4 + 4*a^2*b^2 - 8*b^4)*cos(d*x + c)^4 + a^4 + 4*a^2*b^2 - 8*b^4 - 2*(a^4 + 4*a^2*b^2 - 8*b^4)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 16*(3*a*b^3*cos(d*x + c) + (a^3*b - 3*a*b^3)*cos(d*x + c)^3)*sin(d*x + c))/(a^5*d*cos(d*x + c)^4 - 2*a^5*d*cos(d*x + c)^2 + a^5*d)]","B",0
1294,1,959,0,1.974733," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{240 \, a b^{4} \cos\left(d x + c\right) - 16 \, {\left(2 \, a^{5} + 5 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 80 \, {\left(a^{5} + a^{3} b^{2} - 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 120 \, {\left(b^{4} \cos\left(d x + c\right)^{4} - 2 \, b^{4} \cos\left(d x + c\right)^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) + 15 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5} + {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5} + {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left({\left(a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{4} b + 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{6} d \cos\left(d x + c\right)^{4} - 2 \, a^{6} d \cos\left(d x + c\right)^{2} + a^{6} d\right)} \sin\left(d x + c\right)}, -\frac{240 \, a b^{4} \cos\left(d x + c\right) - 16 \, {\left(2 \, a^{5} + 5 \, a^{3} b^{2} - 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 80 \, {\left(a^{5} + a^{3} b^{2} - 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 240 \, {\left(b^{4} \cos\left(d x + c\right)^{4} - 2 \, b^{4} \cos\left(d x + c\right)^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) + 15 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5} + {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5} + {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b + 4 \, a^{2} b^{3} - 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left({\left(a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{4} b + 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{6} d \cos\left(d x + c\right)^{4} - 2 \, a^{6} d \cos\left(d x + c\right)^{2} + a^{6} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/240*(240*a*b^4*cos(d*x + c) - 16*(2*a^5 + 5*a^3*b^2 - 15*a*b^4)*cos(d*x + c)^5 + 80*(a^5 + a^3*b^2 - 6*a*b^4)*cos(d*x + c)^3 - 120*(b^4*cos(d*x + c)^4 - 2*b^4*cos(d*x + c)^2 + b^4)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) + 15*(a^4*b + 4*a^2*b^3 - 8*b^5 + (a^4*b + 4*a^2*b^3 - 8*b^5)*cos(d*x + c)^4 - 2*(a^4*b + 4*a^2*b^3 - 8*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(a^4*b + 4*a^2*b^3 - 8*b^5 + (a^4*b + 4*a^2*b^3 - 8*b^5)*cos(d*x + c)^4 - 2*(a^4*b + 4*a^2*b^3 - 8*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*((a^4*b - 4*a^2*b^3)*cos(d*x + c)^3 + (a^4*b + 4*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6*d*cos(d*x + c)^4 - 2*a^6*d*cos(d*x + c)^2 + a^6*d)*sin(d*x + c)), -1/240*(240*a*b^4*cos(d*x + c) - 16*(2*a^5 + 5*a^3*b^2 - 15*a*b^4)*cos(d*x + c)^5 + 80*(a^5 + a^3*b^2 - 6*a*b^4)*cos(d*x + c)^3 - 240*(b^4*cos(d*x + c)^4 - 2*b^4*cos(d*x + c)^2 + b^4)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) + 15*(a^4*b + 4*a^2*b^3 - 8*b^5 + (a^4*b + 4*a^2*b^3 - 8*b^5)*cos(d*x + c)^4 - 2*(a^4*b + 4*a^2*b^3 - 8*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(a^4*b + 4*a^2*b^3 - 8*b^5 + (a^4*b + 4*a^2*b^3 - 8*b^5)*cos(d*x + c)^4 - 2*(a^4*b + 4*a^2*b^3 - 8*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*((a^4*b - 4*a^2*b^3)*cos(d*x + c)^3 + (a^4*b + 4*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6*d*cos(d*x + c)^4 - 2*a^6*d*cos(d*x + c)^2 + a^6*d)*sin(d*x + c))]","A",0
1295,1,127,0,1.397859," ","integrate(cos(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{15 \, a b^{4} \cos\left(d x + c\right)^{4} - 30 \, a^{3} b^{2} \cos\left(d x + c\right)^{2} + 60 \, {\left(a^{5} - a^{3} b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 4 \, {\left(3 \, b^{5} \cos\left(d x + c\right)^{4} + 15 \, a^{4} b - 10 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, b^{6} d}"," ",0,"1/60*(15*a*b^4*cos(d*x + c)^4 - 30*a^3*b^2*cos(d*x + c)^2 + 60*(a^5 - a^3*b^2)*log(b*sin(d*x + c) + a) - 4*(3*b^5*cos(d*x + c)^4 + 15*a^4*b - 10*a^2*b^3 - 2*b^5 - (5*a^2*b^3 + b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^6*d)","A",0
1296,1,97,0,1.299188," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, b^{4} \cos\left(d x + c\right)^{4} - 6 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} + 12 \, {\left(a^{4} - a^{2} b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{3} b + 2 \, a b^{3}\right)} \sin\left(d x + c\right)}{12 \, b^{5} d}"," ",0,"-1/12*(3*b^4*cos(d*x + c)^4 - 6*a^2*b^2*cos(d*x + c)^2 + 12*(a^4 - a^2*b^2)*log(b*sin(d*x + c) + a) + 4*(a*b^3*cos(d*x + c)^2 - 3*a^3*b + 2*a*b^3)*sin(d*x + c))/(b^5*d)","A",0
1297,1,78,0,1.345827," ","integrate(cos(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a b^{2} \cos\left(d x + c\right)^{2} - 6 \, {\left(a^{3} - a b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, {\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)}{6 \, b^{4} d}"," ",0,"-1/6*(3*a*b^2*cos(d*x + c)^2 - 6*(a^3 - a*b^2)*log(b*sin(d*x + c) + a) - 2*(b^3*cos(d*x + c)^2 - 3*a^2*b + 2*b^3)*sin(d*x + c))/(b^4*d)","A",0
1298,1,55,0,1.404588," ","integrate(cos(d*x+c)^3*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{b^{2} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - a b \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a b^{2} d}"," ",0,"(b^2*log(-1/2*sin(d*x + c)) - a*b*sin(d*x + c) + (a^2 - b^2)*log(b*sin(d*x + c) + a))/(a*b^2*d)","A",0
1299,1,69,0,1.374479," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b^{2} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) + a b}{a^{2} b d \sin\left(d x + c\right)}"," ",0,"-(b^2*log(1/2*sin(d*x + c))*sin(d*x + c) + (a^2 - b^2)*log(b*sin(d*x + c) + a)*sin(d*x + c) + a*b)/(a^2*b*d*sin(d*x + c))","A",0
1300,1,118,0,1.417791," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a b \sin\left(d x + c\right) - a^{2} - 2 \, {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right)}{2 \, {\left(a^{3} d \cos\left(d x + c\right)^{2} - a^{3} d\right)}}"," ",0,"-1/2*(2*a*b*sin(d*x + c) - a^2 - 2*((a^2 - b^2)*cos(d*x + c)^2 - a^2 + b^2)*log(b*sin(d*x + c) + a) + 2*((a^2 - b^2)*cos(d*x + c)^2 - a^2 + b^2)*log(-1/2*sin(d*x + c)))/(a^3*d*cos(d*x + c)^2 - a^3*d)","A",0
1301,1,526,0,1.440785," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{48 \, a b^{5} \cos\left(d x + c\right)^{5} - 80 \, a^{3} b^{3} \cos\left(d x + c\right)^{3} + 15 \, {\left(16 \, a^{6} - 24 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + b^{6}\right)} d x - 120 \, {\left(a^{5} - a^{3} b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 240 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(d x + c\right) - 5 \, {\left(8 \, b^{6} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b^{2} - 6 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, b^{7} d}, \frac{48 \, a b^{5} \cos\left(d x + c\right)^{5} - 80 \, a^{3} b^{3} \cos\left(d x + c\right)^{3} + 15 \, {\left(16 \, a^{6} - 24 \, a^{4} b^{2} + 6 \, a^{2} b^{4} + b^{6}\right)} d x + 240 \, {\left(a^{5} - a^{3} b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 240 \, {\left(a^{5} b - a^{3} b^{3}\right)} \cos\left(d x + c\right) - 5 \, {\left(8 \, b^{6} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b^{2} - 6 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, b^{7} d}\right]"," ",0,"[1/240*(48*a*b^5*cos(d*x + c)^5 - 80*a^3*b^3*cos(d*x + c)^3 + 15*(16*a^6 - 24*a^4*b^2 + 6*a^2*b^4 + b^6)*d*x - 120*(a^5 - a^3*b^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 240*(a^5*b - a^3*b^3)*cos(d*x + c) - 5*(8*b^6*cos(d*x + c)^5 - 2*(6*a^2*b^4 + b^6)*cos(d*x + c)^3 + 3*(8*a^4*b^2 - 6*a^2*b^4 - b^6)*cos(d*x + c))*sin(d*x + c))/(b^7*d), 1/240*(48*a*b^5*cos(d*x + c)^5 - 80*a^3*b^3*cos(d*x + c)^3 + 15*(16*a^6 - 24*a^4*b^2 + 6*a^2*b^4 + b^6)*d*x + 240*(a^5 - a^3*b^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 240*(a^5*b - a^3*b^3)*cos(d*x + c) - 5*(8*b^6*cos(d*x + c)^5 - 2*(6*a^2*b^4 + b^6)*cos(d*x + c)^3 + 3*(8*a^4*b^2 - 6*a^2*b^4 - b^6)*cos(d*x + c))*sin(d*x + c))/(b^7*d)]","A",0
1302,1,457,0,1.564126," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{24 \, b^{5} \cos\left(d x + c\right)^{5} - 40 \, a^{2} b^{3} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{5} - 12 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d x + 60 \, {\left(a^{4} - a^{2} b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 120 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right) + 15 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, b^{6} d}, -\frac{24 \, b^{5} \cos\left(d x + c\right)^{5} - 40 \, a^{2} b^{3} \cos\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{5} - 12 \, a^{3} b^{2} + 3 \, a b^{4}\right)} d x + 120 \, {\left(a^{4} - a^{2} b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 120 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right) + 15 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, b^{6} d}\right]"," ",0,"[-1/120*(24*b^5*cos(d*x + c)^5 - 40*a^2*b^3*cos(d*x + c)^3 + 15*(8*a^5 - 12*a^3*b^2 + 3*a*b^4)*d*x + 60*(a^4 - a^2*b^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 120*(a^4*b - a^2*b^3)*cos(d*x + c) + 15*(2*a*b^4*cos(d*x + c)^3 - (4*a^3*b^2 - 3*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^6*d), -1/120*(24*b^5*cos(d*x + c)^5 - 40*a^2*b^3*cos(d*x + c)^3 + 15*(8*a^5 - 12*a^3*b^2 + 3*a*b^4)*d*x + 120*(a^4 - a^2*b^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 120*(a^4*b - a^2*b^3)*cos(d*x + c) + 15*(2*a*b^4*cos(d*x + c)^3 - (4*a^3*b^2 - 3*a*b^4)*cos(d*x + c))*sin(d*x + c))/(b^6*d)]","A",0
1303,1,414,0,1.298448," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{8 \, a b^{3} \cos\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} - 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} d x + 12 \, {\left(a^{3} - a b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 24 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) - 3 \, {\left(2 \, b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, b^{5} d}, -\frac{8 \, a b^{3} \cos\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} - 12 \, a^{2} b^{2} + 3 \, b^{4}\right)} d x - 24 \, {\left(a^{3} - a b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 24 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right) - 3 \, {\left(2 \, b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, b^{5} d}\right]"," ",0,"[-1/24*(8*a*b^3*cos(d*x + c)^3 - 3*(8*a^4 - 12*a^2*b^2 + 3*b^4)*d*x + 12*(a^3 - a*b^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 24*(a^3*b - a*b^3)*cos(d*x + c) - 3*(2*b^4*cos(d*x + c)^3 - (4*a^2*b^2 - 3*b^4)*cos(d*x + c))*sin(d*x + c))/(b^5*d), -1/24*(8*a*b^3*cos(d*x + c)^3 - 3*(8*a^4 - 12*a^2*b^2 + 3*b^4)*d*x - 24*(a^3 - a*b^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 24*(a^3*b - a*b^3)*cos(d*x + c) - 3*(2*b^4*cos(d*x + c)^3 - (4*a^2*b^2 - 3*b^4)*cos(d*x + c))*sin(d*x + c))/(b^5*d)]","A",0
1304,1,350,0,1.621492," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} b \cos\left(d x + c\right) + b^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d x - {\left(-a^{2} + b^{2}\right)}^{\frac{3}{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right)}{2 \, a b^{3} d}, -\frac{a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) - 2 \, a^{2} b \cos\left(d x + c\right) + b^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - b^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(2 \, a^{3} - 3 \, a b^{2}\right)} d x - 2 \, {\left(a^{2} - b^{2}\right)}^{\frac{3}{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right)}{2 \, a b^{3} d}\right]"," ",0,"[-1/2*(a*b^2*cos(d*x + c)*sin(d*x + c) - 2*a^2*b*cos(d*x + c) + b^3*log(1/2*cos(d*x + c) + 1/2) - b^3*log(-1/2*cos(d*x + c) + 1/2) - (2*a^3 - 3*a*b^2)*d*x - (-a^2 + b^2)^(3/2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)))/(a*b^3*d), -1/2*(a*b^2*cos(d*x + c)*sin(d*x + c) - 2*a^2*b*cos(d*x + c) + b^3*log(1/2*cos(d*x + c) + 1/2) - b^3*log(-1/2*cos(d*x + c) + 1/2) - (2*a^3 - 3*a*b^2)*d*x - 2*(a^2 - b^2)^(3/2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))))/(a*b^3*d)]","A",0
1305,1,396,0,1.655105," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{b^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - b^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, a b^{2} \cos\left(d x + c\right) - {\left(a^{2} - b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{3} d x + a^{2} b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, a^{2} b^{2} d \sin\left(d x + c\right)}, \frac{b^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - b^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, a b^{2} \cos\left(d x + c\right) - 2 \, {\left(a^{2} - b^{2}\right)}^{\frac{3}{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - 2 \, {\left(a^{3} d x + a^{2} b \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, a^{2} b^{2} d \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(b^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - b^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*a*b^2*cos(d*x + c) - (a^2 - b^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 2*(a^3*d*x + a^2*b*cos(d*x + c))*sin(d*x + c))/(a^2*b^2*d*sin(d*x + c)), 1/2*(b^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - b^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*a*b^2*cos(d*x + c) - 2*(a^2 - b^2)^(3/2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - 2*(a^3*d*x + a^2*b*cos(d*x + c))*sin(d*x + c))/(a^2*b^2*d*sin(d*x + c))]","A",0
1306,1,572,0,1.829331," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{4 \, a^{3} d x \cos\left(d x + c\right)^{2} - 4 \, a^{3} d x - 4 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, a^{2} b \cos\left(d x + c\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(a^{3} b d \cos\left(d x + c\right)^{2} - a^{3} b d\right)}}, \frac{4 \, a^{3} d x \cos\left(d x + c\right)^{2} - 4 \, a^{3} d x - 4 \, a b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, a^{2} b \cos\left(d x + c\right) + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(a^{3} b d \cos\left(d x + c\right)^{2} - a^{3} b d\right)}}\right]"," ",0,"[1/4*(4*a^3*d*x*cos(d*x + c)^2 - 4*a^3*d*x - 4*a*b^2*cos(d*x + c)*sin(d*x + c) + 2*a^2*b*cos(d*x + c) - 2*((a^2 - b^2)*cos(d*x + c)^2 - a^2 + b^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - (3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + (3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/(a^3*b*d*cos(d*x + c)^2 - a^3*b*d), 1/4*(4*a^3*d*x*cos(d*x + c)^2 - 4*a^3*d*x - 4*a*b^2*cos(d*x + c)*sin(d*x + c) + 2*a^2*b*cos(d*x + c) + 4*((a^2 - b^2)*cos(d*x + c)^2 - a^2 + b^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + (3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2))/(a^3*b*d*cos(d*x + c)^2 - a^3*b*d)]","B",0
1307,1,633,0,1.807660," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, a^{2} b \cos\left(d x + c\right) \sin\left(d x + c\right) - 4 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 6 \, {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 3 \, {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 12 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)}{12 \, {\left(a^{4} d \cos\left(d x + c\right)^{2} - a^{4} d\right)} \sin\left(d x + c\right)}, -\frac{6 \, a^{2} b \cos\left(d x + c\right) \sin\left(d x + c\right) - 4 \, {\left(4 \, a^{3} - 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} + 12 \, {\left({\left(a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - 3 \, {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(3 \, a^{2} b - 2 \, b^{3} - {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 12 \, {\left(a^{3} - a b^{2}\right)} \cos\left(d x + c\right)}{12 \, {\left(a^{4} d \cos\left(d x + c\right)^{2} - a^{4} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/12*(6*a^2*b*cos(d*x + c)*sin(d*x + c) - 4*(4*a^3 - 3*a*b^2)*cos(d*x + c)^3 + 6*((a^2 - b^2)*cos(d*x + c)^2 - a^2 + b^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 3*(3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 12*(a^3 - a*b^2)*cos(d*x + c))/((a^4*d*cos(d*x + c)^2 - a^4*d)*sin(d*x + c)), -1/12*(6*a^2*b*cos(d*x + c)*sin(d*x + c) - 4*(4*a^3 - 3*a*b^2)*cos(d*x + c)^3 + 12*((a^2 - b^2)*cos(d*x + c)^2 - a^2 + b^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - 3*(3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(3*a^2*b - 2*b^3 - (3*a^2*b - 2*b^3)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 12*(a^3 - a*b^2)*cos(d*x + c))/((a^4*d*cos(d*x + c)^2 - a^4*d)*sin(d*x + c))]","A",0
1308,1,904,0,2.354037," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(5 \, a^{4} - 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} + 24 \, {\left({\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} + a^{2} b - b^{3} - 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(3 \, a^{4} - 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left({\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4} - 2 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4} - 2 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left({\left(4 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{5} d \cos\left(d x + c\right)^{4} - 2 \, a^{5} d \cos\left(d x + c\right)^{2} + a^{5} d\right)}}, -\frac{6 \, {\left(5 \, a^{4} - 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)^{3} - 48 \, {\left({\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} + a^{2} b - b^{3} - 2 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 6 \, {\left(3 \, a^{4} - 4 \, a^{2} b^{2}\right)} \cos\left(d x + c\right) + 3 \, {\left({\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4} - 2 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{4} + 3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4} - 2 \, {\left(3 \, a^{4} - 12 \, a^{2} b^{2} + 8 \, b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left({\left(4 \, a^{3} b - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{5} d \cos\left(d x + c\right)^{4} - 2 \, a^{5} d \cos\left(d x + c\right)^{2} + a^{5} d\right)}}\right]"," ",0,"[-1/48*(6*(5*a^4 - 4*a^2*b^2)*cos(d*x + c)^3 + 24*((a^2*b - b^3)*cos(d*x + c)^4 + a^2*b - b^3 - 2*(a^2*b - b^3)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(3*a^4 - 4*a^2*b^2)*cos(d*x + c) + 3*((3*a^4 - 12*a^2*b^2 + 8*b^4)*cos(d*x + c)^4 + 3*a^4 - 12*a^2*b^2 + 8*b^4 - 2*(3*a^4 - 12*a^2*b^2 + 8*b^4)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - 3*((3*a^4 - 12*a^2*b^2 + 8*b^4)*cos(d*x + c)^4 + 3*a^4 - 12*a^2*b^2 + 8*b^4 - 2*(3*a^4 - 12*a^2*b^2 + 8*b^4)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 16*((4*a^3*b - 3*a*b^3)*cos(d*x + c)^3 - 3*(a^3*b - a*b^3)*cos(d*x + c))*sin(d*x + c))/(a^5*d*cos(d*x + c)^4 - 2*a^5*d*cos(d*x + c)^2 + a^5*d), -1/48*(6*(5*a^4 - 4*a^2*b^2)*cos(d*x + c)^3 - 48*((a^2*b - b^3)*cos(d*x + c)^4 + a^2*b - b^3 - 2*(a^2*b - b^3)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 6*(3*a^4 - 4*a^2*b^2)*cos(d*x + c) + 3*((3*a^4 - 12*a^2*b^2 + 8*b^4)*cos(d*x + c)^4 + 3*a^4 - 12*a^2*b^2 + 8*b^4 - 2*(3*a^4 - 12*a^2*b^2 + 8*b^4)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - 3*((3*a^4 - 12*a^2*b^2 + 8*b^4)*cos(d*x + c)^4 + 3*a^4 - 12*a^2*b^2 + 8*b^4 - 2*(3*a^4 - 12*a^2*b^2 + 8*b^4)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 16*((4*a^3*b - 3*a*b^3)*cos(d*x + c)^3 - 3*(a^3*b - a*b^3)*cos(d*x + c))*sin(d*x + c))/(a^5*d*cos(d*x + c)^4 - 2*a^5*d*cos(d*x + c)^2 + a^5*d)]","B",0
1309,1,1051,0,3.758617," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{16 \, {\left(3 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 80 \, {\left(7 \, a^{3} b^{2} - 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 120 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{2} b^{2} - b^{4} - 2 \, {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 15 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 240 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right) - 30 \, {\left({\left(5 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{6} d \cos\left(d x + c\right)^{4} - 2 \, a^{6} d \cos\left(d x + c\right)^{2} + a^{6} d\right)} \sin\left(d x + c\right)}, -\frac{16 \, {\left(3 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} + 80 \, {\left(7 \, a^{3} b^{2} - 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} + 240 \, {\left({\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{2} b^{2} - b^{4} - 2 \, {\left(a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - 15 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5} + {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{4} b - 12 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 240 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right) - 30 \, {\left({\left(5 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{6} d \cos\left(d x + c\right)^{4} - 2 \, a^{6} d \cos\left(d x + c\right)^{2} + a^{6} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/240*(16*(3*a^5 - 20*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 + 80*(7*a^3*b^2 - 6*a*b^4)*cos(d*x + c)^3 + 120*((a^2*b^2 - b^4)*cos(d*x + c)^4 + a^2*b^2 - b^4 - 2*(a^2*b^2 - b^4)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 15*(3*a^4*b - 12*a^2*b^3 + 8*b^5 + (3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(3*a^4*b - 12*a^2*b^3 + 8*b^5 + (3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 240*(a^3*b^2 - a*b^4)*cos(d*x + c) - 30*((5*a^4*b - 4*a^2*b^3)*cos(d*x + c)^3 - (3*a^4*b - 4*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6*d*cos(d*x + c)^4 - 2*a^6*d*cos(d*x + c)^2 + a^6*d)*sin(d*x + c)), -1/240*(16*(3*a^5 - 20*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 + 80*(7*a^3*b^2 - 6*a*b^4)*cos(d*x + c)^3 + 240*((a^2*b^2 - b^4)*cos(d*x + c)^4 + a^2*b^2 - b^4 - 2*(a^2*b^2 - b^4)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - 15*(3*a^4*b - 12*a^2*b^3 + 8*b^5 + (3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(3*a^4*b - 12*a^2*b^3 + 8*b^5 + (3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(3*a^4*b - 12*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 240*(a^3*b^2 - a*b^4)*cos(d*x + c) - 30*((5*a^4*b - 4*a^2*b^3)*cos(d*x + c)^3 - (3*a^4*b - 4*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6*d*cos(d*x + c)^4 - 2*a^6*d*cos(d*x + c)^2 + a^6*d)*sin(d*x + c))]","B",0
1310,1,199,0,1.902471," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{70 \, a b^{6} \cos\left(d x + c\right)^{6} - 105 \, a^{3} b^{4} \cos\left(d x + c\right)^{4} + 210 \, {\left(a^{5} b^{2} - a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} - 420 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 4 \, {\left(15 \, b^{7} \cos\left(d x + c\right)^{6} - 105 \, a^{6} b + 175 \, a^{4} b^{3} - 56 \, a^{2} b^{5} - 8 \, b^{7} - 3 \, {\left(7 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(35 \, a^{4} b^{3} - 28 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{420 \, b^{8} d}"," ",0,"1/420*(70*a*b^6*cos(d*x + c)^6 - 105*a^3*b^4*cos(d*x + c)^4 + 210*(a^5*b^2 - a^3*b^4)*cos(d*x + c)^2 - 420*(a^7 - 2*a^5*b^2 + a^3*b^4)*log(b*sin(d*x + c) + a) - 4*(15*b^7*cos(d*x + c)^6 - 105*a^6*b + 175*a^4*b^3 - 56*a^2*b^5 - 8*b^7 - 3*(7*a^2*b^5 + b^7)*cos(d*x + c)^4 + (35*a^4*b^3 - 28*a^2*b^5 - 4*b^7)*cos(d*x + c)^2)*sin(d*x + c))/(b^8*d)","A",0
1311,1,164,0,1.304724," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{10 \, b^{6} \cos\left(d x + c\right)^{6} - 15 \, a^{2} b^{4} \cos\left(d x + c\right)^{4} + 30 \, {\left(a^{4} b^{2} - a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - 60 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 4 \, {\left(3 \, a b^{5} \cos\left(d x + c\right)^{4} + 15 \, a^{5} b - 25 \, a^{3} b^{3} + 8 \, a b^{5} - {\left(5 \, a^{3} b^{3} - 4 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, b^{7} d}"," ",0,"-1/60*(10*b^6*cos(d*x + c)^6 - 15*a^2*b^4*cos(d*x + c)^4 + 30*(a^4*b^2 - a^2*b^4)*cos(d*x + c)^2 - 60*(a^6 - 2*a^4*b^2 + a^2*b^4)*log(b*sin(d*x + c) + a) + 4*(3*a*b^5*cos(d*x + c)^4 + 15*a^5*b - 25*a^3*b^3 + 8*a*b^5 - (5*a^3*b^3 - 4*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^7*d)","A",0
1312,1,142,0,1.723054," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, a b^{4} \cos\left(d x + c\right)^{4} - 30 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + 60 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 4 \, {\left(3 \, b^{5} \cos\left(d x + c\right)^{4} + 15 \, a^{4} b - 25 \, a^{2} b^{3} + 8 \, b^{5} - {\left(5 \, a^{2} b^{3} - 4 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, b^{6} d}"," ",0,"-1/60*(15*a*b^4*cos(d*x + c)^4 - 30*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 + 60*(a^5 - 2*a^3*b^2 + a*b^4)*log(b*sin(d*x + c) + a) - 4*(3*b^5*cos(d*x + c)^4 + 15*a^4*b - 25*a^2*b^3 + 8*b^5 - (5*a^2*b^3 - 4*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^6*d)","A",0
1313,1,104,0,1.373829," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} + 6 \, b^{4} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{3} b + 5 \, a b^{3}\right)} \sin\left(d x + c\right)}{6 \, a b^{4} d}"," ",0,"1/6*(3*a^2*b^2*cos(d*x + c)^2 + 6*b^4*log(-1/2*sin(d*x + c)) - 6*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a) - 2*(a*b^3*cos(d*x + c)^2 - 3*a^3*b + 5*a*b^3)*sin(d*x + c))/(a*b^4*d)","A",0
1314,1,133,0,1.845062," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, a^{3} b \cos\left(d x + c\right)^{2} - 4 \, b^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 4 \, a^{3} b - 4 \, a b^{3} + 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) - {\left(2 \, a^{2} b^{2} \cos\left(d x + c\right)^{2} - a^{2} b^{2}\right)} \sin\left(d x + c\right)}{4 \, a^{2} b^{3} d \sin\left(d x + c\right)}"," ",0,"1/4*(4*a^3*b*cos(d*x + c)^2 - 4*b^4*log(1/2*sin(d*x + c))*sin(d*x + c) - 4*a^3*b - 4*a*b^3 + 4*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)*sin(d*x + c) - (2*a^2*b^2*cos(d*x + c)^2 - a^2*b^2)*sin(d*x + c))/(a^2*b^3*d*sin(d*x + c))","A",0
1315,1,174,0,1.734545," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a^{2} b^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 2 \, {\left(2 \, a^{2} b^{2} - b^{4} - {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) + 2 \, {\left(a^{3} b \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{3} b^{2} d \cos\left(d x + c\right)^{2} - a^{3} b^{2} d\right)}}"," ",0,"1/2*(a^2*b^2 + 2*(a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*log(b*sin(d*x + c) + a) + 2*(2*a^2*b^2 - b^4 - (2*a^2*b^2 - b^4)*cos(d*x + c)^2)*log(-1/2*sin(d*x + c)) + 2*(a^3*b*cos(d*x + c)^2 - a^3*b - a*b^3)*sin(d*x + c))/(a^3*b^2*d*cos(d*x + c)^2 - a^3*b^2*d)","A",0
1316,1,198,0,1.289723," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, a^{2} b^{2} \sin\left(d x + c\right) + 10 \, a^{3} b - 6 \, a b^{3} - 6 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) + 6 \, {\left(2 \, a^{2} b^{2} - b^{4} - {\left(2 \, a^{2} b^{2} - b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right)}{6 \, {\left(a^{4} b d \cos\left(d x + c\right)^{2} - a^{4} b d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(3*a^2*b^2*sin(d*x + c) + 10*a^3*b - 6*a*b^3 - 6*(2*a^3*b - a*b^3)*cos(d*x + c)^2 + 6*(a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*log(b*sin(d*x + c) + a)*sin(d*x + c) + 6*(2*a^2*b^2 - b^4 - (2*a^2*b^2 - b^4)*cos(d*x + c)^2)*log(1/2*sin(d*x + c))*sin(d*x + c))/((a^4*b*d*cos(d*x + c)^2 - a^4*b*d)*sin(d*x + c))","A",0
1317,1,271,0,0.968599," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{9 \, a^{4} - 6 \, a^{2} b^{2} - 6 \, {\left(2 \, a^{4} - a^{2} b^{2}\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 12 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, {\left(5 \, a^{3} b - 3 \, a b^{3} - 3 \, {\left(2 \, a^{3} b - a b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{5} d \cos\left(d x + c\right)^{4} - 2 \, a^{5} d \cos\left(d x + c\right)^{2} + a^{5} d\right)}}"," ",0,"1/12*(9*a^4 - 6*a^2*b^2 - 6*(2*a^4 - a^2*b^2)*cos(d*x + c)^2 - 12*((a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*log(b*sin(d*x + c) + a) + 12*((a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*log(-1/2*sin(d*x + c)) - 4*(5*a^3*b - 3*a*b^3 - 3*(2*a^3*b - a*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(a^5*d*cos(d*x + c)^4 - 2*a^5*d*cos(d*x + c)^2 + a^5*d)","A",0
1318,1,346,0,1.422247," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{32 \, a^{5} - 100 \, a^{3} b^{2} + 60 \, a b^{4} + 60 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{4} - 20 \, {\left(4 \, a^{5} - 11 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} - 60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) + 60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 15 \, {\left(3 \, a^{4} b - 2 \, a^{2} b^{3} - 2 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{6} d \cos\left(d x + c\right)^{4} - 2 \, a^{6} d \cos\left(d x + c\right)^{2} + a^{6} d\right)} \sin\left(d x + c\right)}"," ",0,"-1/60*(32*a^5 - 100*a^3*b^2 + 60*a*b^4 + 60*(a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c)^4 - 20*(4*a^5 - 11*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^2 - 60*(a^4*b - 2*a^2*b^3 + b^5 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^4 - 2*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^2)*log(b*sin(d*x + c) + a)*sin(d*x + c) + 60*(a^4*b - 2*a^2*b^3 + b^5 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^4 - 2*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^2)*log(1/2*sin(d*x + c))*sin(d*x + c) + 15*(3*a^4*b - 2*a^2*b^3 - 2*(2*a^4*b - a^2*b^3)*cos(d*x + c)^2)*sin(d*x + c))/((a^6*d*cos(d*x + c)^4 - 2*a^6*d*cos(d*x + c)^2 + a^6*d)*sin(d*x + c))","B",0
1319,1,464,0,1.510202," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, a^{6} - 45 \, a^{4} b^{2} + 30 \, a^{2} b^{4} + 30 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{4} - 15 \, {\left(2 \, a^{6} - 7 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - 60 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{4} b^{2} + 2 \, a^{2} b^{4} - b^{6} - 3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 60 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{4} b^{2} + 2 \, a^{2} b^{4} - b^{6} - 3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - 4 \, {\left(8 \, a^{5} b - 25 \, a^{3} b^{3} + 15 \, a b^{5} + 15 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{4} - 5 \, {\left(4 \, a^{5} b - 11 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, {\left(a^{7} d \cos\left(d x + c\right)^{6} - 3 \, a^{7} d \cos\left(d x + c\right)^{4} + 3 \, a^{7} d \cos\left(d x + c\right)^{2} - a^{7} d\right)}}"," ",0,"1/60*(10*a^6 - 45*a^4*b^2 + 30*a^2*b^4 + 30*(a^6 - 2*a^4*b^2 + a^2*b^4)*cos(d*x + c)^4 - 15*(2*a^6 - 7*a^4*b^2 + 4*a^2*b^4)*cos(d*x + c)^2 - 60*((a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^6 - a^4*b^2 + 2*a^2*b^4 - b^6 - 3*(a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^4 + 3*(a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2)*log(b*sin(d*x + c) + a) + 60*((a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^6 - a^4*b^2 + 2*a^2*b^4 - b^6 - 3*(a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^4 + 3*(a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2)*log(-1/2*sin(d*x + c)) - 4*(8*a^5*b - 25*a^3*b^3 + 15*a*b^5 + 15*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c)^4 - 5*(4*a^5*b - 11*a^3*b^3 + 6*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(a^7*d*cos(d*x + c)^6 - 3*a^7*d*cos(d*x + c)^4 + 3*a^7*d*cos(d*x + c)^2 - a^7*d)","B",0
1320,1,706,0,1.741066," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{1920 \, a b^{7} \cos\left(d x + c\right)^{7} - 2688 \, a^{3} b^{5} \cos\left(d x + c\right)^{5} + 4480 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(128 \, a^{8} - 320 \, a^{6} b^{2} + 240 \, a^{4} b^{4} - 40 \, a^{2} b^{6} - 5 \, b^{8}\right)} d x + 6720 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 13440 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right) - 35 \, {\left(48 \, b^{8} \cos\left(d x + c\right)^{7} - 8 \, {\left(8 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(48 \, a^{4} b^{4} - 40 \, a^{2} b^{6} - 5 \, b^{8}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(64 \, a^{6} b^{2} - 112 \, a^{4} b^{4} + 40 \, a^{2} b^{6} + 5 \, b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{13440 \, b^{9} d}, \frac{1920 \, a b^{7} \cos\left(d x + c\right)^{7} - 2688 \, a^{3} b^{5} \cos\left(d x + c\right)^{5} + 4480 \, {\left(a^{5} b^{3} - a^{3} b^{5}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(128 \, a^{8} - 320 \, a^{6} b^{2} + 240 \, a^{4} b^{4} - 40 \, a^{2} b^{6} - 5 \, b^{8}\right)} d x - 13440 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 13440 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5}\right)} \cos\left(d x + c\right) - 35 \, {\left(48 \, b^{8} \cos\left(d x + c\right)^{7} - 8 \, {\left(8 \, a^{2} b^{6} + b^{8}\right)} \cos\left(d x + c\right)^{5} + 2 \, {\left(48 \, a^{4} b^{4} - 40 \, a^{2} b^{6} - 5 \, b^{8}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(64 \, a^{6} b^{2} - 112 \, a^{4} b^{4} + 40 \, a^{2} b^{6} + 5 \, b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{13440 \, b^{9} d}\right]"," ",0,"[1/13440*(1920*a*b^7*cos(d*x + c)^7 - 2688*a^3*b^5*cos(d*x + c)^5 + 4480*(a^5*b^3 - a^3*b^5)*cos(d*x + c)^3 - 105*(128*a^8 - 320*a^6*b^2 + 240*a^4*b^4 - 40*a^2*b^6 - 5*b^8)*d*x + 6720*(a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 13440*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c) - 35*(48*b^8*cos(d*x + c)^7 - 8*(8*a^2*b^6 + b^8)*cos(d*x + c)^5 + 2*(48*a^4*b^4 - 40*a^2*b^6 - 5*b^8)*cos(d*x + c)^3 - 3*(64*a^6*b^2 - 112*a^4*b^4 + 40*a^2*b^6 + 5*b^8)*cos(d*x + c))*sin(d*x + c))/(b^9*d), 1/13440*(1920*a*b^7*cos(d*x + c)^7 - 2688*a^3*b^5*cos(d*x + c)^5 + 4480*(a^5*b^3 - a^3*b^5)*cos(d*x + c)^3 - 105*(128*a^8 - 320*a^6*b^2 + 240*a^4*b^4 - 40*a^2*b^6 - 5*b^8)*d*x - 13440*(a^7 - 2*a^5*b^2 + a^3*b^4)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 13440*(a^7*b - 2*a^5*b^3 + a^3*b^5)*cos(d*x + c) - 35*(48*b^8*cos(d*x + c)^7 - 8*(8*a^2*b^6 + b^8)*cos(d*x + c)^5 + 2*(48*a^4*b^4 - 40*a^2*b^6 - 5*b^8)*cos(d*x + c)^3 - 3*(64*a^6*b^2 - 112*a^4*b^4 + 40*a^2*b^6 + 5*b^8)*cos(d*x + c))*sin(d*x + c))/(b^9*d)]","A",0
1321,1,619,0,1.194560," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{240 \, b^{7} \cos\left(d x + c\right)^{7} - 336 \, a^{2} b^{5} \cos\left(d x + c\right)^{5} + 560 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(16 \, a^{7} - 40 \, a^{5} b^{2} + 30 \, a^{3} b^{4} - 5 \, a b^{6}\right)} d x - 840 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 1680 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right) + 35 \, {\left(8 \, a b^{6} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{3} b^{4} - 5 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{5} b^{2} - 14 \, a^{3} b^{4} + 5 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, b^{8} d}, -\frac{240 \, b^{7} \cos\left(d x + c\right)^{7} - 336 \, a^{2} b^{5} \cos\left(d x + c\right)^{5} + 560 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} - 105 \, {\left(16 \, a^{7} - 40 \, a^{5} b^{2} + 30 \, a^{3} b^{4} - 5 \, a b^{6}\right)} d x - 1680 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 1680 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \cos\left(d x + c\right) + 35 \, {\left(8 \, a b^{6} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{3} b^{4} - 5 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{5} b^{2} - 14 \, a^{3} b^{4} + 5 \, a b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{1680 \, b^{8} d}\right]"," ",0,"[-1/1680*(240*b^7*cos(d*x + c)^7 - 336*a^2*b^5*cos(d*x + c)^5 + 560*(a^4*b^3 - a^2*b^5)*cos(d*x + c)^3 - 105*(16*a^7 - 40*a^5*b^2 + 30*a^3*b^4 - 5*a*b^6)*d*x - 840*(a^6 - 2*a^4*b^2 + a^2*b^4)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 1680*(a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c) + 35*(8*a*b^6*cos(d*x + c)^5 - 2*(6*a^3*b^4 - 5*a*b^6)*cos(d*x + c)^3 + 3*(8*a^5*b^2 - 14*a^3*b^4 + 5*a*b^6)*cos(d*x + c))*sin(d*x + c))/(b^8*d), -1/1680*(240*b^7*cos(d*x + c)^7 - 336*a^2*b^5*cos(d*x + c)^5 + 560*(a^4*b^3 - a^2*b^5)*cos(d*x + c)^3 - 105*(16*a^7 - 40*a^5*b^2 + 30*a^3*b^4 - 5*a*b^6)*d*x - 1680*(a^6 - 2*a^4*b^2 + a^2*b^4)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 1680*(a^6*b - 2*a^4*b^3 + a^2*b^5)*cos(d*x + c) + 35*(8*a*b^6*cos(d*x + c)^5 - 2*(6*a^3*b^4 - 5*a*b^6)*cos(d*x + c)^3 + 3*(8*a^5*b^2 - 14*a^3*b^4 + 5*a*b^6)*cos(d*x + c))*sin(d*x + c))/(b^8*d)]","A",0
1322,1,570,0,1.053937," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{48 \, a b^{5} \cos\left(d x + c\right)^{5} - 80 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(16 \, a^{6} - 40 \, a^{4} b^{2} + 30 \, a^{2} b^{4} - 5 \, b^{6}\right)} d x - 120 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 240 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - 5 \, {\left(8 \, b^{6} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{2} b^{4} - 5 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 5 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, b^{7} d}, -\frac{48 \, a b^{5} \cos\left(d x + c\right)^{5} - 80 \, {\left(a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(16 \, a^{6} - 40 \, a^{4} b^{2} + 30 \, a^{2} b^{4} - 5 \, b^{6}\right)} d x + 240 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 240 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right) - 5 \, {\left(8 \, b^{6} \cos\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{2} b^{4} - 5 \, b^{6}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b^{2} - 14 \, a^{2} b^{4} + 5 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, b^{7} d}\right]"," ",0,"[-1/240*(48*a*b^5*cos(d*x + c)^5 - 80*(a^3*b^3 - a*b^5)*cos(d*x + c)^3 + 15*(16*a^6 - 40*a^4*b^2 + 30*a^2*b^4 - 5*b^6)*d*x - 120*(a^5 - 2*a^3*b^2 + a*b^4)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 240*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c) - 5*(8*b^6*cos(d*x + c)^5 - 2*(6*a^2*b^4 - 5*b^6)*cos(d*x + c)^3 + 3*(8*a^4*b^2 - 14*a^2*b^4 + 5*b^6)*cos(d*x + c))*sin(d*x + c))/(b^7*d), -1/240*(48*a*b^5*cos(d*x + c)^5 - 80*(a^3*b^3 - a*b^5)*cos(d*x + c)^3 + 15*(16*a^6 - 40*a^4*b^2 + 30*a^2*b^4 - 5*b^6)*d*x + 240*(a^5 - 2*a^3*b^2 + a*b^4)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 240*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c) - 5*(8*b^6*cos(d*x + c)^5 - 2*(6*a^2*b^4 - 5*b^6)*cos(d*x + c)^3 + 3*(8*a^4*b^2 - 14*a^2*b^4 + 5*b^6)*cos(d*x + c))*sin(d*x + c))/(b^7*d)]","A",0
1323,1,508,0,2.101025," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{8 \, a^{2} b^{3} \cos\left(d x + c\right)^{3} - 12 \, b^{5} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, b^{5} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} d x + 12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 24 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(d x + c\right) - 3 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} - 7 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, a b^{5} d}, \frac{8 \, a^{2} b^{3} \cos\left(d x + c\right)^{3} - 12 \, b^{5} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 12 \, b^{5} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(8 \, a^{5} - 20 \, a^{3} b^{2} + 15 \, a b^{4}\right)} d x - 24 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 24 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(d x + c\right) - 3 \, {\left(2 \, a b^{4} \cos\left(d x + c\right)^{3} - {\left(4 \, a^{3} b^{2} - 7 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, a b^{5} d}\right]"," ",0,"[1/24*(8*a^2*b^3*cos(d*x + c)^3 - 12*b^5*log(1/2*cos(d*x + c) + 1/2) + 12*b^5*log(-1/2*cos(d*x + c) + 1/2) - 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*d*x + 12*(a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 24*(a^4*b - 2*a^2*b^3)*cos(d*x + c) - 3*(2*a*b^4*cos(d*x + c)^3 - (4*a^3*b^2 - 7*a*b^4)*cos(d*x + c))*sin(d*x + c))/(a*b^5*d), 1/24*(8*a^2*b^3*cos(d*x + c)^3 - 12*b^5*log(1/2*cos(d*x + c) + 1/2) + 12*b^5*log(-1/2*cos(d*x + c) + 1/2) - 3*(8*a^5 - 20*a^3*b^2 + 15*a*b^4)*d*x - 24*(a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 24*(a^4*b - 2*a^2*b^3)*cos(d*x + c) - 3*(2*a*b^4*cos(d*x + c)^3 - (4*a^3*b^2 - 7*a*b^4)*cos(d*x + c))*sin(d*x + c))/(a*b^5*d)]","A",0
1324,1,549,0,1.692121," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{3 \, a^{3} b^{2} \cos\left(d x + c\right)^{3} + 3 \, b^{5} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, b^{5} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 3 \, {\left(a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right) - {\left(2 \, a^{2} b^{3} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{5} - 5 \, a^{3} b^{2}\right)} d x - 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, a^{2} b^{4} d \sin\left(d x + c\right)}, \frac{3 \, a^{3} b^{2} \cos\left(d x + c\right)^{3} + 3 \, b^{5} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, b^{5} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - 3 \, {\left(a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right) - {\left(2 \, a^{2} b^{3} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{5} - 5 \, a^{3} b^{2}\right)} d x - 6 \, {\left(a^{4} b - 2 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, a^{2} b^{4} d \sin\left(d x + c\right)}\right]"," ",0,"[1/6*(3*a^3*b^2*cos(d*x + c)^3 + 3*b^5*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*b^5*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(a^4 - 2*a^2*b^2 + b^4)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 3*(a^3*b^2 + 2*a*b^4)*cos(d*x + c) - (2*a^2*b^3*cos(d*x + c)^3 - 3*(2*a^5 - 5*a^3*b^2)*d*x - 6*(a^4*b - 2*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(a^2*b^4*d*sin(d*x + c)), 1/6*(3*a^3*b^2*cos(d*x + c)^3 + 3*b^5*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*b^5*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*(a^4 - 2*a^2*b^2 + b^4)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - 3*(a^3*b^2 + 2*a*b^4)*cos(d*x + c) - (2*a^2*b^3*cos(d*x + c)^3 - 3*(2*a^5 - 5*a^3*b^2)*d*x - 6*(a^4*b - 2*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/(a^2*b^4*d*sin(d*x + c))]","A",0
1325,1,770,0,2.306400," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{4 \, a^{4} b \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{5} - 5 \, a^{3} b^{2}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{5} - 5 \, a^{3} b^{2}\right)} d x + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right) + {\left(5 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(5 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{3} b^{2} \cos\left(d x + c\right)^{3} - {\left(a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{3} b^{3} d \cos\left(d x + c\right)^{2} - a^{3} b^{3} d\right)}}, -\frac{4 \, a^{4} b \cos\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{5} - 5 \, a^{3} b^{2}\right)} d x \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{5} - 5 \, a^{3} b^{2}\right)} d x - 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 2 \, {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right) + {\left(5 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(5 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{3} b^{2} \cos\left(d x + c\right)^{3} - {\left(a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{3} b^{3} d \cos\left(d x + c\right)^{2} - a^{3} b^{3} d\right)}}\right]"," ",0,"[-1/4*(4*a^4*b*cos(d*x + c)^3 + 2*(2*a^5 - 5*a^3*b^2)*d*x*cos(d*x + c)^2 - 2*(2*a^5 - 5*a^3*b^2)*d*x + 2*(a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^4*b + a^2*b^3)*cos(d*x + c) + (5*a^2*b^3 - 2*b^5 - (5*a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - (5*a^2*b^3 - 2*b^5 - (5*a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^3*b^2*cos(d*x + c)^3 - (a^3*b^2 + 2*a*b^4)*cos(d*x + c))*sin(d*x + c))/(a^3*b^3*d*cos(d*x + c)^2 - a^3*b^3*d), -1/4*(4*a^4*b*cos(d*x + c)^3 + 2*(2*a^5 - 5*a^3*b^2)*d*x*cos(d*x + c)^2 - 2*(2*a^5 - 5*a^3*b^2)*d*x - 4*(a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 2*(2*a^4*b + a^2*b^3)*cos(d*x + c) + (5*a^2*b^3 - 2*b^5 - (5*a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - (5*a^2*b^3 - 2*b^5 - (5*a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^3*b^2*cos(d*x + c)^3 - (a^3*b^2 + 2*a*b^4)*cos(d*x + c))*sin(d*x + c))/(a^3*b^3*d*cos(d*x + c)^2 - a^3*b^3*d)]","B",0
1326,1,801,0,2.320276," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(7 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) + 3 \, {\left(5 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(5 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 12 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right) + 6 \, {\left(2 \, a^{5} d x \cos\left(d x + c\right)^{2} + 2 \, a^{4} b \cos\left(d x + c\right)^{3} - 2 \, a^{5} d x - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{4} b^{2} d \cos\left(d x + c\right)^{2} - a^{4} b^{2} d\right)} \sin\left(d x + c\right)}, \frac{4 \, {\left(7 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) + 3 \, {\left(5 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left(5 \, a^{2} b^{3} - 2 \, b^{5} - {\left(5 \, a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 12 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right) + 6 \, {\left(2 \, a^{5} d x \cos\left(d x + c\right)^{2} + 2 \, a^{4} b \cos\left(d x + c\right)^{3} - 2 \, a^{5} d x - {\left(2 \, a^{4} b + a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{12 \, {\left(a^{4} b^{2} d \cos\left(d x + c\right)^{2} - a^{4} b^{2} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[1/12*(4*(7*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^3 - 6*(a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) + 3*(5*a^2*b^3 - 2*b^5 - (5*a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(5*a^2*b^3 - 2*b^5 - (5*a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 12*(2*a^3*b^2 - a*b^4)*cos(d*x + c) + 6*(2*a^5*d*x*cos(d*x + c)^2 + 2*a^4*b*cos(d*x + c)^3 - 2*a^5*d*x - (2*a^4*b + a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^4*b^2*d*cos(d*x + c)^2 - a^4*b^2*d)*sin(d*x + c)), 1/12*(4*(7*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^3 - 12*(a^4 - 2*a^2*b^2 + b^4 - (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) + 3*(5*a^2*b^3 - 2*b^5 - (5*a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*(5*a^2*b^3 - 2*b^5 - (5*a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 12*(2*a^3*b^2 - a*b^4)*cos(d*x + c) + 6*(2*a^5*d*x*cos(d*x + c)^2 + 2*a^4*b*cos(d*x + c)^3 - 2*a^5*d*x - (2*a^4*b + a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^4*b^2*d*cos(d*x + c)^2 - a^4*b^2*d)*sin(d*x + c))]","A",0
1327,1,1034,0,2.538160," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{48 \, a^{5} d x \cos\left(d x + c\right)^{4} - 96 \, a^{5} d x \cos\left(d x + c\right)^{2} + 48 \, a^{5} d x + 6 \, {\left(9 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - 24 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(7 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right) + 3 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5} + {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5} + {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left({\left(7 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{5} b d \cos\left(d x + c\right)^{4} - 2 \, a^{5} b d \cos\left(d x + c\right)^{2} + a^{5} b d\right)}}, -\frac{48 \, a^{5} d x \cos\left(d x + c\right)^{4} - 96 \, a^{5} d x \cos\left(d x + c\right)^{2} + 48 \, a^{5} d x + 6 \, {\left(9 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} + 48 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 6 \, {\left(7 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right) + 3 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5} + {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5} + {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 16 \, {\left({\left(7 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{48 \, {\left(a^{5} b d \cos\left(d x + c\right)^{4} - 2 \, a^{5} b d \cos\left(d x + c\right)^{2} + a^{5} b d\right)}}\right]"," ",0,"[-1/48*(48*a^5*d*x*cos(d*x + c)^4 - 96*a^5*d*x*cos(d*x + c)^2 + 48*a^5*d*x + 6*(9*a^4*b - 4*a^2*b^3)*cos(d*x + c)^3 - 24*((a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(7*a^4*b - 4*a^2*b^3)*cos(d*x + c) + 3*(15*a^4*b - 20*a^2*b^3 + 8*b^5 + (15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - 3*(15*a^4*b - 20*a^2*b^3 + 8*b^5 + (15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 16*((7*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^3 - 3*(2*a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/(a^5*b*d*cos(d*x + c)^4 - 2*a^5*b*d*cos(d*x + c)^2 + a^5*b*d), -1/48*(48*a^5*d*x*cos(d*x + c)^4 - 96*a^5*d*x*cos(d*x + c)^2 + 48*a^5*d*x + 6*(9*a^4*b - 4*a^2*b^3)*cos(d*x + c)^3 + 48*((a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 6*(7*a^4*b - 4*a^2*b^3)*cos(d*x + c) + 3*(15*a^4*b - 20*a^2*b^3 + 8*b^5 + (15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - 3*(15*a^4*b - 20*a^2*b^3 + 8*b^5 + (15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 16*((7*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^3 - 3*(2*a^3*b^2 - a*b^4)*cos(d*x + c))*sin(d*x + c))/(a^5*b*d*cos(d*x + c)^4 - 2*a^5*b*d*cos(d*x + c)^2 + a^5*b*d)]","B",0
1328,1,1079,0,2.310516," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{16 \, {\left(23 \, a^{5} - 35 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} - 80 \, {\left(7 \, a^{5} - 13 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 120 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 15 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5} + {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5} + {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 240 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - 30 \, {\left({\left(9 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(7 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{6} d \cos\left(d x + c\right)^{4} - 2 \, a^{6} d \cos\left(d x + c\right)^{2} + a^{6} d\right)} \sin\left(d x + c\right)}, -\frac{16 \, {\left(23 \, a^{5} - 35 \, a^{3} b^{2} + 15 \, a b^{4}\right)} \cos\left(d x + c\right)^{5} - 80 \, {\left(7 \, a^{5} - 13 \, a^{3} b^{2} + 6 \, a b^{4}\right)} \cos\left(d x + c\right)^{3} - 240 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{4} + a^{4} - 2 \, a^{2} b^{2} + b^{4} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) - 15 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5} + {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 15 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5} + {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{4} b - 20 \, a^{2} b^{3} + 8 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 240 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right) - 30 \, {\left({\left(9 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(7 \, a^{4} b - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, {\left(a^{6} d \cos\left(d x + c\right)^{4} - 2 \, a^{6} d \cos\left(d x + c\right)^{2} + a^{6} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[-1/240*(16*(23*a^5 - 35*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 - 80*(7*a^5 - 13*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^3 - 120*((a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 15*(15*a^4*b - 20*a^2*b^3 + 8*b^5 + (15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(15*a^4*b - 20*a^2*b^3 + 8*b^5 + (15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 240*(a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c) - 30*((9*a^4*b - 4*a^2*b^3)*cos(d*x + c)^3 - (7*a^4*b - 4*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6*d*cos(d*x + c)^4 - 2*a^6*d*cos(d*x + c)^2 + a^6*d)*sin(d*x + c)), -1/240*(16*(23*a^5 - 35*a^3*b^2 + 15*a*b^4)*cos(d*x + c)^5 - 80*(7*a^5 - 13*a^3*b^2 + 6*a*b^4)*cos(d*x + c)^3 - 240*((a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) - 15*(15*a^4*b - 20*a^2*b^3 + 8*b^5 + (15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 15*(15*a^4*b - 20*a^2*b^3 + 8*b^5 + (15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^4 - 2*(15*a^4*b - 20*a^2*b^3 + 8*b^5)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 240*(a^5 - 2*a^3*b^2 + a*b^4)*cos(d*x + c) - 30*((9*a^4*b - 4*a^2*b^3)*cos(d*x + c)^3 - (7*a^4*b - 4*a^2*b^3)*cos(d*x + c))*sin(d*x + c))/((a^6*d*cos(d*x + c)^4 - 2*a^6*d*cos(d*x + c)^2 + a^6*d)*sin(d*x + c))]","B",0
1329,1,1462,0,2.867879," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{30 \, {\left(11 \, a^{6} - 18 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{5} - 80 \, {\left(5 \, a^{6} - 12 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} + 240 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{6} - a^{4} b + 2 \, a^{2} b^{3} - b^{5} - 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 30 \, {\left(5 \, a^{6} - 14 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 5 \, a^{6} + 30 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 16 \, b^{6} - 3 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 5 \, a^{6} + 30 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 16 \, b^{6} - 3 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left({\left(23 \, a^{5} b - 35 \, a^{3} b^{3} + 15 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 5 \, {\left(7 \, a^{5} b - 13 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(a^{7} d \cos\left(d x + c\right)^{6} - 3 \, a^{7} d \cos\left(d x + c\right)^{4} + 3 \, a^{7} d \cos\left(d x + c\right)^{2} - a^{7} d\right)}}, \frac{30 \, {\left(11 \, a^{6} - 18 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{5} - 80 \, {\left(5 \, a^{6} - 12 \, a^{4} b^{2} + 6 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 480 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{6} - a^{4} b + 2 \, a^{2} b^{3} - b^{5} - 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 30 \, {\left(5 \, a^{6} - 14 \, a^{4} b^{2} + 8 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) + 15 \, {\left({\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 5 \, a^{6} + 30 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 16 \, b^{6} - 3 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 15 \, {\left({\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{6} - 5 \, a^{6} + 30 \, a^{4} b^{2} - 40 \, a^{2} b^{4} + 16 \, b^{6} - 3 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{6} - 30 \, a^{4} b^{2} + 40 \, a^{2} b^{4} - 16 \, b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 32 \, {\left({\left(23 \, a^{5} b - 35 \, a^{3} b^{3} + 15 \, a b^{5}\right)} \cos\left(d x + c\right)^{5} - 5 \, {\left(7 \, a^{5} b - 13 \, a^{3} b^{3} + 6 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} + 15 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{480 \, {\left(a^{7} d \cos\left(d x + c\right)^{6} - 3 \, a^{7} d \cos\left(d x + c\right)^{4} + 3 \, a^{7} d \cos\left(d x + c\right)^{2} - a^{7} d\right)}}\right]"," ",0,"[1/480*(30*(11*a^6 - 18*a^4*b^2 + 8*a^2*b^4)*cos(d*x + c)^5 - 80*(5*a^6 - 12*a^4*b^2 + 6*a^2*b^4)*cos(d*x + c)^3 + 240*((a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^6 - a^4*b + 2*a^2*b^3 - b^5 - 3*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^4 + 3*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 30*(5*a^6 - 14*a^4*b^2 + 8*a^2*b^4)*cos(d*x + c) + 15*((5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^6 - 5*a^6 + 30*a^4*b^2 - 40*a^2*b^4 + 16*b^6 - 3*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^4 + 3*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - 15*((5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^6 - 5*a^6 + 30*a^4*b^2 - 40*a^2*b^4 + 16*b^6 - 3*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^4 + 3*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 32*((23*a^5*b - 35*a^3*b^3 + 15*a*b^5)*cos(d*x + c)^5 - 5*(7*a^5*b - 13*a^3*b^3 + 6*a*b^5)*cos(d*x + c)^3 + 15*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^7*d*cos(d*x + c)^6 - 3*a^7*d*cos(d*x + c)^4 + 3*a^7*d*cos(d*x + c)^2 - a^7*d), 1/480*(30*(11*a^6 - 18*a^4*b^2 + 8*a^2*b^4)*cos(d*x + c)^5 - 80*(5*a^6 - 12*a^4*b^2 + 6*a^2*b^4)*cos(d*x + c)^3 - 480*((a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^6 - a^4*b + 2*a^2*b^3 - b^5 - 3*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^4 + 3*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 30*(5*a^6 - 14*a^4*b^2 + 8*a^2*b^4)*cos(d*x + c) + 15*((5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^6 - 5*a^6 + 30*a^4*b^2 - 40*a^2*b^4 + 16*b^6 - 3*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^4 + 3*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) - 15*((5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^6 - 5*a^6 + 30*a^4*b^2 - 40*a^2*b^4 + 16*b^6 - 3*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^4 + 3*(5*a^6 - 30*a^4*b^2 + 40*a^2*b^4 - 16*b^6)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 32*((23*a^5*b - 35*a^3*b^3 + 15*a*b^5)*cos(d*x + c)^5 - 5*(7*a^5*b - 13*a^3*b^3 + 6*a*b^5)*cos(d*x + c)^3 + 15*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c))*sin(d*x + c))/(a^7*d*cos(d*x + c)^6 - 3*a^7*d*cos(d*x + c)^4 + 3*a^7*d*cos(d*x + c)^2 - a^7*d)]","B",0
1330,1,1645,0,2.924492," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{32 \, {\left(15 \, a^{7} - 161 \, a^{5} b^{2} + 245 \, a^{3} b^{4} - 105 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} + 224 \, {\left(58 \, a^{5} b^{2} - 100 \, a^{3} b^{4} + 45 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 1120 \, {\left(10 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 9 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 1680 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{4} b^{2} + 2 \, a^{2} b^{4} - b^{6} - 3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) + 105 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7} - {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 105 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7} - {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3360 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) - 70 \, {\left(3 \, {\left(11 \, a^{6} b - 18 \, a^{4} b^{3} + 8 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{5} - 8 \, {\left(5 \, a^{6} b - 12 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{6} b - 14 \, a^{4} b^{3} + 8 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3360 \, {\left(a^{8} d \cos\left(d x + c\right)^{6} - 3 \, a^{8} d \cos\left(d x + c\right)^{4} + 3 \, a^{8} d \cos\left(d x + c\right)^{2} - a^{8} d\right)} \sin\left(d x + c\right)}, \frac{32 \, {\left(15 \, a^{7} - 161 \, a^{5} b^{2} + 245 \, a^{3} b^{4} - 105 \, a b^{6}\right)} \cos\left(d x + c\right)^{7} + 224 \, {\left(58 \, a^{5} b^{2} - 100 \, a^{3} b^{4} + 45 \, a b^{6}\right)} \cos\left(d x + c\right)^{5} - 1120 \, {\left(10 \, a^{5} b^{2} - 19 \, a^{3} b^{4} + 9 \, a b^{6}\right)} \cos\left(d x + c\right)^{3} + 3360 \, {\left({\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{6} - a^{4} b^{2} + 2 \, a^{2} b^{4} - b^{6} - 3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \sin\left(d x + c\right) + 105 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7} - {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 105 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7} - {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(5 \, a^{6} b - 30 \, a^{4} b^{3} + 40 \, a^{2} b^{5} - 16 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3360 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right) - 70 \, {\left(3 \, {\left(11 \, a^{6} b - 18 \, a^{4} b^{3} + 8 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{5} - 8 \, {\left(5 \, a^{6} b - 12 \, a^{4} b^{3} + 6 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{6} b - 14 \, a^{4} b^{3} + 8 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{3360 \, {\left(a^{8} d \cos\left(d x + c\right)^{6} - 3 \, a^{8} d \cos\left(d x + c\right)^{4} + 3 \, a^{8} d \cos\left(d x + c\right)^{2} - a^{8} d\right)} \sin\left(d x + c\right)}\right]"," ",0,"[1/3360*(32*(15*a^7 - 161*a^5*b^2 + 245*a^3*b^4 - 105*a*b^6)*cos(d*x + c)^7 + 224*(58*a^5*b^2 - 100*a^3*b^4 + 45*a*b^6)*cos(d*x + c)^5 - 1120*(10*a^5*b^2 - 19*a^3*b^4 + 9*a*b^6)*cos(d*x + c)^3 + 1680*((a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^6 - a^4*b^2 + 2*a^2*b^4 - b^6 - 3*(a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^4 + 3*(a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) + 105*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7 - (5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^6 + 3*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^4 - 3*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 105*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7 - (5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^6 + 3*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^4 - 3*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3360*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c) - 70*(3*(11*a^6*b - 18*a^4*b^3 + 8*a^2*b^5)*cos(d*x + c)^5 - 8*(5*a^6*b - 12*a^4*b^3 + 6*a^2*b^5)*cos(d*x + c)^3 + 3*(5*a^6*b - 14*a^4*b^3 + 8*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*d*cos(d*x + c)^6 - 3*a^8*d*cos(d*x + c)^4 + 3*a^8*d*cos(d*x + c)^2 - a^8*d)*sin(d*x + c)), 1/3360*(32*(15*a^7 - 161*a^5*b^2 + 245*a^3*b^4 - 105*a*b^6)*cos(d*x + c)^7 + 224*(58*a^5*b^2 - 100*a^3*b^4 + 45*a*b^6)*cos(d*x + c)^5 - 1120*(10*a^5*b^2 - 19*a^3*b^4 + 9*a*b^6)*cos(d*x + c)^3 + 3360*((a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^6 - a^4*b^2 + 2*a^2*b^4 - b^6 - 3*(a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^4 + 3*(a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*sin(d*x + c) + 105*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7 - (5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^6 + 3*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^4 - 3*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 105*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7 - (5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^6 + 3*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^4 - 3*(5*a^6*b - 30*a^4*b^3 + 40*a^2*b^5 - 16*b^7)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3360*(a^5*b^2 - 2*a^3*b^4 + a*b^6)*cos(d*x + c) - 70*(3*(11*a^6*b - 18*a^4*b^3 + 8*a^2*b^5)*cos(d*x + c)^5 - 8*(5*a^6*b - 12*a^4*b^3 + 6*a^2*b^5)*cos(d*x + c)^3 + 3*(5*a^6*b - 14*a^4*b^3 + 8*a^2*b^5)*cos(d*x + c))*sin(d*x + c))/((a^8*d*cos(d*x + c)^6 - 3*a^8*d*cos(d*x + c)^4 + 3*a^8*d*cos(d*x + c)^2 - a^8*d)*sin(d*x + c))]","A",0
1331,1,2082,0,4.847744," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{210 \, {\left(5 \, a^{8} - 88 \, a^{6} b^{2} + 144 \, a^{4} b^{4} - 64 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{7} + 70 \, {\left(73 \, a^{8} + 584 \, a^{6} b^{2} - 1200 \, a^{4} b^{4} + 576 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{5} - 70 \, {\left(55 \, a^{8} + 440 \, a^{6} b^{2} - 1104 \, a^{4} b^{4} + 576 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} - 13440 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{8} + a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} - 4 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 210 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 112 \, a^{4} b^{4} + 64 \, a^{2} b^{6}\right)} \cos\left(d x + c\right) - 105 \, {\left({\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8} - 4 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left({\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8} - 4 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 256 \, {\left({\left(15 \, a^{7} b - 161 \, a^{5} b^{3} + 245 \, a^{3} b^{5} - 105 \, a b^{7}\right)} \cos\left(d x + c\right)^{7} + 7 \, {\left(58 \, a^{5} b^{3} - 100 \, a^{3} b^{5} + 45 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} - 35 \, {\left(10 \, a^{5} b^{3} - 19 \, a^{3} b^{5} + 9 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 105 \, {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{26880 \, {\left(a^{9} d \cos\left(d x + c\right)^{8} - 4 \, a^{9} d \cos\left(d x + c\right)^{6} + 6 \, a^{9} d \cos\left(d x + c\right)^{4} - 4 \, a^{9} d \cos\left(d x + c\right)^{2} + a^{9} d\right)}}, -\frac{210 \, {\left(5 \, a^{8} - 88 \, a^{6} b^{2} + 144 \, a^{4} b^{4} - 64 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{7} + 70 \, {\left(73 \, a^{8} + 584 \, a^{6} b^{2} - 1200 \, a^{4} b^{4} + 576 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{5} - 70 \, {\left(55 \, a^{8} + 440 \, a^{6} b^{2} - 1104 \, a^{4} b^{4} + 576 \, a^{2} b^{6}\right)} \cos\left(d x + c\right)^{3} + 26880 \, {\left({\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{8} + a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} - 4 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 210 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 112 \, a^{4} b^{4} + 64 \, a^{2} b^{6}\right)} \cos\left(d x + c\right) - 105 \, {\left({\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8} - 4 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 105 \, {\left({\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{8} + 5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8} - 4 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(5 \, a^{8} + 40 \, a^{6} b^{2} - 240 \, a^{4} b^{4} + 320 \, a^{2} b^{6} - 128 \, b^{8}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 256 \, {\left({\left(15 \, a^{7} b - 161 \, a^{5} b^{3} + 245 \, a^{3} b^{5} - 105 \, a b^{7}\right)} \cos\left(d x + c\right)^{7} + 7 \, {\left(58 \, a^{5} b^{3} - 100 \, a^{3} b^{5} + 45 \, a b^{7}\right)} \cos\left(d x + c\right)^{5} - 35 \, {\left(10 \, a^{5} b^{3} - 19 \, a^{3} b^{5} + 9 \, a b^{7}\right)} \cos\left(d x + c\right)^{3} + 105 \, {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{26880 \, {\left(a^{9} d \cos\left(d x + c\right)^{8} - 4 \, a^{9} d \cos\left(d x + c\right)^{6} + 6 \, a^{9} d \cos\left(d x + c\right)^{4} - 4 \, a^{9} d \cos\left(d x + c\right)^{2} + a^{9} d\right)}}\right]"," ",0,"[-1/26880*(210*(5*a^8 - 88*a^6*b^2 + 144*a^4*b^4 - 64*a^2*b^6)*cos(d*x + c)^7 + 70*(73*a^8 + 584*a^6*b^2 - 1200*a^4*b^4 + 576*a^2*b^6)*cos(d*x + c)^5 - 70*(55*a^8 + 440*a^6*b^2 - 1104*a^4*b^4 + 576*a^2*b^6)*cos(d*x + c)^3 - 13440*((a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^8 + a^4*b^3 - 2*a^2*b^5 + b^7 - 4*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^6 + 6*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^4 - 4*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 210*(5*a^8 + 40*a^6*b^2 - 112*a^4*b^4 + 64*a^2*b^6)*cos(d*x + c) - 105*((5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^8 + 5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8 - 4*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^6 + 6*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^4 - 4*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 105*((5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^8 + 5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8 - 4*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^6 + 6*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^4 - 4*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 256*((15*a^7*b - 161*a^5*b^3 + 245*a^3*b^5 - 105*a*b^7)*cos(d*x + c)^7 + 7*(58*a^5*b^3 - 100*a^3*b^5 + 45*a*b^7)*cos(d*x + c)^5 - 35*(10*a^5*b^3 - 19*a^3*b^5 + 9*a*b^7)*cos(d*x + c)^3 + 105*(a^5*b^3 - 2*a^3*b^5 + a*b^7)*cos(d*x + c))*sin(d*x + c))/(a^9*d*cos(d*x + c)^8 - 4*a^9*d*cos(d*x + c)^6 + 6*a^9*d*cos(d*x + c)^4 - 4*a^9*d*cos(d*x + c)^2 + a^9*d), -1/26880*(210*(5*a^8 - 88*a^6*b^2 + 144*a^4*b^4 - 64*a^2*b^6)*cos(d*x + c)^7 + 70*(73*a^8 + 584*a^6*b^2 - 1200*a^4*b^4 + 576*a^2*b^6)*cos(d*x + c)^5 - 70*(55*a^8 + 440*a^6*b^2 - 1104*a^4*b^4 + 576*a^2*b^6)*cos(d*x + c)^3 + 26880*((a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^8 + a^4*b^3 - 2*a^2*b^5 + b^7 - 4*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^6 + 6*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^4 - 4*(a^4*b^3 - 2*a^2*b^5 + b^7)*cos(d*x + c)^2)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 210*(5*a^8 + 40*a^6*b^2 - 112*a^4*b^4 + 64*a^2*b^6)*cos(d*x + c) - 105*((5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^8 + 5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8 - 4*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^6 + 6*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^4 - 4*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^2)*log(1/2*cos(d*x + c) + 1/2) + 105*((5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^8 + 5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8 - 4*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^6 + 6*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^4 - 4*(5*a^8 + 40*a^6*b^2 - 240*a^4*b^4 + 320*a^2*b^6 - 128*b^8)*cos(d*x + c)^2)*log(-1/2*cos(d*x + c) + 1/2) - 256*((15*a^7*b - 161*a^5*b^3 + 245*a^3*b^5 - 105*a*b^7)*cos(d*x + c)^7 + 7*(58*a^5*b^3 - 100*a^3*b^5 + 45*a*b^7)*cos(d*x + c)^5 - 35*(10*a^5*b^3 - 19*a^3*b^5 + 9*a*b^7)*cos(d*x + c)^3 + 105*(a^5*b^3 - 2*a^3*b^5 + a*b^7)*cos(d*x + c))*sin(d*x + c))/(a^9*d*cos(d*x + c)^8 - 4*a^9*d*cos(d*x + c)^6 + 6*a^9*d*cos(d*x + c)^4 - 4*a^9*d*cos(d*x + c)^2 + a^9*d)]","B",0
1332,1,100,0,0.837937," ","integrate(sec(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a^{3} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(a b^{2} + b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a b^{2} - b^{3}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} - b^{4}\right)} d}"," ",0,"1/2*(2*a^3*log(b*sin(d*x + c) + a) - (a*b^2 + b^3)*log(sin(d*x + c) + 1) - (a*b^2 - b^3)*log(-sin(d*x + c) + 1) - 2*(a^2*b - b^3)*sin(d*x + c))/((a^2*b^2 - b^4)*d)","A",0
1333,1,74,0,1.282624," ","integrate(sec(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{2} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(a b + b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a b - b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{2} b - b^{3}\right)} d}"," ",0,"-1/2*(2*a^2*log(b*sin(d*x + c) + a) - (a*b + b^2)*log(sin(d*x + c) + 1) + (a*b - b^2)*log(-sin(d*x + c) + 1))/((a^2*b - b^3)*d)","A",0
1334,1,63,0,0.980118," ","integrate(sec(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, a \log\left(b \sin\left(d x + c\right) + a\right) - {\left(a + b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a - b\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}"," ",0,"1/2*(2*a*log(b*sin(d*x + c) + a) - (a + b)*log(sin(d*x + c) + 1) - (a - b)*log(-sin(d*x + c) + 1))/((a^2 - b^2)*d)","A",0
1335,1,93,0,1.214123," ","integrate(csc(d*x+c)*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, b^{2} \log\left(b \sin\left(d x + c\right) + a\right) + 2 \, {\left(a^{2} - b^{2}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(a^{2} + a b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} - a b\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{3} - a b^{2}\right)} d}"," ",0,"1/2*(2*b^2*log(b*sin(d*x + c) + a) + 2*(a^2 - b^2)*log(-1/2*sin(d*x + c)) - (a^2 + a*b)*log(sin(d*x + c) + 1) - (a^2 - a*b)*log(-sin(d*x + c) + 1))/((a^3 - a*b^2)*d)","A",0
1336,1,143,0,1.696711," ","integrate(csc(d*x+c)^2*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b^{3} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) + 2 \, a^{3} - 2 \, a b^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(a^{3} + a^{2} b\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(a^{3} - a^{2} b\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right)}{2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \sin\left(d x + c\right)}"," ",0,"-1/2*(2*b^3*log(b*sin(d*x + c) + a)*sin(d*x + c) + 2*a^3 - 2*a*b^2 + 2*(a^2*b - b^3)*log(1/2*sin(d*x + c))*sin(d*x + c) - (a^3 + a^2*b)*log(sin(d*x + c) + 1)*sin(d*x + c) + (a^3 - a^2*b)*log(-sin(d*x + c) + 1)*sin(d*x + c))/((a^4 - a^2*b^2)*d*sin(d*x + c))","A",0
1337,1,224,0,1.830103," ","integrate(csc(d*x+c)^3*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{a^{4} - a^{2} b^{2} + 2 \, {\left(b^{4} \cos\left(d x + c\right)^{2} - b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, {\left(a^{4} - b^{4} - {\left(a^{4} - b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) + {\left(a^{4} + a^{3} b - {\left(a^{4} + a^{3} b\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{4} - a^{3} b - {\left(a^{4} - a^{3} b\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{5} - a^{3} b^{2}\right)} d \cos\left(d x + c\right)^{2} - {\left(a^{5} - a^{3} b^{2}\right)} d\right)}}"," ",0,"1/2*(a^4 - a^2*b^2 + 2*(b^4*cos(d*x + c)^2 - b^4)*log(b*sin(d*x + c) + a) - 2*(a^4 - b^4 - (a^4 - b^4)*cos(d*x + c)^2)*log(-1/2*sin(d*x + c)) + (a^4 + a^3*b - (a^4 + a^3*b)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + (a^4 - a^3*b - (a^4 - a^3*b)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^3*b - a*b^3)*sin(d*x + c))/((a^5 - a^3*b^2)*d*cos(d*x + c)^2 - (a^5 - a^3*b^2)*d)","A",0
1338,1,521,0,1.326264," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} a^{5} \cos\left(d x + c\right) \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, a^{3} b^{3} - 2 \, a b^{5} - {\left(2 \, a^{6} - a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} d x \cos\left(d x + c\right) - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(2 \, a^{2} b^{4} - 2 \, b^{6} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)}, -\frac{2 \, \sqrt{a^{2} - b^{2}} a^{5} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) - 2 \, a^{3} b^{3} + 2 \, a b^{5} + {\left(2 \, a^{6} - a^{4} b^{2} - 4 \, a^{2} b^{4} + 3 \, b^{6}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{4} - 2 \, b^{6} - {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*a^5*cos(d*x + c)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*a^3*b^3 - 2*a*b^5 - (2*a^6 - a^4*b^2 - 4*a^2*b^4 + 3*b^6)*d*x*cos(d*x + c) - 2*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c)^2 - (2*a^2*b^4 - 2*b^6 - (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d*cos(d*x + c)), -1/2*(2*sqrt(a^2 - b^2)*a^5*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c) - 2*a^3*b^3 + 2*a*b^5 + (2*a^6 - a^4*b^2 - 4*a^2*b^4 + 3*b^6)*d*x*cos(d*x + c) + 2*(a^5*b - 2*a^3*b^3 + a*b^5)*cos(d*x + c)^2 + (2*a^2*b^4 - 2*b^6 - (a^4*b^2 - 2*a^2*b^4 + b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^4*b^3 - 2*a^2*b^5 + b^7)*d*cos(d*x + c))]","A",0
1339,1,431,0,1.046383," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} a^{4} \cos\left(d x + c\right) \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, a^{2} b^{3} + 2 \, b^{5} + 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)}, \frac{\sqrt{a^{2} - b^{2}} a^{4} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) - a^{2} b^{3} + b^{5} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d x \cos\left(d x + c\right) + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*a^4*cos(d*x + c)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*a^2*b^3 + 2*b^5 + 2*(a^5 - 2*a^3*b^2 + a*b^4)*d*x*cos(d*x + c) + 2*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^2 + 2*(a^3*b^2 - a*b^4)*sin(d*x + c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d*cos(d*x + c)), (sqrt(a^2 - b^2)*a^4*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c) - a^2*b^3 + b^5 + (a^5 - 2*a^3*b^2 + a*b^4)*d*x*cos(d*x + c) + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^2 + (a^3*b^2 - a*b^4)*sin(d*x + c))/((a^4*b^2 - 2*a^2*b^4 + b^6)*d*cos(d*x + c))]","A",0
1340,1,369,0,1.000746," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} a^{3} \cos\left(d x + c\right) \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, a^{3} b - 2 \, a b^{3} - 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d x \cos\left(d x + c\right) - 2 \, {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)}, -\frac{\sqrt{a^{2} - b^{2}} a^{3} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) - a^{3} b + a b^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d x \cos\left(d x + c\right) + {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*a^3*cos(d*x + c)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*a^3*b - 2*a*b^3 - 2*(a^4 - 2*a^2*b^2 + b^4)*d*x*cos(d*x + c) - 2*(a^2*b^2 - b^4)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c)), -(sqrt(a^2 - b^2)*a^3*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c) - a^3*b + a*b^3 + (a^4 - 2*a^2*b^2 + b^4)*d*x*cos(d*x + c) + (a^2*b^2 - b^4)*sin(d*x + c))/((a^4*b - 2*a^2*b^3 + b^5)*d*cos(d*x + c))]","A",0
1341,1,305,0,1.216455," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} a^{2} \cos\left(d x + c\right) \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, a^{2} b + 2 \, b^{3} + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}, \frac{\sqrt{a^{2} - b^{2}} a^{2} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) - a^{2} b + b^{3} + {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*a^2*cos(d*x + c)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*a^2*b + 2*b^3 + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)), (sqrt(a^2 - b^2)*a^2*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c) - a^2*b + b^3 + (a^3 - a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c))]","A",0
1342,1,308,0,0.949633," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} a b \cos\left(d x + c\right) \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, a^{3} - 2 \, a b^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}, -\frac{\sqrt{a^{2} - b^{2}} a b \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) - a^{3} + a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*a*b*cos(d*x + c)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*a^3 - 2*a*b^2 - 2*(a^2*b - b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)), -(sqrt(a^2 - b^2)*a*b*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c) - a^3 + a*b^2 + (a^2*b - b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c))]","A",0
1343,1,457,0,1.501420," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} b^{3} \cos\left(d x + c\right) \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, a^{4} - 2 \, a^{2} b^{2} - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)}, -\frac{2 \, \sqrt{a^{2} - b^{2}} b^{3} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) - 2 \, a^{4} + 2 \, a^{2} b^{2} + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*b^3*cos(d*x + c)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*a^4 - 2*a^2*b^2 - (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2) + (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^3*b - a*b^3)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c)), -1/2*(2*sqrt(a^2 - b^2)*b^3*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c) - 2*a^4 + 2*a^2*b^2 + (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2) - (a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2) + 2*(a^3*b - a*b^3)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c))]","A",0
1344,1,582,0,1.505883," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a^{2} + b^{2}} b^{4} \cos\left(d x + c\right) \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) + 2 \, a^{5} - 2 \, a^{3} b^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right)}, \frac{2 \, \sqrt{a^{2} - b^{2}} b^{4} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, a^{5} - 2 \, a^{3} b^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)}{2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right)}\right]"," ",0,"[1/2*(sqrt(-a^2 + b^2)*b^4*cos(d*x + c)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) + 2*a^5 - 2*a^3*b^2 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*(2*a^5 - 3*a^3*b^2 + a*b^4)*cos(d*x + c)^2 - 2*(a^4*b - a^2*b^3)*sin(d*x + c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*d*cos(d*x + c)*sin(d*x + c)), 1/2*(2*sqrt(a^2 - b^2)*b^4*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)*sin(d*x + c) + 2*a^5 - 2*a^3*b^2 + (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - (a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*(2*a^5 - 3*a^3*b^2 + a*b^4)*cos(d*x + c)^2 - 2*(a^4*b - a^2*b^3)*sin(d*x + c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*d*cos(d*x + c)*sin(d*x + c))]","B",0
1345,1,878,0,2.366227," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{4 \, a^{6} - 4 \, a^{4} b^{2} - 2 \, {\left(3 \, a^{6} - 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(b^{5} \cos\left(d x + c\right)^{3} - b^{5} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + {\left({\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left({\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, {\left(a^{5} b - a^{3} b^{3} - {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{4 \, a^{6} - 4 \, a^{4} b^{2} - 2 \, {\left(3 \, a^{6} - 4 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(b^{5} \cos\left(d x + c\right)^{3} - b^{5} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left({\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left({\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{6} - 4 \, a^{4} b^{2} - a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, {\left(a^{5} b - a^{3} b^{3} - {\left(2 \, a^{5} b - 3 \, a^{3} b^{3} + a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^6 - 4*a^4*b^2 - 2*(3*a^6 - 4*a^4*b^2 + a^2*b^4)*cos(d*x + c)^2 - 2*(b^5*cos(d*x + c)^3 - b^5*cos(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + ((3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c)^3 - (3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - ((3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c)^3 - (3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 4*(a^5*b - a^3*b^3 - (2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c)^3 - (a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c)), -1/4*(4*a^6 - 4*a^4*b^2 - 2*(3*a^6 - 4*a^4*b^2 + a^2*b^4)*cos(d*x + c)^2 + 4*(b^5*cos(d*x + c)^3 - b^5*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + ((3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c)^3 - (3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - ((3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c)^3 - (3*a^6 - 4*a^4*b^2 - a^2*b^4 + 2*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 4*(a^5*b - a^3*b^3 - (2*a^5*b - 3*a^3*b^3 + a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c)^3 - (a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c))]","B",0
1346,1,157,0,0.925411," ","integrate(sec(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a^{3} \cos\left(d x + c\right)^{2} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(2 \, a^{3} - 3 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, a^{3} + 2 \, a b^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/4*(4*a^3*cos(d*x + c)^2*log(b*sin(d*x + c) + a) - (2*a^3 + 3*a^2*b - b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (2*a^3 - 3*a^2*b + b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*a^3 + 2*a*b^2 + 2*(a^2*b - b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2)","A",0
1347,1,154,0,1.356416," ","integrate(sec(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, a^{2} b \cos\left(d x + c\right)^{2} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, a^{2} b + 2 \, b^{3} + 2 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(4*a^2*b*cos(d*x + c)^2*log(b*sin(d*x + c) + a) - (a^3 + 2*a^2*b + a*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (a^3 - 2*a^2*b + a*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*a^2*b + 2*b^3 + 2*(a^3 - a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2)","A",0
1348,1,155,0,1.406179," ","integrate(sec(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a b^{2} \cos\left(d x + c\right)^{2} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, a^{3} + 2 \, a b^{2} + 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/4*(4*a*b^2*cos(d*x + c)^2*log(b*sin(d*x + c) + a) - (a^2*b + 2*a*b^2 + b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (a^2*b - 2*a*b^2 + b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) - 2*a^3 + 2*a*b^2 + 2*(a^2*b - b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2)","A",0
1349,1,213,0,2.808881," ","integrate(csc(d*x+c)*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, b^{4} \cos\left(d x + c\right)^{2} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, a^{4} + 2 \, a^{2} b^{2} - 4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) + {\left(2 \, a^{4} + a^{3} b - 4 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(2 \, a^{4} - a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"-1/4*(4*b^4*cos(d*x + c)^2*log(b*sin(d*x + c) + a) - 2*a^4 + 2*a^2*b^2 - 4*(a^4 - 2*a^2*b^2 + b^4)*cos(d*x + c)^2*log(-1/2*sin(d*x + c)) + (2*a^4 + a^3*b - 4*a^2*b^2 - 3*a*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) + (2*a^4 - a^3*b - 4*a^2*b^2 + 3*a*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(a^3*b - a*b^3)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*d*cos(d*x + c)^2)","A",0
1350,1,287,0,3.546184," ","integrate(csc(d*x+c)^2*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, b^{5} \cos\left(d x + c\right)^{2} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) + 2 \, a^{5} - 2 \, a^{3} b^{2} - 4 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(3 \, a^{5} + 2 \, a^{4} b - 5 \, a^{3} b^{2} - 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 2 \, {\left(3 \, a^{5} - 5 \, a^{3} b^{2} + 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)}"," ",0,"1/4*(4*b^5*cos(d*x + c)^2*log(b*sin(d*x + c) + a)*sin(d*x + c) + 2*a^5 - 2*a^3*b^2 - 4*(a^4*b - 2*a^2*b^3 + b^5)*cos(d*x + c)^2*log(1/2*sin(d*x + c))*sin(d*x + c) + (3*a^5 + 2*a^4*b - 5*a^3*b^2 - 4*a^2*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1)*sin(d*x + c) - (3*a^5 - 2*a^4*b - 5*a^3*b^2 + 4*a^2*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1)*sin(d*x + c) - 2*(3*a^5 - 5*a^3*b^2 + 2*a*b^4)*cos(d*x + c)^2 - 2*(a^4*b - a^2*b^3)*sin(d*x + c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*d*cos(d*x + c)^2*sin(d*x + c))","A",0
1351,1,440,0,5.458598," ","integrate(csc(d*x+c)^3*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, a^{6} - 2 \, a^{4} b^{2} - 2 \, {\left(2 \, a^{6} - 3 \, a^{4} b^{2} + a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(b^{6} \cos\left(d x + c\right)^{4} - b^{6} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 4 \, {\left({\left(2 \, a^{6} - 3 \, a^{4} b^{2} + b^{6}\right)} \cos\left(d x + c\right)^{4} - {\left(2 \, a^{6} - 3 \, a^{4} b^{2} + b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) + {\left({\left(4 \, a^{6} + 3 \, a^{5} b - 6 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{6} + 3 \, a^{5} b - 6 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(4 \, a^{6} - 3 \, a^{5} b - 6 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{6} - 3 \, a^{5} b - 6 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(a^{5} b - a^{3} b^{3} - {\left(3 \, a^{5} b - 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{4} - {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"-1/4*(2*a^6 - 2*a^4*b^2 - 2*(2*a^6 - 3*a^4*b^2 + a^2*b^4)*cos(d*x + c)^2 + 4*(b^6*cos(d*x + c)^4 - b^6*cos(d*x + c)^2)*log(b*sin(d*x + c) + a) - 4*((2*a^6 - 3*a^4*b^2 + b^6)*cos(d*x + c)^4 - (2*a^6 - 3*a^4*b^2 + b^6)*cos(d*x + c)^2)*log(-1/2*sin(d*x + c)) + ((4*a^6 + 3*a^5*b - 6*a^4*b^2 - 5*a^3*b^3)*cos(d*x + c)^4 - (4*a^6 + 3*a^5*b - 6*a^4*b^2 - 5*a^3*b^3)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) + ((4*a^6 - 3*a^5*b - 6*a^4*b^2 + 5*a^3*b^3)*cos(d*x + c)^4 - (4*a^6 - 3*a^5*b - 6*a^4*b^2 + 5*a^3*b^3)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) - 2*(a^5*b - a^3*b^3 - (3*a^5*b - 5*a^3*b^3 + 2*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c)^4 - (a^7 - 2*a^5*b^2 + a^3*b^4)*d*cos(d*x + c)^2)","B",0
1352,1,476,0,1.453030," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} + b^{2}} a^{4} \cos\left(d x + c\right)^{3} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} - 6 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(4 \, a^{5} - 5 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}, -\frac{3 \, \sqrt{a^{2} - b^{2}} a^{4} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} + a^{4} b - 2 \, a^{2} b^{3} + b^{5} - 3 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(4 \, a^{5} - 5 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/6*(3*sqrt(-a^2 + b^2)*a^4*cos(d*x + c)^3*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*a^4*b - 4*a^2*b^3 + 2*b^5 - 6*(2*a^4*b - 3*a^2*b^3 + b^5)*cos(d*x + c)^2 - 2*(a^5 - 2*a^3*b^2 + a*b^4 - (4*a^5 - 5*a^3*b^2 + a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3), -1/3*(3*sqrt(a^2 - b^2)*a^4*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)^3 + a^4*b - 2*a^2*b^3 + b^5 - 3*(2*a^4*b - 3*a^2*b^3 + b^5)*cos(d*x + c)^2 - (a^5 - 2*a^3*b^2 + a*b^4 - (4*a^5 - 5*a^3*b^2 + a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","A",0
1353,1,465,0,1.284826," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} + b^{2}} a^{3} b \cos\left(d x + c\right)^{3} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, a^{5} + 4 \, a^{3} b^{2} - 2 \, a b^{4} + 6 \, {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}, \frac{3 \, \sqrt{a^{2} - b^{2}} a^{3} b \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} + a^{5} - 2 \, a^{3} b^{2} + a b^{4} - 3 \, {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} - {\left(4 \, a^{4} b - 5 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/6*(3*sqrt(-a^2 + b^2)*a^3*b*cos(d*x + c)^3*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*a^5 + 4*a^3*b^2 - 2*a*b^4 + 6*(a^5 - a^3*b^2)*cos(d*x + c)^2 + 2*(a^4*b - 2*a^2*b^3 + b^5 - (4*a^4*b - 5*a^2*b^3 + b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3), 1/3*(3*sqrt(a^2 - b^2)*a^3*b*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)^3 + a^5 - 2*a^3*b^2 + a*b^4 - 3*(a^5 - a^3*b^2)*cos(d*x + c)^2 - (a^4*b - 2*a^2*b^3 + b^5 - (4*a^4*b - 5*a^2*b^3 + b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","A",0
1354,1,470,0,1.474392," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} + b^{2}} a^{2} b^{2} \cos\left(d x + c\right)^{3} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} - 6 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}, -\frac{3 \, \sqrt{a^{2} - b^{2}} a^{2} b^{2} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} + a^{4} b - 2 \, a^{2} b^{3} + b^{5} - 3 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/6*(3*sqrt(-a^2 + b^2)*a^2*b^2*cos(d*x + c)^3*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*a^4*b - 4*a^2*b^3 + 2*b^5 - 6*(a^4*b - a^2*b^3)*cos(d*x + c)^2 - 2*(a^5 - 2*a^3*b^2 + a*b^4 - (a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3), -1/3*(3*sqrt(a^2 - b^2)*a^2*b^2*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)^3 + a^4*b - 2*a^2*b^3 + b^5 - 3*(a^4*b - a^2*b^3)*cos(d*x + c)^2 - (a^5 - 2*a^3*b^2 + a*b^4 - (a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","A",0
1355,1,469,0,1.334532," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} + b^{2}} a b^{3} \cos\left(d x + c\right)^{3} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, a^{5} + 4 \, a^{3} b^{2} - 2 \, a b^{4} + 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} - {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}, \frac{3 \, \sqrt{a^{2} - b^{2}} a b^{3} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} + a^{5} - 2 \, a^{3} b^{2} + a b^{4} - 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5} - {\left(a^{4} b + a^{2} b^{3} - 2 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/6*(3*sqrt(-a^2 + b^2)*a*b^3*cos(d*x + c)^3*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*a^5 + 4*a^3*b^2 - 2*a*b^4 + 6*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 + 2*(a^4*b - 2*a^2*b^3 + b^5 - (a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3), 1/3*(3*sqrt(a^2 - b^2)*a*b^3*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)^3 + a^5 - 2*a^3*b^2 + a*b^4 - 3*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 - (a^4*b - 2*a^2*b^3 + b^5 - (a^4*b + a^2*b^3 - 2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^3)]","A",0
1356,1,680,0,3.066314," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} + b^{2}} b^{5} \cos\left(d x + c\right)^{3} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, a^{6} + 4 \, a^{4} b^{2} - 2 \, a^{2} b^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5} + {\left(2 \, a^{5} b - 7 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{3}}, \frac{6 \, \sqrt{a^{2} - b^{2}} b^{5} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} + 2 \, a^{6} - 4 \, a^{4} b^{2} + 2 \, a^{2} b^{4} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 6 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5} + {\left(2 \, a^{5} b - 7 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{3}}\right]"," ",0,"[-1/6*(3*sqrt(-a^2 + b^2)*b^5*cos(d*x + c)^3*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*a^6 + 4*a^4*b^2 - 2*a^2*b^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(d*x + c)^3*log(1/2*cos(d*x + c) + 1/2) - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(d*x + c)^3*log(-1/2*cos(d*x + c) + 1/2) - 6*(a^6 - 3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c)^2 + 2*(a^5*b - 2*a^3*b^3 + a*b^5 + (2*a^5*b - 7*a^3*b^3 + 5*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)^3), 1/6*(6*sqrt(a^2 - b^2)*b^5*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)^3 + 2*a^6 - 4*a^4*b^2 + 2*a^2*b^4 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(d*x + c)^3*log(1/2*cos(d*x + c) + 1/2) + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(d*x + c)^3*log(-1/2*cos(d*x + c) + 1/2) + 6*(a^6 - 3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c)^2 - 2*(a^5*b - 2*a^3*b^3 + a*b^5 + (2*a^5*b - 7*a^3*b^3 + 5*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)^3)]","A",0
1357,1,831,0,3.628394," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{3 \, \sqrt{-a^{2} + b^{2}} b^{6} \cos\left(d x + c\right)^{3} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) \sin\left(d x + c\right) - 2 \, a^{7} + 4 \, a^{5} b^{2} - 2 \, a^{3} b^{4} - 3 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(8 \, a^{7} - 22 \, a^{5} b^{2} + 17 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{7} - 11 \, a^{5} b^{2} + 7 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5} + 3 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)}, -\frac{6 \, \sqrt{a^{2} - b^{2}} b^{6} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 2 \, a^{7} + 4 \, a^{5} b^{2} - 2 \, a^{3} b^{4} - 3 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 2 \, {\left(8 \, a^{7} - 22 \, a^{5} b^{2} + 17 \, a^{3} b^{4} - 3 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{7} - 11 \, a^{5} b^{2} + 7 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5} + 3 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{6 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d \cos\left(d x + c\right)^{3} \sin\left(d x + c\right)}\right]"," ",0,"[-1/6*(3*sqrt(-a^2 + b^2)*b^6*cos(d*x + c)^3*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2))*sin(d*x + c) - 2*a^7 + 4*a^5*b^2 - 2*a^3*b^4 - 3*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*(8*a^7 - 22*a^5*b^2 + 17*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^4 - 2*(4*a^7 - 11*a^5*b^2 + 7*a^3*b^4)*cos(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5 + 3*(a^6*b - 3*a^4*b^3 + 2*a^2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*cos(d*x + c)^3*sin(d*x + c)), -1/6*(6*sqrt(a^2 - b^2)*b^6*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c)))*cos(d*x + c)^3*sin(d*x + c) - 2*a^7 + 4*a^5*b^2 - 2*a^3*b^4 - 3*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 2*(8*a^7 - 22*a^5*b^2 + 17*a^3*b^4 - 3*a*b^6)*cos(d*x + c)^4 - 2*(4*a^7 - 11*a^5*b^2 + 7*a^3*b^4)*cos(d*x + c)^2 + 2*(a^6*b - 2*a^4*b^3 + a^2*b^5 + 3*(a^6*b - 3*a^4*b^3 + 2*a^2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*cos(d*x + c)^3*sin(d*x + c))]","A",0
1358,1,1182,0,5.717030," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\left[-\frac{4 \, a^{8} - 8 \, a^{6} b^{2} + 4 \, a^{4} b^{4} - 6 \, {\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 8 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(b^{7} \cos\left(d x + c\right)^{5} - b^{7} \cos\left(d x + c\right)^{3}\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 3 \, {\left({\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + a^{2} b^{6} - 2 \, b^{8}\right)} \cos\left(d x + c\right)^{5} - {\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + a^{2} b^{6} - 2 \, b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + a^{2} b^{6} - 2 \, b^{8}\right)} \cos\left(d x + c\right)^{5} - {\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + a^{2} b^{6} - 2 \, b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5} - {\left(8 \, a^{7} b - 22 \, a^{5} b^{3} + 17 \, a^{3} b^{5} - 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{7} b - 11 \, a^{5} b^{3} + 7 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{5} - {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{3}\right)}}, -\frac{4 \, a^{8} - 8 \, a^{6} b^{2} + 4 \, a^{4} b^{4} - 6 \, {\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 8 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{2} - 12 \, {\left(b^{7} \cos\left(d x + c\right)^{5} - b^{7} \cos\left(d x + c\right)^{3}\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 3 \, {\left({\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + a^{2} b^{6} - 2 \, b^{8}\right)} \cos\left(d x + c\right)^{5} - {\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + a^{2} b^{6} - 2 \, b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + a^{2} b^{6} - 2 \, b^{8}\right)} \cos\left(d x + c\right)^{5} - {\left(5 \, a^{8} - 13 \, a^{6} b^{2} + 9 \, a^{4} b^{4} + a^{2} b^{6} - 2 \, b^{8}\right)} \cos\left(d x + c\right)^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5} - {\left(8 \, a^{7} b - 22 \, a^{5} b^{3} + 17 \, a^{3} b^{5} - 3 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(4 \, a^{7} b - 11 \, a^{5} b^{3} + 7 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{5} - {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[-1/12*(4*a^8 - 8*a^6*b^2 + 4*a^4*b^4 - 6*(5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 - a^2*b^6)*cos(d*x + c)^4 + 4*(5*a^8 - 13*a^6*b^2 + 8*a^4*b^4)*cos(d*x + c)^2 + 6*(b^7*cos(d*x + c)^5 - b^7*cos(d*x + c)^3)*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 3*((5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 + a^2*b^6 - 2*b^8)*cos(d*x + c)^5 - (5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 + a^2*b^6 - 2*b^8)*cos(d*x + c)^3)*log(1/2*cos(d*x + c) + 1/2) - 3*((5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 + a^2*b^6 - 2*b^8)*cos(d*x + c)^5 - (5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 + a^2*b^6 - 2*b^8)*cos(d*x + c)^3)*log(-1/2*cos(d*x + c) + 1/2) - 4*(a^7*b - 2*a^5*b^3 + a^3*b^5 - (8*a^7*b - 22*a^5*b^3 + 17*a^3*b^5 - 3*a*b^7)*cos(d*x + c)^4 + (4*a^7*b - 11*a^5*b^3 + 7*a^3*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c)^5 - (a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c)^3), -1/12*(4*a^8 - 8*a^6*b^2 + 4*a^4*b^4 - 6*(5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 - a^2*b^6)*cos(d*x + c)^4 + 4*(5*a^8 - 13*a^6*b^2 + 8*a^4*b^4)*cos(d*x + c)^2 - 12*(b^7*cos(d*x + c)^5 - b^7*cos(d*x + c)^3)*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 3*((5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 + a^2*b^6 - 2*b^8)*cos(d*x + c)^5 - (5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 + a^2*b^6 - 2*b^8)*cos(d*x + c)^3)*log(1/2*cos(d*x + c) + 1/2) - 3*((5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 + a^2*b^6 - 2*b^8)*cos(d*x + c)^5 - (5*a^8 - 13*a^6*b^2 + 9*a^4*b^4 + a^2*b^6 - 2*b^8)*cos(d*x + c)^3)*log(-1/2*cos(d*x + c) + 1/2) - 4*(a^7*b - 2*a^5*b^3 + a^3*b^5 - (8*a^7*b - 22*a^5*b^3 + 17*a^3*b^5 - 3*a*b^7)*cos(d*x + c)^4 + (4*a^7*b - 11*a^5*b^3 + 7*a^3*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c)^5 - (a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c)^3)]","A",0
1359,1,429,0,2.117138," ","integrate(sec(d*x+c)^5*sin(d*x+c)^8/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a^{8} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) + 4 \, a^{4} b^{4} - 8 \, a^{2} b^{6} + 4 \, b^{8} - 8 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{6} - {\left(35 \, a^{5} b^{3} + 48 \, a^{4} b^{4} - 42 \, a^{3} b^{5} - 64 \, a^{2} b^{6} + 15 \, a b^{7} + 24 \, b^{8}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(35 \, a^{5} b^{3} - 48 \, a^{4} b^{4} - 42 \, a^{3} b^{5} + 64 \, a^{2} b^{6} + 15 \, a b^{7} - 24 \, b^{8}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(4 \, a^{4} b^{4} - 7 \, a^{2} b^{6} + 3 \, b^{8}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{5} b^{3} - 4 \, a^{3} b^{5} + 2 \, a b^{7} + 8 \, {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(13 \, a^{5} b^{3} - 22 \, a^{3} b^{5} + 9 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*(16*a^8*cos(d*x + c)^4*log(b*sin(d*x + c) + a) + 4*a^4*b^4 - 8*a^2*b^6 + 4*b^8 - 8*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^6 - (35*a^5*b^3 + 48*a^4*b^4 - 42*a^3*b^5 - 64*a^2*b^6 + 15*a*b^7 + 24*b^8)*cos(d*x + c)^4*log(sin(d*x + c) + 1) + (35*a^5*b^3 - 48*a^4*b^4 - 42*a^3*b^5 + 64*a^2*b^6 + 15*a*b^7 - 24*b^8)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^4 - 8*(4*a^4*b^4 - 7*a^2*b^6 + 3*b^8)*cos(d*x + c)^2 - 2*(2*a^5*b^3 - 4*a^3*b^5 + 2*a*b^7 + 8*(a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c)^4 - (13*a^5*b^3 - 22*a^3*b^5 + 9*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d*cos(d*x + c)^4)","A",0
1360,1,351,0,2.253207," ","integrate(sec(d*x+c)^5*sin(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, a^{7} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) + 4 \, a^{5} b^{2} - 8 \, a^{3} b^{4} + 4 \, a b^{6} - {\left(24 \, a^{5} b^{2} + 35 \, a^{4} b^{3} - 24 \, a^{3} b^{4} - 42 \, a^{2} b^{5} + 8 \, a b^{6} + 15 \, b^{7}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(24 \, a^{5} b^{2} - 35 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 42 \, a^{2} b^{5} + 8 \, a b^{6} - 15 \, b^{7}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 8 \, {\left(3 \, a^{5} b^{2} - 5 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{4} b^{3} - 4 \, a^{2} b^{5} + 2 \, b^{7} + 8 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} - {\left(13 \, a^{4} b^{3} - 22 \, a^{2} b^{5} + 9 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*a^7*cos(d*x + c)^4*log(b*sin(d*x + c) + a) + 4*a^5*b^2 - 8*a^3*b^4 + 4*a*b^6 - (24*a^5*b^2 + 35*a^4*b^3 - 24*a^3*b^4 - 42*a^2*b^5 + 8*a*b^6 + 15*b^7)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (24*a^5*b^2 - 35*a^4*b^3 - 24*a^3*b^4 + 42*a^2*b^5 + 8*a*b^6 - 15*b^7)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 8*(3*a^5*b^2 - 5*a^3*b^4 + 2*a*b^6)*cos(d*x + c)^2 - 2*(2*a^4*b^3 - 4*a^2*b^5 + 2*b^7 + 8*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)^4 - (13*a^4*b^3 - 22*a^2*b^5 + 9*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*d*cos(d*x + c)^4)","A",0
1361,1,303,0,2.563978," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a^{6} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) + 4 \, a^{4} b^{2} - 8 \, a^{2} b^{4} + 4 \, b^{6} - {\left(15 \, a^{5} b + 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} - 24 \, a^{2} b^{4} + 3 \, a b^{5} + 8 \, b^{6}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(15 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 3 \, a b^{5} - 8 \, b^{6}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 8 \, {\left(3 \, a^{4} b^{2} - 5 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{5} b - 4 \, a^{3} b^{3} + 2 \, a b^{5} - {\left(9 \, a^{5} b - 14 \, a^{3} b^{3} + 5 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*(16*a^6*cos(d*x + c)^4*log(b*sin(d*x + c) + a) + 4*a^4*b^2 - 8*a^2*b^4 + 4*b^6 - (15*a^5*b + 24*a^4*b^2 - 10*a^3*b^3 - 24*a^2*b^4 + 3*a*b^5 + 8*b^6)*cos(d*x + c)^4*log(sin(d*x + c) + 1) + (15*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 3*a*b^5 - 8*b^6)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 8*(3*a^4*b^2 - 5*a^2*b^4 + 2*b^6)*cos(d*x + c)^2 - 2*(2*a^5*b - 4*a^3*b^3 + 2*a*b^5 - (9*a^5*b - 14*a^3*b^3 + 5*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)^4)","A",0
1362,1,261,0,2.132897," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, a^{5} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(8 \, a^{5} + 15 \, a^{4} b - 10 \, a^{2} b^{3} + 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(8 \, a^{5} - 15 \, a^{4} b + 10 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a^{5} - 8 \, a^{3} b^{2} + 4 \, a b^{4} - 8 \, {\left(2 \, a^{5} - 3 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} - {\left(9 \, a^{4} b - 14 \, a^{2} b^{3} + 5 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*a^5*cos(d*x + c)^4*log(b*sin(d*x + c) + a) - (8*a^5 + 15*a^4*b - 10*a^2*b^3 + 3*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (8*a^5 - 15*a^4*b + 10*a^2*b^3 - 3*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*a^5 - 8*a^3*b^2 + 4*a*b^4 - 8*(2*a^5 - 3*a^3*b^2 + a*b^4)*cos(d*x + c)^2 - 2*(2*a^4*b - 4*a^2*b^3 + 2*b^5 - (9*a^4*b - 14*a^2*b^3 + 5*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^4)","A",0
1363,1,261,0,1.850089," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a^{4} b \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(3 \, a^{5} + 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(3 \, a^{5} - 8 \, a^{4} b + 6 \, a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a^{4} b - 8 \, a^{2} b^{3} + 4 \, b^{5} - 8 \, {\left(2 \, a^{4} b - 3 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{5} - 4 \, a^{3} b^{2} + 2 \, a b^{4} - {\left(5 \, a^{5} - 6 \, a^{3} b^{2} + a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*(16*a^4*b*cos(d*x + c)^4*log(b*sin(d*x + c) + a) - (3*a^5 + 8*a^4*b + 6*a^3*b^2 - a*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) + (3*a^5 - 8*a^4*b + 6*a^3*b^2 - a*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*a^4*b - 8*a^2*b^3 + 4*b^5 - 8*(2*a^4*b - 3*a^2*b^3 + b^5)*cos(d*x + c)^2 - 2*(2*a^5 - 4*a^3*b^2 + 2*a*b^4 - (5*a^5 - 6*a^3*b^2 + a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^4)","A",0
1364,1,260,0,1.508133," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, a^{3} b^{2} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(3 \, a^{4} b + 8 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(3 \, a^{4} b - 8 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a^{5} - 8 \, a^{3} b^{2} + 4 \, a b^{4} - 8 \, {\left(a^{5} - a^{3} b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} - {\left(5 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*a^3*b^2*cos(d*x + c)^4*log(b*sin(d*x + c) + a) - (3*a^4*b + 8*a^3*b^2 + 6*a^2*b^3 - b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) + (3*a^4*b - 8*a^3*b^2 + 6*a^2*b^3 - b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*a^5 - 8*a^3*b^2 + 4*a*b^4 - 8*(a^5 - a^3*b^2)*cos(d*x + c)^2 - 2*(2*a^4*b - 4*a^2*b^3 + 2*b^5 - (5*a^4*b - 6*a^2*b^3 + b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^4)","A",0
1365,1,258,0,1.516634," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, a^{2} b^{3} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(a^{5} - 6 \, a^{3} b^{2} - 8 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{5} - 6 \, a^{3} b^{2} + 8 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a^{4} b - 8 \, a^{2} b^{3} + 4 \, b^{5} - 8 \, {\left(a^{4} b - a^{2} b^{3}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{5} - 4 \, a^{3} b^{2} + 2 \, a b^{4} - {\left(a^{5} + 2 \, a^{3} b^{2} - 3 \, a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*(16*a^2*b^3*cos(d*x + c)^4*log(b*sin(d*x + c) + a) + (a^5 - 6*a^3*b^2 - 8*a^2*b^3 - 3*a*b^4)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (a^5 - 6*a^3*b^2 + 8*a^2*b^3 - 3*a*b^4)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*a^4*b - 8*a^2*b^3 + 4*b^5 - 8*(a^4*b - a^2*b^3)*cos(d*x + c)^2 - 2*(2*a^5 - 4*a^3*b^2 + 2*a*b^4 - (a^5 + 2*a^3*b^2 - 3*a*b^4)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^4)","A",0
1366,1,255,0,1.319123," ","integrate(sec(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, a b^{4} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(a^{4} b - 6 \, a^{2} b^{3} - 8 \, a b^{4} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{4} b - 6 \, a^{2} b^{3} + 8 \, a b^{4} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a^{5} - 8 \, a^{3} b^{2} + 4 \, a b^{4} - 8 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} - {\left(a^{4} b + 2 \, a^{2} b^{3} - 3 \, b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*a*b^4*cos(d*x + c)^4*log(b*sin(d*x + c) + a) + (a^4*b - 6*a^2*b^3 - 8*a*b^4 - 3*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (a^4*b - 6*a^2*b^3 + 8*a*b^4 - 3*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*a^5 - 8*a^3*b^2 + 4*a*b^4 - 8*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 - 2*(2*a^4*b - 4*a^2*b^3 + 2*b^5 - (a^4*b + 2*a^2*b^3 - 3*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^4)","A",0
1367,1,344,0,5.586240," ","integrate(csc(d*x+c)*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, b^{6} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) + 4 \, a^{6} - 8 \, a^{4} b^{2} + 4 \, a^{2} b^{4} + 16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right)^{4} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(8 \, a^{6} + 3 \, a^{5} b - 24 \, a^{4} b^{2} - 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} + 15 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(8 \, a^{6} - 3 \, a^{5} b - 24 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 15 \, a b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{5} b - 4 \, a^{3} b^{3} + 2 \, a b^{5} + {\left(3 \, a^{5} b - 10 \, a^{3} b^{3} + 7 \, a b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*b^6*cos(d*x + c)^4*log(b*sin(d*x + c) + a) + 4*a^6 - 8*a^4*b^2 + 4*a^2*b^4 + 16*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*cos(d*x + c)^4*log(-1/2*sin(d*x + c)) - (8*a^6 + 3*a^5*b - 24*a^4*b^2 - 10*a^3*b^3 + 24*a^2*b^4 + 15*a*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (8*a^6 - 3*a^5*b - 24*a^4*b^2 + 10*a^3*b^3 + 24*a^2*b^4 - 15*a*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 8*(a^6 - 3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c)^2 - 2*(2*a^5*b - 4*a^3*b^3 + 2*a*b^5 + (3*a^5*b - 10*a^3*b^3 + 7*a*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)^4)","A",0
1368,1,425,0,8.156399," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, b^{7} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) \sin\left(d x + c\right) - 4 \, a^{7} + 8 \, a^{5} b^{2} - 4 \, a^{3} b^{4} + 16 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right)^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - {\left(15 \, a^{7} + 8 \, a^{6} b - 42 \, a^{5} b^{2} - 24 \, a^{4} b^{3} + 35 \, a^{3} b^{4} + 24 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + {\left(15 \, a^{7} - 8 \, a^{6} b - 42 \, a^{5} b^{2} + 24 \, a^{4} b^{3} + 35 \, a^{3} b^{4} - 24 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 2 \, {\left(15 \, a^{7} - 42 \, a^{5} b^{2} + 35 \, a^{3} b^{4} - 8 \, a b^{6}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{7} - 14 \, a^{5} b^{2} + 9 \, a^{3} b^{4}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5} + 2 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 2 \, a^{2} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}\right)} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}"," ",0,"-1/16*(16*b^7*cos(d*x + c)^4*log(b*sin(d*x + c) + a)*sin(d*x + c) - 4*a^7 + 8*a^5*b^2 - 4*a^3*b^4 + 16*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)^4*log(1/2*sin(d*x + c))*sin(d*x + c) - (15*a^7 + 8*a^6*b - 42*a^5*b^2 - 24*a^4*b^3 + 35*a^3*b^4 + 24*a^2*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1)*sin(d*x + c) + (15*a^7 - 8*a^6*b - 42*a^5*b^2 + 24*a^4*b^3 + 35*a^3*b^4 - 24*a^2*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1)*sin(d*x + c) + 2*(15*a^7 - 42*a^5*b^2 + 35*a^3*b^4 - 8*a*b^6)*cos(d*x + c)^4 - 2*(5*a^7 - 14*a^5*b^2 + 9*a^3*b^4)*cos(d*x + c)^2 + 4*(a^6*b - 2*a^4*b^3 + a^2*b^5 + 2*(a^6*b - 3*a^4*b^3 + 2*a^2*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6)*d*cos(d*x + c)^4*sin(d*x + c))","A",0
1369,1,640,0,11.415969," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, a^{8} - 8 \, a^{6} b^{2} + 4 \, a^{4} b^{4} - 8 \, {\left(3 \, a^{8} - 8 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{8} - 8 \, a^{6} b^{2} + 5 \, a^{4} b^{4}\right)} \cos\left(d x + c\right)^{2} - 16 \, {\left(b^{8} \cos\left(d x + c\right)^{6} - b^{8} \cos\left(d x + c\right)^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 16 \, {\left({\left(3 \, a^{8} - 8 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - b^{8}\right)} \cos\left(d x + c\right)^{6} - {\left(3 \, a^{8} - 8 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - b^{8}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\frac{1}{2} \, \sin\left(d x + c\right)\right) + {\left({\left(24 \, a^{8} + 15 \, a^{7} b - 64 \, a^{6} b^{2} - 42 \, a^{5} b^{3} + 48 \, a^{4} b^{4} + 35 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{6} - {\left(24 \, a^{8} + 15 \, a^{7} b - 64 \, a^{6} b^{2} - 42 \, a^{5} b^{3} + 48 \, a^{4} b^{4} + 35 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(24 \, a^{8} - 15 \, a^{7} b - 64 \, a^{6} b^{2} + 42 \, a^{5} b^{3} + 48 \, a^{4} b^{4} - 35 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{6} - {\left(24 \, a^{8} - 15 \, a^{7} b - 64 \, a^{6} b^{2} + 42 \, a^{5} b^{3} + 48 \, a^{4} b^{4} - 35 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, a^{7} b - 4 \, a^{5} b^{3} + 2 \, a^{3} b^{5} - {\left(15 \, a^{7} b - 42 \, a^{5} b^{3} + 35 \, a^{3} b^{5} - 8 \, a b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{7} b - 14 \, a^{5} b^{3} + 9 \, a^{3} b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{6} - {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"-1/16*(4*a^8 - 8*a^6*b^2 + 4*a^4*b^4 - 8*(3*a^8 - 8*a^6*b^2 + 6*a^4*b^4 - a^2*b^6)*cos(d*x + c)^4 + 4*(3*a^8 - 8*a^6*b^2 + 5*a^4*b^4)*cos(d*x + c)^2 - 16*(b^8*cos(d*x + c)^6 - b^8*cos(d*x + c)^4)*log(b*sin(d*x + c) + a) - 16*((3*a^8 - 8*a^6*b^2 + 6*a^4*b^4 - b^8)*cos(d*x + c)^6 - (3*a^8 - 8*a^6*b^2 + 6*a^4*b^4 - b^8)*cos(d*x + c)^4)*log(-1/2*sin(d*x + c)) + ((24*a^8 + 15*a^7*b - 64*a^6*b^2 - 42*a^5*b^3 + 48*a^4*b^4 + 35*a^3*b^5)*cos(d*x + c)^6 - (24*a^8 + 15*a^7*b - 64*a^6*b^2 - 42*a^5*b^3 + 48*a^4*b^4 + 35*a^3*b^5)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) + ((24*a^8 - 15*a^7*b - 64*a^6*b^2 + 42*a^5*b^3 + 48*a^4*b^4 - 35*a^3*b^5)*cos(d*x + c)^6 - (24*a^8 - 15*a^7*b - 64*a^6*b^2 + 42*a^5*b^3 + 48*a^4*b^4 - 35*a^3*b^5)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) - 2*(2*a^7*b - 4*a^5*b^3 + 2*a^3*b^5 - (15*a^7*b - 42*a^5*b^3 + 35*a^3*b^5 - 8*a*b^7)*cos(d*x + c)^4 + (5*a^7*b - 14*a^5*b^3 + 9*a^3*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c)^6 - (a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c)^4)","B",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1374,-1,0,0,0.000000," ","integrate(csc(f*x+e)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1375,-1,0,0,0.000000," ","integrate(csc(f*x+e)^2*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1376,-1,0,0,0.000000," ","integrate(csc(f*x+e)^3*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1393,-1,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1394,-1,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1395,-1,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1400,-1,0,0,0.000000," ","integrate(csc(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1401,-1,0,0,0.000000," ","integrate(csc(f*x+e)^2/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1410,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1411,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1412,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1418,-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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1431,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1432,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1433,-1,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1434,-1,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1438,-1,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1439,-1,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1443,1,72,0,1.166909," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, b \cos\left(d x + c\right)^{4} + 9 \, a d x \cos\left(d x + c\right) - 12 \, b \cos\left(d x + c\right)^{2} - 3 \, {\left(a \cos\left(d x + c\right)^{2} + 2 \, a\right)} \sin\left(d x + c\right) - 6 \, b}{6 \, d \cos\left(d x + c\right)}"," ",0,"-1/6*(2*b*cos(d*x + c)^4 + 9*a*d*x*cos(d*x + c) - 12*b*cos(d*x + c)^2 - 3*(a*cos(d*x + c)^2 + 2*a)*sin(d*x + c) - 6*b)/(d*cos(d*x + c))","A",0
1444,1,61,0,1.230480," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, b d x \cos\left(d x + c\right) - 2 \, a \cos\left(d x + c\right)^{2} - {\left(b \cos\left(d x + c\right)^{2} + 2 \, b\right)} \sin\left(d x + c\right) - 2 \, a}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*(3*b*d*x*cos(d*x + c) - 2*a*cos(d*x + c)^2 - (b*cos(d*x + c)^2 + 2*b)*sin(d*x + c) - 2*a)/(d*cos(d*x + c))","A",0
1445,1,47,0,0.955571," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a d x \cos\left(d x + c\right) - b \cos\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - b}{d \cos\left(d x + c\right)}"," ",0,"-(a*d*x*cos(d*x + c) - b*cos(d*x + c)^2 - a*sin(d*x + c) - b)/(d*cos(d*x + c))","A",0
1446,1,36,0,0.900952," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b d x \cos\left(d x + c\right) - b \sin\left(d x + c\right) - a}{d \cos\left(d x + c\right)}"," ",0,"-(b*d*x*cos(d*x + c) - b*sin(d*x + c) - a)/(d*cos(d*x + c))","A",0
1447,1,65,0,0.995765," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - a \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, b \sin\left(d x + c\right) - 2 \, a}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*(a*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2) - a*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2) - 2*b*sin(d*x + c) - 2*a)/(d*cos(d*x + c))","A",0
1448,1,96,0,0.902444," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - b \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 4 \, a \cos\left(d x + c\right)^{2} - 2 \, b \sin\left(d x + c\right) - 2 \, a}{2 \, d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"-1/2*(b*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - b*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 4*a*cos(d*x + c)^2 - 2*b*sin(d*x + c) - 2*a)/(d*cos(d*x + c)*sin(d*x + c))","A",0
1449,1,128,0,0.989586," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{6 \, a \cos\left(d x + c\right)^{2} - 3 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(a \cos\left(d x + c\right)^{3} - a \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(2 \, b \cos\left(d x + c\right)^{2} - b\right)} \sin\left(d x + c\right) - 4 \, a}{4 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(6*a*cos(d*x + c)^2 - 3*(a*cos(d*x + c)^3 - a*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(a*cos(d*x + c)^3 - a*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(2*b*cos(d*x + c)^2 - b)*sin(d*x + c) - 4*a)/(d*cos(d*x + c)^3 - d*cos(d*x + c))","A",0
1450,1,91,0,0.983816," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{b^{2} \cos\left(d x + c\right)^{4} + 9 \, a b d x \cos\left(d x + c\right) - 3 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 3 \, a^{2} - 3 \, b^{2} - 3 \, {\left(a b \cos\left(d x + c\right)^{2} + 2 \, a b\right)} \sin\left(d x + c\right)}{3 \, d \cos\left(d x + c\right)}"," ",0,"-1/3*(b^2*cos(d*x + c)^4 + 9*a*b*d*x*cos(d*x + c) - 3*(a^2 + 2*b^2)*cos(d*x + c)^2 - 3*a^2 - 3*b^2 - 3*(a*b*cos(d*x + c)^2 + 2*a*b)*sin(d*x + c))/(d*cos(d*x + c))","A",0
1451,1,81,0,0.897036," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, a^{2} + 3 \, b^{2}\right)} d x \cos\left(d x + c\right) - 4 \, a b \cos\left(d x + c\right)^{2} - 4 \, a b - {\left(b^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*((2*a^2 + 3*b^2)*d*x*cos(d*x + c) - 4*a*b*cos(d*x + c)^2 - 4*a*b - (b^2*cos(d*x + c)^2 + 2*a^2 + 2*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
1452,1,59,0,1.043412," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, a b d x \cos\left(d x + c\right) - b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}{d \cos\left(d x + c\right)}"," ",0,"-(2*a*b*d*x*cos(d*x + c) - b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)/(d*cos(d*x + c))","A",0
1453,1,77,0,1.128019," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a^{2} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - a^{2} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 4 \, a b \sin\left(d x + c\right) - 2 \, a^{2} - 2 \, b^{2}}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*(a^2*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2) - a^2*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2) - 4*a*b*sin(d*x + c) - 2*a^2 - 2*b^2)/(d*cos(d*x + c))","A",0
1454,1,113,0,1.198024," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a b \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - a b \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + {\left(2 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}{d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"-(a*b*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - a*b*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + (2*a^2 + b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)/(d*cos(d*x + c)*sin(d*x + c))","A",0
1455,1,186,0,1.095011," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 4 \, a^{2} - 4 \, b^{2} - {\left({\left(3 \, a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(3 \, a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 8 \, {\left(2 \, a b \cos\left(d x + c\right)^{2} - a b\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)}}"," ",0,"1/4*(2*(3*a^2 + 2*b^2)*cos(d*x + c)^2 - 4*a^2 - 4*b^2 - ((3*a^2 + 2*b^2)*cos(d*x + c)^3 - (3*a^2 + 2*b^2)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + ((3*a^2 + 2*b^2)*cos(d*x + c)^3 - (3*a^2 + 2*b^2)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 8*(2*a*b*cos(d*x + c)^2 - a*b)*sin(d*x + c))/(d*cos(d*x + c)^3 - d*cos(d*x + c))","A",0
1456,1,192,0,1.053412," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 6 \, {\left(4 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 9 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 9 \, {\left(a b \cos\left(d x + c\right)^{3} - a b \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, a^{2} + 6 \, b^{2} - 6 \, {\left(3 \, a b \cos\left(d x + c\right)^{2} - 2 \, a b\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(4*(4*a^2 + 3*b^2)*cos(d*x + c)^4 - 6*(4*a^2 + 3*b^2)*cos(d*x + c)^2 + 9*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 9*(a*b*cos(d*x + c)^3 - a*b*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*a^2 + 6*b^2 - 6*(3*a*b*cos(d*x + c)^2 - 2*a*b)*sin(d*x + c))/((d*cos(d*x + c)^3 - d*cos(d*x + c))*sin(d*x + c))","A",0
1457,1,135,0,1.149431," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, a b^{2} \cos\left(d x + c\right)^{4} + 3 \, {\left(12 \, a^{2} b + 5 \, b^{3}\right)} d x \cos\left(d x + c\right) - 8 \, a^{3} - 24 \, a b^{2} - 8 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + {\left(2 \, b^{3} \cos\left(d x + c\right)^{4} - 24 \, a^{2} b - 8 \, b^{3} - 3 \, {\left(4 \, a^{2} b + 3 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{8 \, d \cos\left(d x + c\right)}"," ",0,"-1/8*(8*a*b^2*cos(d*x + c)^4 + 3*(12*a^2*b + 5*b^3)*d*x*cos(d*x + c) - 8*a^3 - 24*a*b^2 - 8*(a^3 + 6*a*b^2)*cos(d*x + c)^2 + (2*b^3*cos(d*x + c)^4 - 24*a^2*b - 8*b^3 - 3*(4*a^2*b + 3*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
1458,1,116,0,0.962677," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} \cos\left(d x + c\right)^{4} + 3 \, {\left(2 \, a^{3} + 9 \, a b^{2}\right)} d x \cos\left(d x + c\right) - 18 \, a^{2} b - 6 \, b^{3} - 6 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{3} + 6 \, a b^{2}\right)} \sin\left(d x + c\right)}{6 \, d \cos\left(d x + c\right)}"," ",0,"-1/6*(2*b^3*cos(d*x + c)^4 + 3*(2*a^3 + 9*a*b^2)*d*x*cos(d*x + c) - 18*a^2*b - 6*b^3 - 6*(3*a^2*b + 2*b^3)*cos(d*x + c)^2 - 3*(3*a*b^2*cos(d*x + c)^2 + 2*a^3 + 6*a*b^2)*sin(d*x + c))/(d*cos(d*x + c))","A",0
1459,1,90,0,1.190742," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{6 \, a b^{2} \cos\left(d x + c\right)^{2} - 3 \, {\left(2 \, a^{2} b + b^{3}\right)} d x \cos\left(d x + c\right) + 2 \, a^{3} + 6 \, a b^{2} + {\left(b^{3} \cos\left(d x + c\right)^{2} + 6 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"1/2*(6*a*b^2*cos(d*x + c)^2 - 3*(2*a^2*b + b^3)*d*x*cos(d*x + c) + 2*a^3 + 6*a*b^2 + (b^3*cos(d*x + c)^2 + 6*a^2*b + 2*b^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
1460,1,99,0,0.848800," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{2 \, b^{3} d x \cos\left(d x + c\right) + a^{3} \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - a^{3} \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, a^{3} - 6 \, a b^{2} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right)}"," ",0,"-1/2*(2*b^3*d*x*cos(d*x + c) + a^3*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2) - a^3*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2) - 2*a^3 - 6*a*b^2 - 2*(3*a^2*b + b^3)*sin(d*x + c))/(d*cos(d*x + c))","A",0
1461,1,131,0,0.823149," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, a^{2} b \cos\left(d x + c\right) \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, a^{2} b \cos\left(d x + c\right) \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, a^{3} - 6 \, a b^{2} + 2 \, {\left(2 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(3 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{2 \, d \cos\left(d x + c\right) \sin\left(d x + c\right)}"," ",0,"-1/2*(3*a^2*b*cos(d*x + c)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*a^2*b*cos(d*x + c)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*a^3 - 6*a*b^2 + 2*(2*a^3 + 3*a*b^2)*cos(d*x + c)^2 - 2*(3*a^2*b + b^3)*sin(d*x + c))/(d*cos(d*x + c)*sin(d*x + c))","A",0
1462,1,196,0,0.638233," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{4 \, a^{3} + 12 \, a b^{2} - 6 \, {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{3} + 2 \, a b^{2}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 4 \, {\left(3 \, a^{2} b + b^{3} - {\left(6 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)}}"," ",0,"-1/4*(4*a^3 + 12*a*b^2 - 6*(a^3 + 2*a*b^2)*cos(d*x + c)^2 + 3*((a^3 + 2*a*b^2)*cos(d*x + c)^3 - (a^3 + 2*a*b^2)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*((a^3 + 2*a*b^2)*cos(d*x + c)^3 - (a^3 + 2*a*b^2)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) + 4*(3*a^2*b + b^3 - (6*a^2*b + b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^3 - d*cos(d*x + c))","A",0
1463,1,252,0,0.925912," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + 12 \, a^{3} + 36 \, a b^{2} - 12 \, {\left(4 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(9 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(9 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 3 \, {\left({\left(9 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{3} - {\left(9 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, {\left(6 \, a^{2} b + 2 \, b^{3} - {\left(9 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, {\left(d \cos\left(d x + c\right)^{3} - d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}"," ",0,"-1/12*(8*(4*a^3 + 9*a*b^2)*cos(d*x + c)^4 + 12*a^3 + 36*a*b^2 - 12*(4*a^3 + 9*a*b^2)*cos(d*x + c)^2 + 3*((9*a^2*b + 2*b^3)*cos(d*x + c)^3 - (9*a^2*b + 2*b^3)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 3*((9*a^2*b + 2*b^3)*cos(d*x + c)^3 - (9*a^2*b + 2*b^3)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*(6*a^2*b + 2*b^3 - (9*a^2*b + 2*b^3)*cos(d*x + c)^2)*sin(d*x + c))/((d*cos(d*x + c)^3 - d*cos(d*x + c))*sin(d*x + c))","A",0
1464,1,724,0,0.965456," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{4} b^{3} - 4 \, a^{2} b^{5} + 2 \, b^{7} + 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d x \cos\left(d x + c\right) + 2 \, {\left(a^{6} b - b^{7}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} - {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d x \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{a^{4} b^{3} - 2 \, a^{2} b^{5} + b^{7} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d x \cos\left(d x + c\right) + {\left(a^{6} b - b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{5} b - 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{6} - 4 \, a^{4} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(a^{5} b^{2} - 2 \, a^{3} b^{4} + a b^{6} - {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d x \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{{\left(a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} b^{2} - 3 \, a^{5} b^{4} + 3 \, a^{3} b^{6} - a b^{8}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(2*a^4*b^3 - 4*a^2*b^5 + 2*b^7 + 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*x*cos(d*x + c) + 2*(a^6*b - b^7)*cos(d*x + c)^2 - ((a^5*b - 4*a^3*b^3)*cos(d*x + c)*sin(d*x + c) + (a^6 - 4*a^4*b^2)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(a^5*b^2 - 2*a^3*b^4 + a*b^6 - (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*x*cos(d*x + c))*sin(d*x + c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d*cos(d*x + c)*sin(d*x + c) + (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d*cos(d*x + c)), -(a^4*b^3 - 2*a^2*b^5 + b^7 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*x*cos(d*x + c) + (a^6*b - b^7)*cos(d*x + c)^2 + ((a^5*b - 4*a^3*b^3)*cos(d*x + c)*sin(d*x + c) + (a^6 - 4*a^4*b^2)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (a^5*b^2 - 2*a^3*b^4 + a*b^6 - (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*x*cos(d*x + c))*sin(d*x + c))/((a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9)*d*cos(d*x + c)*sin(d*x + c) + (a^7*b^2 - 3*a^5*b^4 + 3*a^3*b^6 - a*b^8)*d*cos(d*x + c))]","A",0
1465,1,534,0,1.073623," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{5} - 4 \, a^{3} b^{2} + 2 \, a b^{4} + 2 \, {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{2} b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + a^{3} b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)\right)}}, \frac{a^{5} - 2 \, a^{3} b^{2} + a b^{4} + {\left(a^{5} + a^{3} b^{2} - 2 \, a b^{4}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(a^{2} b^{2} \cos\left(d x + c\right) \sin\left(d x + c\right) + a^{3} b \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(2*a^5 - 4*a^3*b^2 + 2*a*b^4 + 2*(a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2 - 3*(a^2*b^2*cos(d*x + c)*sin(d*x + c) + a^3*b*cos(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)), (a^5 - 2*a^3*b^2 + a*b^4 + (a^5 + a^3*b^2 - 2*a*b^4)*cos(d*x + c)^2 - 3*(a^2*b^2*cos(d*x + c)*sin(d*x + c) + a^3*b*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c))]","A",0
1466,1,569,0,0.987748," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{4} b - 4 \, a^{2} b^{3} + 2 \, b^{5} + 2 \, {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{a^{4} b - 2 \, a^{2} b^{3} + b^{5} + {\left(2 \, a^{4} b - a^{2} b^{3} - b^{5}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(a^{3} b + 2 \, a b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{4} + 2 \, a^{2} b^{2}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{{\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(2*a^4*b - 4*a^2*b^3 + 2*b^5 + 2*(2*a^4*b - a^2*b^3 - b^5)*cos(d*x + c)^2 + ((a^3*b + 2*a*b^3)*cos(d*x + c)*sin(d*x + c) + (a^4 + 2*a^2*b^2)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)), -(a^4*b - 2*a^2*b^3 + b^5 + (2*a^4*b - a^2*b^3 - b^5)*cos(d*x + c)^2 - ((a^3*b + 2*a*b^3)*cos(d*x + c)*sin(d*x + c) + (a^4 + 2*a^2*b^2)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c))]","A",0
1467,1,557,0,0.714072," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{5} - 4 \, a^{3} b^{2} + 2 \, a b^{4} + 6 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)\right)}}, \frac{a^{5} - 2 \, a^{3} b^{2} + a b^{4} + 3 \, {\left(a^{3} b^{2} - a b^{4}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(2 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(2 \, a^{3} b + a b^{3}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}{{\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[1/2*(2*a^5 - 4*a^3*b^2 + 2*a*b^4 + 6*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 - ((2*a^2*b^2 + b^4)*cos(d*x + c)*sin(d*x + c) + (2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)), (a^5 - 2*a^3*b^2 + a*b^4 + 3*(a^3*b^2 - a*b^4)*cos(d*x + c)^2 - ((2*a^2*b^2 + b^4)*cos(d*x + c)*sin(d*x + c) + (2*a^3*b + a*b^3)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c))]","A",0
1468,1,957,0,2.460731," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{7} - 4 \, a^{5} b^{2} + 2 \, a^{3} b^{4} + 2 \, {\left(2 \, a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(4 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right)\right)}}, \frac{2 \, a^{7} - 4 \, a^{5} b^{2} + 2 \, a^{3} b^{4} + 2 \, {\left(2 \, a^{5} b^{2} - a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left({\left(4 \, a^{2} b^{4} - b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(4 \, a^{3} b^{3} - a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{6} b - 2 \, a^{4} b^{3} + a^{2} b^{5}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b - 3 \, a^{6} b^{3} + 3 \, a^{4} b^{5} - a^{2} b^{7}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) + {\left(a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/2*(2*a^7 - 4*a^5*b^2 + 2*a^3*b^4 + 2*(2*a^5*b^2 - a^3*b^4 - a*b^6)*cos(d*x + c)^2 + ((4*a^2*b^4 - b^6)*cos(d*x + c)*sin(d*x + c) + (4*a^3*b^3 - a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - ((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + ((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*sin(d*x + c))/((a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c)), 1/2*(2*a^7 - 4*a^5*b^2 + 2*a^3*b^4 + 2*(2*a^5*b^2 - a^3*b^4 - a*b^6)*cos(d*x + c)^2 - 2*((4*a^2*b^4 - b^6)*cos(d*x + c)*sin(d*x + c) + (4*a^3*b^3 - a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - ((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + ((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*cos(d*x + c)*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^6*b - 2*a^4*b^3 + a^2*b^5)*sin(d*x + c))/((a^8*b - 3*a^6*b^3 + 3*a^4*b^5 - a^2*b^7)*d*cos(d*x + c)*sin(d*x + c) + (a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6)*d*cos(d*x + c))]","B",0
1469,1,1355,0,2.464626," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, a^{8} - 4 \, a^{6} b^{2} + 2 \, a^{4} b^{4} - 2 \, {\left(2 \, a^{8} - 5 \, a^{6} b^{2} + 4 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(5 \, a^{2} b^{5} - 2 \, b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(5 \, a^{2} b^{5} - 2 \, b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 2 \, {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5} + {\left(2 \, a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - 2 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{a^{8} - 2 \, a^{6} b^{2} + a^{4} b^{4} - {\left(2 \, a^{8} - 5 \, a^{6} b^{2} + 4 \, a^{4} b^{4} - a^{2} b^{6}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(5 \, a^{2} b^{5} - 2 \, b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(5 \, a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(5 \, a^{2} b^{5} - 2 \, b^{7}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left({\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(a^{7} b - 2 \, a^{5} b^{3} + a^{3} b^{5} + {\left(2 \, a^{7} b - 3 \, a^{5} b^{3} + 3 \, a^{3} b^{5} - 2 \, a b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{{\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{10} - 3 \, a^{8} b^{2} + 3 \, a^{6} b^{4} - a^{4} b^{6}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{9} b - 3 \, a^{7} b^{3} + 3 \, a^{5} b^{5} - a^{3} b^{7}\right)} d \cos\left(d x + c\right)}\right]"," ",0,"[-1/2*(2*a^8 - 4*a^6*b^2 + 2*a^4*b^4 - 2*(2*a^8 - 5*a^6*b^2 + 4*a^4*b^4 - a^2*b^6)*cos(d*x + c)^2 - ((5*a^2*b^5 - 2*b^7)*cos(d*x + c)^3 - (5*a^3*b^4 - 2*a*b^6)*cos(d*x + c)*sin(d*x + c) - (5*a^2*b^5 - 2*b^7)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^3 - (a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c)*sin(d*x + c) - (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 2*((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^3 - (a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c)*sin(d*x + c) - (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(a^7*b - 2*a^5*b^3 + a^3*b^5 + (2*a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - 2*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d*cos(d*x + c)^3 - (a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*d*cos(d*x + c)*sin(d*x + c) - (a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d*cos(d*x + c)), -(a^8 - 2*a^6*b^2 + a^4*b^4 - (2*a^8 - 5*a^6*b^2 + 4*a^4*b^4 - a^2*b^6)*cos(d*x + c)^2 - ((5*a^2*b^5 - 2*b^7)*cos(d*x + c)^3 - (5*a^3*b^4 - 2*a*b^6)*cos(d*x + c)*sin(d*x + c) - (5*a^2*b^5 - 2*b^7)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - ((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^3 - (a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c)*sin(d*x + c) - (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + ((a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c)^3 - (a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - a*b^7)*cos(d*x + c)*sin(d*x + c) - (a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - (a^7*b - 2*a^5*b^3 + a^3*b^5 + (2*a^7*b - 3*a^5*b^3 + 3*a^3*b^5 - 2*a*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d*cos(d*x + c)^3 - (a^10 - 3*a^8*b^2 + 3*a^6*b^4 - a^4*b^6)*d*cos(d*x + c)*sin(d*x + c) - (a^9*b - 3*a^7*b^3 + 3*a^5*b^5 - a^3*b^7)*d*cos(d*x + c))]","B",0
1470,1,1844,0,4.691042," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{9} - 8 \, a^{7} b^{2} + 4 \, a^{5} b^{4} - 4 \, {\left(4 \, a^{7} b^{2} - 8 \, a^{5} b^{4} + 7 \, a^{3} b^{6} - 3 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - 6 \, {\left(a^{9} - 5 \, a^{7} b^{2} + 7 \, a^{5} b^{4} - 5 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left({\left(2 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right) + {\left({\left(2 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 3 \, {\left({\left(a^{9} - a^{7} b^{2} - 3 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{9} - a^{7} b^{2} - 3 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right) + {\left({\left(a^{8} b - a^{6} b^{3} - 3 \, a^{4} b^{5} + 5 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{8} b - a^{6} b^{3} - 3 \, a^{4} b^{5} + 5 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(a^{9} - a^{7} b^{2} - 3 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{9} - a^{7} b^{2} - 3 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right) + {\left({\left(a^{8} b - a^{6} b^{3} - 3 \, a^{4} b^{5} + 5 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{8} b - a^{6} b^{3} - 3 \, a^{4} b^{5} + 5 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, a^{8} b - 4 \, a^{6} b^{3} + 2 \, a^{4} b^{5} - {\left(5 \, a^{8} b - 13 \, a^{6} b^{3} + 11 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cos\left(d x + c\right) + {\left({\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}, -\frac{4 \, a^{9} - 8 \, a^{7} b^{2} + 4 \, a^{5} b^{4} - 4 \, {\left(4 \, a^{7} b^{2} - 8 \, a^{5} b^{4} + 7 \, a^{3} b^{6} - 3 \, a b^{8}\right)} \cos\left(d x + c\right)^{4} - 6 \, {\left(a^{9} - 5 \, a^{7} b^{2} + 7 \, a^{5} b^{4} - 5 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \cos\left(d x + c\right)^{2} + 12 \, {\left({\left(2 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{3} b^{5} - a b^{7}\right)} \cos\left(d x + c\right) + {\left({\left(2 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(2 \, a^{2} b^{6} - b^{8}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + 3 \, {\left({\left(a^{9} - a^{7} b^{2} - 3 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{9} - a^{7} b^{2} - 3 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right) + {\left({\left(a^{8} b - a^{6} b^{3} - 3 \, a^{4} b^{5} + 5 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{8} b - a^{6} b^{3} - 3 \, a^{4} b^{5} + 5 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, {\left({\left(a^{9} - a^{7} b^{2} - 3 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{9} - a^{7} b^{2} - 3 \, a^{5} b^{4} + 5 \, a^{3} b^{6} - 2 \, a b^{8}\right)} \cos\left(d x + c\right) + {\left({\left(a^{8} b - a^{6} b^{3} - 3 \, a^{4} b^{5} + 5 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{8} b - a^{6} b^{3} - 3 \, a^{4} b^{5} + 5 \, a^{2} b^{7} - 2 \, b^{9}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, a^{8} b - 4 \, a^{6} b^{3} + 2 \, a^{4} b^{5} - {\left(5 \, a^{8} b - 13 \, a^{6} b^{3} + 11 \, a^{4} b^{5} - 3 \, a^{2} b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{11} - 3 \, a^{9} b^{2} + 3 \, a^{7} b^{4} - a^{5} b^{6}\right)} d \cos\left(d x + c\right) + {\left({\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 3 \, a^{8} b^{3} + 3 \, a^{6} b^{5} - a^{4} b^{7}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^9 - 8*a^7*b^2 + 4*a^5*b^4 - 4*(4*a^7*b^2 - 8*a^5*b^4 + 7*a^3*b^6 - 3*a*b^8)*cos(d*x + c)^4 - 6*(a^9 - 5*a^7*b^2 + 7*a^5*b^4 - 5*a^3*b^6 + 2*a*b^8)*cos(d*x + c)^2 - 6*((2*a^3*b^5 - a*b^7)*cos(d*x + c)^3 - (2*a^3*b^5 - a*b^7)*cos(d*x + c) + ((2*a^2*b^6 - b^8)*cos(d*x + c)^3 - (2*a^2*b^6 - b^8)*cos(d*x + c))*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 3*((a^9 - a^7*b^2 - 3*a^5*b^4 + 5*a^3*b^6 - 2*a*b^8)*cos(d*x + c)^3 - (a^9 - a^7*b^2 - 3*a^5*b^4 + 5*a^3*b^6 - 2*a*b^8)*cos(d*x + c) + ((a^8*b - a^6*b^3 - 3*a^4*b^5 + 5*a^2*b^7 - 2*b^9)*cos(d*x + c)^3 - (a^8*b - a^6*b^3 - 3*a^4*b^5 + 5*a^2*b^7 - 2*b^9)*cos(d*x + c))*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*((a^9 - a^7*b^2 - 3*a^5*b^4 + 5*a^3*b^6 - 2*a*b^8)*cos(d*x + c)^3 - (a^9 - a^7*b^2 - 3*a^5*b^4 + 5*a^3*b^6 - 2*a*b^8)*cos(d*x + c) + ((a^8*b - a^6*b^3 - 3*a^4*b^5 + 5*a^2*b^7 - 2*b^9)*cos(d*x + c)^3 - (a^8*b - a^6*b^3 - 3*a^4*b^5 + 5*a^2*b^7 - 2*b^9)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*a^8*b - 4*a^6*b^3 + 2*a^4*b^5 - (5*a^8*b - 13*a^6*b^3 + 11*a^4*b^5 - 3*a^2*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cos(d*x + c)^3 - (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cos(d*x + c) + ((a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c)^3 - (a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c))*sin(d*x + c)), -1/4*(4*a^9 - 8*a^7*b^2 + 4*a^5*b^4 - 4*(4*a^7*b^2 - 8*a^5*b^4 + 7*a^3*b^6 - 3*a*b^8)*cos(d*x + c)^4 - 6*(a^9 - 5*a^7*b^2 + 7*a^5*b^4 - 5*a^3*b^6 + 2*a*b^8)*cos(d*x + c)^2 + 12*((2*a^3*b^5 - a*b^7)*cos(d*x + c)^3 - (2*a^3*b^5 - a*b^7)*cos(d*x + c) + ((2*a^2*b^6 - b^8)*cos(d*x + c)^3 - (2*a^2*b^6 - b^8)*cos(d*x + c))*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + 3*((a^9 - a^7*b^2 - 3*a^5*b^4 + 5*a^3*b^6 - 2*a*b^8)*cos(d*x + c)^3 - (a^9 - a^7*b^2 - 3*a^5*b^4 + 5*a^3*b^6 - 2*a*b^8)*cos(d*x + c) + ((a^8*b - a^6*b^3 - 3*a^4*b^5 + 5*a^2*b^7 - 2*b^9)*cos(d*x + c)^3 - (a^8*b - a^6*b^3 - 3*a^4*b^5 + 5*a^2*b^7 - 2*b^9)*cos(d*x + c))*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 3*((a^9 - a^7*b^2 - 3*a^5*b^4 + 5*a^3*b^6 - 2*a*b^8)*cos(d*x + c)^3 - (a^9 - a^7*b^2 - 3*a^5*b^4 + 5*a^3*b^6 - 2*a*b^8)*cos(d*x + c) + ((a^8*b - a^6*b^3 - 3*a^4*b^5 + 5*a^2*b^7 - 2*b^9)*cos(d*x + c)^3 - (a^8*b - a^6*b^3 - 3*a^4*b^5 + 5*a^2*b^7 - 2*b^9)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*a^8*b - 4*a^6*b^3 + 2*a^4*b^5 - (5*a^8*b - 13*a^6*b^3 + 11*a^4*b^5 - 3*a^2*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cos(d*x + c)^3 - (a^11 - 3*a^9*b^2 + 3*a^7*b^4 - a^5*b^6)*d*cos(d*x + c) + ((a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c)^3 - (a^10*b - 3*a^8*b^3 + 3*a^6*b^5 - a^4*b^7)*d*cos(d*x + c))*sin(d*x + c))]","B",0
1471,1,906,0,1.137821," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, a^{6} b - 12 \, a^{4} b^{3} + 12 \, a^{2} b^{5} - 4 \, b^{7} + 2 \, {\left(11 \, a^{6} b - 5 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b + 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{6} + 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} + {\left(a^{7} - 11 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}, \frac{2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} + {\left(11 \, a^{6} b - 5 \, a^{4} b^{3} - 8 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{5} b + 4 \, a^{3} b^{3}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{6} + 5 \, a^{4} b^{2} + 4 \, a^{2} b^{4}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} + {\left(a^{7} - 11 \, a^{5} b^{2} + 4 \, a^{3} b^{4} + 6 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a^6*b - 12*a^4*b^3 + 12*a^2*b^5 - 4*b^7 + 2*(11*a^6*b - 5*a^4*b^3 - 8*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + 3*((a^4*b^2 + 4*a^2*b^4)*cos(d*x + c)^3 - 2*(a^5*b + 4*a^3*b^3)*cos(d*x + c)*sin(d*x + c) - (a^6 + 5*a^4*b^2 + 4*a^2*b^4)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 + (a^7 - 11*a^5*b^2 + 4*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c)), 1/2*(2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 + (11*a^6*b - 5*a^4*b^3 - 8*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + 3*((a^4*b^2 + 4*a^2*b^4)*cos(d*x + c)^3 - 2*(a^5*b + 4*a^3*b^3)*cos(d*x + c)*sin(d*x + c) - (a^6 + 5*a^4*b^2 + 4*a^2*b^4)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 + (a^7 - 11*a^5*b^2 + 4*a^3*b^4 + 6*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c))]","A",0
1472,1,917,0,1.104751," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{7} - 12 \, a^{5} b^{2} + 12 \, a^{3} b^{4} - 4 \, a b^{6} + 2 \, {\left(2 \, a^{7} + 13 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} - {\left(a^{6} b + 11 \, a^{4} b^{3} - 10 \, a^{2} b^{5} - 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} + {\left(2 \, a^{7} + 13 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(3 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(3 \, a^{4} b^{2} + 2 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(3 \, a^{5} b + 5 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} - {\left(a^{6} b + 11 \, a^{4} b^{3} - 10 \, a^{2} b^{5} - 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^7 - 12*a^5*b^2 + 12*a^3*b^4 - 4*a*b^6 + 2*(2*a^7 + 13*a^5*b^2 - 17*a^3*b^4 + 2*a*b^6)*cos(d*x + c)^2 - 3*((3*a^3*b^3 + 2*a*b^5)*cos(d*x + c)^3 - 2*(3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c)*sin(d*x + c) - (3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 - (a^6*b + 11*a^4*b^3 - 10*a^2*b^5 - 2*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c)), -1/2*(2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 + (2*a^7 + 13*a^5*b^2 - 17*a^3*b^4 + 2*a*b^6)*cos(d*x + c)^2 + 3*((3*a^3*b^3 + 2*a*b^5)*cos(d*x + c)^3 - 2*(3*a^4*b^2 + 2*a^2*b^4)*cos(d*x + c)*sin(d*x + c) - (3*a^5*b + 5*a^3*b^3 + 2*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 - (a^6*b + 11*a^4*b^3 - 10*a^2*b^5 - 2*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c))]","A",0
1473,1,934,0,1.073069," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, a^{6} b - 12 \, a^{4} b^{3} + 12 \, a^{2} b^{5} - 4 \, b^{7} + 2 \, {\left(8 \, a^{6} b + a^{4} b^{3} - 11 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, a^{4} b^{2} + 11 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{5} b + 11 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(2 \, a^{6} + 13 \, a^{4} b^{2} + 13 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} - 5 \, {\left(a^{5} b^{2} + a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}, \frac{2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} + {\left(8 \, a^{6} b + a^{4} b^{3} - 11 \, a^{2} b^{5} + 2 \, b^{7}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(2 \, a^{4} b^{2} + 11 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{5} b + 11 \, a^{3} b^{3} + 2 \, a b^{5}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(2 \, a^{6} + 13 \, a^{4} b^{2} + 13 \, a^{2} b^{4} + 2 \, b^{6}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} - 5 \, {\left(a^{5} b^{2} + a^{3} b^{4} - 2 \, a b^{6}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a^6*b - 12*a^4*b^3 + 12*a^2*b^5 - 4*b^7 + 2*(8*a^6*b + a^4*b^3 - 11*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + ((2*a^4*b^2 + 11*a^2*b^4 + 2*b^6)*cos(d*x + c)^3 - 2*(2*a^5*b + 11*a^3*b^3 + 2*a*b^5)*cos(d*x + c)*sin(d*x + c) - (2*a^6 + 13*a^4*b^2 + 13*a^2*b^4 + 2*b^6)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 - 5*(a^5*b^2 + a^3*b^4 - 2*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c)), 1/2*(2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 + (8*a^6*b + a^4*b^3 - 11*a^2*b^5 + 2*b^7)*cos(d*x + c)^2 + ((2*a^4*b^2 + 11*a^2*b^4 + 2*b^6)*cos(d*x + c)^3 - 2*(2*a^5*b + 11*a^3*b^3 + 2*a*b^5)*cos(d*x + c)*sin(d*x + c) - (2*a^6 + 13*a^4*b^2 + 13*a^2*b^4 + 2*b^6)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 - 5*(a^5*b^2 + a^3*b^4 - 2*a*b^6)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c))]","A",0
1474,1,895,0,1.152786," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{7} - 12 \, a^{5} b^{2} + 12 \, a^{3} b^{4} - 4 \, a b^{6} + 2 \, {\left(16 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left({\left(2 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(2 \, a^{5} b + 5 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 2 \, {\left(2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} - {\left(11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{2 \, a^{7} - 6 \, a^{5} b^{2} + 6 \, a^{3} b^{4} - 2 \, a b^{6} + {\left(16 \, a^{5} b^{2} - 17 \, a^{3} b^{4} + a b^{6}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(2 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(2 \, a^{5} b + 5 \, a^{3} b^{3} + 3 \, a b^{5}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - {\left(2 \, a^{6} b - 6 \, a^{4} b^{3} + 6 \, a^{2} b^{5} - 2 \, b^{7} - {\left(11 \, a^{4} b^{3} - 7 \, a^{2} b^{5} - 4 \, b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^7 - 12*a^5*b^2 + 12*a^3*b^4 - 4*a*b^6 + 2*(16*a^5*b^2 - 17*a^3*b^4 + a*b^6)*cos(d*x + c)^2 - 3*((2*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3 - 2*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)*sin(d*x + c) - (2*a^5*b + 5*a^3*b^3 + 3*a*b^5)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 2*(2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 - (11*a^4*b^3 - 7*a^2*b^5 - 4*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c)), -1/2*(2*a^7 - 6*a^5*b^2 + 6*a^3*b^4 - 2*a*b^6 + (16*a^5*b^2 - 17*a^3*b^4 + a*b^6)*cos(d*x + c)^2 + 3*((2*a^3*b^3 + 3*a*b^5)*cos(d*x + c)^3 - 2*(2*a^4*b^2 + 3*a^2*b^4)*cos(d*x + c)*sin(d*x + c) - (2*a^5*b + 5*a^3*b^3 + 3*a*b^5)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - (2*a^6*b - 6*a^4*b^3 + 6*a^2*b^5 - 2*b^7 - (11*a^4*b^3 - 7*a^2*b^5 - 4*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*d*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*d*cos(d*x + c))]","B",0
1475,1,1623,0,6.104195," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{10} - 12 \, a^{8} b^{2} + 12 \, a^{6} b^{4} - 4 \, a^{4} b^{6} + 2 \, {\left(10 \, a^{8} b^{2} - 2 \, a^{6} b^{4} - 11 \, a^{4} b^{6} + 3 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} - {\left({\left(20 \, a^{4} b^{5} - 7 \, a^{2} b^{7} + 2 \, b^{9}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(20 \, a^{5} b^{4} - 7 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(20 \, a^{6} b^{3} + 13 \, a^{4} b^{5} - 5 \, a^{2} b^{7} + 2 \, b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) + 2 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, a^{9} b - 6 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 2 \, a^{3} b^{7} - {\left(6 \, a^{7} b^{3} + 5 \, a^{5} b^{5} - 13 \, a^{3} b^{7} + 2 \, a b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{11} b^{2} - 4 \, a^{9} b^{4} + 6 \, a^{7} b^{6} - 4 \, a^{5} b^{8} + a^{3} b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{12} b - 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} - 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{13} - 3 \, a^{11} b^{2} + 2 \, a^{9} b^{4} + 2 \, a^{7} b^{6} - 3 \, a^{5} b^{8} + a^{3} b^{10}\right)} d \cos\left(d x + c\right)\right)}}, -\frac{2 \, a^{10} - 6 \, a^{8} b^{2} + 6 \, a^{6} b^{4} - 2 \, a^{4} b^{6} + {\left(10 \, a^{8} b^{2} - 2 \, a^{6} b^{4} - 11 \, a^{4} b^{6} + 3 \, a^{2} b^{8}\right)} \cos\left(d x + c\right)^{2} + {\left({\left(20 \, a^{4} b^{5} - 7 \, a^{2} b^{7} + 2 \, b^{9}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(20 \, a^{5} b^{4} - 7 \, a^{3} b^{6} + 2 \, a b^{8}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(20 \, a^{6} b^{3} + 13 \, a^{4} b^{5} - 5 \, a^{2} b^{7} + 2 \, b^{9}\right)} \cos\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) + {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left({\left(a^{8} b^{2} - 4 \, a^{6} b^{4} + 6 \, a^{4} b^{6} - 4 \, a^{2} b^{8} + b^{10}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b - 4 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 4 \, a^{3} b^{7} + a b^{9}\right)} \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{10} - 3 \, a^{8} b^{2} + 2 \, a^{6} b^{4} + 2 \, a^{4} b^{6} - 3 \, a^{2} b^{8} + b^{10}\right)} \cos\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(2 \, a^{9} b - 6 \, a^{7} b^{3} + 6 \, a^{5} b^{5} - 2 \, a^{3} b^{7} - {\left(6 \, a^{7} b^{3} + 5 \, a^{5} b^{5} - 13 \, a^{3} b^{7} + 2 \, a b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left({\left(a^{11} b^{2} - 4 \, a^{9} b^{4} + 6 \, a^{7} b^{6} - 4 \, a^{5} b^{8} + a^{3} b^{10}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{12} b - 4 \, a^{10} b^{3} + 6 \, a^{8} b^{5} - 4 \, a^{6} b^{7} + a^{4} b^{9}\right)} d \cos\left(d x + c\right) \sin\left(d x + c\right) - {\left(a^{13} - 3 \, a^{11} b^{2} + 2 \, a^{9} b^{4} + 2 \, a^{7} b^{6} - 3 \, a^{5} b^{8} + a^{3} b^{10}\right)} d \cos\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^10 - 12*a^8*b^2 + 12*a^6*b^4 - 4*a^4*b^6 + 2*(10*a^8*b^2 - 2*a^6*b^4 - 11*a^4*b^6 + 3*a^2*b^8)*cos(d*x + c)^2 - ((20*a^4*b^5 - 7*a^2*b^7 + 2*b^9)*cos(d*x + c)^3 - 2*(20*a^5*b^4 - 7*a^3*b^6 + 2*a*b^8)*cos(d*x + c)*sin(d*x + c) - (20*a^6*b^3 + 13*a^4*b^5 - 5*a^2*b^7 + 2*b^9)*cos(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) + 2*((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - 2*((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*a^9*b - 6*a^7*b^3 + 6*a^5*b^5 - 2*a^3*b^7 - (6*a^7*b^3 + 5*a^5*b^5 - 13*a^3*b^7 + 2*a*b^9)*cos(d*x + c)^2)*sin(d*x + c))/((a^11*b^2 - 4*a^9*b^4 + 6*a^7*b^6 - 4*a^5*b^8 + a^3*b^10)*d*cos(d*x + c)^3 - 2*(a^12*b - 4*a^10*b^3 + 6*a^8*b^5 - 4*a^6*b^7 + a^4*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^13 - 3*a^11*b^2 + 2*a^9*b^4 + 2*a^7*b^6 - 3*a^5*b^8 + a^3*b^10)*d*cos(d*x + c)), -1/2*(2*a^10 - 6*a^8*b^2 + 6*a^6*b^4 - 2*a^4*b^6 + (10*a^8*b^2 - 2*a^6*b^4 - 11*a^4*b^6 + 3*a^2*b^8)*cos(d*x + c)^2 + ((20*a^4*b^5 - 7*a^2*b^7 + 2*b^9)*cos(d*x + c)^3 - 2*(20*a^5*b^4 - 7*a^3*b^6 + 2*a*b^8)*cos(d*x + c)*sin(d*x + c) - (20*a^6*b^3 + 13*a^4*b^5 - 5*a^2*b^7 + 2*b^9)*cos(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) + ((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*cos(d*x + c))*log(1/2*cos(d*x + c) + 1/2) - ((a^8*b^2 - 4*a^6*b^4 + 6*a^4*b^6 - 4*a^2*b^8 + b^10)*cos(d*x + c)^3 - 2*(a^9*b - 4*a^7*b^3 + 6*a^5*b^5 - 4*a^3*b^7 + a*b^9)*cos(d*x + c)*sin(d*x + c) - (a^10 - 3*a^8*b^2 + 2*a^6*b^4 + 2*a^4*b^6 - 3*a^2*b^8 + b^10)*cos(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - (2*a^9*b - 6*a^7*b^3 + 6*a^5*b^5 - 2*a^3*b^7 - (6*a^7*b^3 + 5*a^5*b^5 - 13*a^3*b^7 + 2*a*b^9)*cos(d*x + c)^2)*sin(d*x + c))/((a^11*b^2 - 4*a^9*b^4 + 6*a^7*b^6 - 4*a^5*b^8 + a^3*b^10)*d*cos(d*x + c)^3 - 2*(a^12*b - 4*a^10*b^3 + 6*a^8*b^5 - 4*a^6*b^7 + a^4*b^9)*d*cos(d*x + c)*sin(d*x + c) - (a^13 - 3*a^11*b^2 + 2*a^9*b^4 + 2*a^7*b^6 - 3*a^5*b^8 + a^3*b^10)*d*cos(d*x + c))]","B",0
1476,1,2140,0,5.468282," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{11} - 12 \, a^{9} b^{2} + 12 \, a^{7} b^{4} - 4 \, a^{5} b^{6} + 2 \, {\left(4 \, a^{9} b^{2} - 4 \, a^{7} b^{4} + 17 \, a^{5} b^{6} - 23 \, a^{3} b^{8} + 6 \, a b^{10}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{11} - 10 \, a^{9} b^{2} + 14 \, a^{7} b^{4} + 7 \, a^{5} b^{6} - 21 \, a^{3} b^{8} + 6 \, a b^{10}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(2 \, {\left(10 \, a^{5} b^{5} - 7 \, a^{3} b^{7} + 2 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(10 \, a^{5} b^{5} - 7 \, a^{3} b^{7} + 2 \, a b^{9}\right)} \cos\left(d x + c\right) + {\left({\left(10 \, a^{4} b^{6} - 7 \, a^{2} b^{8} + 2 \, b^{10}\right)} \cos\left(d x + c\right)^{3} - {\left(10 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - 5 \, a^{2} b^{8} + 2 \, b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 6 \, {\left(2 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} + 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 6 \, {\left(2 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} + 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, a^{10} b - 6 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 2 \, a^{4} b^{7} + {\left(8 \, a^{10} b - 14 \, a^{8} b^{3} + 28 \, a^{6} b^{5} - 31 \, a^{4} b^{7} + 9 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left(2 \, {\left(a^{13} b - 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} - 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{13} b - 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} - 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d \cos\left(d x + c\right) + {\left({\left(a^{12} b^{2} - 4 \, a^{10} b^{4} + 6 \, a^{8} b^{6} - 4 \, a^{6} b^{8} + a^{4} b^{10}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{14} - 3 \, a^{12} b^{2} + 2 \, a^{10} b^{4} + 2 \, a^{8} b^{6} - 3 \, a^{6} b^{8} + a^{4} b^{10}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}, -\frac{2 \, a^{11} - 6 \, a^{9} b^{2} + 6 \, a^{7} b^{4} - 2 \, a^{5} b^{6} + {\left(4 \, a^{9} b^{2} - 4 \, a^{7} b^{4} + 17 \, a^{5} b^{6} - 23 \, a^{3} b^{8} + 6 \, a b^{10}\right)} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{11} - 10 \, a^{9} b^{2} + 14 \, a^{7} b^{4} + 7 \, a^{5} b^{6} - 21 \, a^{3} b^{8} + 6 \, a b^{10}\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(2 \, {\left(10 \, a^{5} b^{5} - 7 \, a^{3} b^{7} + 2 \, a b^{9}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(10 \, a^{5} b^{5} - 7 \, a^{3} b^{7} + 2 \, a b^{9}\right)} \cos\left(d x + c\right) + {\left({\left(10 \, a^{4} b^{6} - 7 \, a^{2} b^{8} + 2 \, b^{10}\right)} \cos\left(d x + c\right)^{3} - {\left(10 \, a^{6} b^{4} + 3 \, a^{4} b^{6} - 5 \, a^{2} b^{8} + 2 \, b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left(2 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} + 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left(2 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{9} b^{2} - 4 \, a^{7} b^{4} + 6 \, a^{5} b^{6} - 4 \, a^{3} b^{8} + a b^{10}\right)} \cos\left(d x + c\right) + {\left({\left(a^{8} b^{3} - 4 \, a^{6} b^{5} + 6 \, a^{4} b^{7} - 4 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{10} b - 3 \, a^{8} b^{3} + 2 \, a^{6} b^{5} + 2 \, a^{4} b^{7} - 3 \, a^{2} b^{9} + b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(2 \, a^{10} b - 6 \, a^{8} b^{3} + 6 \, a^{6} b^{5} - 2 \, a^{4} b^{7} + {\left(8 \, a^{10} b - 14 \, a^{8} b^{3} + 28 \, a^{6} b^{5} - 31 \, a^{4} b^{7} + 9 \, a^{2} b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2 \, {\left(2 \, {\left(a^{13} b - 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} - 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d \cos\left(d x + c\right)^{3} - 2 \, {\left(a^{13} b - 4 \, a^{11} b^{3} + 6 \, a^{9} b^{5} - 4 \, a^{7} b^{7} + a^{5} b^{9}\right)} d \cos\left(d x + c\right) + {\left({\left(a^{12} b^{2} - 4 \, a^{10} b^{4} + 6 \, a^{8} b^{6} - 4 \, a^{6} b^{8} + a^{4} b^{10}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{14} - 3 \, a^{12} b^{2} + 2 \, a^{10} b^{4} + 2 \, a^{8} b^{6} - 3 \, a^{6} b^{8} + a^{4} b^{10}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^11 - 12*a^9*b^2 + 12*a^7*b^4 - 4*a^5*b^6 + 2*(4*a^9*b^2 - 4*a^7*b^4 + 17*a^5*b^6 - 23*a^3*b^8 + 6*a*b^10)*cos(d*x + c)^4 - 2*(4*a^11 - 10*a^9*b^2 + 14*a^7*b^4 + 7*a^5*b^6 - 21*a^3*b^8 + 6*a*b^10)*cos(d*x + c)^2 - 3*(2*(10*a^5*b^5 - 7*a^3*b^7 + 2*a*b^9)*cos(d*x + c)^3 - 2*(10*a^5*b^5 - 7*a^3*b^7 + 2*a*b^9)*cos(d*x + c) + ((10*a^4*b^6 - 7*a^2*b^8 + 2*b^10)*cos(d*x + c)^3 - (10*a^6*b^4 + 3*a^4*b^6 - 5*a^2*b^8 + 2*b^10)*cos(d*x + c))*sin(d*x + c))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 + 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 6*(2*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c)^3 - 2*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c) + ((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*cos(d*x + c)^3 - (a^10*b - 3*a^8*b^3 + 2*a^6*b^5 + 2*a^4*b^7 - 3*a^2*b^9 + b^11)*cos(d*x + c))*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 6*(2*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c)^3 - 2*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c) + ((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*cos(d*x + c)^3 - (a^10*b - 3*a^8*b^3 + 2*a^6*b^5 + 2*a^4*b^7 - 3*a^2*b^9 + b^11)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*a^10*b - 6*a^8*b^3 + 6*a^6*b^5 - 2*a^4*b^7 + (8*a^10*b - 14*a^8*b^3 + 28*a^6*b^5 - 31*a^4*b^7 + 9*a^2*b^9)*cos(d*x + c)^2)*sin(d*x + c))/(2*(a^13*b - 4*a^11*b^3 + 6*a^9*b^5 - 4*a^7*b^7 + a^5*b^9)*d*cos(d*x + c)^3 - 2*(a^13*b - 4*a^11*b^3 + 6*a^9*b^5 - 4*a^7*b^7 + a^5*b^9)*d*cos(d*x + c) + ((a^12*b^2 - 4*a^10*b^4 + 6*a^8*b^6 - 4*a^6*b^8 + a^4*b^10)*d*cos(d*x + c)^3 - (a^14 - 3*a^12*b^2 + 2*a^10*b^4 + 2*a^8*b^6 - 3*a^6*b^8 + a^4*b^10)*d*cos(d*x + c))*sin(d*x + c)), -1/2*(2*a^11 - 6*a^9*b^2 + 6*a^7*b^4 - 2*a^5*b^6 + (4*a^9*b^2 - 4*a^7*b^4 + 17*a^5*b^6 - 23*a^3*b^8 + 6*a*b^10)*cos(d*x + c)^4 - (4*a^11 - 10*a^9*b^2 + 14*a^7*b^4 + 7*a^5*b^6 - 21*a^3*b^8 + 6*a*b^10)*cos(d*x + c)^2 - 3*(2*(10*a^5*b^5 - 7*a^3*b^7 + 2*a*b^9)*cos(d*x + c)^3 - 2*(10*a^5*b^5 - 7*a^3*b^7 + 2*a*b^9)*cos(d*x + c) + ((10*a^4*b^6 - 7*a^2*b^8 + 2*b^10)*cos(d*x + c)^3 - (10*a^6*b^4 + 3*a^4*b^6 - 5*a^2*b^8 + 2*b^10)*cos(d*x + c))*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*(2*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c)^3 - 2*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c) + ((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*cos(d*x + c)^3 - (a^10*b - 3*a^8*b^3 + 2*a^6*b^5 + 2*a^4*b^7 - 3*a^2*b^9 + b^11)*cos(d*x + c))*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*(2*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c)^3 - 2*(a^9*b^2 - 4*a^7*b^4 + 6*a^5*b^6 - 4*a^3*b^8 + a*b^10)*cos(d*x + c) + ((a^8*b^3 - 4*a^6*b^5 + 6*a^4*b^7 - 4*a^2*b^9 + b^11)*cos(d*x + c)^3 - (a^10*b - 3*a^8*b^3 + 2*a^6*b^5 + 2*a^4*b^7 - 3*a^2*b^9 + b^11)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - (2*a^10*b - 6*a^8*b^3 + 6*a^6*b^5 - 2*a^4*b^7 + (8*a^10*b - 14*a^8*b^3 + 28*a^6*b^5 - 31*a^4*b^7 + 9*a^2*b^9)*cos(d*x + c)^2)*sin(d*x + c))/(2*(a^13*b - 4*a^11*b^3 + 6*a^9*b^5 - 4*a^7*b^7 + a^5*b^9)*d*cos(d*x + c)^3 - 2*(a^13*b - 4*a^11*b^3 + 6*a^9*b^5 - 4*a^7*b^7 + a^5*b^9)*d*cos(d*x + c) + ((a^12*b^2 - 4*a^10*b^4 + 6*a^8*b^6 - 4*a^6*b^8 + a^4*b^10)*d*cos(d*x + c)^3 - (a^14 - 3*a^12*b^2 + 2*a^10*b^4 + 2*a^8*b^6 - 3*a^6*b^8 + a^4*b^10)*d*cos(d*x + c))*sin(d*x + c))]","B",0
1477,1,2672,0,9.293741," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\left[\frac{4 \, a^{12} - 12 \, a^{10} b^{2} + 12 \, a^{8} b^{4} - 4 \, a^{6} b^{6} - 2 \, {\left(21 \, a^{10} b^{2} - 56 \, a^{8} b^{4} + 82 \, a^{6} b^{6} - 65 \, a^{4} b^{8} + 18 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{12} - 31 \, a^{10} b^{2} + 68 \, a^{8} b^{4} - 88 \, a^{6} b^{6} + 66 \, a^{4} b^{8} - 18 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} + 3 \, {\left({\left(14 \, a^{4} b^{7} - 13 \, a^{2} b^{9} + 4 \, b^{11}\right)} \cos\left(d x + c\right)^{5} - {\left(14 \, a^{6} b^{5} + 15 \, a^{4} b^{7} - 22 \, a^{2} b^{9} + 8 \, b^{11}\right)} \cos\left(d x + c\right)^{3} + {\left(14 \, a^{6} b^{5} + a^{4} b^{7} - 9 \, a^{2} b^{9} + 4 \, b^{11}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(14 \, a^{5} b^{6} - 13 \, a^{3} b^{8} + 4 \, a b^{10}\right)} \cos\left(d x + c\right)^{3} - {\left(14 \, a^{5} b^{6} - 13 \, a^{3} b^{8} + 4 \, a b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(-\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2} - 2 \, {\left(a \cos\left(d x + c\right) \sin\left(d x + c\right) + b \cos\left(d x + c\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(d x + c\right)^{2} - 2 \, a b \sin\left(d x + c\right) - a^{2} - b^{2}}\right) - 3 \, {\left({\left(a^{10} b^{2} - 10 \, a^{6} b^{6} + 20 \, a^{4} b^{8} - 15 \, a^{2} b^{10} + 4 \, b^{12}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{12} + 2 \, a^{10} b^{2} - 10 \, a^{8} b^{4} + 25 \, a^{4} b^{8} - 26 \, a^{2} b^{10} + 8 \, b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{12} + a^{10} b^{2} - 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 11 \, a^{2} b^{10} + 4 \, b^{12}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{11} b - 10 \, a^{7} b^{5} + 20 \, a^{5} b^{7} - 15 \, a^{3} b^{9} + 4 \, a b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{11} b - 10 \, a^{7} b^{5} + 20 \, a^{5} b^{7} - 15 \, a^{3} b^{9} + 4 \, a b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(a^{10} b^{2} - 10 \, a^{6} b^{6} + 20 \, a^{4} b^{8} - 15 \, a^{2} b^{10} + 4 \, b^{12}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{12} + 2 \, a^{10} b^{2} - 10 \, a^{8} b^{4} + 25 \, a^{4} b^{8} - 26 \, a^{2} b^{10} + 8 \, b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{12} + a^{10} b^{2} - 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 11 \, a^{2} b^{10} + 4 \, b^{12}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{11} b - 10 \, a^{7} b^{5} + 20 \, a^{5} b^{7} - 15 \, a^{3} b^{9} + 4 \, a b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{11} b - 10 \, a^{7} b^{5} + 20 \, a^{5} b^{7} - 15 \, a^{3} b^{9} + 4 \, a b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, a^{11} b - 6 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 2 \, a^{5} b^{7} + {\left(12 \, a^{9} b^{3} - 28 \, a^{7} b^{5} + 47 \, a^{5} b^{7} - 43 \, a^{3} b^{9} + 12 \, a b^{11}\right)} \cos\left(d x + c\right)^{4} - {\left(6 \, a^{11} b - 10 \, a^{9} b^{3} + 2 \, a^{7} b^{5} + 29 \, a^{5} b^{7} - 39 \, a^{3} b^{9} + 12 \, a b^{11}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{13} b^{2} - 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} - 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right)^{5} - {\left(a^{15} - 2 \, a^{13} b^{2} - 2 \, a^{11} b^{4} + 8 \, a^{9} b^{6} - 7 \, a^{7} b^{8} + 2 \, a^{5} b^{10}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{15} - 3 \, a^{13} b^{2} + 2 \, a^{11} b^{4} + 2 \, a^{9} b^{6} - 3 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right) - 2 \, {\left({\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}, \frac{4 \, a^{12} - 12 \, a^{10} b^{2} + 12 \, a^{8} b^{4} - 4 \, a^{6} b^{6} - 2 \, {\left(21 \, a^{10} b^{2} - 56 \, a^{8} b^{4} + 82 \, a^{6} b^{6} - 65 \, a^{4} b^{8} + 18 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{12} - 31 \, a^{10} b^{2} + 68 \, a^{8} b^{4} - 88 \, a^{6} b^{6} + 66 \, a^{4} b^{8} - 18 \, a^{2} b^{10}\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left({\left(14 \, a^{4} b^{7} - 13 \, a^{2} b^{9} + 4 \, b^{11}\right)} \cos\left(d x + c\right)^{5} - {\left(14 \, a^{6} b^{5} + 15 \, a^{4} b^{7} - 22 \, a^{2} b^{9} + 8 \, b^{11}\right)} \cos\left(d x + c\right)^{3} + {\left(14 \, a^{6} b^{5} + a^{4} b^{7} - 9 \, a^{2} b^{9} + 4 \, b^{11}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(14 \, a^{5} b^{6} - 13 \, a^{3} b^{8} + 4 \, a b^{10}\right)} \cos\left(d x + c\right)^{3} - {\left(14 \, a^{5} b^{6} - 13 \, a^{3} b^{8} + 4 \, a b^{10}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(d x + c\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(d x + c\right)}\right) - 3 \, {\left({\left(a^{10} b^{2} - 10 \, a^{6} b^{6} + 20 \, a^{4} b^{8} - 15 \, a^{2} b^{10} + 4 \, b^{12}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{12} + 2 \, a^{10} b^{2} - 10 \, a^{8} b^{4} + 25 \, a^{4} b^{8} - 26 \, a^{2} b^{10} + 8 \, b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{12} + a^{10} b^{2} - 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 11 \, a^{2} b^{10} + 4 \, b^{12}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{11} b - 10 \, a^{7} b^{5} + 20 \, a^{5} b^{7} - 15 \, a^{3} b^{9} + 4 \, a b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{11} b - 10 \, a^{7} b^{5} + 20 \, a^{5} b^{7} - 15 \, a^{3} b^{9} + 4 \, a b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 3 \, {\left({\left(a^{10} b^{2} - 10 \, a^{6} b^{6} + 20 \, a^{4} b^{8} - 15 \, a^{2} b^{10} + 4 \, b^{12}\right)} \cos\left(d x + c\right)^{5} - {\left(a^{12} + 2 \, a^{10} b^{2} - 10 \, a^{8} b^{4} + 25 \, a^{4} b^{8} - 26 \, a^{2} b^{10} + 8 \, b^{12}\right)} \cos\left(d x + c\right)^{3} + {\left(a^{12} + a^{10} b^{2} - 10 \, a^{8} b^{4} + 10 \, a^{6} b^{6} + 5 \, a^{4} b^{8} - 11 \, a^{2} b^{10} + 4 \, b^{12}\right)} \cos\left(d x + c\right) - 2 \, {\left({\left(a^{11} b - 10 \, a^{7} b^{5} + 20 \, a^{5} b^{7} - 15 \, a^{3} b^{9} + 4 \, a b^{11}\right)} \cos\left(d x + c\right)^{3} - {\left(a^{11} b - 10 \, a^{7} b^{5} + 20 \, a^{5} b^{7} - 15 \, a^{3} b^{9} + 4 \, a b^{11}\right)} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(2 \, a^{11} b - 6 \, a^{9} b^{3} + 6 \, a^{7} b^{5} - 2 \, a^{5} b^{7} + {\left(12 \, a^{9} b^{3} - 28 \, a^{7} b^{5} + 47 \, a^{5} b^{7} - 43 \, a^{3} b^{9} + 12 \, a b^{11}\right)} \cos\left(d x + c\right)^{4} - {\left(6 \, a^{11} b - 10 \, a^{9} b^{3} + 2 \, a^{7} b^{5} + 29 \, a^{5} b^{7} - 39 \, a^{3} b^{9} + 12 \, a b^{11}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{13} b^{2} - 4 \, a^{11} b^{4} + 6 \, a^{9} b^{6} - 4 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right)^{5} - {\left(a^{15} - 2 \, a^{13} b^{2} - 2 \, a^{11} b^{4} + 8 \, a^{9} b^{6} - 7 \, a^{7} b^{8} + 2 \, a^{5} b^{10}\right)} d \cos\left(d x + c\right)^{3} + {\left(a^{15} - 3 \, a^{13} b^{2} + 2 \, a^{11} b^{4} + 2 \, a^{9} b^{6} - 3 \, a^{7} b^{8} + a^{5} b^{10}\right)} d \cos\left(d x + c\right) - 2 \, {\left({\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right)^{3} - {\left(a^{14} b - 4 \, a^{12} b^{3} + 6 \, a^{10} b^{5} - 4 \, a^{8} b^{7} + a^{6} b^{9}\right)} d \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a^12 - 12*a^10*b^2 + 12*a^8*b^4 - 4*a^6*b^6 - 2*(21*a^10*b^2 - 56*a^8*b^4 + 82*a^6*b^6 - 65*a^4*b^8 + 18*a^2*b^10)*cos(d*x + c)^4 - 2*(3*a^12 - 31*a^10*b^2 + 68*a^8*b^4 - 88*a^6*b^6 + 66*a^4*b^8 - 18*a^2*b^10)*cos(d*x + c)^2 + 3*((14*a^4*b^7 - 13*a^2*b^9 + 4*b^11)*cos(d*x + c)^5 - (14*a^6*b^5 + 15*a^4*b^7 - 22*a^2*b^9 + 8*b^11)*cos(d*x + c)^3 + (14*a^6*b^5 + a^4*b^7 - 9*a^2*b^9 + 4*b^11)*cos(d*x + c) - 2*((14*a^5*b^6 - 13*a^3*b^8 + 4*a*b^10)*cos(d*x + c)^3 - (14*a^5*b^6 - 13*a^3*b^8 + 4*a*b^10)*cos(d*x + c))*sin(d*x + c))*sqrt(-a^2 + b^2)*log(-((2*a^2 - b^2)*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2 - 2*(a*cos(d*x + c)*sin(d*x + c) + b*cos(d*x + c))*sqrt(-a^2 + b^2))/(b^2*cos(d*x + c)^2 - 2*a*b*sin(d*x + c) - a^2 - b^2)) - 3*((a^10*b^2 - 10*a^6*b^6 + 20*a^4*b^8 - 15*a^2*b^10 + 4*b^12)*cos(d*x + c)^5 - (a^12 + 2*a^10*b^2 - 10*a^8*b^4 + 25*a^4*b^8 - 26*a^2*b^10 + 8*b^12)*cos(d*x + c)^3 + (a^12 + a^10*b^2 - 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 - 11*a^2*b^10 + 4*b^12)*cos(d*x + c) - 2*((a^11*b - 10*a^7*b^5 + 20*a^5*b^7 - 15*a^3*b^9 + 4*a*b^11)*cos(d*x + c)^3 - (a^11*b - 10*a^7*b^5 + 20*a^5*b^7 - 15*a^3*b^9 + 4*a*b^11)*cos(d*x + c))*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*((a^10*b^2 - 10*a^6*b^6 + 20*a^4*b^8 - 15*a^2*b^10 + 4*b^12)*cos(d*x + c)^5 - (a^12 + 2*a^10*b^2 - 10*a^8*b^4 + 25*a^4*b^8 - 26*a^2*b^10 + 8*b^12)*cos(d*x + c)^3 + (a^12 + a^10*b^2 - 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 - 11*a^2*b^10 + 4*b^12)*cos(d*x + c) - 2*((a^11*b - 10*a^7*b^5 + 20*a^5*b^7 - 15*a^3*b^9 + 4*a*b^11)*cos(d*x + c)^3 - (a^11*b - 10*a^7*b^5 + 20*a^5*b^7 - 15*a^3*b^9 + 4*a*b^11)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*a^11*b - 6*a^9*b^3 + 6*a^7*b^5 - 2*a^5*b^7 + (12*a^9*b^3 - 28*a^7*b^5 + 47*a^5*b^7 - 43*a^3*b^9 + 12*a*b^11)*cos(d*x + c)^4 - (6*a^11*b - 10*a^9*b^3 + 2*a^7*b^5 + 29*a^5*b^7 - 39*a^3*b^9 + 12*a*b^11)*cos(d*x + c)^2)*sin(d*x + c))/((a^13*b^2 - 4*a^11*b^4 + 6*a^9*b^6 - 4*a^7*b^8 + a^5*b^10)*d*cos(d*x + c)^5 - (a^15 - 2*a^13*b^2 - 2*a^11*b^4 + 8*a^9*b^6 - 7*a^7*b^8 + 2*a^5*b^10)*d*cos(d*x + c)^3 + (a^15 - 3*a^13*b^2 + 2*a^11*b^4 + 2*a^9*b^6 - 3*a^7*b^8 + a^5*b^10)*d*cos(d*x + c) - 2*((a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c)^3 - (a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c))*sin(d*x + c)), 1/4*(4*a^12 - 12*a^10*b^2 + 12*a^8*b^4 - 4*a^6*b^6 - 2*(21*a^10*b^2 - 56*a^8*b^4 + 82*a^6*b^6 - 65*a^4*b^8 + 18*a^2*b^10)*cos(d*x + c)^4 - 2*(3*a^12 - 31*a^10*b^2 + 68*a^8*b^4 - 88*a^6*b^6 + 66*a^4*b^8 - 18*a^2*b^10)*cos(d*x + c)^2 - 6*((14*a^4*b^7 - 13*a^2*b^9 + 4*b^11)*cos(d*x + c)^5 - (14*a^6*b^5 + 15*a^4*b^7 - 22*a^2*b^9 + 8*b^11)*cos(d*x + c)^3 + (14*a^6*b^5 + a^4*b^7 - 9*a^2*b^9 + 4*b^11)*cos(d*x + c) - 2*((14*a^5*b^6 - 13*a^3*b^8 + 4*a*b^10)*cos(d*x + c)^3 - (14*a^5*b^6 - 13*a^3*b^8 + 4*a*b^10)*cos(d*x + c))*sin(d*x + c))*sqrt(a^2 - b^2)*arctan(-(a*sin(d*x + c) + b)/(sqrt(a^2 - b^2)*cos(d*x + c))) - 3*((a^10*b^2 - 10*a^6*b^6 + 20*a^4*b^8 - 15*a^2*b^10 + 4*b^12)*cos(d*x + c)^5 - (a^12 + 2*a^10*b^2 - 10*a^8*b^4 + 25*a^4*b^8 - 26*a^2*b^10 + 8*b^12)*cos(d*x + c)^3 + (a^12 + a^10*b^2 - 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 - 11*a^2*b^10 + 4*b^12)*cos(d*x + c) - 2*((a^11*b - 10*a^7*b^5 + 20*a^5*b^7 - 15*a^3*b^9 + 4*a*b^11)*cos(d*x + c)^3 - (a^11*b - 10*a^7*b^5 + 20*a^5*b^7 - 15*a^3*b^9 + 4*a*b^11)*cos(d*x + c))*sin(d*x + c))*log(1/2*cos(d*x + c) + 1/2) + 3*((a^10*b^2 - 10*a^6*b^6 + 20*a^4*b^8 - 15*a^2*b^10 + 4*b^12)*cos(d*x + c)^5 - (a^12 + 2*a^10*b^2 - 10*a^8*b^4 + 25*a^4*b^8 - 26*a^2*b^10 + 8*b^12)*cos(d*x + c)^3 + (a^12 + a^10*b^2 - 10*a^8*b^4 + 10*a^6*b^6 + 5*a^4*b^8 - 11*a^2*b^10 + 4*b^12)*cos(d*x + c) - 2*((a^11*b - 10*a^7*b^5 + 20*a^5*b^7 - 15*a^3*b^9 + 4*a*b^11)*cos(d*x + c)^3 - (a^11*b - 10*a^7*b^5 + 20*a^5*b^7 - 15*a^3*b^9 + 4*a*b^11)*cos(d*x + c))*sin(d*x + c))*log(-1/2*cos(d*x + c) + 1/2) - 2*(2*a^11*b - 6*a^9*b^3 + 6*a^7*b^5 - 2*a^5*b^7 + (12*a^9*b^3 - 28*a^7*b^5 + 47*a^5*b^7 - 43*a^3*b^9 + 12*a*b^11)*cos(d*x + c)^4 - (6*a^11*b - 10*a^9*b^3 + 2*a^7*b^5 + 29*a^5*b^7 - 39*a^3*b^9 + 12*a*b^11)*cos(d*x + c)^2)*sin(d*x + c))/((a^13*b^2 - 4*a^11*b^4 + 6*a^9*b^6 - 4*a^7*b^8 + a^5*b^10)*d*cos(d*x + c)^5 - (a^15 - 2*a^13*b^2 - 2*a^11*b^4 + 8*a^9*b^6 - 7*a^7*b^8 + 2*a^5*b^10)*d*cos(d*x + c)^3 + (a^15 - 3*a^13*b^2 + 2*a^11*b^4 + 2*a^9*b^6 - 3*a^7*b^8 + a^5*b^10)*d*cos(d*x + c) - 2*((a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c)^3 - (a^14*b - 4*a^12*b^3 + 6*a^10*b^5 - 4*a^8*b^7 + a^6*b^9)*d*cos(d*x + c))*sin(d*x + c))]","B",0
1478,0,0,0,0.952856," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e))^(1/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right)} \sec\left(f x + e\right)^{2}}{d \sin\left(f x + e\right)}, x\right)"," ",0,"integral(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))*sec(f*x + e)^2/(d*sin(f*x + e)), x)","F",0
1479,0,0,0,0.851694," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b \sec\left(f x + e\right)^{2} \sin\left(f x + e\right) + a \sec\left(f x + e\right)^{2}\right)} \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right)}}{d \sin\left(f x + e\right)}, x\right)"," ",0,"integral((b*sec(f*x + e)^2*sin(f*x + e) + a*sec(f*x + e)^2)*sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))/(d*sin(f*x + e)), x)","F",0
1480,0,0,0,0.912954," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(2 \, a b \sec\left(f x + e\right)^{4} \sin\left(f x + e\right) - {\left(b^{2} \cos\left(f x + e\right)^{2} - a^{2} - b^{2}\right)} \sec\left(f x + e\right)^{4}\right)} \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right)}}{d \sin\left(f x + e\right)}, x\right)"," ",0,"integral((2*a*b*sec(f*x + e)^4*sin(f*x + e) - (b^2*cos(f*x + e)^2 - a^2 - b^2)*sec(f*x + e)^4)*sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))/(d*sin(f*x + e)), x)","F",0
1481,1,149,0,0.733091," ","integrate(sec(d*x+c)^5*sin(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{24 \, a \cos\left(d x + c\right)^{6} - 3 \, {\left(24 \, a - 35 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(24 \, a + 35 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 12 \, a \cos\left(d x + c\right)^{4} - 72 \, a \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, b \cos\left(d x + c\right)^{6} - 80 \, b \cos\left(d x + c\right)^{4} - 39 \, b \cos\left(d x + c\right)^{2} + 6 \, b\right)} \sin\left(d x + c\right) + 12 \, a}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(24*a*cos(d*x + c)^6 - 3*(24*a - 35*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(24*a + 35*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 12*a*cos(d*x + c)^4 - 72*a*cos(d*x + c)^2 + 2*(8*b*cos(d*x + c)^6 - 80*b*cos(d*x + c)^4 - 39*b*cos(d*x + c)^2 + 6*b)*sin(d*x + c) + 12*a)/(d*cos(d*x + c)^4)","A",0
1482,1,138,0,0.886173," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{8 \, b \cos\left(d x + c\right)^{6} + 3 \, {\left(5 \, a - 8 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, a + 8 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 4 \, b \cos\left(d x + c\right)^{4} - 24 \, b \cos\left(d x + c\right)^{2} - 2 \, {\left(8 \, a \cos\left(d x + c\right)^{4} + 9 \, a \cos\left(d x + c\right)^{2} - 2 \, a\right)} \sin\left(d x + c\right) + 4 \, b}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(8*b*cos(d*x + c)^6 + 3*(5*a - 8*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(5*a + 8*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 4*b*cos(d*x + c)^4 - 24*b*cos(d*x + c)^2 - 2*(8*a*cos(d*x + c)^4 + 9*a*cos(d*x + c)^2 - 2*a)*sin(d*x + c) + 4*b)/(d*cos(d*x + c)^4)","A",0
1483,1,114,0,0.945915," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(8 \, a - 15 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(8 \, a + 15 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 16 \, a \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, b \cos\left(d x + c\right)^{4} + 9 \, b \cos\left(d x + c\right)^{2} - 2 \, b\right)} \sin\left(d x + c\right) - 4 \, a}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*((8*a - 15*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) + (8*a + 15*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 16*a*cos(d*x + c)^2 + 2*(8*b*cos(d*x + c)^4 + 9*b*cos(d*x + c)^2 - 2*b)*sin(d*x + c) - 4*a)/(d*cos(d*x + c)^4)","A",0
1484,1,104,0,0.943909," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, a - 8 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, a + 8 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 16 \, b \cos\left(d x + c\right)^{2} - 2 \, {\left(5 \, a \cos\left(d x + c\right)^{2} - 2 \, a\right)} \sin\left(d x + c\right) + 4 \, b}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*((3*a - 8*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (3*a + 8*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 16*b*cos(d*x + c)^2 - 2*(5*a*cos(d*x + c)^2 - 2*a)*sin(d*x + c) + 4*b)/(d*cos(d*x + c)^4)","A",0
1485,1,93,0,0.964930," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, b \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, b \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 8 \, a \cos\left(d x + c\right)^{2} - 2 \, {\left(5 \, b \cos\left(d x + c\right)^{2} - 2 \, b\right)} \sin\left(d x + c\right) + 4 \, a}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(3*b*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*b*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 8*a*cos(d*x + c)^2 - 2*(5*b*cos(d*x + c)^2 - 2*b)*sin(d*x + c) + 4*a)/(d*cos(d*x + c)^4)","A",0
1486,1,91,0,0.633475," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{a \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - a \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, b \cos\left(d x + c\right)^{2} + 2 \, {\left(a \cos\left(d x + c\right)^{2} - 2 \, a\right)} \sin\left(d x + c\right) - 4 \, b}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*(a*cos(d*x + c)^4*log(sin(d*x + c) + 1) - a*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 8*b*cos(d*x + c)^2 + 2*(a*cos(d*x + c)^2 - 2*a)*sin(d*x + c) - 4*b)/(d*cos(d*x + c)^4)","A",0
1487,1,80,0,0.892448," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{b \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - b \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(b \cos\left(d x + c\right)^{2} - 2 \, b\right)} \sin\left(d x + c\right) - 4 \, a}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*(b*cos(d*x + c)^4*log(sin(d*x + c) + 1) - b*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 2*(b*cos(d*x + c)^2 - 2*b)*sin(d*x + c) - 4*a)/(d*cos(d*x + c)^4)","A",0
1488,1,125,0,0.959878," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, a \cos\left(d x + c\right)^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(8 \, a - 3 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(8 \, a + 3 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, a \cos\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cos\left(d x + c\right)^{2} + 2 \, b\right)} \sin\left(d x + c\right) + 4 \, a}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*a*cos(d*x + c)^4*log(1/2*sin(d*x + c)) - (8*a - 3*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (8*a + 3*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 8*a*cos(d*x + c)^2 + 2*(3*b*cos(d*x + c)^2 + 2*b)*sin(d*x + c) + 4*a)/(d*cos(d*x + c)^4)","A",0
1489,1,159,0,1.000072," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, b \cos\left(d x + c\right)^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(15 \, a - 8 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - {\left(15 \, a + 8 \, b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 30 \, a \cos\left(d x + c\right)^{4} + 10 \, a \cos\left(d x + c\right)^{2} + 4 \, {\left(2 \, b \cos\left(d x + c\right)^{2} + b\right)} \sin\left(d x + c\right) + 4 \, a}{16 \, d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}"," ",0,"1/16*(16*b*cos(d*x + c)^4*log(1/2*sin(d*x + c))*sin(d*x + c) + (15*a - 8*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1)*sin(d*x + c) - (15*a + 8*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1)*sin(d*x + c) - 30*a*cos(d*x + c)^4 + 10*a*cos(d*x + c)^2 + 4*(2*b*cos(d*x + c)^2 + b)*sin(d*x + c) + 4*a)/(d*cos(d*x + c)^4*sin(d*x + c))","A",0
1490,1,211,0,1.017462," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{24 \, a \cos\left(d x + c\right)^{4} - 12 \, a \cos\left(d x + c\right)^{2} + 48 \, {\left(a \cos\left(d x + c\right)^{6} - a \cos\left(d x + c\right)^{4}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 3 \, {\left({\left(8 \, a - 5 \, b\right)} \cos\left(d x + c\right)^{6} - {\left(8 \, a - 5 \, b\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(8 \, a + 5 \, b\right)} \cos\left(d x + c\right)^{6} - {\left(8 \, a + 5 \, b\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(15 \, b \cos\left(d x + c\right)^{4} - 5 \, b \cos\left(d x + c\right)^{2} - 2 \, b\right)} \sin\left(d x + c\right) - 4 \, a}{16 \, {\left(d \cos\left(d x + c\right)^{6} - d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/16*(24*a*cos(d*x + c)^4 - 12*a*cos(d*x + c)^2 + 48*(a*cos(d*x + c)^6 - a*cos(d*x + c)^4)*log(1/2*sin(d*x + c)) - 3*((8*a - 5*b)*cos(d*x + c)^6 - (8*a - 5*b)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - 3*((8*a + 5*b)*cos(d*x + c)^6 - (8*a + 5*b)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) + 2*(15*b*cos(d*x + c)^4 - 5*b*cos(d*x + c)^2 - 2*b)*sin(d*x + c) - 4*a)/(d*cos(d*x + c)^6 - d*cos(d*x + c)^4)","A",0
1491,1,248,0,0.900706," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{210 \, a \cos\left(d x + c\right)^{6} - 280 \, a \cos\left(d x + c\right)^{4} + 42 \, a \cos\left(d x + c\right)^{2} - 144 \, {\left(b \cos\left(d x + c\right)^{6} - b \cos\left(d x + c\right)^{4}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) - 3 \, {\left({\left(35 \, a - 24 \, b\right)} \cos\left(d x + c\right)^{6} - {\left(35 \, a - 24 \, b\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) + 3 \, {\left({\left(35 \, a + 24 \, b\right)} \cos\left(d x + c\right)^{6} - {\left(35 \, a + 24 \, b\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 12 \, {\left(6 \, b \cos\left(d x + c\right)^{4} - 3 \, b \cos\left(d x + c\right)^{2} - b\right)} \sin\left(d x + c\right) + 12 \, a}{48 \, {\left(d \cos\left(d x + c\right)^{6} - d \cos\left(d x + c\right)^{4}\right)} \sin\left(d x + c\right)}"," ",0,"-1/48*(210*a*cos(d*x + c)^6 - 280*a*cos(d*x + c)^4 + 42*a*cos(d*x + c)^2 - 144*(b*cos(d*x + c)^6 - b*cos(d*x + c)^4)*log(1/2*sin(d*x + c))*sin(d*x + c) - 3*((35*a - 24*b)*cos(d*x + c)^6 - (35*a - 24*b)*cos(d*x + c)^4)*log(sin(d*x + c) + 1)*sin(d*x + c) + 3*((35*a + 24*b)*cos(d*x + c)^6 - (35*a + 24*b)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1)*sin(d*x + c) - 12*(6*b*cos(d*x + c)^4 - 3*b*cos(d*x + c)^2 - b)*sin(d*x + c) + 12*a)/((d*cos(d*x + c)^6 - d*cos(d*x + c)^4)*sin(d*x + c))","A",0
1492,1,198,0,1.030029," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{48 \, a b \cos\left(d x + c\right)^{6} - 24 \, a b \cos\left(d x + c\right)^{4} + 3 \, {\left(15 \, a^{2} - 48 \, a b + 35 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(15 \, a^{2} + 48 \, a b + 35 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 144 \, a b \cos\left(d x + c\right)^{2} + 24 \, a b + 2 \, {\left(8 \, b^{2} \cos\left(d x + c\right)^{6} - 8 \, {\left(3 \, a^{2} + 10 \, b^{2}\right)} \cos\left(d x + c\right)^{4} - 3 \, {\left(9 \, a^{2} + 13 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 6 \, a^{2} + 6 \, b^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(48*a*b*cos(d*x + c)^6 - 24*a*b*cos(d*x + c)^4 + 3*(15*a^2 - 48*a*b + 35*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(15*a^2 + 48*a*b + 35*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 144*a*b*cos(d*x + c)^2 + 24*a*b + 2*(8*b^2*cos(d*x + c)^6 - 8*(3*a^2 + 10*b^2)*cos(d*x + c)^4 - 3*(9*a^2 + 13*b^2)*cos(d*x + c)^2 + 6*a^2 + 6*b^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1493,1,178,0,0.998831," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, b^{2} \cos\left(d x + c\right)^{6} - 2 \, b^{2} \cos\left(d x + c\right)^{4} - {\left(4 \, a^{2} - 15 \, a b + 12 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 4 \, {\left(2 \, a^{2} + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, b^{2} - 2 \, {\left(8 \, a b \cos\left(d x + c\right)^{4} + 9 \, a b \cos\left(d x + c\right)^{2} - 2 \, a b\right)} \sin\left(d x + c\right)}{8 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/8*(4*b^2*cos(d*x + c)^6 - 2*b^2*cos(d*x + c)^4 - (4*a^2 - 15*a*b + 12*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (4*a^2 + 15*a*b + 12*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 4*(2*a^2 + 3*b^2)*cos(d*x + c)^2 + 2*a^2 + 2*b^2 - 2*(8*a*b*cos(d*x + c)^4 + 9*a*b*cos(d*x + c)^2 - 2*a*b)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1494,1,151,0,0.962646," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} - 16 \, a b + 15 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, a^{2} + 16 \, a b + 15 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 32 \, a b \cos\left(d x + c\right)^{2} + 8 \, a b - 2 \, {\left(8 \, b^{2} \cos\left(d x + c\right)^{4} + {\left(5 \, a^{2} + 9 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*((3*a^2 - 16*a*b + 15*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (3*a^2 + 16*a*b + 15*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 32*a*b*cos(d*x + c)^2 + 8*a*b - 2*(8*b^2*cos(d*x + c)^4 + (5*a^2 + 9*b^2)*cos(d*x + c)^2 - 2*a^2 - 2*b^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1495,1,127,0,0.946847," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{{\left(3 \, a b - 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, a b + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 4 \, {\left(a^{2} + 2 \, b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, b^{2} - 2 \, {\left(5 \, a b \cos\left(d x + c\right)^{2} - 2 \, a b\right)} \sin\left(d x + c\right)}{8 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/8*((3*a*b - 4*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (3*a*b + 4*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 4*(a^2 + 2*b^2)*cos(d*x + c)^2 + 2*a^2 + 2*b^2 - 2*(5*a*b*cos(d*x + c)^2 - 2*a*b)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1496,1,124,0,0.755859," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} - 3 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 16 \, a b \cos\left(d x + c\right)^{2} - 8 \, a b + 2 \, {\left({\left(a^{2} + 5 \, b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*((a^2 - 3*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (a^2 - 3*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 16*a*b*cos(d*x + c)^2 - 8*a*b + 2*((a^2 + 5*b^2)*cos(d*x + c)^2 - 2*a^2 - 2*b^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1497,1,104,0,0.852082," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{a b \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - a b \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, b^{2} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - 2 \, b^{2} + 2 \, {\left(a b \cos\left(d x + c\right)^{2} - 2 \, a b\right)} \sin\left(d x + c\right)}{8 \, d \cos\left(d x + c\right)^{4}}"," ",0,"-1/8*(a*b*cos(d*x + c)^4*log(sin(d*x + c) + 1) - a*b*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*b^2*cos(d*x + c)^2 - 2*a^2 - 2*b^2 + 2*(a*b*cos(d*x + c)^2 - 2*a*b)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1498,1,144,0,0.748690," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{8 \, a^{2} \cos\left(d x + c\right)^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(4 \, a^{2} - 3 \, a b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(4 \, a^{2} + 3 \, a b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a^{2} \cos\left(d x + c\right)^{2} + 2 \, a^{2} + 2 \, b^{2} + 2 \, {\left(3 \, a b \cos\left(d x + c\right)^{2} + 2 \, a b\right)} \sin\left(d x + c\right)}{8 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/8*(8*a^2*cos(d*x + c)^4*log(1/2*sin(d*x + c)) - (4*a^2 - 3*a*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (4*a^2 + 3*a*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*a^2*cos(d*x + c)^2 + 2*a^2 + 2*b^2 + 2*(3*a*b*cos(d*x + c)^2 + 2*a*b)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1499,1,202,0,0.912906," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{32 \, a b \cos\left(d x + c\right)^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + {\left(15 \, a^{2} - 16 \, a b + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - {\left(15 \, a^{2} + 16 \, a b + 3 \, b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 6 \, {\left(5 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, a^{2} + 4 \, b^{2} + 8 \, {\left(2 \, a b \cos\left(d x + c\right)^{2} + a b\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}"," ",0,"1/16*(32*a*b*cos(d*x + c)^4*log(1/2*sin(d*x + c))*sin(d*x + c) + (15*a^2 - 16*a*b + 3*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1)*sin(d*x + c) - (15*a^2 + 16*a*b + 3*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1)*sin(d*x + c) - 6*(5*a^2 + b^2)*cos(d*x + c)^4 + 2*(5*a^2 + b^2)*cos(d*x + c)^2 + 4*a^2 + 4*b^2 + 8*(2*a*b*cos(d*x + c)^2 + a*b)*sin(d*x + c))/(d*cos(d*x + c)^4*sin(d*x + c))","A",0
1500,1,285,0,1.018808," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, a^{2} - 2 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{6} - {\left(3 \, a^{2} + b^{2}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left({\left(12 \, a^{2} - 15 \, a b + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - {\left(12 \, a^{2} - 15 \, a b + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(12 \, a^{2} + 15 \, a b + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{6} - {\left(12 \, a^{2} + 15 \, a b + 4 \, b^{2}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(15 \, a b \cos\left(d x + c\right)^{4} - 5 \, a b \cos\left(d x + c\right)^{2} - 2 \, a b\right)} \sin\left(d x + c\right)}{8 \, {\left(d \cos\left(d x + c\right)^{6} - d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/8*(4*(3*a^2 + b^2)*cos(d*x + c)^4 - 2*(3*a^2 + b^2)*cos(d*x + c)^2 - 2*a^2 - 2*b^2 + 8*((3*a^2 + b^2)*cos(d*x + c)^6 - (3*a^2 + b^2)*cos(d*x + c)^4)*log(1/2*sin(d*x + c)) - ((12*a^2 - 15*a*b + 4*b^2)*cos(d*x + c)^6 - (12*a^2 - 15*a*b + 4*b^2)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - ((12*a^2 + 15*a*b + 4*b^2)*cos(d*x + c)^6 - (12*a^2 + 15*a*b + 4*b^2)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) + 2*(15*a*b*cos(d*x + c)^4 - 5*a*b*cos(d*x + c)^2 - 2*a*b)*sin(d*x + c))/(d*cos(d*x + c)^6 - d*cos(d*x + c)^4)","A",0
1501,1,238,0,1.096046," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{72 \, a b^{2} \cos\left(d x + c\right)^{6} - 36 \, a b^{2} \cos\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 45 \, a^{2} b + 72 \, a b^{2} - 35 \, b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(8 \, a^{3} + 45 \, a^{2} b + 72 \, a b^{2} + 35 \, b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 12 \, a^{3} + 36 \, a b^{2} - 24 \, {\left(2 \, a^{3} + 9 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, b^{3} \cos\left(d x + c\right)^{6} - 8 \, {\left(9 \, a^{2} b + 10 \, b^{3}\right)} \cos\left(d x + c\right)^{4} + 18 \, a^{2} b + 6 \, b^{3} - 3 \, {\left(27 \, a^{2} b + 13 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{48 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/48*(72*a*b^2*cos(d*x + c)^6 - 36*a*b^2*cos(d*x + c)^4 - 3*(8*a^3 - 45*a^2*b + 72*a*b^2 - 35*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(8*a^3 + 45*a^2*b + 72*a*b^2 + 35*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 12*a^3 + 36*a*b^2 - 24*(2*a^3 + 9*a*b^2)*cos(d*x + c)^2 + 2*(8*b^3*cos(d*x + c)^6 - 8*(9*a^2*b + 10*b^3)*cos(d*x + c)^4 + 18*a^2*b + 6*b^3 - 3*(27*a^2*b + 13*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1502,1,208,0,0.741681," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{8 \, b^{3} \cos\left(d x + c\right)^{6} - 4 \, b^{3} \cos\left(d x + c\right)^{4} + 3 \, {\left(a^{3} - 8 \, a^{2} b + 15 \, a b^{2} - 8 \, b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{3} + 8 \, a^{2} b + 15 \, a b^{2} + 8 \, b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 12 \, a^{2} b + 4 \, b^{3} - 24 \, {\left(2 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(24 \, a b^{2} \cos\left(d x + c\right)^{4} - 2 \, a^{3} - 6 \, a b^{2} + {\left(5 \, a^{3} + 27 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(8*b^3*cos(d*x + c)^6 - 4*b^3*cos(d*x + c)^4 + 3*(a^3 - 8*a^2*b + 15*a*b^2 - 8*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(a^3 + 8*a^2*b + 15*a*b^2 + 8*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 12*a^2*b + 4*b^3 - 24*(2*a^2*b + b^3)*cos(d*x + c)^2 - 2*(24*a*b^2*cos(d*x + c)^4 - 2*a^3 - 6*a*b^2 + (5*a^3 + 27*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1503,1,176,0,0.777176," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{3 \, {\left(3 \, a^{2} b - 8 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, a^{3} + 12 \, a b^{2} - 8 \, {\left(a^{3} + 6 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(8 \, b^{3} \cos\left(d x + c\right)^{4} - 6 \, a^{2} b - 2 \, b^{3} + 3 \, {\left(5 \, a^{2} b + 3 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(3*(3*a^2*b - 8*a*b^2 + 5*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(3*a^2*b + 8*a*b^2 + 5*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*a^3 + 12*a*b^2 - 8*(a^3 + 6*a*b^2)*cos(d*x + c)^2 - 2*(8*b^3*cos(d*x + c)^4 - 6*a^2*b - 2*b^3 + 3*(5*a^2*b + 3*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1504,1,156,0,0.978233," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(a^{3} - 9 \, a b^{2} + 8 \, b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{3} - 9 \, a b^{2} - 8 \, b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 12 \, a^{2} b - 4 \, b^{3} + 8 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \cos\left(d x + c\right)^{2} - 2 \, {\left(2 \, a^{3} + 6 \, a b^{2} - {\left(a^{3} + 15 \, a b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*((a^3 - 9*a*b^2 + 8*b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (a^3 - 9*a*b^2 - 8*b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 12*a^2*b - 4*b^3 + 8*(3*a^2*b + 2*b^3)*cos(d*x + c)^2 - 2*(2*a^3 + 6*a*b^2 - (a^3 + 15*a*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1505,1,143,0,0.985911," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 24 \, a b^{2} \cos\left(d x + c\right)^{2} - 4 \, a^{3} - 12 \, a b^{2} - 2 \, {\left(6 \, a^{2} b + 2 \, b^{3} - {\left(3 \, a^{2} b + 5 \, b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"-1/16*(3*(a^2*b - b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - 3*(a^2*b - b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 24*a*b^2*cos(d*x + c)^2 - 4*a^3 - 12*a*b^2 - 2*(6*a^2*b + 2*b^3 - (3*a^2*b + 5*b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1506,1,173,0,0.998470," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{16 \, a^{3} \cos\left(d x + c\right)^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - {\left(8 \, a^{3} - 9 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(8 \, a^{3} + 9 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 8 \, a^{3} \cos\left(d x + c\right)^{2} + 4 \, a^{3} + 12 \, a b^{2} + 2 \, {\left(6 \, a^{2} b + 2 \, b^{3} + {\left(9 \, a^{2} b - b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(16*a^3*cos(d*x + c)^4*log(1/2*sin(d*x + c)) - (8*a^3 - 9*a^2*b + b^3)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (8*a^3 + 9*a^2*b - b^3)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 8*a^3*cos(d*x + c)^2 + 4*a^3 + 12*a*b^2 + 2*(6*a^2*b + 2*b^3 + (9*a^2*b - b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1507,1,226,0,1.034591," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{48 \, a^{2} b \cos\left(d x + c\right)^{4} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) \sin\left(d x + c\right) + 3 \, {\left(5 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 3 \, {\left(5 \, a^{3} + 8 \, a^{2} b + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) \sin\left(d x + c\right) - 6 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{4} + 4 \, a^{3} + 12 \, a b^{2} + 2 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(6 \, a^{2} b \cos\left(d x + c\right)^{2} + 3 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}"," ",0,"1/16*(48*a^2*b*cos(d*x + c)^4*log(1/2*sin(d*x + c))*sin(d*x + c) + 3*(5*a^3 - 8*a^2*b + 3*a*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1)*sin(d*x + c) - 3*(5*a^3 + 8*a^2*b + 3*a*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1)*sin(d*x + c) - 6*(5*a^3 + 3*a*b^2)*cos(d*x + c)^4 + 4*a^3 + 12*a*b^2 + 2*(5*a^3 + 3*a*b^2)*cos(d*x + c)^2 + 4*(6*a^2*b*cos(d*x + c)^2 + 3*a^2*b + b^3)*sin(d*x + c))/(d*cos(d*x + c)^4*sin(d*x + c))","A",0
1508,1,337,0,0.985947," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{24 \, {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, a^{3} - 12 \, a b^{2} - 12 \, {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{2} + 48 \, {\left({\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{6} - {\left(a^{3} + a b^{2}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\frac{1}{2} \, \sin\left(d x + c\right)\right) - 3 \, {\left({\left(8 \, a^{3} - 15 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{6} - {\left(8 \, a^{3} - 15 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(8 \, a^{3} + 15 \, a^{2} b + 8 \, a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{6} - {\left(8 \, a^{3} + 15 \, a^{2} b + 8 \, a b^{2} + b^{3}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(3 \, {\left(15 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{4} - 6 \, a^{2} b - 2 \, b^{3} - {\left(15 \, a^{2} b + b^{3}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(d \cos\left(d x + c\right)^{6} - d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/16*(24*(a^3 + a*b^2)*cos(d*x + c)^4 - 4*a^3 - 12*a*b^2 - 12*(a^3 + a*b^2)*cos(d*x + c)^2 + 48*((a^3 + a*b^2)*cos(d*x + c)^6 - (a^3 + a*b^2)*cos(d*x + c)^4)*log(1/2*sin(d*x + c)) - 3*((8*a^3 - 15*a^2*b + 8*a*b^2 - b^3)*cos(d*x + c)^6 - (8*a^3 - 15*a^2*b + 8*a*b^2 - b^3)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - 3*((8*a^3 + 15*a^2*b + 8*a*b^2 + b^3)*cos(d*x + c)^6 - (8*a^3 + 15*a^2*b + 8*a*b^2 + b^3)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) + 2*(3*(15*a^2*b + b^3)*cos(d*x + c)^4 - 6*a^2*b - 2*b^3 - (15*a^2*b + b^3)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6 - d*cos(d*x + c)^4)","A",0
1509,0,0,0,0.924840," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^4,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(4 \, {\left(a b^{3} \cos\left(d x + c\right)^{2} - a^{3} b - a b^{3}\right)} \sec\left(d x + c\right)^{5} \sin\left(d x + c\right) - {\left(b^{4} \cos\left(d x + c\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \sec\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-(4*(a*b^3*cos(d*x + c)^2 - a^3*b - a*b^3)*sec(d*x + c)^5*sin(d*x + c) - (b^4*cos(d*x + c)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(d*x + c)^2)*sec(d*x + c)^5)*sin(d*x + c)^n, x)","F",0
1510,0,0,0,0.964121," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left({\left(b^{3} \cos\left(d x + c\right)^{2} - 3 \, a^{2} b - b^{3}\right)} \sec\left(d x + c\right)^{5} \sin\left(d x + c\right) + {\left(3 \, a b^{2} \cos\left(d x + c\right)^{2} - a^{3} - 3 \, a b^{2}\right)} \sec\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral(-((b^3*cos(d*x + c)^2 - 3*a^2*b - b^3)*sec(d*x + c)^5*sin(d*x + c) + (3*a*b^2*cos(d*x + c)^2 - a^3 - 3*a*b^2)*sec(d*x + c)^5)*sin(d*x + c)^n, x)","F",0
1511,0,0,0,0.952701," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, a b \sec\left(d x + c\right)^{5} \sin\left(d x + c\right) - {\left(b^{2} \cos\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \sec\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral((2*a*b*sec(d*x + c)^5*sin(d*x + c) - (b^2*cos(d*x + c)^2 - a^2 - b^2)*sec(d*x + c)^5)*sin(d*x + c)^n, x)","F",0
1512,0,0,0,0.870670," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sec\left(d x + c\right)^{5} \sin\left(d x + c\right) + a \sec\left(d x + c\right)^{5}\right)} \sin\left(d x + c\right)^{n}, x\right)"," ",0,"integral((b*sec(d*x + c)^5*sin(d*x + c) + a*sec(d*x + c)^5)*sin(d*x + c)^n, x)","F",0
1513,0,0,0,0.937199," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}}{b \sin\left(d x + c\right) + a}, x\right)"," ",0,"integral(sin(d*x + c)^n*sec(d*x + c)^5/(b*sin(d*x + c) + a), x)","F",0
1514,0,0,0,2.782728," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(d x + c\right) + a\right)}^{p} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}, x\right)"," ",0,"integral((b*sin(d*x + c) + a)^p*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1515,0,0,0,1.088552," ","integrate(sec(f*x+e)^6*(a+b*sin(f*x+e))^(9/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(4 \, {\left(a b^{3} \cos\left(f x + e\right)^{2} - a^{3} b - a b^{3}\right)} \sec\left(f x + e\right)^{6} \sin\left(f x + e\right) - {\left(b^{4} \cos\left(f x + e\right)^{4} + a^{4} + 6 \, a^{2} b^{2} + b^{4} - 2 \, {\left(3 \, a^{2} b^{2} + b^{4}\right)} \cos\left(f x + e\right)^{2}\right)} \sec\left(f x + e\right)^{6}\right)} \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right)}}{d \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(4*(a*b^3*cos(f*x + e)^2 - a^3*b - a*b^3)*sec(f*x + e)^6*sin(f*x + e) - (b^4*cos(f*x + e)^4 + a^4 + 6*a^2*b^2 + b^4 - 2*(3*a^2*b^2 + b^4)*cos(f*x + e)^2)*sec(f*x + e)^6)*sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))/(d*sin(f*x + e)), x)","F",0
1516,0,0,0,1.175599," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(-{\left({\left(b^{2} c + 2 \, a b d\right)} \cos\left(f x + e\right)^{4} - {\left(2 \, a b d + {\left(a^{2} + b^{2}\right)} c\right)} \cos\left(f x + e\right)^{2} + {\left(b^{2} d \cos\left(f x + e\right)^{4} - {\left(2 \, a b c + {\left(a^{2} + b^{2}\right)} d\right)} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral(-((b^2*c + 2*a*b*d)*cos(f*x + e)^4 - (2*a*b*d + (a^2 + b^2)*c)*cos(f*x + e)^2 + (b^2*d*cos(f*x + e)^4 - (2*a*b*c + (a^2 + b^2)*d)*cos(f*x + e)^2)*sin(f*x + e))*(d*sin(f*x + e) + c)^(1/3), x)","F",0
1517,0,0,0,0.850751," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b d \cos\left(f x + e\right)^{4} - {\left(b c + a d\right)} \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - {\left(a c + b d\right)} \cos\left(f x + e\right)^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral(-(b*d*cos(f*x + e)^4 - (b*c + a*d)*cos(f*x + e)^2*sin(f*x + e) - (a*c + b*d)*cos(f*x + e)^2)*(d*sin(f*x + e) + c)^(1/3), x)","F",0
1518,0,0,0,0.998770," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(d \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) + c \cos\left(f x + e\right)^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{1}{3}}, x\right)"," ",0,"integral((d*cos(f*x + e)^2*sin(f*x + e) + c*cos(f*x + e)^2)*(d*sin(f*x + e) + c)^(1/3), 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, algorithm=""fricas"")","\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, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1521,0,0,0,6.362863," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1522,0,0,0,2.462221," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(4/3),x, algorithm=""fricas"")","{\rm integral}\left({\left(d \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) + c \cos\left(f x + e\right)^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{1}{3}} {\left(b \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((d*cos(f*x + e)^2*sin(f*x + e) + c*cos(f*x + e)^2)*(d*sin(f*x + e) + c)^(1/3)*(b*sin(f*x + e) + a)^m, x)","F",0
1523,0,0,0,1.275660," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(b^{2} \cos\left(f x + e\right)^{4} - 2 \, a b \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) - {\left(a^{2} + b^{2}\right)} \cos\left(f x + e\right)^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(b^2*cos(f*x + e)^4 - 2*a*b*cos(f*x + e)^2*sin(f*x + e) - (a^2 + b^2)*cos(f*x + e)^2)*(d*sin(f*x + e) + c)^n, x)","F",0
1524,0,0,0,1.203192," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cos\left(f x + e\right)^{2} \sin\left(f x + e\right) + a \cos\left(f x + e\right)^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((b*cos(f*x + e)^2*sin(f*x + e) + a*cos(f*x + e)^2)*(d*sin(f*x + e) + c)^n, x)","F",0
1525,0,0,0,1.126384," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}, x\right)"," ",0,"integral((d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1526,0,0,0,1.054068," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1527,0,0,0,1.510438," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{b^{2} \cos\left(f x + e\right)^{2} - 2 \, a b \sin\left(f x + e\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(b^2*cos(f*x + e)^2 - 2*a*b*sin(f*x + e) - a^2 - b^2), x)","F",0
1528,1,106,0,0.750295," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{315 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{8} + 8 \, {\left(35 \, B b \cos\left(d x + c\right)^{8} - 5 \, {\left(9 \, A a + B b\right)} \cos\left(d x + c\right)^{6} - 6 \, {\left(9 \, A a + B b\right)} \cos\left(d x + c\right)^{4} - 8 \, {\left(9 \, A a + B b\right)} \cos\left(d x + c\right)^{2} - 144 \, A a - 16 \, B b\right)} \sin\left(d x + c\right)}{2520 \, d}"," ",0,"-1/2520*(315*(B*a + A*b)*cos(d*x + c)^8 + 8*(35*B*b*cos(d*x + c)^8 - 5*(9*A*a + B*b)*cos(d*x + c)^6 - 6*(9*A*a + B*b)*cos(d*x + c)^4 - 8*(9*A*a + B*b)*cos(d*x + c)^2 - 144*A*a - 16*B*b)*sin(d*x + c))/d","A",0
1529,1,88,0,0.953522," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{35 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(15 \, B b \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, A a + B b\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(7 \, A a + B b\right)} \cos\left(d x + c\right)^{2} - 56 \, A a - 8 \, B b\right)} \sin\left(d x + c\right)}{210 \, d}"," ",0,"-1/210*(35*(B*a + A*b)*cos(d*x + c)^6 + 2*(15*B*b*cos(d*x + c)^6 - 3*(7*A*a + B*b)*cos(d*x + c)^4 - 4*(7*A*a + B*b)*cos(d*x + c)^2 - 56*A*a - 8*B*b)*sin(d*x + c))/d","A",0
1530,1,70,0,1.003508," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(3 \, B b \cos\left(d x + c\right)^{4} - {\left(5 \, A a + B b\right)} \cos\left(d x + c\right)^{2} - 10 \, A a - 2 \, B b\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(15*(B*a + A*b)*cos(d*x + c)^4 + 4*(3*B*b*cos(d*x + c)^4 - (5*A*a + B*b)*cos(d*x + c)^2 - 10*A*a - 2*B*b)*sin(d*x + c))/d","A",0
1531,1,51,0,0.998995," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(B a + A b\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(B b \cos\left(d x + c\right)^{2} - 3 \, A a - B b\right)} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(3*(B*a + A*b)*cos(d*x + c)^2 + 2*(B*b*cos(d*x + c)^2 - 3*A*a - B*b)*sin(d*x + c))/d","A",0
1532,1,66,0,0.947948," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, B b \sin\left(d x + c\right) - {\left({\left(A - B\right)} a - {\left(A - B\right)} b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A + B\right)} a + {\left(A + B\right)} b\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, d}"," ",0,"-1/2*(2*B*b*sin(d*x + c) - ((A - B)*a - (A - B)*b)*log(sin(d*x + c) + 1) + ((A + B)*a + (A + B)*b)*log(-sin(d*x + c) + 1))/d","A",0
1533,1,92,0,0.951842," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(A a - B b\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a - B b\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B a + 2 \, A b + 2 \, {\left(A a + B b\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((A*a - B*b)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a - B*b)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*B*a + 2*A*b + 2*(A*a + B*b)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
1534,1,114,0,0.912119," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, A a - B b\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A a - B b\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) + 4 \, B a + 4 \, A b + 2 \, {\left({\left(3 \, A a - B b\right)} \cos\left(d x + c\right)^{2} + 2 \, A a + 2 \, B b\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*((3*A*a - B*b)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (3*A*a - B*b)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) + 4*B*a + 4*A*b + 2*((3*A*a - B*b)*cos(d*x + c)^2 + 2*A*a + 2*B*b)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1535,1,135,0,0.907033," ","integrate(sec(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, A a - B b\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A a - B b\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 16 \, B a + 16 \, A b + 2 \, {\left(3 \, {\left(5 \, A a - B b\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, A a - B b\right)} \cos\left(d x + c\right)^{2} + 8 \, A a + 8 \, B b\right)} \sin\left(d x + c\right)}{96 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/96*(3*(5*A*a - B*b)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 3*(5*A*a - B*b)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 16*B*a + 16*A*b + 2*(3*(5*A*a - B*b)*cos(d*x + c)^4 + 2*(5*A*a - B*b)*cos(d*x + c)^2 + 8*A*a + 8*B*b)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
1536,1,174,0,0.702092," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{252 \, B b^{2} \cos\left(d x + c\right)^{10} - 315 \, {\left(B a^{2} + 2 \, A a b + B b^{2}\right)} \cos\left(d x + c\right)^{8} - 8 \, {\left(35 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{8} - 5 \, {\left(9 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{6} - 6 \, {\left(9 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{4} - 144 \, A a^{2} - 32 \, B a b - 16 \, A b^{2} - 8 \, {\left(9 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{2520 \, d}"," ",0,"1/2520*(252*B*b^2*cos(d*x + c)^10 - 315*(B*a^2 + 2*A*a*b + B*b^2)*cos(d*x + c)^8 - 8*(35*(2*B*a*b + A*b^2)*cos(d*x + c)^8 - 5*(9*A*a^2 + 2*B*a*b + A*b^2)*cos(d*x + c)^6 - 6*(9*A*a^2 + 2*B*a*b + A*b^2)*cos(d*x + c)^4 - 144*A*a^2 - 32*B*a*b - 16*A*b^2 - 8*(9*A*a^2 + 2*B*a*b + A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
1537,1,147,0,0.970416," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{105 \, B b^{2} \cos\left(d x + c\right)^{8} - 140 \, {\left(B a^{2} + 2 \, A a b + B b^{2}\right)} \cos\left(d x + c\right)^{6} - 8 \, {\left(15 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{6} - 3 \, {\left(7 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{4} - 56 \, A a^{2} - 16 \, B a b - 8 \, A b^{2} - 4 \, {\left(7 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*B*b^2*cos(d*x + c)^8 - 140*(B*a^2 + 2*A*a*b + B*b^2)*cos(d*x + c)^6 - 8*(15*(2*B*a*b + A*b^2)*cos(d*x + c)^6 - 3*(7*A*a^2 + 2*B*a*b + A*b^2)*cos(d*x + c)^4 - 56*A*a^2 - 16*B*a*b - 8*A*b^2 - 4*(7*A*a^2 + 2*B*a*b + A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
1538,1,120,0,0.987839," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{10 \, B b^{2} \cos\left(d x + c\right)^{6} - 15 \, {\left(B a^{2} + 2 \, A a b + B b^{2}\right)} \cos\left(d x + c\right)^{4} - 4 \, {\left(3 \, {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{4} - 10 \, A a^{2} - 4 \, B a b - 2 \, A b^{2} - {\left(5 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*B*b^2*cos(d*x + c)^6 - 15*(B*a^2 + 2*A*a*b + B*b^2)*cos(d*x + c)^4 - 4*(3*(2*B*a*b + A*b^2)*cos(d*x + c)^4 - 10*A*a^2 - 4*B*a*b - 2*A*b^2 - (5*A*a^2 + 2*B*a*b + A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
1539,1,92,0,1.036640," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, B b^{2} \cos\left(d x + c\right)^{4} - 6 \, {\left(B a^{2} + 2 \, A a b + B b^{2}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(3 \, A a^{2} + 2 \, B a b + A b^{2} - {\left(2 \, B a b + A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*b^2*cos(d*x + c)^4 - 6*(B*a^2 + 2*A*a*b + B*b^2)*cos(d*x + c)^2 + 4*(3*A*a^2 + 2*B*a*b + A*b^2 - (2*B*a*b + A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/d","A",0
1540,1,111,0,1.116819," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{B b^{2} \cos\left(d x + c\right)^{2} + {\left({\left(A - B\right)} a^{2} - 2 \, {\left(A - B\right)} a b + {\left(A - B\right)} b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A + B\right)} a^{2} + 2 \, {\left(A + B\right)} a b + {\left(A + B\right)} b^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) - 2 \, {\left(2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(B*b^2*cos(d*x + c)^2 + ((A - B)*a^2 - 2*(A - B)*a*b + (A - B)*b^2)*log(sin(d*x + c) + 1) - ((A + B)*a^2 + 2*(A + B)*a*b + (A + B)*b^2)*log(-sin(d*x + c) + 1) - 2*(2*B*a*b + A*b^2)*sin(d*x + c))/d","A",0
1541,1,136,0,1.205073," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(A a^{2} - 2 \, B a b - {\left(A - 2 \, B\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{2} - 2 \, B a b - {\left(A + 2 \, B\right)} b^{2}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, B a^{2} + 4 \, A a b + 2 \, B b^{2} + 2 \, {\left(A a^{2} + 2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)}{4 \, d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*((A*a^2 - 2*B*a*b - (A - 2*B)*b^2)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a^2 - 2*B*a*b - (A + 2*B)*b^2)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*B*a^2 + 4*A*a*b + 2*B*b^2 + 2*(A*a^2 + 2*B*a*b + A*b^2)*sin(d*x + c))/(d*cos(d*x + c)^2)","A",0
1542,1,173,0,1.190649," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{{\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 8 \, B b^{2} \cos\left(d x + c\right)^{2} + 4 \, B a^{2} + 8 \, A a b + 4 \, B b^{2} + 2 \, {\left(2 \, A a^{2} + 4 \, B a b + 2 \, A b^{2} + {\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*((3*A*a^2 - 2*B*a*b - A*b^2)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (3*A*a^2 - 2*B*a*b - A*b^2)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 8*B*b^2*cos(d*x + c)^2 + 4*B*a^2 + 8*A*a*b + 4*B*b^2 + 2*(2*A*a^2 + 4*B*a*b + 2*A*b^2 + (3*A*a^2 - 2*B*a*b - A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^4)","A",0
1543,1,203,0,1.122604," ","integrate(sec(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) - 24 \, B b^{2} \cos\left(d x + c\right)^{2} + 16 \, B a^{2} + 32 \, A a b + 16 \, B b^{2} + 2 \, {\left(3 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \cos\left(d x + c\right)^{4} + 8 \, A a^{2} + 16 \, B a b + 8 \, A b^{2} + 2 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{96 \, d \cos\left(d x + c\right)^{6}}"," ",0,"1/96*(3*(5*A*a^2 - 2*B*a*b - A*b^2)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 3*(5*A*a^2 - 2*B*a*b - A*b^2)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) - 24*B*b^2*cos(d*x + c)^2 + 16*B*a^2 + 32*A*a*b + 16*B*b^2 + 2*(3*(5*A*a^2 - 2*B*a*b - A*b^2)*cos(d*x + c)^4 + 8*A*a^2 + 16*B*a*b + 8*A*b^2 + 2*(5*A*a^2 - 2*B*a*b - A*b^2)*cos(d*x + c)^2)*sin(d*x + c))/(d*cos(d*x + c)^6)","A",0
1544,1,366,0,1.089709," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{70 \, {\left(B a b^{6} - A b^{7}\right)} \cos\left(d x + c\right)^{6} - 105 \, {\left(B a^{3} b^{4} - A a^{2} b^{5} - B a b^{6} + A b^{7}\right)} \cos\left(d x + c\right)^{4} + 210 \, {\left(B a^{5} b^{2} - A a^{4} b^{3} - 2 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5} + B a b^{6} - A b^{7}\right)} \cos\left(d x + c\right)^{2} - 420 \, {\left(B a^{7} - A a^{6} b - 3 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3} + 3 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5} - B a b^{6} + A b^{7}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 4 \, {\left(15 \, B b^{7} \cos\left(d x + c\right)^{6} - 105 \, B a^{6} b + 105 \, A a^{5} b^{2} + 280 \, B a^{4} b^{3} - 280 \, A a^{3} b^{4} - 231 \, B a^{2} b^{5} + 231 \, A a b^{6} + 48 \, B b^{7} - 3 \, {\left(7 \, B a^{2} b^{5} - 7 \, A a b^{6} - 6 \, B b^{7}\right)} \cos\left(d x + c\right)^{4} + {\left(35 \, B a^{4} b^{3} - 35 \, A a^{3} b^{4} - 63 \, B a^{2} b^{5} + 63 \, A a b^{6} + 24 \, B b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{420 \, b^{8} d}"," ",0,"-1/420*(70*(B*a*b^6 - A*b^7)*cos(d*x + c)^6 - 105*(B*a^3*b^4 - A*a^2*b^5 - B*a*b^6 + A*b^7)*cos(d*x + c)^4 + 210*(B*a^5*b^2 - A*a^4*b^3 - 2*B*a^3*b^4 + 2*A*a^2*b^5 + B*a*b^6 - A*b^7)*cos(d*x + c)^2 - 420*(B*a^7 - A*a^6*b - 3*B*a^5*b^2 + 3*A*a^4*b^3 + 3*B*a^3*b^4 - 3*A*a^2*b^5 - B*a*b^6 + A*b^7)*log(b*sin(d*x + c) + a) - 4*(15*B*b^7*cos(d*x + c)^6 - 105*B*a^6*b + 105*A*a^5*b^2 + 280*B*a^4*b^3 - 280*A*a^3*b^4 - 231*B*a^2*b^5 + 231*A*a*b^6 + 48*B*b^7 - 3*(7*B*a^2*b^5 - 7*A*a*b^6 - 6*B*b^7)*cos(d*x + c)^4 + (35*B*a^4*b^3 - 35*A*a^3*b^4 - 63*B*a^2*b^5 + 63*A*a*b^6 + 24*B*b^7)*cos(d*x + c)^2)*sin(d*x + c))/(b^8*d)","A",0
1545,1,222,0,1.022592," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{15 \, {\left(B a b^{4} - A b^{5}\right)} \cos\left(d x + c\right)^{4} - 30 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)^{2} + 60 \, {\left(B a^{5} - A a^{4} b - 2 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3} + B a b^{4} - A b^{5}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 4 \, {\left(3 \, B b^{5} \cos\left(d x + c\right)^{4} + 15 \, B a^{4} b - 15 \, A a^{3} b^{2} - 25 \, B a^{2} b^{3} + 25 \, A a b^{4} + 8 \, B b^{5} - {\left(5 \, B a^{2} b^{3} - 5 \, A a b^{4} - 4 \, B b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{60 \, b^{6} d}"," ",0,"-1/60*(15*(B*a*b^4 - A*b^5)*cos(d*x + c)^4 - 30*(B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c)^2 + 60*(B*a^5 - A*a^4*b - 2*B*a^3*b^2 + 2*A*a^2*b^3 + B*a*b^4 - A*b^5)*log(b*sin(d*x + c) + a) - 4*(3*B*b^5*cos(d*x + c)^4 + 15*B*a^4*b - 15*A*a^3*b^2 - 25*B*a^2*b^3 + 25*A*a*b^4 + 8*B*b^5 - (5*B*a^2*b^3 - 5*A*a*b^4 - 4*B*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^6*d)","A",0
1546,1,112,0,0.934039," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{3 \, {\left(B a b^{2} - A b^{3}\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)} \log\left(b \sin\left(d x + c\right) + a\right) - 2 \, {\left(B b^{3} \cos\left(d x + c\right)^{2} - 3 \, B a^{2} b + 3 \, A a b^{2} + 2 \, B b^{3}\right)} \sin\left(d x + c\right)}{6 \, b^{4} d}"," ",0,"-1/6*(3*(B*a*b^2 - A*b^3)*cos(d*x + c)^2 - 6*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*log(b*sin(d*x + c) + a) - 2*(B*b^3*cos(d*x + c)^2 - 3*B*a^2*b + 3*A*a*b^2 + 2*B*b^3)*sin(d*x + c))/(b^4*d)","A",0
1547,1,38,0,0.633030," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{B b \sin\left(d x + c\right) - {\left(B a - A b\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{2} d}"," ",0,"(B*b*sin(d*x + c) - (B*a - A*b)*log(b*sin(d*x + c) + a))/(b^2*d)","A",0
1548,1,88,0,0.859462," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(B a - A b\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left({\left(A - B\right)} a + {\left(A - B\right)} b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A + B\right)} a - {\left(A + B\right)} b\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left(a^{2} - b^{2}\right)} d}"," ",0,"1/2*(2*(B*a - A*b)*log(b*sin(d*x + c) + a) + ((A - B)*a + (A - B)*b)*log(sin(d*x + c) + 1) - ((A + B)*a - (A + B)*b)*log(-sin(d*x + c) + 1))/((a^2 - b^2)*d)","A",0
1549,1,234,0,1.523290," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, B a^{3} - 2 \, A a^{2} b - 2 \, B a b^{2} + 2 \, A b^{3} - 4 \, {\left(B a b^{2} - A b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(A a^{3} + B a^{2} b - {\left(3 \, A - 2 \, B\right)} a b^{2} - {\left(2 \, A - B\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a^{3} + B a^{2} b - {\left(3 \, A + 2 \, B\right)} a b^{2} + {\left(2 \, A + B\right)} b^{3}\right)} \cos\left(d x + c\right)^{2} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{3} - B a^{2} b - A a b^{2} + B b^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cos\left(d x + c\right)^{2}}"," ",0,"1/4*(2*B*a^3 - 2*A*a^2*b - 2*B*a*b^2 + 2*A*b^3 - 4*(B*a*b^2 - A*b^3)*cos(d*x + c)^2*log(b*sin(d*x + c) + a) + (A*a^3 + B*a^2*b - (3*A - 2*B)*a*b^2 - (2*A - B)*b^3)*cos(d*x + c)^2*log(sin(d*x + c) + 1) - (A*a^3 + B*a^2*b - (3*A + 2*B)*a*b^2 + (2*A + B)*b^3)*cos(d*x + c)^2*log(-sin(d*x + c) + 1) + 2*(A*a^3 - B*a^2*b - A*a*b^2 + B*b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cos(d*x + c)^2)","A",0
1550,1,413,0,3.603155," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{4 \, B a^{5} - 4 \, A a^{4} b - 8 \, B a^{3} b^{2} + 8 \, A a^{2} b^{3} + 4 \, B a b^{4} - 4 \, A b^{5} + 16 \, {\left(B a b^{4} - A b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(3 \, A a^{5} + B a^{4} b - 10 \, A a^{3} b^{2} - 6 \, B a^{2} b^{3} + {\left(15 \, A - 8 \, B\right)} a b^{4} + {\left(8 \, A - 3 \, B\right)} b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A a^{5} + B a^{4} b - 10 \, A a^{3} b^{2} - 6 \, B a^{2} b^{3} + {\left(15 \, A + 8 \, B\right)} a b^{4} - {\left(8 \, A + 3 \, B\right)} b^{5}\right)} \cos\left(d x + c\right)^{4} \log\left(-\sin\left(d x + c\right) + 1\right) - 8 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - B a b^{4} + A b^{5}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(2 \, A a^{5} - 2 \, B a^{4} b - 4 \, A a^{3} b^{2} + 4 \, B a^{2} b^{3} + 2 \, A a b^{4} - 2 \, B b^{5} + {\left(3 \, A a^{5} + B a^{4} b - 10 \, A a^{3} b^{2} + 2 \, B a^{2} b^{3} + 7 \, A a b^{4} - 3 \, B b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} d \cos\left(d x + c\right)^{4}}"," ",0,"1/16*(4*B*a^5 - 4*A*a^4*b - 8*B*a^3*b^2 + 8*A*a^2*b^3 + 4*B*a*b^4 - 4*A*b^5 + 16*(B*a*b^4 - A*b^5)*cos(d*x + c)^4*log(b*sin(d*x + c) + a) + (3*A*a^5 + B*a^4*b - 10*A*a^3*b^2 - 6*B*a^2*b^3 + (15*A - 8*B)*a*b^4 + (8*A - 3*B)*b^5)*cos(d*x + c)^4*log(sin(d*x + c) + 1) - (3*A*a^5 + B*a^4*b - 10*A*a^3*b^2 - 6*B*a^2*b^3 + (15*A + 8*B)*a*b^4 - (8*A + 3*B)*b^5)*cos(d*x + c)^4*log(-sin(d*x + c) + 1) - 8*(B*a^3*b^2 - A*a^2*b^3 - B*a*b^4 + A*b^5)*cos(d*x + c)^2 + 2*(2*A*a^5 - 2*B*a^4*b - 4*A*a^3*b^2 + 4*B*a^2*b^3 + 2*A*a*b^4 - 2*B*b^5 + (3*A*a^5 + B*a^4*b - 10*A*a^3*b^2 + 2*B*a^2*b^3 + 7*A*a*b^4 - 3*B*b^5)*cos(d*x + c)^2)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*d*cos(d*x + c)^4)","A",0
1551,1,643,0,8.470583," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""fricas"")","\frac{16 \, B a^{7} - 16 \, A a^{6} b - 48 \, B a^{5} b^{2} + 48 \, A a^{4} b^{3} + 48 \, B a^{3} b^{4} - 48 \, A a^{2} b^{5} - 16 \, B a b^{6} + 16 \, A b^{7} - 96 \, {\left(B a b^{6} - A b^{7}\right)} \cos\left(d x + c\right)^{6} \log\left(b \sin\left(d x + c\right) + a\right) + 3 \, {\left(5 \, A a^{7} + B a^{6} b - 21 \, A a^{5} b^{2} - 5 \, B a^{4} b^{3} + 35 \, A a^{3} b^{4} + 15 \, B a^{2} b^{5} - {\left(35 \, A - 16 \, B\right)} a b^{6} - {\left(16 \, A - 5 \, B\right)} b^{7}\right)} \cos\left(d x + c\right)^{6} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A a^{7} + B a^{6} b - 21 \, A a^{5} b^{2} - 5 \, B a^{4} b^{3} + 35 \, A a^{3} b^{4} + 15 \, B a^{2} b^{5} - {\left(35 \, A + 16 \, B\right)} a b^{6} + {\left(16 \, A + 5 \, B\right)} b^{7}\right)} \cos\left(d x + c\right)^{6} \log\left(-\sin\left(d x + c\right) + 1\right) + 48 \, {\left(B a^{3} b^{4} - A a^{2} b^{5} - B a b^{6} + A b^{7}\right)} \cos\left(d x + c\right)^{4} - 24 \, {\left(B a^{5} b^{2} - A a^{4} b^{3} - 2 \, B a^{3} b^{4} + 2 \, A a^{2} b^{5} + B a b^{6} - A b^{7}\right)} \cos\left(d x + c\right)^{2} + 2 \, {\left(8 \, A a^{7} - 8 \, B a^{6} b - 24 \, A a^{5} b^{2} + 24 \, B a^{4} b^{3} + 24 \, A a^{3} b^{4} - 24 \, B a^{2} b^{5} - 8 \, A a b^{6} + 8 \, B b^{7} + 3 \, {\left(5 \, A a^{7} + B a^{6} b - 21 \, A a^{5} b^{2} - 5 \, B a^{4} b^{3} + 35 \, A a^{3} b^{4} - B a^{2} b^{5} - 19 \, A a b^{6} + 5 \, B b^{7}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, A a^{7} + B a^{6} b - 21 \, A a^{5} b^{2} + 3 \, B a^{4} b^{3} + 27 \, A a^{3} b^{4} - 9 \, B a^{2} b^{5} - 11 \, A a b^{6} + 5 \, B b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{96 \, {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d \cos\left(d x + c\right)^{6}}"," ",0,"1/96*(16*B*a^7 - 16*A*a^6*b - 48*B*a^5*b^2 + 48*A*a^4*b^3 + 48*B*a^3*b^4 - 48*A*a^2*b^5 - 16*B*a*b^6 + 16*A*b^7 - 96*(B*a*b^6 - A*b^7)*cos(d*x + c)^6*log(b*sin(d*x + c) + a) + 3*(5*A*a^7 + B*a^6*b - 21*A*a^5*b^2 - 5*B*a^4*b^3 + 35*A*a^3*b^4 + 15*B*a^2*b^5 - (35*A - 16*B)*a*b^6 - (16*A - 5*B)*b^7)*cos(d*x + c)^6*log(sin(d*x + c) + 1) - 3*(5*A*a^7 + B*a^6*b - 21*A*a^5*b^2 - 5*B*a^4*b^3 + 35*A*a^3*b^4 + 15*B*a^2*b^5 - (35*A + 16*B)*a*b^6 + (16*A + 5*B)*b^7)*cos(d*x + c)^6*log(-sin(d*x + c) + 1) + 48*(B*a^3*b^4 - A*a^2*b^5 - B*a*b^6 + A*b^7)*cos(d*x + c)^4 - 24*(B*a^5*b^2 - A*a^4*b^3 - 2*B*a^3*b^4 + 2*A*a^2*b^5 + B*a*b^6 - A*b^7)*cos(d*x + c)^2 + 2*(8*A*a^7 - 8*B*a^6*b - 24*A*a^5*b^2 + 24*B*a^4*b^3 + 24*A*a^3*b^4 - 24*B*a^2*b^5 - 8*A*a*b^6 + 8*B*b^7 + 3*(5*A*a^7 + B*a^6*b - 21*A*a^5*b^2 - 5*B*a^4*b^3 + 35*A*a^3*b^4 - B*a^2*b^5 - 19*A*a*b^6 + 5*B*b^7)*cos(d*x + c)^4 + 2*(5*A*a^7 + B*a^6*b - 21*A*a^5*b^2 + 3*B*a^4*b^3 + 27*A*a^3*b^4 - 9*B*a^2*b^5 - 11*A*a*b^6 + 5*B*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d*cos(d*x + c)^6)","A",0
1552,1,508,0,1.093380," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{480 \, B a^{7} - 480 \, A a^{6} b - 3720 \, B a^{5} b^{2} + 3360 \, A a^{4} b^{3} + 5705 \, B a^{3} b^{4} - 4710 \, A a^{2} b^{5} - 2402 \, B a b^{6} + 1536 \, A b^{7} + 16 \, {\left(7 \, B a b^{6} - 6 \, A b^{7}\right)} \cos\left(d x + c\right)^{6} - 8 \, {\left(35 \, B a^{3} b^{4} - 30 \, A a^{2} b^{5} - 33 \, B a b^{6} + 24 \, A b^{7}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(105 \, B a^{5} b^{2} - 90 \, A a^{4} b^{3} - 190 \, B a^{3} b^{4} + 150 \, A a^{2} b^{5} + 81 \, B a b^{6} - 48 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 480 \, {\left(7 \, B a^{7} - 6 \, A a^{6} b - 15 \, B a^{5} b^{2} + 12 \, A a^{4} b^{3} + 9 \, B a^{3} b^{4} - 6 \, A a^{2} b^{5} - B a b^{6} + {\left(7 \, B a^{6} b - 6 \, A a^{5} b^{2} - 15 \, B a^{4} b^{3} + 12 \, A a^{3} b^{4} + 9 \, B a^{2} b^{5} - 6 \, A a b^{6} - B b^{7}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(80 \, B b^{7} \cos\left(d x + c\right)^{6} + 2880 \, B a^{6} b - 2400 \, A a^{5} b^{2} - 5720 \, B a^{4} b^{3} + 4320 \, A a^{3} b^{4} + 2967 \, B a^{2} b^{5} - 1626 \, A a b^{6} - 190 \, B b^{7} - 24 \, {\left(7 \, B a^{2} b^{5} - 6 \, A a b^{6} - 5 \, B b^{7}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(35 \, B a^{4} b^{3} - 30 \, A a^{3} b^{4} - 54 \, B a^{2} b^{5} + 42 \, A a b^{6} + 15 \, B b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{480 \, {\left(b^{9} d \sin\left(d x + c\right) + a b^{8} d\right)}}"," ",0,"-1/480*(480*B*a^7 - 480*A*a^6*b - 3720*B*a^5*b^2 + 3360*A*a^4*b^3 + 5705*B*a^3*b^4 - 4710*A*a^2*b^5 - 2402*B*a*b^6 + 1536*A*b^7 + 16*(7*B*a*b^6 - 6*A*b^7)*cos(d*x + c)^6 - 8*(35*B*a^3*b^4 - 30*A*a^2*b^5 - 33*B*a*b^6 + 24*A*b^7)*cos(d*x + c)^4 + 16*(105*B*a^5*b^2 - 90*A*a^4*b^3 - 190*B*a^3*b^4 + 150*A*a^2*b^5 + 81*B*a*b^6 - 48*A*b^7)*cos(d*x + c)^2 + 480*(7*B*a^7 - 6*A*a^6*b - 15*B*a^5*b^2 + 12*A*a^4*b^3 + 9*B*a^3*b^4 - 6*A*a^2*b^5 - B*a*b^6 + (7*B*a^6*b - 6*A*a^5*b^2 - 15*B*a^4*b^3 + 12*A*a^3*b^4 + 9*B*a^2*b^5 - 6*A*a*b^6 - B*b^7)*sin(d*x + c))*log(b*sin(d*x + c) + a) - (80*B*b^7*cos(d*x + c)^6 + 2880*B*a^6*b - 2400*A*a^5*b^2 - 5720*B*a^4*b^3 + 4320*A*a^3*b^4 + 2967*B*a^2*b^5 - 1626*A*a*b^6 - 190*B*b^7 - 24*(7*B*a^2*b^5 - 6*A*a*b^6 - 5*B*b^7)*cos(d*x + c)^4 + 16*(35*B*a^4*b^3 - 30*A*a^3*b^4 - 54*B*a^2*b^5 + 42*A*a*b^6 + 15*B*b^7)*cos(d*x + c)^2)*sin(d*x + c))/(b^9*d*sin(d*x + c) + a*b^8*d)","A",0
1553,1,322,0,1.118294," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{96 \, B a^{5} - 96 \, A a^{4} b - 504 \, B a^{3} b^{2} + 432 \, A a^{2} b^{3} + 383 \, B a b^{4} - 256 \, A b^{5} - 8 \, {\left(5 \, B a b^{4} - 4 \, A b^{5}\right)} \cos\left(d x + c\right)^{4} + 16 \, {\left(15 \, B a^{3} b^{2} - 12 \, A a^{2} b^{3} - 13 \, B a b^{4} + 8 \, A b^{5}\right)} \cos\left(d x + c\right)^{2} + 96 \, {\left(5 \, B a^{5} - 4 \, A a^{4} b - 6 \, B a^{3} b^{2} + 4 \, A a^{2} b^{3} + B a b^{4} + {\left(5 \, B a^{4} b - 4 \, A a^{3} b^{2} - 6 \, B a^{2} b^{3} + 4 \, A a b^{4} + B b^{5}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left(24 \, B b^{5} \cos\left(d x + c\right)^{4} - 384 \, B a^{4} b + 288 \, A a^{3} b^{2} + 392 \, B a^{2} b^{3} - 208 \, A a b^{4} - 33 \, B b^{5} - 16 \, {\left(5 \, B a^{2} b^{3} - 4 \, A a b^{4} - 3 \, B b^{5}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{96 \, {\left(b^{7} d \sin\left(d x + c\right) + a b^{6} d\right)}}"," ",0,"1/96*(96*B*a^5 - 96*A*a^4*b - 504*B*a^3*b^2 + 432*A*a^2*b^3 + 383*B*a*b^4 - 256*A*b^5 - 8*(5*B*a*b^4 - 4*A*b^5)*cos(d*x + c)^4 + 16*(15*B*a^3*b^2 - 12*A*a^2*b^3 - 13*B*a*b^4 + 8*A*b^5)*cos(d*x + c)^2 + 96*(5*B*a^5 - 4*A*a^4*b - 6*B*a^3*b^2 + 4*A*a^2*b^3 + B*a*b^4 + (5*B*a^4*b - 4*A*a^3*b^2 - 6*B*a^2*b^3 + 4*A*a*b^4 + B*b^5)*sin(d*x + c))*log(b*sin(d*x + c) + a) + (24*B*b^5*cos(d*x + c)^4 - 384*B*a^4*b + 288*A*a^3*b^2 + 392*B*a^2*b^3 - 208*A*a*b^4 - 33*B*b^5 - 16*(5*B*a^2*b^3 - 4*A*a*b^4 - 3*B*b^5)*cos(d*x + c)^2)*sin(d*x + c))/(b^7*d*sin(d*x + c) + a*b^6*d)","A",0
1554,1,178,0,0.884384," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{4 \, B a^{3} - 4 \, A a^{2} b - 11 \, B a b^{2} + 8 \, A b^{3} + 2 \, {\left(3 \, B a b^{2} - 2 \, A b^{3}\right)} \cos\left(d x + c\right)^{2} + 4 \, {\left(3 \, B a^{3} - 2 \, A a^{2} b - B a b^{2} + {\left(3 \, B a^{2} b - 2 \, A a b^{2} - B b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) - {\left(2 \, B b^{3} \cos\left(d x + c\right)^{2} + 8 \, B a^{2} b - 4 \, A a b^{2} - B b^{3}\right)} \sin\left(d x + c\right)}{4 \, {\left(b^{5} d \sin\left(d x + c\right) + a b^{4} d\right)}}"," ",0,"-1/4*(4*B*a^3 - 4*A*a^2*b - 11*B*a*b^2 + 8*A*b^3 + 2*(3*B*a*b^2 - 2*A*b^3)*cos(d*x + c)^2 + 4*(3*B*a^3 - 2*A*a^2*b - B*a*b^2 + (3*B*a^2*b - 2*A*a*b^2 - B*b^3)*sin(d*x + c))*log(b*sin(d*x + c) + a) - (2*B*b^3*cos(d*x + c)^2 + 8*B*a^2*b - 4*A*a*b^2 - B*b^3)*sin(d*x + c))/(b^5*d*sin(d*x + c) + a*b^4*d)","A",0
1555,1,54,0,0.934031," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{B a - A b + {\left(B b \sin\left(d x + c\right) + B a\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{3} d \sin\left(d x + c\right) + a b^{2} d}"," ",0,"(B*a - A*b + (B*b*sin(d*x + c) + B*a)*log(b*sin(d*x + c) + a))/(b^3*d*sin(d*x + c) + a*b^2*d)","A",0
1556,1,283,0,1.341404," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","-\frac{2 \, B a^{3} - 2 \, A a^{2} b - 2 \, B a b^{2} + 2 \, A b^{3} - 2 \, {\left(B a^{3} - 2 \, A a^{2} b + B a b^{2} + {\left(B a^{2} b - 2 \, A a b^{2} + B b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(b \sin\left(d x + c\right) + a\right) - {\left({\left(A - B\right)} a^{3} + 2 \, {\left(A - B\right)} a^{2} b + {\left(A - B\right)} a b^{2} + {\left({\left(A - B\right)} a^{2} b + 2 \, {\left(A - B\right)} a b^{2} + {\left(A - B\right)} b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left({\left(A + B\right)} a^{3} - 2 \, {\left(A + B\right)} a^{2} b + {\left(A + B\right)} a b^{2} + {\left({\left(A + B\right)} a^{2} b - 2 \, {\left(A + B\right)} a b^{2} + {\left(A + B\right)} b^{3}\right)} \sin\left(d x + c\right)\right)} \log\left(-\sin\left(d x + c\right) + 1\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} d \sin\left(d x + c\right) + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} d\right)}}"," ",0,"-1/2*(2*B*a^3 - 2*A*a^2*b - 2*B*a*b^2 + 2*A*b^3 - 2*(B*a^3 - 2*A*a^2*b + B*a*b^2 + (B*a^2*b - 2*A*a*b^2 + B*b^3)*sin(d*x + c))*log(b*sin(d*x + c) + a) - ((A - B)*a^3 + 2*(A - B)*a^2*b + (A - B)*a*b^2 + ((A - B)*a^2*b + 2*(A - B)*a*b^2 + (A - B)*b^3)*sin(d*x + c))*log(sin(d*x + c) + 1) + ((A + B)*a^3 - 2*(A + B)*a^2*b + (A + B)*a*b^2 + ((A + B)*a^2*b - 2*(A + B)*a*b^2 + (A + B)*b^3)*sin(d*x + c))*log(-sin(d*x + c) + 1))/((a^4*b - 2*a^2*b^3 + b^5)*d*sin(d*x + c) + (a^5 - 2*a^3*b^2 + a*b^4)*d)","B",0
1557,1,598,0,2.591074," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{2 \, B a^{5} - 2 \, A a^{4} b - 4 \, B a^{3} b^{2} + 4 \, A a^{2} b^{3} + 2 \, B a b^{4} - 2 \, A b^{5} - 2 \, {\left(A a^{4} b - 4 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3} + 4 \, B a b^{4} - 3 \, A b^{5}\right)} \cos\left(d x + c\right)^{2} - 4 \, {\left({\left(3 \, B a^{2} b^{3} - 4 \, A a b^{4} + B b^{5}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(3 \, B a^{3} b^{2} - 4 \, A a^{2} b^{3} + B a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left({\left(A a^{4} b + 2 \, B a^{3} b^{2} - 6 \, {\left(A - B\right)} a^{2} b^{3} - 2 \, {\left(4 \, A - 3 \, B\right)} a b^{4} - {\left(3 \, A - 2 \, B\right)} b^{5}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(A a^{5} + 2 \, B a^{4} b - 6 \, {\left(A - B\right)} a^{3} b^{2} - 2 \, {\left(4 \, A - 3 \, B\right)} a^{2} b^{3} - {\left(3 \, A - 2 \, B\right)} a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(A a^{4} b + 2 \, B a^{3} b^{2} - 6 \, {\left(A + B\right)} a^{2} b^{3} + 2 \, {\left(4 \, A + 3 \, B\right)} a b^{4} - {\left(3 \, A + 2 \, B\right)} b^{5}\right)} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(A a^{5} + 2 \, B a^{4} b - 6 \, {\left(A + B\right)} a^{3} b^{2} + 2 \, {\left(4 \, A + 3 \, B\right)} a^{2} b^{3} - {\left(3 \, A + 2 \, B\right)} a b^{4}\right)} \cos\left(d x + c\right)^{2}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(A a^{5} - B a^{4} b - 2 \, A a^{3} b^{2} + 2 \, B a^{2} b^{3} + A a b^{4} - B b^{5}\right)} \sin\left(d x + c\right)}{4 \, {\left({\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} d \cos\left(d x + c\right)^{2} \sin\left(d x + c\right) + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} d \cos\left(d x + c\right)^{2}\right)}}"," ",0,"1/4*(2*B*a^5 - 2*A*a^4*b - 4*B*a^3*b^2 + 4*A*a^2*b^3 + 2*B*a*b^4 - 2*A*b^5 - 2*(A*a^4*b - 4*B*a^3*b^2 + 2*A*a^2*b^3 + 4*B*a*b^4 - 3*A*b^5)*cos(d*x + c)^2 - 4*((3*B*a^2*b^3 - 4*A*a*b^4 + B*b^5)*cos(d*x + c)^2*sin(d*x + c) + (3*B*a^3*b^2 - 4*A*a^2*b^3 + B*a*b^4)*cos(d*x + c)^2)*log(b*sin(d*x + c) + a) + ((A*a^4*b + 2*B*a^3*b^2 - 6*(A - B)*a^2*b^3 - 2*(4*A - 3*B)*a*b^4 - (3*A - 2*B)*b^5)*cos(d*x + c)^2*sin(d*x + c) + (A*a^5 + 2*B*a^4*b - 6*(A - B)*a^3*b^2 - 2*(4*A - 3*B)*a^2*b^3 - (3*A - 2*B)*a*b^4)*cos(d*x + c)^2)*log(sin(d*x + c) + 1) - ((A*a^4*b + 2*B*a^3*b^2 - 6*(A + B)*a^2*b^3 + 2*(4*A + 3*B)*a*b^4 - (3*A + 2*B)*b^5)*cos(d*x + c)^2*sin(d*x + c) + (A*a^5 + 2*B*a^4*b - 6*(A + B)*a^3*b^2 + 2*(4*A + 3*B)*a^2*b^3 - (3*A + 2*B)*a*b^4)*cos(d*x + c)^2)*log(-sin(d*x + c) + 1) + 2*(A*a^5 - B*a^4*b - 2*A*a^3*b^2 + 2*B*a^2*b^3 + A*a*b^4 - B*b^5)*sin(d*x + c))/((a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*d*cos(d*x + c)^2*sin(d*x + c) + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*d*cos(d*x + c)^2)","B",0
1558,1,881,0,6.561249," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{4 \, B a^{7} - 4 \, A a^{6} b - 12 \, B a^{5} b^{2} + 12 \, A a^{4} b^{3} + 12 \, B a^{3} b^{4} - 12 \, A a^{2} b^{5} - 4 \, B a b^{6} + 4 \, A b^{7} - 2 \, {\left(3 \, A a^{6} b + 2 \, B a^{5} b^{2} - 15 \, A a^{4} b^{3} + 20 \, B a^{3} b^{4} - 3 \, A a^{2} b^{5} - 22 \, B a b^{6} + 15 \, A b^{7}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(A a^{6} b - 6 \, B a^{5} b^{2} + 3 \, A a^{4} b^{3} + 12 \, B a^{3} b^{4} - 9 \, A a^{2} b^{5} - 6 \, B a b^{6} + 5 \, A b^{7}\right)} \cos\left(d x + c\right)^{2} + 16 \, {\left({\left(5 \, B a^{2} b^{5} - 6 \, A a b^{6} + B b^{7}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(5 \, B a^{3} b^{4} - 6 \, A a^{2} b^{5} + B a b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + {\left({\left(3 \, A a^{6} b + 2 \, B a^{5} b^{2} - 15 \, A a^{4} b^{3} - 20 \, B a^{3} b^{4} + 5 \, {\left(9 \, A - 8 \, B\right)} a^{2} b^{5} + 6 \, {\left(8 \, A - 5 \, B\right)} a b^{6} + {\left(15 \, A - 8 \, B\right)} b^{7}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(3 \, A a^{7} + 2 \, B a^{6} b - 15 \, A a^{5} b^{2} - 20 \, B a^{4} b^{3} + 5 \, {\left(9 \, A - 8 \, B\right)} a^{3} b^{4} + 6 \, {\left(8 \, A - 5 \, B\right)} a^{2} b^{5} + {\left(15 \, A - 8 \, B\right)} a b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left({\left(3 \, A a^{6} b + 2 \, B a^{5} b^{2} - 15 \, A a^{4} b^{3} - 20 \, B a^{3} b^{4} + 5 \, {\left(9 \, A + 8 \, B\right)} a^{2} b^{5} - 6 \, {\left(8 \, A + 5 \, B\right)} a b^{6} + {\left(15 \, A + 8 \, B\right)} b^{7}\right)} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(3 \, A a^{7} + 2 \, B a^{6} b - 15 \, A a^{5} b^{2} - 20 \, B a^{4} b^{3} + 5 \, {\left(9 \, A + 8 \, B\right)} a^{3} b^{4} - 6 \, {\left(8 \, A + 5 \, B\right)} a^{2} b^{5} + {\left(15 \, A + 8 \, B\right)} a b^{6}\right)} \cos\left(d x + c\right)^{4}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(2 \, A a^{7} - 2 \, B a^{6} b - 6 \, A a^{5} b^{2} + 6 \, B a^{4} b^{3} + 6 \, A a^{3} b^{4} - 6 \, B a^{2} b^{5} - 2 \, A a b^{6} + 2 \, B b^{7} + {\left(3 \, A a^{7} + 2 \, B a^{6} b - 15 \, A a^{5} b^{2} + 21 \, A a^{3} b^{4} - 6 \, B a^{2} b^{5} - 9 \, A a b^{6} + 4 \, B b^{7}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{16 \, {\left({\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} d \cos\left(d x + c\right)^{4} \sin\left(d x + c\right) + {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} d \cos\left(d x + c\right)^{4}\right)}}"," ",0,"1/16*(4*B*a^7 - 4*A*a^6*b - 12*B*a^5*b^2 + 12*A*a^4*b^3 + 12*B*a^3*b^4 - 12*A*a^2*b^5 - 4*B*a*b^6 + 4*A*b^7 - 2*(3*A*a^6*b + 2*B*a^5*b^2 - 15*A*a^4*b^3 + 20*B*a^3*b^4 - 3*A*a^2*b^5 - 22*B*a*b^6 + 15*A*b^7)*cos(d*x + c)^4 + 2*(A*a^6*b - 6*B*a^5*b^2 + 3*A*a^4*b^3 + 12*B*a^3*b^4 - 9*A*a^2*b^5 - 6*B*a*b^6 + 5*A*b^7)*cos(d*x + c)^2 + 16*((5*B*a^2*b^5 - 6*A*a*b^6 + B*b^7)*cos(d*x + c)^4*sin(d*x + c) + (5*B*a^3*b^4 - 6*A*a^2*b^5 + B*a*b^6)*cos(d*x + c)^4)*log(b*sin(d*x + c) + a) + ((3*A*a^6*b + 2*B*a^5*b^2 - 15*A*a^4*b^3 - 20*B*a^3*b^4 + 5*(9*A - 8*B)*a^2*b^5 + 6*(8*A - 5*B)*a*b^6 + (15*A - 8*B)*b^7)*cos(d*x + c)^4*sin(d*x + c) + (3*A*a^7 + 2*B*a^6*b - 15*A*a^5*b^2 - 20*B*a^4*b^3 + 5*(9*A - 8*B)*a^3*b^4 + 6*(8*A - 5*B)*a^2*b^5 + (15*A - 8*B)*a*b^6)*cos(d*x + c)^4)*log(sin(d*x + c) + 1) - ((3*A*a^6*b + 2*B*a^5*b^2 - 15*A*a^4*b^3 - 20*B*a^3*b^4 + 5*(9*A + 8*B)*a^2*b^5 - 6*(8*A + 5*B)*a*b^6 + (15*A + 8*B)*b^7)*cos(d*x + c)^4*sin(d*x + c) + (3*A*a^7 + 2*B*a^6*b - 15*A*a^5*b^2 - 20*B*a^4*b^3 + 5*(9*A + 8*B)*a^3*b^4 - 6*(8*A + 5*B)*a^2*b^5 + (15*A + 8*B)*a*b^6)*cos(d*x + c)^4)*log(-sin(d*x + c) + 1) + 2*(2*A*a^7 - 2*B*a^6*b - 6*A*a^5*b^2 + 6*B*a^4*b^3 + 6*A*a^3*b^4 - 6*B*a^2*b^5 - 2*A*a*b^6 + 2*B*b^7 + (3*A*a^7 + 2*B*a^6*b - 15*A*a^5*b^2 + 21*A*a^3*b^4 - 6*B*a^2*b^5 - 9*A*a*b^6 + 4*B*b^7)*cos(d*x + c)^2)*sin(d*x + c))/((a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*d*cos(d*x + c)^4*sin(d*x + c) + (a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*d*cos(d*x + c)^4)","B",0
1559,1,1244,0,16.283413," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""fricas"")","\frac{16 \, B a^{9} - 16 \, A a^{8} b - 64 \, B a^{7} b^{2} + 64 \, A a^{6} b^{3} + 96 \, B a^{5} b^{4} - 96 \, A a^{4} b^{5} - 64 \, B a^{3} b^{6} + 64 \, A a^{2} b^{7} + 16 \, B a b^{8} - 16 \, A b^{9} - 6 \, {\left(5 \, A a^{8} b + 2 \, B a^{7} b^{2} - 28 \, A a^{6} b^{3} - 14 \, B a^{5} b^{4} + 70 \, A a^{4} b^{5} - 42 \, B a^{3} b^{6} - 12 \, A a^{2} b^{7} + 54 \, B a b^{8} - 35 \, A b^{9}\right)} \cos\left(d x + c\right)^{6} + 2 \, {\left(5 \, A a^{8} b + 2 \, B a^{7} b^{2} - 28 \, A a^{6} b^{3} + 42 \, B a^{5} b^{4} + 6 \, A a^{4} b^{5} - 90 \, B a^{3} b^{6} + 52 \, A a^{2} b^{7} + 46 \, B a b^{8} - 35 \, A b^{9}\right)} \cos\left(d x + c\right)^{4} + 4 \, {\left(A a^{8} b - 8 \, B a^{7} b^{2} + 4 \, A a^{6} b^{3} + 24 \, B a^{5} b^{4} - 18 \, A a^{4} b^{5} - 24 \, B a^{3} b^{6} + 20 \, A a^{2} b^{7} + 8 \, B a b^{8} - 7 \, A b^{9}\right)} \cos\left(d x + c\right)^{2} - 96 \, {\left({\left(7 \, B a^{2} b^{7} - 8 \, A a b^{8} + B b^{9}\right)} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + {\left(7 \, B a^{3} b^{6} - 8 \, A a^{2} b^{7} + B a b^{8}\right)} \cos\left(d x + c\right)^{6}\right)} \log\left(b \sin\left(d x + c\right) + a\right) + 3 \, {\left({\left(5 \, A a^{8} b + 2 \, B a^{7} b^{2} - 28 \, A a^{6} b^{3} - 14 \, B a^{5} b^{4} + 70 \, A a^{4} b^{5} + 70 \, B a^{3} b^{6} - 28 \, {\left(5 \, A - 4 \, B\right)} a^{2} b^{7} - 2 \, {\left(64 \, A - 35 \, B\right)} a b^{8} - {\left(35 \, A - 16 \, B\right)} b^{9}\right)} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + {\left(5 \, A a^{9} + 2 \, B a^{8} b - 28 \, A a^{7} b^{2} - 14 \, B a^{6} b^{3} + 70 \, A a^{5} b^{4} + 70 \, B a^{4} b^{5} - 28 \, {\left(5 \, A - 4 \, B\right)} a^{3} b^{6} - 2 \, {\left(64 \, A - 35 \, B\right)} a^{2} b^{7} - {\left(35 \, A - 16 \, B\right)} a b^{8}\right)} \cos\left(d x + c\right)^{6}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left({\left(5 \, A a^{8} b + 2 \, B a^{7} b^{2} - 28 \, A a^{6} b^{3} - 14 \, B a^{5} b^{4} + 70 \, A a^{4} b^{5} + 70 \, B a^{3} b^{6} - 28 \, {\left(5 \, A + 4 \, B\right)} a^{2} b^{7} + 2 \, {\left(64 \, A + 35 \, B\right)} a b^{8} - {\left(35 \, A + 16 \, B\right)} b^{9}\right)} \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + {\left(5 \, A a^{9} + 2 \, B a^{8} b - 28 \, A a^{7} b^{2} - 14 \, B a^{6} b^{3} + 70 \, A a^{5} b^{4} + 70 \, B a^{4} b^{5} - 28 \, {\left(5 \, A + 4 \, B\right)} a^{3} b^{6} + 2 \, {\left(64 \, A + 35 \, B\right)} a^{2} b^{7} - {\left(35 \, A + 16 \, B\right)} a b^{8}\right)} \cos\left(d x + c\right)^{6}\right)} \log\left(-\sin\left(d x + c\right) + 1\right) + 2 \, {\left(8 \, A a^{9} - 8 \, B a^{8} b - 32 \, A a^{7} b^{2} + 32 \, B a^{6} b^{3} + 48 \, A a^{5} b^{4} - 48 \, B a^{4} b^{5} - 32 \, A a^{3} b^{6} + 32 \, B a^{2} b^{7} + 8 \, A a b^{8} - 8 \, B b^{9} + 3 \, {\left(5 \, A a^{9} + 2 \, B a^{8} b - 28 \, A a^{7} b^{2} - 14 \, B a^{6} b^{3} + 70 \, A a^{5} b^{4} + 14 \, B a^{4} b^{5} - 76 \, A a^{3} b^{6} + 6 \, B a^{2} b^{7} + 29 \, A a b^{8} - 8 \, B b^{9}\right)} \cos\left(d x + c\right)^{4} + 2 \, {\left(5 \, A a^{9} + 2 \, B a^{8} b - 28 \, A a^{7} b^{2} + 54 \, A a^{5} b^{4} - 12 \, B a^{4} b^{5} - 44 \, A a^{3} b^{6} + 16 \, B a^{2} b^{7} + 13 \, A a b^{8} - 6 \, B b^{9}\right)} \cos\left(d x + c\right)^{2}\right)} \sin\left(d x + c\right)}{96 \, {\left({\left(a^{10} b - 5 \, a^{8} b^{3} + 10 \, a^{6} b^{5} - 10 \, a^{4} b^{7} + 5 \, a^{2} b^{9} - b^{11}\right)} d \cos\left(d x + c\right)^{6} \sin\left(d x + c\right) + {\left(a^{11} - 5 \, a^{9} b^{2} + 10 \, a^{7} b^{4} - 10 \, a^{5} b^{6} + 5 \, a^{3} b^{8} - a b^{10}\right)} d \cos\left(d x + c\right)^{6}\right)}}"," ",0,"1/96*(16*B*a^9 - 16*A*a^8*b - 64*B*a^7*b^2 + 64*A*a^6*b^3 + 96*B*a^5*b^4 - 96*A*a^4*b^5 - 64*B*a^3*b^6 + 64*A*a^2*b^7 + 16*B*a*b^8 - 16*A*b^9 - 6*(5*A*a^8*b + 2*B*a^7*b^2 - 28*A*a^6*b^3 - 14*B*a^5*b^4 + 70*A*a^4*b^5 - 42*B*a^3*b^6 - 12*A*a^2*b^7 + 54*B*a*b^8 - 35*A*b^9)*cos(d*x + c)^6 + 2*(5*A*a^8*b + 2*B*a^7*b^2 - 28*A*a^6*b^3 + 42*B*a^5*b^4 + 6*A*a^4*b^5 - 90*B*a^3*b^6 + 52*A*a^2*b^7 + 46*B*a*b^8 - 35*A*b^9)*cos(d*x + c)^4 + 4*(A*a^8*b - 8*B*a^7*b^2 + 4*A*a^6*b^3 + 24*B*a^5*b^4 - 18*A*a^4*b^5 - 24*B*a^3*b^6 + 20*A*a^2*b^7 + 8*B*a*b^8 - 7*A*b^9)*cos(d*x + c)^2 - 96*((7*B*a^2*b^7 - 8*A*a*b^8 + B*b^9)*cos(d*x + c)^6*sin(d*x + c) + (7*B*a^3*b^6 - 8*A*a^2*b^7 + B*a*b^8)*cos(d*x + c)^6)*log(b*sin(d*x + c) + a) + 3*((5*A*a^8*b + 2*B*a^7*b^2 - 28*A*a^6*b^3 - 14*B*a^5*b^4 + 70*A*a^4*b^5 + 70*B*a^3*b^6 - 28*(5*A - 4*B)*a^2*b^7 - 2*(64*A - 35*B)*a*b^8 - (35*A - 16*B)*b^9)*cos(d*x + c)^6*sin(d*x + c) + (5*A*a^9 + 2*B*a^8*b - 28*A*a^7*b^2 - 14*B*a^6*b^3 + 70*A*a^5*b^4 + 70*B*a^4*b^5 - 28*(5*A - 4*B)*a^3*b^6 - 2*(64*A - 35*B)*a^2*b^7 - (35*A - 16*B)*a*b^8)*cos(d*x + c)^6)*log(sin(d*x + c) + 1) - 3*((5*A*a^8*b + 2*B*a^7*b^2 - 28*A*a^6*b^3 - 14*B*a^5*b^4 + 70*A*a^4*b^5 + 70*B*a^3*b^6 - 28*(5*A + 4*B)*a^2*b^7 + 2*(64*A + 35*B)*a*b^8 - (35*A + 16*B)*b^9)*cos(d*x + c)^6*sin(d*x + c) + (5*A*a^9 + 2*B*a^8*b - 28*A*a^7*b^2 - 14*B*a^6*b^3 + 70*A*a^5*b^4 + 70*B*a^4*b^5 - 28*(5*A + 4*B)*a^3*b^6 + 2*(64*A + 35*B)*a^2*b^7 - (35*A + 16*B)*a*b^8)*cos(d*x + c)^6)*log(-sin(d*x + c) + 1) + 2*(8*A*a^9 - 8*B*a^8*b - 32*A*a^7*b^2 + 32*B*a^6*b^3 + 48*A*a^5*b^4 - 48*B*a^4*b^5 - 32*A*a^3*b^6 + 32*B*a^2*b^7 + 8*A*a*b^8 - 8*B*b^9 + 3*(5*A*a^9 + 2*B*a^8*b - 28*A*a^7*b^2 - 14*B*a^6*b^3 + 70*A*a^5*b^4 + 14*B*a^4*b^5 - 76*A*a^3*b^6 + 6*B*a^2*b^7 + 29*A*a*b^8 - 8*B*b^9)*cos(d*x + c)^4 + 2*(5*A*a^9 + 2*B*a^8*b - 28*A*a^7*b^2 + 54*A*a^5*b^4 - 12*B*a^4*b^5 - 44*A*a^3*b^6 + 16*B*a^2*b^7 + 13*A*a*b^8 - 6*B*b^9)*cos(d*x + c)^2)*sin(d*x + c))/((a^10*b - 5*a^8*b^3 + 10*a^6*b^5 - 10*a^4*b^7 + 5*a^2*b^9 - b^11)*d*cos(d*x + c)^6*sin(d*x + c) + (a^11 - 5*a^9*b^2 + 10*a^7*b^4 - 10*a^5*b^6 + 5*a^3*b^8 - a*b^10)*d*cos(d*x + c)^6)","B",0
1560,0,0,0,1.078276," ","integrate((g*cos(f*x+e))^(-1-m)*(a+b*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} \left(g \cos\left(f x + e\right)\right)^{-m - 1} {\left(b \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(g*cos(f*x + e))^(-m - 1)*(b*sin(f*x + e) + a)^m, x)","F",0
1561,0,0,0,0.935161," ","integrate((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(g \cos\left(f x + e\right)\right)^{p}}{b d \cos\left(f x + e\right)^{2} - a c - b d - {\left(b c + a d\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(g*cos(f*x + e))^p/(b*d*cos(f*x + e)^2 - a*c - b*d - (b*c + a*d)*sin(f*x + e)), x)","F",0
1562,0,0,0,0.978686," ","integrate((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\left(g \cos\left(f x + e\right)\right)^{p}}{a c^{2} + 2 \, b c d + a d^{2} - {\left(2 \, b c d + a d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(b d^{2} \cos\left(f x + e\right)^{2} - b c^{2} - 2 \, a c d - b d^{2}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((g*cos(f*x + e))^p/(a*c^2 + 2*b*c*d + a*d^2 - (2*b*c*d + a*d^2)*cos(f*x + e)^2 - (b*d^2*cos(f*x + e)^2 - b*c^2 - 2*a*c*d - b*d^2)*sin(f*x + e)), x)","F",0
1563,0,0,0,1.041373," ","integrate((g*sec(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\left(g \sec\left(f x + e\right)\right)^{p}}{b d \cos\left(f x + e\right)^{2} - a c - b d - {\left(b c + a d\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(g*sec(f*x + e))^p/(b*d*cos(f*x + e)^2 - a*c - b*d - (b*c + a*d)*sin(f*x + e)), x)","F",0
