1,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2)*cos(f*x + e)^2, x)","F",0
2,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)*cos(f*x + e)^2, x)","F",0
3,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)*cos(f*x + e)^2, x)","F",0
4,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2, x)","F",0
5,1,387,0,0.495590," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{a} \sqrt{c} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{c + \frac{2 \, c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} - \frac{2 \, \sqrt{a} \sqrt{c} - \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{c + \frac{2 \, c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{2 \, {\left(\frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{c + \frac{2 \, c \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{c \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}}}{2 \, f}"," ",0,"-1/2*((2*sqrt(a)*sqrt(c) + sqrt(a)*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sqrt(a)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(a)*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(c + 2*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) - (2*sqrt(a)*sqrt(c) - sqrt(a)*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) + sqrt(a)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - sqrt(a)*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(c + 2*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + 2*(sqrt(a)*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) + sqrt(a)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(a)*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(c + 2*c*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + c*sin(f*x + e)^4/(cos(f*x + e) + 1)^4))/f","B",0
6,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
7,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
8,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
9,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(7/2)*cos(f*x + e)^2, x)","F",0
10,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2)*cos(f*x + e)^2, x)","F",0
11,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2)*cos(f*x + e)^2, x)","F",0
12,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2, x)","F",0
13,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*cos(f*x + e)^2/sqrt(-c*sin(f*x + e) + c), x)","F",0
14,1,844,0,0.955240," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\frac{\frac{16 \, a^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{3}{2}}} - \frac{8 \, a^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{3}{2}}} + \frac{10 \, a^{\frac{3}{2}} - \frac{11 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{15 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{20 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{7 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{c^{\frac{3}{2}} - \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} - \frac{10 \, a^{\frac{3}{2}} - \frac{13 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{25 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{20 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{9 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{c^{\frac{3}{2}} - \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} + \frac{2 \, {\left(\frac{5 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{5 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{5 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{c^{\frac{3}{2}} - \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{4 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{2 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}}{2 \, f}"," ",0,"1/2*(16*a^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(3/2) - 8*a^(3/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(3/2) + (10*a^(3/2) - 11*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 15*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 20*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 7*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(c^(3/2) - 2*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) - (10*a^(3/2) - 13*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 25*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 20*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 9*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(c^(3/2) - 2*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) + 2*(5*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) - 5*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 5*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(c^(3/2) - 2*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 4*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6))/f","B",0
15,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
16,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
17,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
18,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(3/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
19,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(7/2)*cos(f*x + e)^2, x)","F",0
20,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2)*cos(f*x + e)^2, x)","F",0
21,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2)*cos(f*x + e)^2, x)","F",0
22,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2, x)","F",0
23,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*cos(f*x + e)^2/sqrt(-c*sin(f*x + e) + c), x)","F",0
24,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
25,1,1120,0,0.508431," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{\frac{144 \, a^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{5}{2}}} - \frac{72 \, a^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{5}{2}}} + \frac{46 \, a^{\frac{5}{2}} - \frac{121 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{149 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{179 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{148 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{43 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{33 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{15 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}{c^{\frac{5}{2}} - \frac{4 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{8 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{12 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{12 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{8 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{4 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}} - \frac{46 \, a^{\frac{5}{2}} - \frac{199 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{335 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{509 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{496 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{373 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{219 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{63 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}{c^{\frac{5}{2}} - \frac{4 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{8 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{12 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{12 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{8 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{4 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}} + \frac{6 \, {\left(\frac{13 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{39 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{55 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{74 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{55 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{39 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{13 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)}}{c^{\frac{5}{2}} - \frac{4 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{8 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{12 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{12 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{8 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{4 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}}}{6 \, f}"," ",0,"-1/6*(144*a^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(5/2) - 72*a^(5/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(5/2) + (46*a^(5/2) - 121*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 149*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 179*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 148*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 43*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 33*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 15*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)/(c^(5/2) - 4*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 8*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 12*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 12*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 8*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 4*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8) - (46*a^(5/2) - 199*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 335*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 509*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 496*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 373*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 219*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 63*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)/(c^(5/2) - 4*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 8*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 12*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 12*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 8*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 4*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8) + 6*(13*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) - 39*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 55*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 74*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 55*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 39*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 13*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)/(c^(5/2) - 4*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 8*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 12*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 12*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 8*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 4*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8))/f","B",0
26,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
27,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
28,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(5/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
29,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(9/2)*cos(f*x + e)^2, x)","F",0
31,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(7/2)*cos(f*x + e)^2, x)","F",0
32,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(5/2)*cos(f*x + e)^2, x)","F",0
33,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(3/2)*cos(f*x + e)^2, x)","F",0
34,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2, x)","F",0
35,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*cos(f*x + e)^2/sqrt(-c*sin(f*x + e) + c), x)","F",0
36,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
37,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
38,1,1396,0,0.536014," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\frac{\frac{1440 \, a^{\frac{7}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{c^{\frac{7}{2}}} - \frac{720 \, a^{\frac{7}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{c^{\frac{7}{2}}} + \frac{334 \, a^{\frac{7}{2}} - \frac{1449 \, a^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{2693 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{3278 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3199 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{2014 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{315 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{10 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{525 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{75 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}}{c^{\frac{7}{2}} - \frac{6 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{17 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{32 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{46 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{52 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{46 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{32 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{17 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{6 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}} - \frac{334 \, a^{\frac{7}{2}} - \frac{2079 \, a^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{6203 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{10698 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15049 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{15354 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{12165 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{7410 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{2985 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{555 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}}{c^{\frac{7}{2}} - \frac{6 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{17 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{32 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{46 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{52 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{46 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{32 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{17 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{6 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}} + \frac{10 \, {\left(\frac{75 \, a^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{375 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{854 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{1257 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{1534 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{1257 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{854 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{375 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{75 \, a^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}\right)}}{c^{\frac{7}{2}} - \frac{6 \, c^{\frac{7}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{17 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{32 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{46 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{52 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{46 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{32 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{17 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{6 \, c^{\frac{7}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{c^{\frac{7}{2}} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}}}{30 \, f}"," ",0,"1/30*(1440*a^(7/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/c^(7/2) - 720*a^(7/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/c^(7/2) + (334*a^(7/2) - 1449*a^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 2693*a^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 3278*a^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3199*a^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2014*a^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 315*a^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 10*a^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 525*a^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 75*a^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)/(c^(7/2) - 6*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 17*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 32*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 46*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 52*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 46*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 32*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 17*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 6*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10) - (334*a^(7/2) - 2079*a^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 6203*a^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 10698*a^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15049*a^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 15354*a^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 12165*a^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 7410*a^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 2985*a^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 555*a^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)/(c^(7/2) - 6*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 17*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 32*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 46*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 52*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 46*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 32*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 17*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 6*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10) + 10*(75*a^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) - 375*a^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 854*a^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 1257*a^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 1534*a^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 1257*a^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 854*a^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 375*a^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 75*a^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)/(c^(7/2) - 6*c^(7/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 17*c^(7/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 32*c^(7/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 46*c^(7/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 52*c^(7/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 46*c^(7/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 32*c^(7/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 17*c^(7/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 6*c^(7/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + c^(7/2)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10))/f","B",0
39,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
40,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^(7/2)*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
41,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(17/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(5/2)*cos(f*x + e)^2/sqrt(a*sin(f*x + e) + a), x)","F",0
45,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(3/2)*cos(f*x + e)^2/sqrt(a*sin(f*x + e) + a), x)","F",0
46,1,388,0,1.631693," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sqrt{a} \sqrt{c} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} - \frac{2 \, \sqrt{a} \sqrt{c} - \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, \sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}}{a + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}} + \frac{2 \, {\left(\frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{\sqrt{a} \sqrt{c} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}}\right)}}{a + \frac{2 \, a \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{a \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}}}}{2 \, f}"," ",0,"-1/2*((2*sqrt(a)*sqrt(c) + sqrt(a)*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) + sqrt(a)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(a)*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) - (2*sqrt(a)*sqrt(c) - sqrt(a)*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*sqrt(a)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - sqrt(a)*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4) + 2*(sqrt(a)*sqrt(c)*sin(f*x + e)/(cos(f*x + e) + 1) - sqrt(a)*sqrt(c)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + sqrt(a)*sqrt(c)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3)/(a + 2*a*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + a*sin(f*x + e)^4/(cos(f*x + e) + 1)^4))/f","B",0
47,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
48,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
49,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
50,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(7/2)*cos(f*x + e)^2/(a*sin(f*x + e) + a)^(3/2), x)","F",0
51,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(5/2)*cos(f*x + e)^2/(a*sin(f*x + e) + a)^(3/2), x)","F",0
52,1,844,0,1.056017," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{\frac{16 \, c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{\frac{3}{2}}} - \frac{8 \, c^{\frac{3}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{a^{\frac{3}{2}}} - \frac{10 \, c^{\frac{3}{2}} + \frac{13 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{25 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{15 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{9 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{\frac{3}{2}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} + \frac{10 \, c^{\frac{3}{2}} + \frac{11 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{15 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{20 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{7 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}}{a^{\frac{3}{2}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}} - \frac{2 \, {\left(\frac{5 \, c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{5 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{5 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{5 \, c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)}}{a^{\frac{3}{2}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{3 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{2 \, a^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}}}{2 \, f}"," ",0,"-1/2*(16*c^(3/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^(3/2) - 8*c^(3/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/a^(3/2) - (10*c^(3/2) + 13*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 25*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 15*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 9*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^(3/2) + 2*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 2*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) + (10*c^(3/2) + 11*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 15*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 20*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 7*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^(3/2) + 2*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 2*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6) - 2*(5*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 5*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 5*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 5*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)/(a^(3/2) + 2*a^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 3*a^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 3*a^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 2*a^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6))/f","B",0
53,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2/(a*sin(f*x + e) + a)^(3/2), x)","F",0
54,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
55,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
56,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
57,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(9/2)*cos(f*x + e)^2/(a*sin(f*x + e) + a)^(5/2), x)","F",0
58,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(7/2)*cos(f*x + e)^2/(a*sin(f*x + e) + a)^(5/2), x)","F",0
59,1,1120,0,1.612612," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\frac{\frac{144 \, c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{a^{\frac{5}{2}}} - \frac{72 \, c^{\frac{5}{2}} \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}{a^{\frac{5}{2}}} - \frac{46 \, c^{\frac{5}{2}} + \frac{199 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{335 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{509 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{496 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{373 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{219 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{63 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}{a^{\frac{5}{2}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{8 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{12 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{8 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{a^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}} + \frac{46 \, c^{\frac{5}{2}} + \frac{121 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{149 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{179 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{148 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{43 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{33 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{15 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}}{a^{\frac{5}{2}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{8 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{12 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{8 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{a^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}} - \frac{6 \, {\left(\frac{13 \, c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{39 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{55 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{74 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{55 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{39 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{13 \, c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)}}{a^{\frac{5}{2}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{8 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{12 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{14 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{12 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{8 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{4 \, a^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{a^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}}}}{6 \, f}"," ",0,"1/6*(144*c^(5/2)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/a^(5/2) - 72*c^(5/2)*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)/a^(5/2) - (46*c^(5/2) + 199*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 335*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 509*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 496*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 373*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 219*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 63*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)/(a^(5/2) + 4*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 8*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 12*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 8*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 4*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + a^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8) + (46*c^(5/2) + 121*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 149*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 179*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 148*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 43*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 33*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 15*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)/(a^(5/2) + 4*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 8*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 12*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 8*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 4*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + a^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8) - 6*(13*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 39*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 55*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 74*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 55*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 39*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 13*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)/(a^(5/2) + 4*a^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) + 8*a^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 12*a^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 14*a^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 12*a^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 8*a^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 4*a^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + a^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8))/f","B",0
60,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((-c*sin(f*x + e) + c)^(3/2)*cos(f*x + e)^2/(a*sin(f*x + e) + a)^(5/2), x)","F",0
61,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\sqrt{-c \sin\left(f x + e\right) + c} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(-c*sin(f*x + e) + c)*cos(f*x + e)^2/(a*sin(f*x + e) + a)^(5/2), x)","F",0
62,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
63,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
64,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
65,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
66,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
67,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\int {\left(c \sin\left(f x + e\right) - c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((c*sin(f*x + e) - c)^2*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
68,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int {\left(c \sin\left(f x + e\right) - c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"-integrate((c*sin(f*x + e) - c)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
69,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
70,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int \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}\,{d x}"," ",0,"-integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c*sin(f*x + e) - c), x)","F",0
71,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \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)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c*sin(f*x + e) - c)^2, x)","F",0
72,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\int \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)}^{3}}\,{d x}"," ",0,"-integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(c*sin(f*x + e) - c)^3, x)","F",0
73,1,558,0,0.661182," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(8 \, m^{3} + 108 \, m^{2} + 526 \, m + 957\right)} a^{m} c^{\frac{5}{2}} - \frac{3 \, {\left(8 \, m^{3} + 76 \, m^{2} + 142 \, m - 315\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{24 \, {\left(4 \, m^{2} + 16 \, m - 81\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{16 \, {\left(4 \, m^{3} + 36 \, m^{2} + 95 \, m + 315\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{6 \, {\left(8 \, m^{3} + 60 \, m^{2} + 206 \, m - 567\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{6 \, {\left(8 \, m^{3} + 60 \, m^{2} + 206 \, m - 567\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{16 \, {\left(4 \, m^{3} + 36 \, m^{2} + 95 \, m + 315\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} - \frac{24 \, {\left(4 \, m^{2} + 16 \, m - 81\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{3 \, {\left(8 \, m^{3} + 76 \, m^{2} + 142 \, m - 315\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{{\left(8 \, m^{3} + 108 \, m^{2} + 526 \, m + 957\right)} a^{m} c^{\frac{5}{2}} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}\right)} e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(16 \, m^{4} + 192 \, m^{3} + 824 \, m^{2} + 1488 \, m + \frac{2 \, {\left(16 \, m^{4} + 192 \, m^{3} + 824 \, m^{2} + 1488 \, m + 945\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(16 \, m^{4} + 192 \, m^{3} + 824 \, m^{2} + 1488 \, m + 945\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 945\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{5}{2}}}"," ",0,"-2*((8*m^3 + 108*m^2 + 526*m + 957)*a^m*c^(5/2) - 3*(8*m^3 + 76*m^2 + 142*m - 315)*a^m*c^(5/2)*sin(f*x + e)/(cos(f*x + e) + 1) - 24*(4*m^2 + 16*m - 81)*a^m*c^(5/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 16*(4*m^3 + 36*m^2 + 95*m + 315)*a^m*c^(5/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 6*(8*m^3 + 60*m^2 + 206*m - 567)*a^m*c^(5/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 6*(8*m^3 + 60*m^2 + 206*m - 567)*a^m*c^(5/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 16*(4*m^3 + 36*m^2 + 95*m + 315)*a^m*c^(5/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 - 24*(4*m^2 + 16*m - 81)*a^m*c^(5/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - 3*(8*m^3 + 76*m^2 + 142*m - 315)*a^m*c^(5/2)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + (8*m^3 + 108*m^2 + 526*m + 957)*a^m*c^(5/2)*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((16*m^4 + 192*m^3 + 824*m^2 + 1488*m + 2*(16*m^4 + 192*m^3 + 824*m^2 + 1488*m + 945)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (16*m^4 + 192*m^3 + 824*m^2 + 1488*m + 945)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 945)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(5/2))","B",0
74,1,423,0,0.517459," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","-\frac{2 \, {\left({\left(4 \, m^{2} + 32 \, m + 71\right)} a^{m} c^{\frac{3}{2}} - \frac{{\left(4 \, m^{2} - 105\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{{\left(12 \, m^{2} + 64 \, m - 91\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(12 \, m^{2} + 32 \, m + 245\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{{\left(12 \, m^{2} + 32 \, m + 245\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{{\left(12 \, m^{2} + 64 \, m - 91\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{{\left(4 \, m^{2} - 105\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{{\left(4 \, m^{2} + 32 \, m + 71\right)} a^{m} c^{\frac{3}{2}} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(8 \, m^{3} + 60 \, m^{2} + 142 \, m + \frac{2 \, {\left(8 \, m^{3} + 60 \, m^{2} + 142 \, m + 105\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(8 \, m^{3} + 60 \, m^{2} + 142 \, m + 105\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 105\right)} f {\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)}^{\frac{3}{2}}}"," ",0,"-2*((4*m^2 + 32*m + 71)*a^m*c^(3/2) - (4*m^2 - 105)*a^m*c^(3/2)*sin(f*x + e)/(cos(f*x + e) + 1) - (12*m^2 + 64*m - 91)*a^m*c^(3/2)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (12*m^2 + 32*m + 245)*a^m*c^(3/2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + (12*m^2 + 32*m + 245)*a^m*c^(3/2)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - (12*m^2 + 64*m - 91)*a^m*c^(3/2)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - (4*m^2 - 105)*a^m*c^(3/2)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + (4*m^2 + 32*m + 71)*a^m*c^(3/2)*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((8*m^3 + 60*m^2 + 142*m + 2*(8*m^3 + 60*m^2 + 142*m + 105)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (8*m^3 + 60*m^2 + 142*m + 105)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 105)*f*(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1)^(3/2))","B",0
75,1,312,0,0.527946," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{2 \, {\left(a^{m} \sqrt{c} {\left(2 \, m + 7\right)} + \frac{a^{m} \sqrt{c} {\left(2 \, m + 15\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{2 \, a^{m} \sqrt{c} {\left(2 \, m - 5\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{2 \, a^{m} \sqrt{c} {\left(2 \, m - 5\right)} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{a^{m} \sqrt{c} {\left(2 \, m + 15\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{a^{m} \sqrt{c} {\left(2 \, m + 7\right)} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}}\right)} e^{\left(2 \, m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(4 \, m^{2} + 16 \, m + \frac{2 \, {\left(4 \, m^{2} + 16 \, m + 15\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{{\left(4 \, m^{2} + 16 \, m + 15\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + 15\right)} f \sqrt{\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1}}"," ",0,"-2*(a^m*sqrt(c)*(2*m + 7) + a^m*sqrt(c)*(2*m + 15)*sin(f*x + e)/(cos(f*x + e) + 1) - 2*a^m*sqrt(c)*(2*m - 5)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 2*a^m*sqrt(c)*(2*m - 5)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + a^m*sqrt(c)*(2*m + 15)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + a^m*sqrt(c)*(2*m + 7)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5)*e^(2*m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((4*m^2 + 16*m + 2*(4*m^2 + 16*m + 15)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + (4*m^2 + 16*m + 15)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 15)*f*sqrt(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))","B",0
76,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \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)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
78,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \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)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
79,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-5-m),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 5} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 5)*cos(f*x + e)^2, x)","F",0
82,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-4-m),x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 4} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 4)*cos(f*x + e)^2, x)","F",0
83,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""maxima"")","\int {\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)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3)*cos(f*x + e)^2, x)","F",0
84,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2)*cos(f*x + e)^2, x)","F",0
85,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1)*cos(f*x + e)^2, x)","F",0
86,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)^2/(-c*sin(f*x + e) + c)^m, x)","F",0
87,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1)*cos(f*x + e)^2, x)","F",0
88,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2), x)","F",0
89,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
90,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
91,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c), x)","F",0
92,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)/sqrt(-c*sin(f*x + e) + c), x)","F",0
93,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
94,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
95,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
96,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{a \sin\left(f x + e\right) + a}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(a*sin(f*x + e) + a)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
97,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
98,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
99,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
100,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
101,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
102,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
103,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
104,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
105,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(3/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
106,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
107,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
108,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
109,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
110,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
111,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
112,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
113,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
114,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
115,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(5/2)/(-c*sin(f*x + e) + c)^(13/2), x)","F",0
116,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(5/2), x)","F",0
117,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)*(-c*sin(f*x + e) + c)^(3/2), x)","F",0
118,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}} \sqrt{-c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)*sqrt(-c*sin(f*x + e) + c), x)","F",0
119,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)/sqrt(-c*sin(f*x + e) + c), x)","F",0
120,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
121,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
122,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(7/2), x)","F",0
123,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(9/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(9/2), x)","F",0
124,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(11/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(11/2), x)","F",0
125,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(13/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{13}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(13/2), x)","F",0
126,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(7/2)/(c-c*sin(f*x+e))^(15/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{\frac{7}{2}}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{15}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^(7/2)/(-c*sin(f*x + e) + c)^(15/2), x)","F",0
127,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(5/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
128,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(3/2)/sqrt(a*sin(f*x + e) + a), x)","F",0
129,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(-c*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
130,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
131,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
132,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
133,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/(sqrt(a*sin(f*x + e) + a)*(-c*sin(f*x + e) + c)^(7/2)), x)","F",0
134,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(7/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
135,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
136,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
137,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(-c*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(3/2), x)","F",0
138,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(3/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
139,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
140,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
141,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(3/2)*(-c*sin(f*x + e) + c)^(7/2)), x)","F",0
142,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{9}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(9/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
143,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(7/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
144,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(5/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
145,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(3/2)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
146,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(-c*sin(f*x + e) + c)/(a*sin(f*x + e) + a)^(5/2), x)","F",0
147,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(5/2)*sqrt(-c*sin(f*x + e) + c)), x)","F",0
148,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(3/2)), x)","F",0
149,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(5/2)), x)","F",0
150,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((a*sin(f*x + e) + a)^(5/2)*(-c*sin(f*x + e) + c)^(7/2)), x)","F",0
151,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
152,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(c \sin\left(f x + e\right) - c\right)}^{3} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"-integrate((g*cos(f*x + e))^(3/2)*(c*sin(f*x + e) - c)^3*(a*sin(f*x + e) + a)^m, x)","F",0
153,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(c \sin\left(f x + e\right) - c\right)}^{2} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(c*sin(f*x + e) - c)^2*(a*sin(f*x + e) + a)^m, x)","F",0
154,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(c \sin\left(f x + e\right) - c\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"-integrate((g*cos(f*x + e))^(3/2)*(c*sin(f*x + e) - c)*(a*sin(f*x + e) + a)^m, x)","F",0
155,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
156,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}\,{d x}"," ",0,"-integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
157,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(c \sin\left(f x + e\right) - c\right)}^{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^2, x)","F",0
158,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^3,x, algorithm=""maxima"")","-\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(c \sin\left(f x + e\right) - c\right)}^{3}}\,{d x}"," ",0,"-integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c)^3, x)","F",0
159,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(5/2)*(a*sin(f*x + e) + a)^m, x)","F",0
160,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(-c*sin(f*x + e) + c)^(3/2)*(a*sin(f*x + e) + a)^m, x)","F",0
161,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
162,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
163,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(3/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(3/2), x)","F",0
164,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(5/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^(5/2), x)","F",0
165,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{-c \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/sqrt(-c*sin(f*x + e) + c), x)","F",0
166,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(c \sin\left(f x + e\right) + c\right)}^{m}}{\sqrt{-a \sin\left(f x + e\right) + a}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(c*sin(f*x + e) + c)^m/sqrt(-a*sin(f*x + e) + a), x)","F",0
167,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 3}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3), x)","F",0
168,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2), x)","F",0
169,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 1}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1), x)","F",0
170,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m/((c-c*sin(f*x+e))^m),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{m}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^m, x)","F",0
171,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1-m),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 1}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1), x)","F",0
172,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2-m),x, algorithm=""maxima"")","\int \left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 2}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 2), x)","F",0
173,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
174,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+m),x, algorithm=""maxima"")","\int \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)}^{m - 1}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-2*m + 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(m - 1), x)","F",0
175,1,978,0,0.981585," ","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=""maxima"")","\frac{{\left({\left(m^{2} - m {\left(2 \, n + 11\right)} + n^{2} + 11 \, n + 32\right)} a^{m} c^{n} g^{5} - \frac{2 \, {\left(m^{2} - m {\left(2 \, n + 15\right)} + n^{2} + 15 \, n + 60\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{{\left(3 \, m^{2} - m {\left(6 \, n + 1\right)} + 3 \, n^{2} + n - 160\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{8 \, {\left(m^{2} - m {\left(2 \, n + 7\right)} + n^{2} + 7 \, n - 20\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{2 \, {\left(m^{2} - m {\left(2 \, n - 5\right)} + n^{2} - 5 \, n + 160\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{4 \, {\left(3 \, m^{2} - m {\left(6 \, n + 13\right)} + 3 \, n^{2} + 13 \, n + 116\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{2 \, {\left(m^{2} - m {\left(2 \, n - 5\right)} + n^{2} - 5 \, n + 160\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{8 \, {\left(m^{2} - m {\left(2 \, n + 7\right)} + n^{2} + 7 \, n - 20\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} - \frac{{\left(3 \, m^{2} - m {\left(6 \, n + 1\right)} + 3 \, n^{2} + n - 160\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} - \frac{2 \, {\left(m^{2} - m {\left(2 \, n + 15\right)} + n^{2} + 15 \, n + 60\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{{\left(m^{2} - m {\left(2 \, n + 11\right)} + n^{2} + 11 \, n + 32\right)} a^{m} c^{n} g^{5} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)} e^{\left(2 \, n \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right) - 2 \, m \log\left(-\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) + m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right) - n \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left({\left(m^{3} - 3 \, m^{2} {\left(n + 4\right)} - n^{3} + {\left(3 \, n^{2} + 24 \, n + 47\right)} m - 12 \, n^{2} - 47 \, n - 60\right)} g^{2 \, m} + \frac{5 \, {\left(m^{3} - 3 \, m^{2} {\left(n + 4\right)} - n^{3} + {\left(3 \, n^{2} + 24 \, n + 47\right)} m - 12 \, n^{2} - 47 \, n - 60\right)} g^{2 \, m} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{10 \, {\left(m^{3} - 3 \, m^{2} {\left(n + 4\right)} - n^{3} + {\left(3 \, n^{2} + 24 \, n + 47\right)} m - 12 \, n^{2} - 47 \, n - 60\right)} g^{2 \, m} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{10 \, {\left(m^{3} - 3 \, m^{2} {\left(n + 4\right)} - n^{3} + {\left(3 \, n^{2} + 24 \, n + 47\right)} m - 12 \, n^{2} - 47 \, n - 60\right)} g^{2 \, m} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{5 \, {\left(m^{3} - 3 \, m^{2} {\left(n + 4\right)} - n^{3} + {\left(3 \, n^{2} + 24 \, n + 47\right)} m - 12 \, n^{2} - 47 \, n - 60\right)} g^{2 \, m} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{{\left(m^{3} - 3 \, m^{2} {\left(n + 4\right)} - n^{3} + {\left(3 \, n^{2} + 24 \, n + 47\right)} m - 12 \, n^{2} - 47 \, n - 60\right)} g^{2 \, m} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}}\right)} f}"," ",0,"((m^2 - m*(2*n + 11) + n^2 + 11*n + 32)*a^m*c^n*g^5 - 2*(m^2 - m*(2*n + 15) + n^2 + 15*n + 60)*a^m*c^n*g^5*sin(f*x + e)/(cos(f*x + e) + 1) - (3*m^2 - m*(6*n + 1) + 3*n^2 + n - 160)*a^m*c^n*g^5*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 8*(m^2 - m*(2*n + 7) + n^2 + 7*n - 20)*a^m*c^n*g^5*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 2*(m^2 - m*(2*n - 5) + n^2 - 5*n + 160)*a^m*c^n*g^5*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 4*(3*m^2 - m*(6*n + 13) + 3*n^2 + 13*n + 116)*a^m*c^n*g^5*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 2*(m^2 - m*(2*n - 5) + n^2 - 5*n + 160)*a^m*c^n*g^5*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 8*(m^2 - m*(2*n + 7) + n^2 + 7*n - 20)*a^m*c^n*g^5*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 - (3*m^2 - m*(6*n + 1) + 3*n^2 + n - 160)*a^m*c^n*g^5*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 - 2*(m^2 - m*(2*n + 15) + n^2 + 15*n + 60)*a^m*c^n*g^5*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + (m^2 - m*(2*n + 11) + n^2 + 11*n + 32)*a^m*c^n*g^5*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)*e^(2*n*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1) - 2*m*log(-sin(f*x + e)/(cos(f*x + e) + 1) + 1) + m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1) - n*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/(((m^3 - 3*m^2*(n + 4) - n^3 + (3*n^2 + 24*n + 47)*m - 12*n^2 - 47*n - 60)*g^(2*m) + 5*(m^3 - 3*m^2*(n + 4) - n^3 + (3*n^2 + 24*n + 47)*m - 12*n^2 - 47*n - 60)*g^(2*m)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 10*(m^3 - 3*m^2*(n + 4) - n^3 + (3*n^2 + 24*n + 47)*m - 12*n^2 - 47*n - 60)*g^(2*m)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 10*(m^3 - 3*m^2*(n + 4) - n^3 + (3*n^2 + 24*n + 47)*m - 12*n^2 - 47*n - 60)*g^(2*m)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 5*(m^3 - 3*m^2*(n + 4) - n^3 + (3*n^2 + 24*n + 47)*m - 12*n^2 - 47*n - 60)*g^(2*m)*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + (m^3 - 3*m^2*(n + 4) - n^3 + (3*n^2 + 24*n + 47)*m - 12*n^2 - 47*n - 60)*g^(2*m)*sin(f*x + e)^10/(cos(f*x + e) + 1)^10)*f)","B",0
176,1,485,0,2.800218," ","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=""maxima"")","\frac{{\left(a^{m} c^{n} g^{3} {\left(m - n - 4\right)} - \frac{2 \, a^{m} c^{n} g^{3} {\left(m - n - 6\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{a^{m} c^{n} g^{3} {\left(m - n + 12\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{4 \, a^{m} c^{n} g^{3} {\left(m - n + 2\right)} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{a^{m} c^{n} g^{3} {\left(m - n + 12\right)} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{2 \, a^{m} c^{n} g^{3} {\left(m - n - 6\right)} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{a^{m} c^{n} g^{3} {\left(m - n - 4\right)} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} e^{\left(2 \, n \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right) - 2 \, m \log\left(-\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) + m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right) - n \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left({\left(m^{2} - m {\left(2 \, n + 5\right)} + n^{2} + 5 \, n + 6\right)} g^{2 \, m} + \frac{3 \, {\left(m^{2} - m {\left(2 \, n + 5\right)} + n^{2} + 5 \, n + 6\right)} g^{2 \, m} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{3 \, {\left(m^{2} - m {\left(2 \, n + 5\right)} + n^{2} + 5 \, n + 6\right)} g^{2 \, m} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{{\left(m^{2} - m {\left(2 \, n + 5\right)} + n^{2} + 5 \, n + 6\right)} g^{2 \, m} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}}\right)} f}"," ",0,"(a^m*c^n*g^3*(m - n - 4) - 2*a^m*c^n*g^3*(m - n - 6)*sin(f*x + e)/(cos(f*x + e) + 1) - a^m*c^n*g^3*(m - n + 12)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 4*a^m*c^n*g^3*(m - n + 2)*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - a^m*c^n*g^3*(m - n + 12)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 2*a^m*c^n*g^3*(m - n - 6)*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + a^m*c^n*g^3*(m - n - 4)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*e^(2*n*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1) - 2*m*log(-sin(f*x + e)/(cos(f*x + e) + 1) + 1) + m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1) - n*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/(((m^2 - m*(2*n + 5) + n^2 + 5*n + 6)*g^(2*m) + 3*(m^2 - m*(2*n + 5) + n^2 + 5*n + 6)*g^(2*m)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 3*(m^2 - m*(2*n + 5) + n^2 + 5*n + 6)*g^(2*m)*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + (m^2 - m*(2*n + 5) + n^2 + 5*n + 6)*g^(2*m)*sin(f*x + e)^6/(cos(f*x + e) + 1)^6)*f)","B",0
177,1,207,0,1.261259," ","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=""maxima"")","\frac{{\left(a^{m} c^{n} g - \frac{2 \, a^{m} c^{n} g \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{a^{m} c^{n} g \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} e^{\left(2 \, n \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right) - 2 \, m \log\left(-\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) + m \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right) - n \log\left(\frac{\sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + 1\right)\right)}}{{\left(g^{2 \, m} {\left(m - n - 1\right)} + \frac{g^{2 \, m} {\left(m - n - 1\right)} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} f}"," ",0,"(a^m*c^n*g - 2*a^m*c^n*g*sin(f*x + e)/(cos(f*x + e) + 1) + a^m*c^n*g*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*e^(2*n*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1) - 2*m*log(-sin(f*x + e)/(cos(f*x + e) + 1) + 1) + m*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1) - n*log(sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 1))/((g^(2*m)*(m - n - 1) + g^(2*m)*(m - n - 1)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*f)","B",0
178,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((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
179,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-3-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((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
180,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-5-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((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
181,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-2*m)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^m,x, algorithm=""maxima"")","\int \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)}^{m}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(-2*m - 1)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^m, x)","F",0
182,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(3+n),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((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
183,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(2+n),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((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
184,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(1+n),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((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
185,1,145,0,0.470508," ","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=""maxima"")","\frac{a^{m} c^{n} g^{-m - n - 1} e^{\left(m \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - n \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) + 2 \, n \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right) - m \log\left(-\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right) - n \log\left(-\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)\right)}}{f {\left(m - n\right)}}"," ",0,"a^m*c^n*g^(-m - n - 1)*e^(m*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) - n*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1) + 2*n*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1) - m*log(-sin(f*x + e)/(cos(f*x + e) + 1) + 1) - n*log(-sin(f*x + e)/(cos(f*x + e) + 1) + 1))/(f*(m - n))","B",0
186,-2,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-1+n),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
187,-2,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-2+n),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
188,-2,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m-n)*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^(-3+n),x, algorithm=""maxima"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.","F(-2)",0
189,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
190,1,28,0,0.296537," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3}}{12 \, d}"," ",0,"1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3)/d","A",0
191,1,28,0,0.305954," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2}}{6 \, d}"," ",0,"1/6*(2*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2)/d","A",0
192,1,22,0,0.304621," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sin\left(d x + c\right)\right) + a \sin\left(d x + c\right)}{d}"," ",0,"(a*log(sin(d*x + c)) + a*sin(d*x + c))/d","A",0
193,1,25,0,0.303809," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \log\left(\sin\left(d x + c\right)\right) - \frac{a}{\sin\left(d x + c\right)}}{d}"," ",0,"(a*log(sin(d*x + c)) - a/sin(d*x + c))/d","A",0
194,1,24,0,0.304610," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, a \sin\left(d x + c\right) + a}{2 \, d \sin\left(d x + c\right)^{2}}"," ",0,"-1/2*(2*a*sin(d*x + c) + a)/(d*sin(d*x + c)^2)","A",0
195,1,26,0,0.301589," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, a \sin\left(d x + c\right) + 2 \, a}{6 \, d \sin\left(d x + c\right)^{3}}"," ",0,"-1/6*(3*a*sin(d*x + c) + 2*a)/(d*sin(d*x + c)^3)","A",0
196,1,26,0,0.302921," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, a \sin\left(d x + c\right) + 3 \, a}{12 \, d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(4*a*sin(d*x + c) + 3*a)/(d*sin(d*x + c)^4)","A",0
197,1,45,0,0.296679," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, a^{2} \sin\left(d x + c\right)^{5} + 15 \, a^{2} \sin\left(d x + c\right)^{4} + 10 \, a^{2} \sin\left(d x + c\right)^{3}}{30 \, d}"," ",0,"1/30*(6*a^2*sin(d*x + c)^5 + 15*a^2*sin(d*x + c)^4 + 10*a^2*sin(d*x + c)^3)/d","A",0
198,1,45,0,0.298139," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} \sin\left(d x + c\right)^{4} + 8 \, a^{2} \sin\left(d x + c\right)^{3} + 6 \, a^{2} \sin\left(d x + c\right)^{2}}{12 \, d}"," ",0,"1/12*(3*a^2*sin(d*x + c)^4 + 8*a^2*sin(d*x + c)^3 + 6*a^2*sin(d*x + c)^2)/d","A",0
199,1,41,0,0.336926," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + 4 \, a^{2} \sin\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a^2*sin(d*x + c)^2 + 2*a^2*log(sin(d*x + c)) + 4*a^2*sin(d*x + c))/d","A",0
200,1,40,0,0.351646," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + a^{2} \sin\left(d x + c\right) - \frac{a^{2}}{\sin\left(d x + c\right)}}{d}"," ",0,"(2*a^2*log(sin(d*x + c)) + a^2*sin(d*x + c) - a^2/sin(d*x + c))/d","A",0
201,1,43,0,0.350522," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, a^{2} \log\left(\sin\left(d x + c\right)\right) - \frac{4 \, a^{2} \sin\left(d x + c\right) + a^{2}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*a^2*log(sin(d*x + c)) - (4*a^2*sin(d*x + c) + a^2)/sin(d*x + c)^2)/d","A",0
202,1,41,0,0.332227," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} \sin\left(d x + c\right)^{2} + 3 \, a^{2} \sin\left(d x + c\right) + a^{2}}{3 \, d \sin\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*a^2*sin(d*x + c)^2 + 3*a^2*sin(d*x + c) + a^2)/(d*sin(d*x + c)^3)","A",0
203,1,43,0,0.308934," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, a^{2} \sin\left(d x + c\right)^{2} + 8 \, a^{2} \sin\left(d x + c\right) + 3 \, a^{2}}{12 \, d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(6*a^2*sin(d*x + c)^2 + 8*a^2*sin(d*x + c) + 3*a^2)/(d*sin(d*x + c)^4)","A",0
204,1,43,0,0.367781," ","integrate(cos(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{10 \, a^{2} \sin\left(d x + c\right)^{2} + 15 \, a^{2} \sin\left(d x + c\right) + 6 \, a^{2}}{30 \, d \sin\left(d x + c\right)^{5}}"," ",0,"-1/30*(10*a^2*sin(d*x + c)^2 + 15*a^2*sin(d*x + c) + 6*a^2)/(d*sin(d*x + c)^5)","A",0
205,1,43,0,0.340443," ","integrate(cos(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{15 \, a^{2} \sin\left(d x + c\right)^{2} + 24 \, a^{2} \sin\left(d x + c\right) + 10 \, a^{2}}{60 \, d \sin\left(d x + c\right)^{6}}"," ",0,"-1/60*(15*a^2*sin(d*x + c)^2 + 24*a^2*sin(d*x + c) + 10*a^2)/(d*sin(d*x + c)^6)","A",0
206,1,58,0,0.312403," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{20 \, a^{3} \sin\left(d x + c\right)^{7} + 70 \, a^{3} \sin\left(d x + c\right)^{6} + 84 \, a^{3} \sin\left(d x + c\right)^{5} + 35 \, a^{3} \sin\left(d x + c\right)^{4}}{140 \, d}"," ",0,"1/140*(20*a^3*sin(d*x + c)^7 + 70*a^3*sin(d*x + c)^6 + 84*a^3*sin(d*x + c)^5 + 35*a^3*sin(d*x + c)^4)/d","A",0
207,1,58,0,0.327693," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{10 \, a^{3} \sin\left(d x + c\right)^{6} + 36 \, a^{3} \sin\left(d x + c\right)^{5} + 45 \, a^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{3} \sin\left(d x + c\right)^{3}}{60 \, d}"," ",0,"1/60*(10*a^3*sin(d*x + c)^6 + 36*a^3*sin(d*x + c)^5 + 45*a^3*sin(d*x + c)^4 + 20*a^3*sin(d*x + c)^3)/d","A",0
208,1,58,0,0.329349," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, a^{3} \sin\left(d x + c\right)^{5} + 15 \, a^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{3} \sin\left(d x + c\right)^{3} + 10 \, a^{3} \sin\left(d x + c\right)^{2}}{20 \, d}"," ",0,"1/20*(4*a^3*sin(d*x + c)^5 + 15*a^3*sin(d*x + c)^4 + 20*a^3*sin(d*x + c)^3 + 10*a^3*sin(d*x + c)^2)/d","A",0
209,1,55,0,0.333507," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, a^{3} \sin\left(d x + c\right)^{3} + 9 \, a^{3} \sin\left(d x + c\right)^{2} + 6 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 18 \, a^{3} \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*a^3*sin(d*x + c)^3 + 9*a^3*sin(d*x + c)^2 + 6*a^3*log(sin(d*x + c)) + 18*a^3*sin(d*x + c))/d","A",0
210,1,54,0,0.311461," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3} \sin\left(d x + c\right)^{2} + 6 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 6 \, a^{3} \sin\left(d x + c\right) - \frac{2 \, a^{3}}{\sin\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(a^3*sin(d*x + c)^2 + 6*a^3*log(sin(d*x + c)) + 6*a^3*sin(d*x + c) - 2*a^3/sin(d*x + c))/d","A",0
211,1,54,0,0.321944," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 2 \, a^{3} \sin\left(d x + c\right) - \frac{6 \, a^{3} \sin\left(d x + c\right) + a^{3}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(6*a^3*log(sin(d*x + c)) + 2*a^3*sin(d*x + c) - (6*a^3*sin(d*x + c) + a^3)/sin(d*x + c)^2)/d","A",0
212,1,58,0,0.418811," ","integrate(cos(d*x+c)*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{6 \, a^{3} \log\left(\sin\left(d x + c\right)\right) - \frac{18 \, a^{3} \sin\left(d x + c\right)^{2} + 9 \, a^{3} \sin\left(d x + c\right) + 2 \, a^{3}}{\sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*a^3*log(sin(d*x + c)) - (18*a^3*sin(d*x + c)^2 + 9*a^3*sin(d*x + c) + 2*a^3)/sin(d*x + c)^3)/d","A",0
213,1,54,0,0.498655," ","integrate(cos(d*x+c)*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, a^{3} \sin\left(d x + c\right)^{3} + 6 \, a^{3} \sin\left(d x + c\right)^{2} + 4 \, a^{3} \sin\left(d x + c\right) + a^{3}}{4 \, d \sin\left(d x + c\right)^{4}}"," ",0,"-1/4*(4*a^3*sin(d*x + c)^3 + 6*a^3*sin(d*x + c)^2 + 4*a^3*sin(d*x + c) + a^3)/(d*sin(d*x + c)^4)","A",0
214,1,56,0,0.509634," ","integrate(cos(d*x+c)*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{10 \, a^{3} \sin\left(d x + c\right)^{3} + 20 \, a^{3} \sin\left(d x + c\right)^{2} + 15 \, a^{3} \sin\left(d x + c\right) + 4 \, a^{3}}{20 \, d \sin\left(d x + c\right)^{5}}"," ",0,"-1/20*(10*a^3*sin(d*x + c)^3 + 20*a^3*sin(d*x + c)^2 + 15*a^3*sin(d*x + c) + 4*a^3)/(d*sin(d*x + c)^5)","A",0
215,1,56,0,0.342921," ","integrate(cos(d*x+c)*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{20 \, a^{3} \sin\left(d x + c\right)^{3} + 45 \, a^{3} \sin\left(d x + c\right)^{2} + 36 \, a^{3} \sin\left(d x + c\right) + 10 \, a^{3}}{60 \, d \sin\left(d x + c\right)^{6}}"," ",0,"-1/60*(20*a^3*sin(d*x + c)^3 + 45*a^3*sin(d*x + c)^2 + 36*a^3*sin(d*x + c) + 10*a^3)/(d*sin(d*x + c)^6)","A",0
216,1,56,0,0.375544," ","integrate(cos(d*x+c)*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{35 \, a^{3} \sin\left(d x + c\right)^{3} + 84 \, a^{3} \sin\left(d x + c\right)^{2} + 70 \, a^{3} \sin\left(d x + c\right) + 20 \, a^{3}}{140 \, d \sin\left(d x + c\right)^{7}}"," ",0,"-1/140*(35*a^3*sin(d*x + c)^3 + 84*a^3*sin(d*x + c)^2 + 70*a^3*sin(d*x + c) + 20*a^3)/(d*sin(d*x + c)^7)","A",0
217,1,71,0,0.315443," ","integrate(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{70 \, a^{4} \sin\left(d x + c\right)^{9} + 315 \, a^{4} \sin\left(d x + c\right)^{8} + 540 \, a^{4} \sin\left(d x + c\right)^{7} + 420 \, a^{4} \sin\left(d x + c\right)^{6} + 126 \, a^{4} \sin\left(d x + c\right)^{5}}{630 \, d}"," ",0,"1/630*(70*a^4*sin(d*x + c)^9 + 315*a^4*sin(d*x + c)^8 + 540*a^4*sin(d*x + c)^7 + 420*a^4*sin(d*x + c)^6 + 126*a^4*sin(d*x + c)^5)/d","A",0
218,1,71,0,0.297328," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{35 \, a^{4} \sin\left(d x + c\right)^{8} + 160 \, a^{4} \sin\left(d x + c\right)^{7} + 280 \, a^{4} \sin\left(d x + c\right)^{6} + 224 \, a^{4} \sin\left(d x + c\right)^{5} + 70 \, a^{4} \sin\left(d x + c\right)^{4}}{280 \, d}"," ",0,"1/280*(35*a^4*sin(d*x + c)^8 + 160*a^4*sin(d*x + c)^7 + 280*a^4*sin(d*x + c)^6 + 224*a^4*sin(d*x + c)^5 + 70*a^4*sin(d*x + c)^4)/d","A",0
219,1,71,0,0.311257," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{15 \, a^{4} \sin\left(d x + c\right)^{7} + 70 \, a^{4} \sin\left(d x + c\right)^{6} + 126 \, a^{4} \sin\left(d x + c\right)^{5} + 105 \, a^{4} \sin\left(d x + c\right)^{4} + 35 \, a^{4} \sin\left(d x + c\right)^{3}}{105 \, d}"," ",0,"1/105*(15*a^4*sin(d*x + c)^7 + 70*a^4*sin(d*x + c)^6 + 126*a^4*sin(d*x + c)^5 + 105*a^4*sin(d*x + c)^4 + 35*a^4*sin(d*x + c)^3)/d","A",0
220,1,71,0,0.585981," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{5 \, a^{4} \sin\left(d x + c\right)^{6} + 24 \, a^{4} \sin\left(d x + c\right)^{5} + 45 \, a^{4} \sin\left(d x + c\right)^{4} + 40 \, a^{4} \sin\left(d x + c\right)^{3} + 15 \, a^{4} \sin\left(d x + c\right)^{2}}{30 \, d}"," ",0,"1/30*(5*a^4*sin(d*x + c)^6 + 24*a^4*sin(d*x + c)^5 + 45*a^4*sin(d*x + c)^4 + 40*a^4*sin(d*x + c)^3 + 15*a^4*sin(d*x + c)^2)/d","A",0
221,1,68,0,0.429534," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 36 \, a^{4} \sin\left(d x + c\right)^{2} + 12 \, a^{4} \log\left(\sin\left(d x + c\right)\right) + 48 \, a^{4} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 36*a^4*sin(d*x + c)^2 + 12*a^4*log(sin(d*x + c)) + 48*a^4*sin(d*x + c))/d","A",0
222,1,67,0,0.403368," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{a^{4} \sin\left(d x + c\right)^{3} + 6 \, a^{4} \sin\left(d x + c\right)^{2} + 12 \, a^{4} \log\left(\sin\left(d x + c\right)\right) + 18 \, a^{4} \sin\left(d x + c\right) - \frac{3 \, a^{4}}{\sin\left(d x + c\right)}}{3 \, d}"," ",0,"1/3*(a^4*sin(d*x + c)^3 + 6*a^4*sin(d*x + c)^2 + 12*a^4*log(sin(d*x + c)) + 18*a^4*sin(d*x + c) - 3*a^4/sin(d*x + c))/d","A",0
223,1,66,0,0.373314," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{a^{4} \sin\left(d x + c\right)^{2} + 12 \, a^{4} \log\left(\sin\left(d x + c\right)\right) + 8 \, a^{4} \sin\left(d x + c\right) - \frac{8 \, a^{4} \sin\left(d x + c\right) + a^{4}}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(a^4*sin(d*x + c)^2 + 12*a^4*log(sin(d*x + c)) + 8*a^4*sin(d*x + c) - (8*a^4*sin(d*x + c) + a^4)/sin(d*x + c)^2)/d","A",0
224,1,63,0,0.405849," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{3 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3} + 6 \, \sin\left(d x + c\right)^{2} - 12 \, \sin\left(d x + c\right)}{a} + \frac{12 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a}}{12 \, d}"," ",0,"1/12*((3*sin(d*x + c)^4 - 4*sin(d*x + c)^3 + 6*sin(d*x + c)^2 - 12*sin(d*x + c))/a + 12*log(sin(d*x + c) + 1)/a)/d","A",0
225,1,53,0,0.305164," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} + 6 \, \sin\left(d x + c\right)}{a} - \frac{6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a}}{6 \, d}"," ",0,"1/6*((2*sin(d*x + c)^3 - 3*sin(d*x + c)^2 + 6*sin(d*x + c))/a - 6*log(sin(d*x + c) + 1)/a)/d","A",0
226,1,41,0,0.312112," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)}{a} + \frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a}}{2 \, d}"," ",0,"1/2*((sin(d*x + c)^2 - 2*sin(d*x + c))/a + 2*log(sin(d*x + c) + 1)/a)/d","A",0
227,1,30,0,0.315057," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\sin\left(d x + c\right)}{a}}{d}"," ",0,"-(log(sin(d*x + c) + 1)/a - sin(d*x + c)/a)/d","A",0
228,1,31,0,0.319173," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\sin\left(d x + c\right)\right)}{a}}{d}"," ",0,"-(log(sin(d*x + c) + 1)/a - log(sin(d*x + c))/a)/d","A",0
229,1,43,0,0.305781," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{\log\left(\sin\left(d x + c\right)\right)}{a} - \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"(log(sin(d*x + c) + 1)/a - log(sin(d*x + c))/a - 1/(a*sin(d*x + c)))/d","A",0
230,1,55,0,0.317625," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a} - \frac{2 \, \sin\left(d x + c\right) - 1}{a \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*log(sin(d*x + c) + 1)/a - 2*log(sin(d*x + c))/a - (2*sin(d*x + c) - 1)/(a*sin(d*x + c)^2))/d","A",0
231,1,65,0,0.313410," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{6 \, \log\left(\sin\left(d x + c\right)\right)}{a} - \frac{6 \, \sin\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) + 2}{a \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*log(sin(d*x + c) + 1)/a - 6*log(sin(d*x + c))/a - (6*sin(d*x + c)^2 - 3*sin(d*x + c) + 2)/(a*sin(d*x + c)^3))/d","A",0
232,1,70,0,0.309834," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{3}{a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} + 9 \, \sin\left(d x + c\right)}{a^{2}} + \frac{12 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}}}{3 \, d}"," ",0,"-1/3*(3/(a^2*sin(d*x + c) + a^2) - (sin(d*x + c)^3 - 3*sin(d*x + c)^2 + 9*sin(d*x + c))/a^2 + 12*log(sin(d*x + c) + 1)/a^2)/d","A",0
233,1,59,0,0.320224," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2}{a^{2} \sin\left(d x + c\right) + a^{2}} + \frac{\sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right)}{a^{2}} + \frac{6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}}}{2 \, d}"," ",0,"1/2*(2/(a^2*sin(d*x + c) + a^2) + (sin(d*x + c)^2 - 4*sin(d*x + c))/a^2 + 6*log(sin(d*x + c) + 1)/a^2)/d","A",0
234,1,47,0,0.378210," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{1}{a^{2} \sin\left(d x + c\right) + a^{2}} + \frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} - \frac{\sin\left(d x + c\right)}{a^{2}}}{d}"," ",0,"-(1/(a^2*sin(d*x + c) + a^2) + 2*log(sin(d*x + c) + 1)/a^2 - sin(d*x + c)/a^2)/d","A",0
235,1,34,0,0.341400," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{1}{a^{2} \sin\left(d x + c\right) + a^{2}} + \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}}}{d}"," ",0,"(1/(a^2*sin(d*x + c) + a^2) + log(sin(d*x + c) + 1)/a^2)/d","A",0
236,1,46,0,0.489624," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{1}{a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{\log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{d}"," ",0,"(1/(a^2*sin(d*x + c) + a^2) - log(sin(d*x + c) + 1)/a^2 + log(sin(d*x + c))/a^2)/d","A",0
237,1,68,0,0.316457," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, \sin\left(d x + c\right) + 1}{a^{2} \sin\left(d x + c\right)^{2} + a^{2} \sin\left(d x + c\right)} - \frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{d}"," ",0,"-((2*sin(d*x + c) + 1)/(a^2*sin(d*x + c)^2 + a^2*sin(d*x + c)) - 2*log(sin(d*x + c) + 1)/a^2 + 2*log(sin(d*x + c))/a^2)/d","A",0
238,1,80,0,0.296352," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{6 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 1}{a^{2} \sin\left(d x + c\right)^{3} + a^{2} \sin\left(d x + c\right)^{2}} - \frac{6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{6 \, \log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{2 \, d}"," ",0,"1/2*((6*sin(d*x + c)^2 + 3*sin(d*x + c) - 1)/(a^2*sin(d*x + c)^3 + a^2*sin(d*x + c)^2) - 6*log(sin(d*x + c) + 1)/a^2 + 6*log(sin(d*x + c))/a^2)/d","A",0
239,1,90,0,0.323017," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{12 \, \sin\left(d x + c\right)^{3} + 6 \, \sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}{a^{2} \sin\left(d x + c\right)^{4} + a^{2} \sin\left(d x + c\right)^{3}} - \frac{12 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{12 \, \log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{3 \, d}"," ",0,"-1/3*((12*sin(d*x + c)^3 + 6*sin(d*x + c)^2 - 2*sin(d*x + c) + 1)/(a^2*sin(d*x + c)^4 + a^2*sin(d*x + c)^3) - 12*log(sin(d*x + c) + 1)/a^2 + 12*log(sin(d*x + c))/a^2)/d","A",0
240,1,95,0,0.318425," ","integrate(cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(10 \, \sin\left(d x + c\right) + 9\right)}}{a^{3} \sin\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) + a^{3}} - \frac{2 \, \sin\left(d x + c\right)^{3} - 9 \, \sin\left(d x + c\right)^{2} + 36 \, \sin\left(d x + c\right)}{a^{3}} + \frac{60 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}}}{6 \, d}"," ",0,"-1/6*(3*(10*sin(d*x + c) + 9)/(a^3*sin(d*x + c)^2 + 2*a^3*sin(d*x + c) + a^3) - (2*sin(d*x + c)^3 - 9*sin(d*x + c)^2 + 36*sin(d*x + c))/a^3 + 60*log(sin(d*x + c) + 1)/a^3)/d","A",0
241,1,81,0,0.311285," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{8 \, \sin\left(d x + c\right) + 7}{a^{3} \sin\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) + a^{3}} + \frac{\sin\left(d x + c\right)^{2} - 6 \, \sin\left(d x + c\right)}{a^{3}} + \frac{12 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((8*sin(d*x + c) + 7)/(a^3*sin(d*x + c)^2 + 2*a^3*sin(d*x + c) + a^3) + (sin(d*x + c)^2 - 6*sin(d*x + c))/a^3 + 12*log(sin(d*x + c) + 1)/a^3)/d","A",0
242,1,71,0,0.299298," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{6 \, \sin\left(d x + c\right) + 5}{a^{3} \sin\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) + a^{3}} + \frac{6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} - \frac{2 \, \sin\left(d x + c\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*((6*sin(d*x + c) + 5)/(a^3*sin(d*x + c)^2 + 2*a^3*sin(d*x + c) + a^3) + 6*log(sin(d*x + c) + 1)/a^3 - 2*sin(d*x + c)/a^3)/d","A",0
243,1,60,0,0.407545," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{4 \, \sin\left(d x + c\right) + 3}{a^{3} \sin\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) + a^{3}} + \frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((4*sin(d*x + c) + 3)/(a^3*sin(d*x + c)^2 + 2*a^3*sin(d*x + c) + a^3) + 2*log(sin(d*x + c) + 1)/a^3)/d","A",0
244,1,44,0,0.393290," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, \sin\left(d x + c\right) + 1}{2 \, {\left(a^{3} \sin\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) + a^{3}\right)} d}"," ",0,"-1/2*(2*sin(d*x + c) + 1)/((a^3*sin(d*x + c)^2 + 2*a^3*sin(d*x + c) + a^3)*d)","A",0
245,1,72,0,0.433178," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, \sin\left(d x + c\right) + 3}{a^{3} \sin\left(d x + c\right)^{2} + 2 \, a^{3} \sin\left(d x + c\right) + a^{3}} - \frac{2 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((2*sin(d*x + c) + 3)/(a^3*sin(d*x + c)^2 + 2*a^3*sin(d*x + c) + a^3) - 2*log(sin(d*x + c) + 1)/a^3 + 2*log(sin(d*x + c))/a^3)/d","A",0
246,1,91,0,0.447887," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{6 \, \sin\left(d x + c\right)^{2} + 9 \, \sin\left(d x + c\right) + 2}{a^{3} \sin\left(d x + c\right)^{3} + 2 \, a^{3} \sin\left(d x + c\right)^{2} + a^{3} \sin\left(d x + c\right)} - \frac{6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{6 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"-1/2*((6*sin(d*x + c)^2 + 9*sin(d*x + c) + 2)/(a^3*sin(d*x + c)^3 + 2*a^3*sin(d*x + c)^2 + a^3*sin(d*x + c)) - 6*log(sin(d*x + c) + 1)/a^3 + 6*log(sin(d*x + c))/a^3)/d","A",0
247,1,103,0,0.313266," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{12 \, \sin\left(d x + c\right)^{3} + 18 \, \sin\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right) - 1}{a^{3} \sin\left(d x + c\right)^{4} + 2 \, a^{3} \sin\left(d x + c\right)^{3} + a^{3} \sin\left(d x + c\right)^{2}} - \frac{12 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{12 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{2 \, d}"," ",0,"1/2*((12*sin(d*x + c)^3 + 18*sin(d*x + c)^2 + 4*sin(d*x + c) - 1)/(a^3*sin(d*x + c)^4 + 2*a^3*sin(d*x + c)^3 + a^3*sin(d*x + c)^2) - 12*log(sin(d*x + c) + 1)/a^3 + 12*log(sin(d*x + c))/a^3)/d","A",0
248,1,113,0,0.314861," ","integrate(cos(d*x+c)*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{60 \, \sin\left(d x + c\right)^{4} + 90 \, \sin\left(d x + c\right)^{3} + 20 \, \sin\left(d x + c\right)^{2} - 5 \, \sin\left(d x + c\right) + 2}{a^{3} \sin\left(d x + c\right)^{5} + 2 \, a^{3} \sin\left(d x + c\right)^{4} + a^{3} \sin\left(d x + c\right)^{3}} - \frac{60 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} + \frac{60 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{6 \, d}"," ",0,"-1/6*((60*sin(d*x + c)^4 + 90*sin(d*x + c)^3 + 20*sin(d*x + c)^2 - 5*sin(d*x + c) + 2)/(a^3*sin(d*x + c)^5 + 2*a^3*sin(d*x + c)^4 + a^3*sin(d*x + c)^3) - 60*log(sin(d*x + c) + 1)/a^3 + 60*log(sin(d*x + c))/a^3)/d","A",0
249,1,105,0,0.347759," ","integrate(cos(d*x+c)*sin(d*x+c)^5/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{60 \, \sin\left(d x + c\right)^{2} + 105 \, \sin\left(d x + c\right) + 47}{a^{4} \sin\left(d x + c\right)^{3} + 3 \, a^{4} \sin\left(d x + c\right)^{2} + 3 \, a^{4} \sin\left(d x + c\right) + a^{4}} + \frac{3 \, {\left(\sin\left(d x + c\right)^{2} - 8 \, \sin\left(d x + c\right)\right)}}{a^{4}} + \frac{60 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}}}{6 \, d}"," ",0,"1/6*((60*sin(d*x + c)^2 + 105*sin(d*x + c) + 47)/(a^4*sin(d*x + c)^3 + 3*a^4*sin(d*x + c)^2 + 3*a^4*sin(d*x + c) + a^4) + 3*(sin(d*x + c)^2 - 8*sin(d*x + c))/a^4 + 60*log(sin(d*x + c) + 1)/a^4)/d","A",0
250,1,94,0,0.379144," ","integrate(cos(d*x+c)*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{18 \, \sin\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right) + 13}{a^{4} \sin\left(d x + c\right)^{3} + 3 \, a^{4} \sin\left(d x + c\right)^{2} + 3 \, a^{4} \sin\left(d x + c\right) + a^{4}} + \frac{12 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} - \frac{3 \, \sin\left(d x + c\right)}{a^{4}}}{3 \, d}"," ",0,"-1/3*((18*sin(d*x + c)^2 + 30*sin(d*x + c) + 13)/(a^4*sin(d*x + c)^3 + 3*a^4*sin(d*x + c)^2 + 3*a^4*sin(d*x + c) + a^4) + 12*log(sin(d*x + c) + 1)/a^4 - 3*sin(d*x + c)/a^4)/d","A",0
251,1,83,0,0.304909," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{18 \, \sin\left(d x + c\right)^{2} + 27 \, \sin\left(d x + c\right) + 11}{a^{4} \sin\left(d x + c\right)^{3} + 3 \, a^{4} \sin\left(d x + c\right)^{2} + 3 \, a^{4} \sin\left(d x + c\right) + a^{4}} + \frac{6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}}}{6 \, d}"," ",0,"1/6*((18*sin(d*x + c)^2 + 27*sin(d*x + c) + 11)/(a^4*sin(d*x + c)^3 + 3*a^4*sin(d*x + c)^2 + 3*a^4*sin(d*x + c) + a^4) + 6*log(sin(d*x + c) + 1)/a^4)/d","A",0
252,1,67,0,0.399619," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) + 1}{3 \, {\left(a^{4} \sin\left(d x + c\right)^{3} + 3 \, a^{4} \sin\left(d x + c\right)^{2} + 3 \, a^{4} \sin\left(d x + c\right) + a^{4}\right)} d}"," ",0,"-1/3*(3*sin(d*x + c)^2 + 3*sin(d*x + c) + 1)/((a^4*sin(d*x + c)^3 + 3*a^4*sin(d*x + c)^2 + 3*a^4*sin(d*x + c) + a^4)*d)","B",0
253,1,57,0,0.311944," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{3 \, \sin\left(d x + c\right) + 1}{6 \, {\left(a^{4} \sin\left(d x + c\right)^{3} + 3 \, a^{4} \sin\left(d x + c\right)^{2} + 3 \, a^{4} \sin\left(d x + c\right) + a^{4}\right)} d}"," ",0,"-1/6*(3*sin(d*x + c) + 1)/((a^4*sin(d*x + c)^3 + 3*a^4*sin(d*x + c)^2 + 3*a^4*sin(d*x + c) + a^4)*d)","A",0
254,1,95,0,0.362647," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{6 \, \sin\left(d x + c\right)^{2} + 15 \, \sin\left(d x + c\right) + 11}{a^{4} \sin\left(d x + c\right)^{3} + 3 \, a^{4} \sin\left(d x + c\right)^{2} + 3 \, a^{4} \sin\left(d x + c\right) + a^{4}} - \frac{6 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} + \frac{6 \, \log\left(\sin\left(d x + c\right)\right)}{a^{4}}}{6 \, d}"," ",0,"1/6*((6*sin(d*x + c)^2 + 15*sin(d*x + c) + 11)/(a^4*sin(d*x + c)^3 + 3*a^4*sin(d*x + c)^2 + 3*a^4*sin(d*x + c) + a^4) - 6*log(sin(d*x + c) + 1)/a^4 + 6*log(sin(d*x + c))/a^4)/d","A",0
255,1,114,0,0.389762," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{12 \, \sin\left(d x + c\right)^{3} + 30 \, \sin\left(d x + c\right)^{2} + 22 \, \sin\left(d x + c\right) + 3}{a^{4} \sin\left(d x + c\right)^{4} + 3 \, a^{4} \sin\left(d x + c\right)^{3} + 3 \, a^{4} \sin\left(d x + c\right)^{2} + a^{4} \sin\left(d x + c\right)} - \frac{12 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} + \frac{12 \, \log\left(\sin\left(d x + c\right)\right)}{a^{4}}}{3 \, d}"," ",0,"-1/3*((12*sin(d*x + c)^3 + 30*sin(d*x + c)^2 + 22*sin(d*x + c) + 3)/(a^4*sin(d*x + c)^4 + 3*a^4*sin(d*x + c)^3 + 3*a^4*sin(d*x + c)^2 + a^4*sin(d*x + c)) - 12*log(sin(d*x + c) + 1)/a^4 + 12*log(sin(d*x + c))/a^4)/d","A",0
256,1,126,0,0.352075," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{60 \, \sin\left(d x + c\right)^{4} + 150 \, \sin\left(d x + c\right)^{3} + 110 \, \sin\left(d x + c\right)^{2} + 15 \, \sin\left(d x + c\right) - 3}{a^{4} \sin\left(d x + c\right)^{5} + 3 \, a^{4} \sin\left(d x + c\right)^{4} + 3 \, a^{4} \sin\left(d x + c\right)^{3} + a^{4} \sin\left(d x + c\right)^{2}} - \frac{60 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} + \frac{60 \, \log\left(\sin\left(d x + c\right)\right)}{a^{4}}}{6 \, d}"," ",0,"1/6*((60*sin(d*x + c)^4 + 150*sin(d*x + c)^3 + 110*sin(d*x + c)^2 + 15*sin(d*x + c) - 3)/(a^4*sin(d*x + c)^5 + 3*a^4*sin(d*x + c)^4 + 3*a^4*sin(d*x + c)^3 + a^4*sin(d*x + c)^2) - 60*log(sin(d*x + c) + 1)/a^4 + 60*log(sin(d*x + c))/a^4)/d","A",0
257,1,61,0,0.405612," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\frac{\sqrt{a} \log\left(\frac{\sqrt{a \sin\left(d x + c\right) + a} - \sqrt{a}}{\sqrt{a \sin\left(d x + c\right) + a} + \sqrt{a}}\right) + 2 \, \sqrt{a \sin\left(d x + c\right) + a}}{d}"," ",0,"(sqrt(a)*log((sqrt(a*sin(d*x + c) + a) - sqrt(a))/(sqrt(a*sin(d*x + c) + a) + sqrt(a))) + 2*sqrt(a*sin(d*x + c) + a))/d","A",0
258,1,103,0,0.310825," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{a^{4} \sin\left(d x + c\right)^{n + 5}}{n + 5} + \frac{4 \, a^{4} \sin\left(d x + c\right)^{n + 4}}{n + 4} + \frac{6 \, a^{4} \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{4 \, a^{4} \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a^{4} \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(a^4*sin(d*x + c)^(n + 5)/(n + 5) + 4*a^4*sin(d*x + c)^(n + 4)/(n + 4) + 6*a^4*sin(d*x + c)^(n + 3)/(n + 3) + 4*a^4*sin(d*x + c)^(n + 2)/(n + 2) + a^4*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
259,1,83,0,0.465812," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{a^{3} \sin\left(d x + c\right)^{n + 4}}{n + 4} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a^{3} \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(a^3*sin(d*x + c)^(n + 4)/(n + 4) + 3*a^3*sin(d*x + c)^(n + 3)/(n + 3) + 3*a^3*sin(d*x + c)^(n + 2)/(n + 2) + a^3*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
260,1,63,0,0.316223," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{a^{2} \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a^{2} \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(a^2*sin(d*x + c)^(n + 3)/(n + 3) + 2*a^2*sin(d*x + c)^(n + 2)/(n + 2) + a^2*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
261,1,39,0,0.443249," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{a \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(a*sin(d*x + c)^(n + 2)/(n + 2) + a*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
262,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a), x)","F",0
263,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a)^2, x)","F",0
264,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a)^3, x)","F",0
265,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)/(a*sin(d*x + c) + a)^4, x)","F",0
266,1,65,0,0.334511," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{64 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{960 \, d}"," ",0,"1/960*(64*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a - 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a)/d","A",0
267,1,52,0,0.313055," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a + 15 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a}{480 \, d}"," ",0,"1/480*(32*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a + 15*(4*d*x + 4*c - sin(4*d*x + 4*c))*a)/d","A",0
268,1,39,0,0.309714," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, a \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a}{96 \, d}"," ",0,"-1/96*(32*a*cos(d*x + c)^3 - 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*a)/d","A",0
269,1,57,0,0.309179," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a + 2 \, a {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a + 2*a*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
270,1,54,0,0.461725," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a - a {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c + 1/tan(d*x + c))*a - a*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
271,1,66,0,0.453637," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a - a {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(4*(d*x + c + 1/tan(d*x + c))*a - a*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)))/d","A",0
272,1,61,0,0.313815," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{4 \, a}{\tan\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"1/12*(3*a*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) - 4*a/tan(d*x + c)^3)/d","A",0
273,1,80,0,0.316115," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, a {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{16 \, a}{\tan\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"-1/48*(3*a*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 16*a/tan(d*x + c)^3)/d","A",0
274,1,92,0,0.319408," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{15 \, a {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{16 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a}{\tan\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"-1/240*(15*a*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 16*(5*tan(d*x + c)^2 + 3)*a/tan(d*x + c)^5)/d","A",0
275,1,105,0,0.330740," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{32 \, {\left(15 \, \cos\left(d x + c\right)^{7} - 42 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3}\right)} a^{2} - 224 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{2} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{3360 \, d}"," ",0,"-1/3360*(32*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*a^2 - 224*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^2 + 35*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a^2)/d","A",0
276,1,93,0,0.331232," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{128 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{2} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} + 30 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{960 \, d}"," ",0,"1/960*(128*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^2 - 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a^2 + 30*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^2)/d","A",0
277,1,69,0,0.336472," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{80 \, a^{2} \cos\left(d x + c\right)^{3} - 16 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{2} - 15 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{240 \, d}"," ",0,"-1/240*(80*a^2*cos(d*x + c)^3 - 16*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^2 - 15*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^2)/d","A",0
278,1,75,0,0.349332," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, a^{2} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 3 \, a^{2} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"-1/6*(2*a^2*cos(d*x + c)^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2 - 3*a^2*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
279,1,79,0,0.439225," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 4 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} + 4 \, a^{2} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a^2 - 4*(d*x + c + 1/tan(d*x + c))*a^2 + 4*a^2*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
280,1,104,0,0.582622," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{8 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} - a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 2 \, a^{2} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(8*(d*x + c + 1/tan(d*x + c))*a^2 - a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) - 2*a^2*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
281,1,83,0,0.422899," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} - 3 \, a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{2 \, a^{2}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c + 1/tan(d*x + c))*a^2 - 3*a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 2*a^2/tan(d*x + c)^3)/d","A",0
282,1,130,0,0.344749," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 12 \, a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{32 \, a^{2}}{\tan\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"-1/48*(3*a^2*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 12*a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 32*a^2/tan(d*x + c)^3)/d","A",0
283,1,109,0,0.344245," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{15 \, a^{2} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{40 \, a^{2}}{\tan\left(d x + c\right)^{3}} + \frac{8 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{2}}{\tan\left(d x + c\right)^{5}}}{120 \, d}"," ",0,"-1/120*(15*a^2*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 40*a^2/tan(d*x + c)^3 + 8*(5*tan(d*x + c)^2 + 3)*a^2/tan(d*x + c)^5)/d","A",0
284,1,187,0,0.353119," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{5 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 30 \, a^{2} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{64 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{2}}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(5*a^2*(2*(3*cos(d*x + c)^5 - 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 30*a^2*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 64*(5*tan(d*x + c)^2 + 3)*a^2/tan(d*x + c)^5)/d","A",0
285,1,129,0,0.329306," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{64 \, {\left(15 \, \cos\left(d x + c\right)^{7} - 42 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3}\right)} a^{3} - 1344 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{3} + 105 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 210 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{6720 \, d}"," ",0,"-1/6720*(64*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*a^3 - 1344*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^3 + 105*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a^3 - 210*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^3)/d","A",0
286,1,106,0,0.311274," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{320 \, a^{3} \cos\left(d x + c\right)^{3} - 192 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{3} + 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 90 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{960 \, d}"," ",0,"-1/960*(320*a^3*cos(d*x + c)^3 - 192*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^3 + 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a^3 - 90*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^3)/d","A",0
287,1,99,0,0.319739," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{32 \, a^{3} \cos\left(d x + c\right)^{3} - {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 16 \, a^{3} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{32 \, d}"," ",0,"-1/32*(32*a^3*cos(d*x + c)^3 - (4*d*x + 4*c - sin(4*d*x + 4*c))*a^3 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 - 16*a^3*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
288,1,93,0,0.426019," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, a^{3} \cos\left(d x + c\right)^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 12 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{3} - 18 \, a^{3} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"-1/12*(4*a^3*cos(d*x + c)^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 + 12*(d*x + c + 1/tan(d*x + c))*a^3 - 18*a^3*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
289,1,124,0,0.428356," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 12 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{3} + a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*a^3 - 12*(d*x + c + 1/tan(d*x + c))*a^3 + a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 6*a^3*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
290,1,117,0,0.430951," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{36 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{3} - 9 \, a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 6 \, a^{3} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{4 \, a^{3}}{\tan\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(36*(d*x + c + 1/tan(d*x + c))*a^3 - 9*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) - 6*a^3*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 4*a^3/tan(d*x + c)^3)/d","A",0
291,1,147,0,0.409123," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{16 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{3} + a^{3} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 12 \, a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{16 \, a^{3}}{\tan\left(d x + c\right)^{3}}}{16 \, d}"," ",0,"-1/16*(16*(d*x + c + 1/tan(d*x + c))*a^3 + a^3*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 12*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 16*a^3/tan(d*x + c)^3)/d","A",0
292,1,155,0,0.330303," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{45 \, a^{3} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 60 \, a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{240 \, a^{3}}{\tan\left(d x + c\right)^{3}} + \frac{16 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{3}}{\tan\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"-1/240*(45*a^3*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 60*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 240*a^3/tan(d*x + c)^3 + 16*(5*tan(d*x + c)^2 + 3)*a^3/tan(d*x + c)^5)/d","A",0
293,1,200,0,0.347677," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{5 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 90 \, a^{3} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{160 \, a^{3}}{\tan\left(d x + c\right)^{3}} + \frac{96 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{3}}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(5*a^3*(2*(3*cos(d*x + c)^5 - 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 90*a^3*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 160*a^3/tan(d*x + c)^3 + 96*(5*tan(d*x + c)^2 + 3)*a^3/tan(d*x + c)^5)/d","A",0
294,1,128,0,0.318744," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{1280 \, a^{4} \cos\left(d x + c\right)^{3} - 256 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{4} + 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} - 180 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4}}{960 \, d}"," ",0,"-1/960*(1280*a^4*cos(d*x + c)^3 - 256*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^4 + 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a^4 - 180*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^4 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4)/d","A",0
295,1,125,0,0.326572," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{240 \, a^{4} \cos\left(d x + c\right)^{3} - 8 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{4} - 15 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 60 \, a^{4} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{120 \, d}"," ",0,"-1/120*(240*a^4*cos(d*x + c)^3 - 8*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^4 - 15*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^4 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 - 60*a^4*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
296,1,117,0,0.425460," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{128 \, a^{4} \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} - 144 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} + 96 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{4} - 192 \, a^{4} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{96 \, d}"," ",0,"-1/96*(128*a^4*cos(d*x + c)^3 - 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^4 - 144*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^4 + 96*(d*x + c + 1/tan(d*x + c))*a^4 - 192*a^4*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
297,1,258,0,0.422913," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{320 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{640 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{210 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{45 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 64}{a + \frac{5 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{60 \, d}"," ",0,"-1/60*((45*sin(d*x + c)/(cos(d*x + c) + 1) - 320*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 210*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 640*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 210*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 45*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 64)/(a + 5*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
298,1,237,0,0.432902," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{64 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{33 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{48 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{33 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{9 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 16}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{12 \, d}"," ",0,"1/12*((9*sin(d*x + c)/(cos(d*x + c) + 1) - 64*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 33*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 48*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 33*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 9*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 16)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
299,1,156,0,0.418740," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{12 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 4}{a + \frac{3 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{3 \, d}"," ",0,"-1/3*((3*sin(d*x + c)/(cos(d*x + c) + 1) - 12*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 4)/(a + 3*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
300,1,133,0,0.413587," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 2}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{d}"," ",0,"((sin(d*x + c)/(cos(d*x + c) + 1) - 2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
301,1,52,0,0.428547," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{d}"," ",0,"-(2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
302,1,70,0,0.330404," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{\cos\left(d x + c\right) + 1}{a \sin\left(d x + c\right)} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*(2*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (cos(d*x + c) + 1)/(a*sin(d*x + c)) - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
303,1,115,0,0.336119," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a} - \frac{4 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{a \sin\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"-1/8*((4*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a - 4*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (4*sin(d*x + c)/(cos(d*x + c) + 1) - 1)*(cos(d*x + c) + 1)^2/(a*sin(d*x + c)^2))/d","B",0
304,1,153,0,0.317559," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{a \sin\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"1/24*((9*sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a - 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (3*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^3/(a*sin(d*x + c)^3))/d","B",0
305,1,195,0,0.327928," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{72 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a} - \frac{72 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{72 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{a \sin\left(d x + c\right)^{4}}}{192 \, d}"," ",0,"-1/192*((72*sin(d*x + c)/(cos(d*x + c) + 1) - 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a - 72*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (8*sin(d*x + c)/(cos(d*x + c) + 1) - 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 72*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3)*(cos(d*x + c) + 1)^4/(a*sin(d*x + c)^4))/d","B",0
306,1,234,0,0.338030," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{300 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{120 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{50 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a} - \frac{360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{50 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{120 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{300 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 6\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a \sin\left(d x + c\right)^{5}}}{960 \, d}"," ",0,"1/960*((300*sin(d*x + c)/(cos(d*x + c) + 1) - 120*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 50*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a - 360*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (15*sin(d*x + c)/(cos(d*x + c) + 1) - 50*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 120*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 300*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6)*(cos(d*x + c) + 1)^5/(a*sin(d*x + c)^5))/d","B",0
307,1,398,0,0.443575," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{47 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{431 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{215 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{471 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{297 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{297 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{81 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{81 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 128}{a^{2} + \frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}} + \frac{81 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{12 \, d}"," ",0,"-1/12*((47*sin(d*x + c)/(cos(d*x + c) + 1) + 431*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 215*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 471*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 297*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 297*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 81*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 81*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 128)/(a^2 + a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 4*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 4*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9) + 81*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
308,1,312,0,0.431126," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{33 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{18 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{24 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{9 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 14}{a^{2} + \frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} + \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{3 \, d}"," ",0,"2/3*((5*sin(d*x + c)/(cos(d*x + c) + 1) + 33*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 18*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 24*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 9*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 9*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 14)/(a^2 + a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) + 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
309,1,226,0,0.432914," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{11 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 8}{a^{2} + \frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{5 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{d}"," ",0,"-((3*sin(d*x + c)/(cos(d*x + c) + 1) + 11*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 8)/(a^2 + a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 2*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 5*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
310,1,139,0,0.444214," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 3}{a^{2} + \frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{d}"," ",0,"2*((sin(d*x + c)/(cos(d*x + c) + 1) + 2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3)/(a^2 + a^2*sin(d*x + c)/(cos(d*x + c) + 1) + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + 2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
311,1,55,0,0.323594," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4}{a^{2} + \frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{d}"," ",0,"(4/(a^2 + a^2*sin(d*x + c)/(cos(d*x + c) + 1)) + log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","A",0
312,1,116,0,0.329059," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}{\frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{4 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{\sin\left(d x + c\right)}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*((9*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/(a^2*sin(d*x + c)/(cos(d*x + c) + 1) + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + 4*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - sin(d*x + c)/(a^2*(cos(d*x + c) + 1)))/d","B",0
313,1,161,0,0.339526," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}{\frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} - \frac{\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{2}} + \frac{20 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{8 \, d}"," ",0,"1/8*((7*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) - (8*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^2 + 20*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
314,1,199,0,0.330089," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{27 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{129 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1}{\frac{a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{72 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{24 \, d}"," ",0,"1/24*((5*sin(d*x + c)/(cos(d*x + c) + 1) - 27*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 129*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/(a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (33*sin(d*x + c)/(cos(d*x + c) + 1) - 6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 72*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
315,1,314,0,0.449482," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{123 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{161 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{210 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{154 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{99 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{33 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 52}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{7 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} + \frac{33 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{3 \, d}"," ",0,"-1/3*((123*sin(d*x + c)/(cos(d*x + c) + 1) + 161*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 210*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 154*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 99*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 33*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 52)/(a^3 + 3*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 7*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 5*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) + 33*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
316,1,228,0,0.428923," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{29 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{27 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{9 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 14}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{3 \, d}"," ",0,"2/3*((33*sin(d*x + c)/(cos(d*x + c) + 1) + 29*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 27*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 9*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14)/(a^3 + 3*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
317,1,142,0,0.440931," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 5}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{3 \, d}"," ",0,"-2/3*((12*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5)/(a^3 + 3*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
318,1,143,0,0.339412," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 7\right)}}{a^{3} + \frac{3 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{3 \, d}"," ",0,"1/3*(2*(12*sin(d*x + c)/(cos(d*x + c) + 1) + 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 7)/(a^3 + 3*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + 3*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
319,1,202,0,0.344639," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{61 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{105 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{63 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 3}{\frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{18 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{3 \, \sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{6 \, d}"," ",0,"-1/6*((61*sin(d*x + c)/(cos(d*x + c) + 1) + 105*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 63*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3)/(a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + 18*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 3*sin(d*x + c)/(a^3*(cos(d*x + c) + 1)))/d","B",0
320,1,247,0,0.336095," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{403 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{681 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{372 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 3}{\frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} - \frac{3 \, {\left(\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{a^{3}} + \frac{132 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{24 \, d}"," ",0,"1/24*((27*sin(d*x + c)/(cos(d*x + c) + 1) + 403*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 681*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 372*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3)/(a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) - 3*(12*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^3 + 132*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
321,1,355,0,0.355832," ","integrate(cos(f*x+e)^2*sin(f*x+e)/(a+a*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{99 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{81 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{609 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{441 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{945 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{315 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{315 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + 11\right)}}{315 \, {\left(a^{6} + \frac{9 \, a^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, a^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{84 \, a^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, a^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{126 \, a^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, a^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{36 \, a^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, a^{6} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{6} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}\right)} f}"," ",0,"-2/315*(99*sin(f*x + e)/(cos(f*x + e) + 1) + 81*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 609*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 441*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 945*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 315*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 315*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 11)/((a^6 + 9*a^6*sin(f*x + e)/(cos(f*x + e) + 1) + 36*a^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 84*a^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*a^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 126*a^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*a^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 36*a^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*a^6*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^6*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)*f)","B",0
322,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^2*sin(d*x + c)^3, x)","F",0
323,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^2*sin(d*x + c)^2, x)","F",0
324,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^2*sin(d*x + c), x)","F",0
325,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^2*csc(d*x + c), x)","F",0
326,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^2*csc(d*x + c)^2, x)","F",0
327,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^2*csc(d*x + c)^3, x)","F",0
328,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^2*csc(d*x + c)^4, x)","F",0
329,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2*sin(d*x + c)^3, x)","F",0
330,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2*sin(d*x + c)^2, x)","F",0
331,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2*sin(d*x + c), x)","F",0
332,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2*csc(d*x + c), x)","F",0
333,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2*csc(d*x + c)^2, x)","F",0
334,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2*csc(d*x + c)^3, x)","F",0
335,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2*csc(d*x + c)^4, x)","F",0
336,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \sin\left(d x + c\right)^{3}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*sin(d*x + c)^3/sqrt(a*sin(d*x + c) + a), x)","F",0
337,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \sin\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*sin(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
338,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \sin\left(d x + c\right)}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*sin(d*x + c)/sqrt(a*sin(d*x + c) + a), x)","F",0
339,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \csc\left(d x + c\right)}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*csc(d*x + c)/sqrt(a*sin(d*x + c) + a), x)","F",0
340,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*csc(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
341,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{3}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*csc(d*x + c)^3/sqrt(a*sin(d*x + c) + a), x)","F",0
342,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{4}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*csc(d*x + c)^4/sqrt(a*sin(d*x + c) + a), x)","F",0
343,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*sin(d*x + c)^3/(a*sin(d*x + c) + a)^(3/2), x)","F",0
344,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*sin(d*x + c)^2/(a*sin(d*x + c) + a)^(3/2), x)","F",0
345,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*sin(d*x + c)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
346,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*csc(d*x + c)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
347,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \csc\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*csc(d*x + c)^2/(a*sin(d*x + c) + a)^(3/2), x)","F",0
348,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
350,1,50,0,0.308894," ","integrate(cos(d*x+c)^3*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, a \sin\left(d x + c\right)^{7} + 70 \, a \sin\left(d x + c\right)^{6} - 84 \, a \sin\left(d x + c\right)^{5} - 105 \, a \sin\left(d x + c\right)^{4}}{420 \, d}"," ",0,"-1/420*(60*a*sin(d*x + c)^7 + 70*a*sin(d*x + c)^6 - 84*a*sin(d*x + c)^5 - 105*a*sin(d*x + c)^4)/d","A",0
351,1,50,0,0.314544," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{10 \, a \sin\left(d x + c\right)^{6} + 12 \, a \sin\left(d x + c\right)^{5} - 15 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3}}{60 \, d}"," ",0,"-1/60*(10*a*sin(d*x + c)^6 + 12*a*sin(d*x + c)^5 - 15*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3)/d","A",0
352,1,50,0,0.313017," ","integrate(cos(d*x+c)^3*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{12 \, a \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3} - 30 \, a \sin\left(d x + c\right)^{2}}{60 \, d}"," ",0,"-1/60*(12*a*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3 - 30*a*sin(d*x + c)^2)/d","A",0
353,1,48,0,0.309592," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 6 \, a \sin\left(d x + c\right)^{2} - 12 \, a \sin\left(d x + c\right)}{12 \, d}"," ",0,"-1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 6*a*sin(d*x + c)^2 - 12*a*sin(d*x + c))/d","A",0
354,1,47,0,0.325801," ","integrate(cos(d*x+c)^3*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - 6 \, a \log\left(\sin\left(d x + c\right)\right) - 6 \, a \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - 6*a*log(sin(d*x + c)) - 6*a*sin(d*x + c))/d","A",0
355,1,46,0,0.310696," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{a \sin\left(d x + c\right)^{2} - 2 \, a \log\left(\sin\left(d x + c\right)\right) + 2 \, a \sin\left(d x + c\right) + \frac{2 \, a}{\sin\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(a*sin(d*x + c)^2 - 2*a*log(sin(d*x + c)) + 2*a*sin(d*x + c) + 2*a/sin(d*x + c))/d","A",0
356,1,45,0,0.333201," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, a \log\left(\sin\left(d x + c\right)\right) + 2 \, a \sin\left(d x + c\right) + \frac{2 \, a \sin\left(d x + c\right) + a}{\sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*a*log(sin(d*x + c)) + 2*a*sin(d*x + c) + (2*a*sin(d*x + c) + a)/sin(d*x + c)^2)/d","A",0
357,1,29,0,0.324795," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3}}{12 \, a d}"," ",0,"-1/12*(3*sin(d*x + c)^4 - 4*sin(d*x + c)^3)/(a*d)","A",0
358,1,29,0,0.310248," ","integrate(cos(d*x+c)^3*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2}}{6 \, a d}"," ",0,"-1/6*(2*sin(d*x + c)^3 - 3*sin(d*x + c)^2)/(a*d)","A",0
359,1,25,0,0.309573," ","integrate(cos(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)}{2 \, a d}"," ",0,"-1/2*(sin(d*x + c)^2 - 2*sin(d*x + c))/(a*d)","A",0
360,1,27,0,0.310748," ","integrate(cos(d*x+c)^3*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\sin\left(d x + c\right)\right)}{a} - \frac{\sin\left(d x + c\right)}{a}}{d}"," ",0,"(log(sin(d*x + c))/a - sin(d*x + c)/a)/d","A",0
361,1,29,0,0.681255," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(\sin\left(d x + c\right)\right)}{a} + \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"-(log(sin(d*x + c))/a + 1/(a*sin(d*x + c)))/d","A",0
362,1,26,0,0.315380," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, \sin\left(d x + c\right) - 1}{2 \, a d \sin\left(d x + c\right)^{2}}"," ",0,"1/2*(2*sin(d*x + c) - 1)/(a*d*sin(d*x + c)^2)","A",0
363,1,26,0,0.312942," ","integrate(cos(d*x+c)^3*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, \sin\left(d x + c\right) - 2}{6 \, a d \sin\left(d x + c\right)^{3}}"," ",0,"1/6*(3*sin(d*x + c) - 2)/(a*d*sin(d*x + c)^3)","A",0
364,1,26,0,0.312345," ","integrate(cos(d*x+c)^3*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, \sin\left(d x + c\right) - 3}{12 \, a d \sin\left(d x + c\right)^{4}}"," ",0,"1/12*(4*sin(d*x + c) - 3)/(a*d*sin(d*x + c)^4)","A",0
365,1,71,0,0.331323," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{1024 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a - 315 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{322560 \, d}"," ",0,"-1/322560*(1024*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a - 315*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a)/d","A",0
366,1,61,0,0.309150," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{1024 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a + 35 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{35840 \, d}"," ",0,"1/35840*(1024*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a + 35*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a)/d","A",0
367,1,65,0,0.321305," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{192 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{6720 \, d}"," ",0,"1/6720*(192*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a + 35*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a)/d","A",0
368,1,52,0,0.309007," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{192 \, a \cos\left(d x + c\right)^{5} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{960 \, d}"," ",0,"-1/960*(192*a*cos(d*x + c)^5 - 5*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a)/d","A",0
369,1,81,0,0.312706," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{96 \, d}"," ",0,"1/96*(16*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a)/d","A",0
370,1,90,0,0.432337," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a - 3 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a}{6 \, d}"," ",0,"1/6*((2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a - 3*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a)/d","A",0
371,1,101,0,0.452354," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a - a {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(2*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a - a*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
372,1,92,0,0.436271," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a + 3 \, a {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(4*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a + 3*a*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
373,1,107,0,0.416234," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a - 3 \, a {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a - 3*a*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
374,1,86,0,0.353035," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, a {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{16 \, a}{\tan\left(d x + c\right)^{5}}}{80 \, d}"," ",0,"-1/80*(5*a*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) + 16*a/tan(d*x + c)^5)/d","A",0
375,1,106,0,0.333935," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{5 \, a {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{96 \, a}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(5*a*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 96*a/tan(d*x + c)^5)/d","A",0
376,1,118,0,0.320637," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{35 \, a {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{96 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a}{\tan\left(d x + c\right)^{7}}}{3360 \, d}"," ",0,"1/3360*(35*a*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 96*(7*tan(d*x + c)^2 + 5)*a/tan(d*x + c)^7)/d","A",0
377,1,138,0,0.317966," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{35 \, a {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{256 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a}{\tan\left(d x + c\right)^{7}}}{8960 \, d}"," ",0,"1/8960*(35*a*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 256*(7*tan(d*x + c)^2 + 5)*a/tan(d*x + c)^7)/d","A",0
378,1,123,0,0.372692," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4096 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a^{2} + 63 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 120 \, d x - 120 \, c - 5 \, \sin\left(8 \, d x + 8 \, c\right) + 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} - 630 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{645120 \, d}"," ",0,"-1/645120*(4096*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^2 + 63*(32*sin(2*d*x + 2*c)^5 - 120*d*x - 120*c - 5*sin(8*d*x + 8*c) + 40*sin(4*d*x + 4*c))*a^2 - 630*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^2)/d","A",0
379,1,101,0,0.341584," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{512 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a^{2} - 4608 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{2} - 315 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{161280 \, d}"," ",0,"-1/161280*(512*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^2 - 4608*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^2 - 315*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^2)/d","A",0
380,1,102,0,0.316182," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6144 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{2} + 560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} + 105 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{107520 \, d}"," ",0,"1/107520*(6144*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^2 + 560*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^2 + 105*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^2)/d","A",0
381,1,82,0,0.354933," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{672 \, a^{2} \cos\left(d x + c\right)^{5} - 96 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{2} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{3360 \, d}"," ",0,"-1/3360*(672*a^2*cos(d*x + c)^5 - 96*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^2 - 35*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^2)/d","A",0
382,1,98,0,0.329065," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{48 \, a^{2} \cos\left(d x + c\right)^{5} - 40 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{240 \, d}"," ",0,"-1/240*(48*a^2*cos(d*x + c)^5 - 40*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^2 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2)/d","A",0
383,1,128,0,0.447782," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{32 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 48 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2}}{96 \, d}"," ",0,"1/96*(32*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^2 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2 - 48*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^2)/d","A",0
384,1,151,0,0.461222," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} - 12 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2} + 3 \, a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(2*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^2 - 12*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^2 + 3*a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
385,1,139,0,0.450333," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2} - 2 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} - 3 \, a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"-1/6*(3*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^2 - 2*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2 - 3*a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
386,1,167,0,0.429553," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} - 3 \, a^{2} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 12 \, a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(32*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2 - 3*a^2*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) + 12*a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
387,1,124,0,0.445973," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{40 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} - 15 \, a^{2} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{24 \, a^{2}}{\tan\left(d x + c\right)^{5}}}{120 \, d}"," ",0,"1/120*(40*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2 - 15*a^2*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 24*a^2/tan(d*x + c)^5)/d","A",0
388,1,181,0,0.351597," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{5 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 30 \, a^{2} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{192 \, a^{2}}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(5*a^2*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 30*a^2*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 192*a^2/tan(d*x + c)^5)/d","A",0
389,1,233,0,0.350786," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{105 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 280 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{1536 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{2}}{\tan\left(d x + c\right)^{7}}}{26880 \, d}"," ",0,"1/26880*(105*a^2*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 280*a^2*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 1536*(7*tan(d*x + c)^2 + 5)*a^2/tan(d*x + c)^7)/d","A",0
390,1,177,0,0.340373," ","integrate(cos(d*x+c)^4*csc(d*x+c)^10*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{315 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{1152 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{2}}{\tan\left(d x + c\right)^{7}} - \frac{128 \, {\left(63 \, \tan\left(d x + c\right)^{4} + 90 \, \tan\left(d x + c\right)^{2} + 35\right)} a^{2}}{\tan\left(d x + c\right)^{9}}}{40320 \, d}"," ",0,"1/40320*(315*a^2*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 1152*(7*tan(d*x + c)^2 + 5)*a^2/tan(d*x + c)^7 - 128*(63*tan(d*x + c)^4 + 90*tan(d*x + c)^2 + 35)*a^2/tan(d*x + c)^9)/d","A",0
391,1,283,0,0.332541," ","integrate(cos(d*x+c)^4*csc(d*x+c)^11*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{63 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 630 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{1024 \, {\left(63 \, \tan\left(d x + c\right)^{4} + 90 \, \tan\left(d x + c\right)^{2} + 35\right)} a^{2}}{\tan\left(d x + c\right)^{9}}}{161280 \, d}"," ",0,"1/161280*(63*a^2*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 630*a^2*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 1024*(63*tan(d*x + c)^4 + 90*tan(d*x + c)^2 + 35)*a^2/tan(d*x + c)^9)/d","A",0
392,1,169,0,0.344967," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2048 \, {\left(105 \, \cos\left(d x + c\right)^{11} - 385 \, \cos\left(d x + c\right)^{9} + 495 \, \cos\left(d x + c\right)^{7} - 231 \, \cos\left(d x + c\right)^{5}\right)} a^{3} - 22528 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a^{3} - 693 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 120 \, d x - 120 \, c - 5 \, \sin\left(8 \, d x + 8 \, c\right) + 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} + 2310 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{2365440 \, d}"," ",0,"1/2365440*(2048*(105*cos(d*x + c)^11 - 385*cos(d*x + c)^9 + 495*cos(d*x + c)^7 - 231*cos(d*x + c)^5)*a^3 - 22528*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^3 - 693*(32*sin(2*d*x + 2*c)^5 - 120*d*x - 120*c - 5*sin(8*d*x + 8*c) + 40*sin(4*d*x + 4*c))*a^3 + 2310*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^3)/d","A",0
393,1,149,0,0.316312," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2048 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a^{3} - 6144 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{3} + 21 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 120 \, d x - 120 \, c - 5 \, \sin\left(8 \, d x + 8 \, c\right) + 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 630 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{215040 \, d}"," ",0,"-1/215040*(2048*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^3 - 6144*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^3 + 21*(32*sin(2*d*x + 2*c)^5 - 120*d*x - 120*c - 5*sin(8*d*x + 8*c) + 40*sin(4*d*x + 4*c))*a^3 - 630*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^3)/d","A",0
394,1,138,0,0.320772," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1024 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a^{3} - 27648 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{3} - 1680 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 945 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{322560 \, d}"," ",0,"-1/322560*(1024*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^3 - 27648*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^3 - 1680*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^3 - 945*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^3)/d","A",0
395,1,115,0,0.319187," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{7168 \, a^{3} \cos\left(d x + c\right)^{5} - 3072 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{3} - 560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 35 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{35840 \, d}"," ",0,"-1/35840*(7168*a^3*cos(d*x + c)^5 - 3072*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^3 - 560*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^3 - 35*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^3)/d","A",0
396,1,135,0,0.321092," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{576 \, a^{3} \cos\left(d x + c\right)^{5} - 160 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{960 \, d}"," ",0,"-1/960*(576*a^3*cos(d*x + c)^5 - 160*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^3 - 5*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^3 - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3)/d","A",0
397,1,141,0,0.446741," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{32 \, a^{3} \cos\left(d x + c\right)^{5} - 80 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 80 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3}}{160 \, d}"," ",0,"-1/160*(32*a^3*cos(d*x + c)^5 - 80*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^3 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 + 80*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^3)/d","A",0
398,1,183,0,0.439941," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{16 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} + {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 48 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3} + 8 \, a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{32 \, d}"," ",0,"1/32*(16*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^3 + (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^3 - 48*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^3 + 8*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
399,1,185,0,0.441332," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 18 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3} + 4 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{3} + 9 \, a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(2*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^3 - 18*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^3 + 4*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^3 + 9*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
400,1,209,0,0.432435," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{8 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3} - 16 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{3} + a^{3} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 12 \, a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{16 \, d}"," ",0,"-1/16*(8*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^3 - 16*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^3 + a^3*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 12*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
401,1,180,0,0.528565," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{80 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{3} - 15 \, a^{3} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 20 \, a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{16 \, a^{3}}{\tan\left(d x + c\right)^{5}}}{80 \, d}"," ",0,"1/80*(80*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^3 - 15*a^3*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) + 20*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 16*a^3/tan(d*x + c)^5)/d","A",0
402,1,215,0,0.422084," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{160 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{3} + 5 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 90 \, a^{3} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{288 \, a^{3}}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(160*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^3 + 5*a^3*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 90*a^3*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 288*a^3/tan(d*x + c)^5)/d","A",0
403,1,206,0,0.347302," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{35 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 70 \, a^{3} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{672 \, a^{3}}{\tan\left(d x + c\right)^{5}} - \frac{32 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{3}}{\tan\left(d x + c\right)^{7}}}{1120 \, d}"," ",0,"1/1120*(35*a^3*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 70*a^3*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 672*a^3/tan(d*x + c)^5 - 32*(7*tan(d*x + c)^2 + 5)*a^3/tan(d*x + c)^7)/d","A",0
404,1,246,0,0.333453," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{35 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 280 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{1792 \, a^{3}}{\tan\left(d x + c\right)^{5}} - \frac{768 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{3}}{\tan\left(d x + c\right)^{7}}}{8960 \, d}"," ",0,"1/8960*(35*a^3*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 280*a^3*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 1792*a^3/tan(d*x + c)^5 - 768*(7*tan(d*x + c)^2 + 5)*a^3/tan(d*x + c)^7)/d","A",0
405,1,268,0,0.354352," ","integrate(cos(d*x+c)^4*csc(d*x+c)^10*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{945 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 840 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{6912 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{3}}{\tan\left(d x + c\right)^{7}} - \frac{256 \, {\left(63 \, \tan\left(d x + c\right)^{4} + 90 \, \tan\left(d x + c\right)^{2} + 35\right)} a^{3}}{\tan\left(d x + c\right)^{9}}}{80640 \, d}"," ",0,"1/80640*(945*a^3*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 840*a^3*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 6912*(7*tan(d*x + c)^2 + 5)*a^3/tan(d*x + c)^7 - 256*(63*tan(d*x + c)^4 + 90*tan(d*x + c)^2 + 35)*a^3/tan(d*x + c)^9)/d","A",0
406,1,308,0,0.357812," ","integrate(cos(d*x+c)^4*csc(d*x+c)^11*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{21 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 630 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{1536 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{3}}{\tan\left(d x + c\right)^{7}} - \frac{512 \, {\left(63 \, \tan\left(d x + c\right)^{4} + 90 \, \tan\left(d x + c\right)^{2} + 35\right)} a^{3}}{\tan\left(d x + c\right)^{9}}}{53760 \, d}"," ",0,"1/53760*(21*a^3*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 630*a^3*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 1536*(7*tan(d*x + c)^2 + 5)*a^3/tan(d*x + c)^7 - 512*(63*tan(d*x + c)^4 + 90*tan(d*x + c)^2 + 35)*a^3/tan(d*x + c)^9)/d","A",0
407,1,186,0,0.351971," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{8192 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} a^{4} - 73728 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{4} + 63 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} - 120 \, d x - 120 \, c - 5 \, \sin\left(8 \, d x + 8 \, c\right) + 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} - 3360 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4} - 3780 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{4}}{645120 \, d}"," ",0,"-1/645120*(8192*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*a^4 - 73728*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^4 + 63*(32*sin(2*d*x + 2*c)^5 - 120*d*x - 120*c - 5*sin(8*d*x + 8*c) + 40*sin(4*d*x + 4*c))*a^4 - 3360*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^4 - 3780*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a^4)/d","A",0
408,1,218,0,0.431320," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{64 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{4} + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 288 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{4} + 32 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{4} + 96 \, a^{4} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{96 \, d}"," ",0,"1/96*(64*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^4 + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^4 - 288*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^4 + 32*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^4 + 96*a^4*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
409,1,380,0,0.439245," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{896 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{700 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2688 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3395 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{4480 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{8960 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{3395 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{700 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{105 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - 128}{a + \frac{7 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{21 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{35 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{35 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{21 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{7 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{840 \, d}"," ",0,"-1/840*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 896*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 700*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2688*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3395*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 4480*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 8960*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 3395*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 700*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 105*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 128)/(a + 7*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 21*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 35*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 35*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 21*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 7*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
410,1,339,0,0.442794," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{192 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{85 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{570 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{320 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{570 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{480 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{85 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{15 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 32}{a + \frac{6 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{120 \, d}"," ",0,"1/120*((15*sin(d*x + c)/(cos(d*x + c) + 1) - 192*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 85*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 570*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 320*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 570*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 480*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 85*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 15*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 32)/(a + 6*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
411,1,278,0,0.439066," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{80 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{90 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{80 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{240 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{90 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{15 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 16}{a + \frac{5 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{60 \, d}"," ",0,"-1/60*((15*sin(d*x + c)/(cos(d*x + c) + 1) - 80*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 90*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 80*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 240*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 90*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 15*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 16)/(a + 5*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
412,1,257,0,0.424882," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{8 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{21 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{24 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{24 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 8}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{12 \, d}"," ",0,"1/12*((3*sin(d*x + c)/(cos(d*x + c) + 1) - 8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 21*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 24*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 24*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 8)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
413,1,156,0,0.426710," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 2}{a + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{d}"," ",0,"-((sin(d*x + c)/(cos(d*x + c) + 1) - 2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2)/(a + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
414,1,154,0,0.423002," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1}{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{4 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{2 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{\sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*((4*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/(a*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + 4*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 2*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
415,1,138,0,0.423603," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a} - \frac{16 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{4 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{a \sin\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"-1/8*((4*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a - 16*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 4*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (4*sin(d*x + c)/(cos(d*x + c) + 1) - 1)*(cos(d*x + c) + 1)^2/(a*sin(d*x + c)^2))/d","B",0
416,1,155,0,0.311690," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{a \sin\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"-1/24*((3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a - 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^3/(a*sin(d*x + c)^3))/d","B",0
417,1,154,0,0.382180," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{24 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a} - \frac{24 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{24 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{a \sin\left(d x + c\right)^{4}}}{192 \, d}"," ",0,"1/192*((24*sin(d*x + c)/(cos(d*x + c) + 1) - 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a - 24*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (8*sin(d*x + c)/(cos(d*x + c) + 1) - 24*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3)*(cos(d*x + c) + 1)^4/(a*sin(d*x + c)^4))/d","B",0
418,1,195,0,0.320117," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{60 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{10 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{60 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 6\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a \sin\left(d x + c\right)^{5}}}{960 \, d}"," ",0,"-1/960*((60*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (15*sin(d*x + c)/(cos(d*x + c) + 1) - 10*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 60*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6)*(cos(d*x + c) + 1)^5/(a*sin(d*x + c)^5))/d","B",0
419,1,274,0,0.357603," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{120 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{12 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}{a} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{120 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 5\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{6}}{a \sin\left(d x + c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*((120*sin(d*x + c)/(cos(d*x + c) + 1) - 15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 12*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)/a - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (12*sin(d*x + c)/(cos(d*x + c) + 1) - 15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 120*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5)*(cos(d*x + c) + 1)^6/(a*sin(d*x + c)^6))/d","B",0
420,1,396,0,0.486349," ","integrate(cos(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{525 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5824 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3500 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{17472 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{9905 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{24640 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{4480 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{9905 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{3500 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{525 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - 832}{a^{2} + \frac{7 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{21 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{35 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{35 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{21 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{7 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}} - \frac{525 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{420 \, d}"," ",0,"1/420*((525*sin(d*x + c)/(cos(d*x + c) + 1) - 5824*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3500*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 17472*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 9905*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 24640*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 4480*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 9905*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 3500*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 525*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 832)/(a^2 + 7*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 21*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 35*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 35*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 21*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 7*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14) - 525*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
421,1,353,0,0.539897," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{165 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1536 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{935 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3840 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1410 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{2560 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1410 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{935 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{165 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 256}{a^{2} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{165 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{120 \, d}"," ",0,"-1/120*((165*sin(d*x + c)/(cos(d*x + c) + 1) - 1536*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 935*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3840*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1410*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2560*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 1410*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 935*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 165*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 256)/(a^2 + 6*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 165*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
422,1,290,0,0.487997," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{120 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{70 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{200 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{40 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{70 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{15 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 24}{a^{2} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{10 \, d}"," ",0,"1/10*((15*sin(d*x + c)/(cos(d*x + c) + 1) - 120*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 70*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 200*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 40*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 70*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 15*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 24)/(a^2 + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
423,1,247,0,0.471723," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{128 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{45 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{96 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{45 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{21 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 32}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{21 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{12 \, d}"," ",0,"-1/12*((21*sin(d*x + c)/(cos(d*x + c) + 1) - 128*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 45*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 96*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 45*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 21*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 32)/(a^2 + 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 21*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
424,1,184,0,0.444470," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{12 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 5}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{3 \, d}"," ",0,"2/3*((3*sin(d*x + c)/(cos(d*x + c) + 1) - 12*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
425,1,82,0,0.452374," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2}{a^{2} + \frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{4 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{d}"," ",0,"-(2/(a^2 + a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + 4*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
426,1,93,0,0.446206," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{4 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{\cos\left(d x + c\right) + 1}{a^{2} \sin\left(d x + c\right)} + \frac{\sin\left(d x + c\right)}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"1/2*(4*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 4*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (cos(d*x + c) + 1)/(a^2*sin(d*x + c)) + sin(d*x + c)/(a^2*(cos(d*x + c) + 1)))/d","B",0
427,1,115,0,0.341075," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{{\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{a^{2} \sin\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"-1/8*((8*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (8*sin(d*x + c)/(cos(d*x + c) + 1) - 1)*(cos(d*x + c) + 1)^2/(a^2*sin(d*x + c)^2))/d","B",0
428,1,153,0,0.340459," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{{\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{21 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{a^{2} \sin\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"1/24*((21*sin(d*x + c)/(cos(d*x + c) + 1) - 6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + (6*sin(d*x + c)/(cos(d*x + c) + 1) - 21*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^3/(a^2*sin(d*x + c)^3))/d","B",0
429,1,195,0,0.351850," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{144 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a^{2}} - \frac{168 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{{\left(\frac{16 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{144 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{a^{2} \sin\left(d x + c\right)^{4}}}{192 \, d}"," ",0,"-1/192*((144*sin(d*x + c)/(cos(d*x + c) + 1) - 48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a^2 - 168*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (16*sin(d*x + c)/(cos(d*x + c) + 1) - 48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 144*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3)*(cos(d*x + c) + 1)^4/(a^2*sin(d*x + c)^4))/d","B",0
430,1,233,0,0.369130," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{110 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{\sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{2}} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{{\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{110 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a^{2} \sin\left(d x + c\right)^{5}}}{160 \, d}"," ",0,"1/160*((110*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^2 - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + (5*sin(d*x + c)/(cos(d*x + c) + 1) - 15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 110*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1)*(cos(d*x + c) + 1)^5/(a^2*sin(d*x + c)^5))/d","B",0
431,1,275,0,0.335179," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{1200 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{465 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{75 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{24 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}{a^{2}} - \frac{1320 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{{\left(\frac{24 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{75 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{200 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{465 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1200 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 5\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{6}}{a^{2} \sin\left(d x + c\right)^{6}}}{1920 \, d}"," ",0,"-1/1920*((1200*sin(d*x + c)/(cos(d*x + c) + 1) - 465*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 200*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 75*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 24*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)/a^2 - 1320*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (24*sin(d*x + c)/(cos(d*x + c) + 1) - 75*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 200*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 465*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1200*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5)*(cos(d*x + c) + 1)^6/(a^2*sin(d*x + c)^6))/d","B",0
432,1,398,0,0.426541," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{29 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{269 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{133 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{309 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{171 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{187 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{51 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{51 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 80}{a^{3} + \frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}} + \frac{51 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{4 \, d}"," ",0,"1/4*((29*sin(d*x + c)/(cos(d*x + c) + 1) + 269*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 133*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 309*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 171*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 187*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 51*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 51*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 80)/(a^3 + a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 4*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 4*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9) + 51*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
433,1,312,0,0.417945," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{19 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{123 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{60 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{96 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{33 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{33 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 52}{a^{3} + \frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} + \frac{33 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{3 \, d}"," ",0,"-1/3*((19*sin(d*x + c)/(cos(d*x + c) + 1) + 123*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 60*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 96*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 33*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 33*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 52)/(a^3 + a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) + 33*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
434,1,225,0,0.422007," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{21 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{7 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{9 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 14}{a^{3} + \frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{d}"," ",0,"((5*sin(d*x + c)/(cos(d*x + c) + 1) + 21*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 7*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 9*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14)/(a^3 + a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
435,1,78,0,0.416059," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{8}{a^{3} + \frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}} + \frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{d}"," ",0,"(8/(a^3 + a^3*sin(d*x + c)/(cos(d*x + c) + 1)) + 2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","A",0
436,1,116,0,0.456463," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{17 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1}{\frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{\sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*((17*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/(a^3*sin(d*x + c)/(cos(d*x + c) + 1) + a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2) + 6*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - sin(d*x + c)/(a^3*(cos(d*x + c) + 1)))/d","B",0
437,1,161,0,0.331739," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{11 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{76 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}{\frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} - \frac{\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{3}} + \frac{36 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{8 \, d}"," ",0,"1/8*((11*sin(d*x + c)/(cos(d*x + c) + 1) + 76*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) - (12*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^3 + 36*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
438,1,199,0,0.484883," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{249 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1}{\frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{\frac{57 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{3}} - \frac{132 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{24 \, d}"," ",0,"1/24*((8*sin(d*x + c)/(cos(d*x + c) + 1) - 48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 249*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/(a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + (57*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^3 - 132*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
439,1,241,0,0.379117," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{32 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{160 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{712 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 1}{\frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} - \frac{\frac{200 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{\sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a^{3}} + \frac{408 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{64 \, d}"," ",0,"1/64*((7*sin(d*x + c)/(cos(d*x + c) + 1) - 32*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 160*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 712*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1)/(a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) - (200*sin(d*x + c)/(cos(d*x + c) + 1) - 40*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a^3 + 408*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
440,1,269,0,0.515695," ","integrate(cos(f*x+e)^4*sin(f*x+e)/(a+a*sin(f*x+e))^6,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{7 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{14 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{70 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{35 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{35 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + 1\right)}}{35 \, {\left(a^{6} + \frac{7 \, a^{6} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{21 \, a^{6} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{35 \, a^{6} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{35 \, a^{6} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{21 \, a^{6} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{7 \, a^{6} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{a^{6} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}}\right)} f}"," ",0,"-2/35*(7*sin(f*x + e)/(cos(f*x + e) + 1) - 14*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 70*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 35*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 35*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 1)/((a^6 + 7*a^6*sin(f*x + e)/(cos(f*x + e) + 1) + 21*a^6*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 35*a^6*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 35*a^6*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 21*a^6*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 7*a^6*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + a^6*sin(f*x + e)^7/(cos(f*x + e) + 1)^7)*f)","B",0
441,1,335,0,0.542656," ","integrate(cos(f*x+e)^4*sin(f*x+e)^2/(a+a*sin(f*x+e))^7,x, algorithm=""maxima"")","-\frac{4 \, {\left(\frac{9 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} - \frac{126 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{441 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} - \frac{315 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{210 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + 1\right)}}{315 \, {\left(a^{7} + \frac{9 \, a^{7} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{36 \, a^{7} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{84 \, a^{7} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{126 \, a^{7} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{126 \, a^{7} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{84 \, a^{7} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{36 \, a^{7} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{9 \, a^{7} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{a^{7} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}}\right)} f}"," ",0,"-4/315*(9*sin(f*x + e)/(cos(f*x + e) + 1) + 36*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 - 126*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 441*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 - 315*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 210*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1)/((a^7 + 9*a^7*sin(f*x + e)/(cos(f*x + e) + 1) + 36*a^7*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 84*a^7*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 126*a^7*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 126*a^7*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 84*a^7*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 36*a^7*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 9*a^7*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + a^7*sin(f*x + e)^9/(cos(f*x + e) + 1)^9)*f)","B",0
442,1,401,0,0.345575," ","integrate(cos(f*x+e)^4*sin(f*x+e)^3/(a+a*sin(f*x+e))^8,x, algorithm=""maxima"")","-\frac{4 \, {\left(\frac{11 \, \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{165 \, \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} - \frac{825 \, \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{2541 \, \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} - \frac{2079 \, \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{1155 \, \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + 1\right)}}{1155 \, {\left(a^{8} + \frac{11 \, a^{8} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{55 \, a^{8} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}} + \frac{165 \, a^{8} \sin\left(f x + e\right)^{3}}{{\left(\cos\left(f x + e\right) + 1\right)}^{3}} + \frac{330 \, a^{8} \sin\left(f x + e\right)^{4}}{{\left(\cos\left(f x + e\right) + 1\right)}^{4}} + \frac{462 \, a^{8} \sin\left(f x + e\right)^{5}}{{\left(\cos\left(f x + e\right) + 1\right)}^{5}} + \frac{462 \, a^{8} \sin\left(f x + e\right)^{6}}{{\left(\cos\left(f x + e\right) + 1\right)}^{6}} + \frac{330 \, a^{8} \sin\left(f x + e\right)^{7}}{{\left(\cos\left(f x + e\right) + 1\right)}^{7}} + \frac{165 \, a^{8} \sin\left(f x + e\right)^{8}}{{\left(\cos\left(f x + e\right) + 1\right)}^{8}} + \frac{55 \, a^{8} \sin\left(f x + e\right)^{9}}{{\left(\cos\left(f x + e\right) + 1\right)}^{9}} + \frac{11 \, a^{8} \sin\left(f x + e\right)^{10}}{{\left(\cos\left(f x + e\right) + 1\right)}^{10}} + \frac{a^{8} \sin\left(f x + e\right)^{11}}{{\left(\cos\left(f x + e\right) + 1\right)}^{11}}\right)} f}"," ",0,"-4/1155*(11*sin(f*x + e)/(cos(f*x + e) + 1) + 55*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 165*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 - 825*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 2541*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 - 2079*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 1155*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 1)/((a^8 + 11*a^8*sin(f*x + e)/(cos(f*x + e) + 1) + 55*a^8*sin(f*x + e)^2/(cos(f*x + e) + 1)^2 + 165*a^8*sin(f*x + e)^3/(cos(f*x + e) + 1)^3 + 330*a^8*sin(f*x + e)^4/(cos(f*x + e) + 1)^4 + 462*a^8*sin(f*x + e)^5/(cos(f*x + e) + 1)^5 + 462*a^8*sin(f*x + e)^6/(cos(f*x + e) + 1)^6 + 330*a^8*sin(f*x + e)^7/(cos(f*x + e) + 1)^7 + 165*a^8*sin(f*x + e)^8/(cos(f*x + e) + 1)^8 + 55*a^8*sin(f*x + e)^9/(cos(f*x + e) + 1)^9 + 11*a^8*sin(f*x + e)^10/(cos(f*x + e) + 1)^10 + a^8*sin(f*x + e)^11/(cos(f*x + e) + 1)^11)*f)","B",0
443,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c)^2, x)","F",0
444,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
445,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*csc(d*x + c), x)","F",0
446,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*csc(d*x + c)^2, x)","F",0
447,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*csc(d*x + c)^3, x)","F",0
448,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*csc(d*x + c)^4, x)","F",0
449,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*csc(d*x + c)^5, x)","F",0
450,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*csc(d*x + c)^6, x)","F",0
451,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*csc(d*x + c)^7, x)","F",0
452,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{a \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{8}\,{d x}"," ",0,"integrate(sqrt(a*sin(d*x + c) + a)*cos(d*x + c)^4*csc(d*x + c)^8, x)","F",0
453,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*sin(d*x + c)^2, x)","F",0
454,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
455,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c), x)","F",0
456,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c)^2, x)","F",0
457,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c)^3, x)","F",0
458,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c)^4, x)","F",0
459,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c)^5, x)","F",0
460,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c)^6, x)","F",0
461,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{7}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c)^7, x)","F",0
462,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{8}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c)^8, x)","F",0
463,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{9}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*csc(d*x + c)^9, x)","F",0
464,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
465,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/sqrt(a*sin(d*x + c) + a), x)","F",0
466,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \csc\left(d x + c\right)}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*csc(d*x + c)/sqrt(a*sin(d*x + c) + a), x)","F",0
467,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{2}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*csc(d*x + c)^2/sqrt(a*sin(d*x + c) + a), x)","F",0
468,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{3}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*csc(d*x + c)^3/sqrt(a*sin(d*x + c) + a), x)","F",0
469,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{4}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*csc(d*x + c)^4/sqrt(a*sin(d*x + c) + a), x)","F",0
470,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \csc\left(d x + c\right)^{5}}{\sqrt{a \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*csc(d*x + c)^5/sqrt(a*sin(d*x + c) + a), x)","F",0
471,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
472,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^3/(a*sin(d*x + c) + a)^(3/2), x)","F",0
473,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/(a*sin(d*x + c) + a)^(3/2), x)","F",0
474,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
475,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*csc(d*x + c)/(a*sin(d*x + c) + a)^(3/2), x)","F",0
476,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
477,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
478,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
479,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
480,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+a*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
481,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{4}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^4/(a*sin(d*x + c) + a)^(5/2), x)","F",0
482,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{3}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^3/(a*sin(d*x + c) + a)^(5/2), x)","F",0
483,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/(a*sin(d*x + c) + a)^(5/2), x)","F",0
484,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/(a*sin(d*x + c) + a)^(5/2), x)","F",0
485,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \csc\left(d x + c\right)}{{\left(a \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*csc(d*x + c)/(a*sin(d*x + c) + a)^(5/2), x)","F",0
486,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
487,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
488,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
489,-1,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+a*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
490,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
491,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
492,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}}{a \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^4/(a*sin(d*x + c) + a), x)","F",0
493,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}}{{\left(a \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^4/(a*sin(d*x + c) + a)^2, x)","F",0
494,1,72,0,0.349349," ","integrate(cos(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{1260 \, a \sin\left(d x + c\right)^{11} + 1386 \, a \sin\left(d x + c\right)^{10} - 3080 \, a \sin\left(d x + c\right)^{9} - 3465 \, a \sin\left(d x + c\right)^{8} + 1980 \, a \sin\left(d x + c\right)^{7} + 2310 \, a \sin\left(d x + c\right)^{6}}{13860 \, d}"," ",0,"1/13860*(1260*a*sin(d*x + c)^11 + 1386*a*sin(d*x + c)^10 - 3080*a*sin(d*x + c)^9 - 3465*a*sin(d*x + c)^8 + 1980*a*sin(d*x + c)^7 + 2310*a*sin(d*x + c)^6)/d","A",0
495,1,72,0,0.503042," ","integrate(cos(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{126 \, a \sin\left(d x + c\right)^{10} + 140 \, a \sin\left(d x + c\right)^{9} - 315 \, a \sin\left(d x + c\right)^{8} - 360 \, a \sin\left(d x + c\right)^{7} + 210 \, a \sin\left(d x + c\right)^{6} + 252 \, a \sin\left(d x + c\right)^{5}}{1260 \, d}"," ",0,"1/1260*(126*a*sin(d*x + c)^10 + 140*a*sin(d*x + c)^9 - 315*a*sin(d*x + c)^8 - 360*a*sin(d*x + c)^7 + 210*a*sin(d*x + c)^6 + 252*a*sin(d*x + c)^5)/d","A",0
496,1,72,0,0.580631," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{280 \, a \sin\left(d x + c\right)^{9} + 315 \, a \sin\left(d x + c\right)^{8} - 720 \, a \sin\left(d x + c\right)^{7} - 840 \, a \sin\left(d x + c\right)^{6} + 504 \, a \sin\left(d x + c\right)^{5} + 630 \, a \sin\left(d x + c\right)^{4}}{2520 \, d}"," ",0,"1/2520*(280*a*sin(d*x + c)^9 + 315*a*sin(d*x + c)^8 - 720*a*sin(d*x + c)^7 - 840*a*sin(d*x + c)^6 + 504*a*sin(d*x + c)^5 + 630*a*sin(d*x + c)^4)/d","A",0
497,1,72,0,0.858085," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{105 \, a \sin\left(d x + c\right)^{8} + 120 \, a \sin\left(d x + c\right)^{7} - 280 \, a \sin\left(d x + c\right)^{6} - 336 \, a \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} + 280 \, a \sin\left(d x + c\right)^{3}}{840 \, d}"," ",0,"1/840*(105*a*sin(d*x + c)^8 + 120*a*sin(d*x + c)^7 - 280*a*sin(d*x + c)^6 - 336*a*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 + 280*a*sin(d*x + c)^3)/d","A",0
498,1,72,0,0.584186," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{30 \, a \sin\left(d x + c\right)^{7} + 35 \, a \sin\left(d x + c\right)^{6} - 84 \, a \sin\left(d x + c\right)^{5} - 105 \, a \sin\left(d x + c\right)^{4} + 70 \, a \sin\left(d x + c\right)^{3} + 105 \, a \sin\left(d x + c\right)^{2}}{210 \, d}"," ",0,"1/210*(30*a*sin(d*x + c)^7 + 35*a*sin(d*x + c)^6 - 84*a*sin(d*x + c)^5 - 105*a*sin(d*x + c)^4 + 70*a*sin(d*x + c)^3 + 105*a*sin(d*x + c)^2)/d","A",0
499,1,69,0,0.541580," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, a \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 40 \, a \sin\left(d x + c\right)^{3} - 60 \, a \sin\left(d x + c\right)^{2} + 60 \, a \log\left(\sin\left(d x + c\right)\right) + 60 \, a \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*a*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 40*a*sin(d*x + c)^3 - 60*a*sin(d*x + c)^2 + 60*a*log(sin(d*x + c)) + 60*a*sin(d*x + c))/d","A",0
500,1,69,0,0.608577," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 12 \, a \sin\left(d x + c\right)^{2} + 12 \, a \log\left(\sin\left(d x + c\right)\right) - 24 \, a \sin\left(d x + c\right) - \frac{12 \, a}{\sin\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 12*a*sin(d*x + c)^2 + 12*a*log(sin(d*x + c)) - 24*a*sin(d*x + c) - 12*a/sin(d*x + c))/d","A",0
501,1,68,0,0.595687," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - 12 \, a \log\left(\sin\left(d x + c\right)\right) - 12 \, a \sin\left(d x + c\right) - \frac{3 \, {\left(2 \, a \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"1/6*(2*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - 12*a*log(sin(d*x + c)) - 12*a*sin(d*x + c) - 3*(2*a*sin(d*x + c) + a)/sin(d*x + c)^2)/d","A",0
502,1,69,0,0.500287," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a \sin\left(d x + c\right)^{2} - 12 \, a \log\left(\sin\left(d x + c\right)\right) + 6 \, a \sin\left(d x + c\right) + \frac{12 \, a \sin\left(d x + c\right)^{2} - 3 \, a \sin\left(d x + c\right) - 2 \, a}{\sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(3*a*sin(d*x + c)^2 - 12*a*log(sin(d*x + c)) + 6*a*sin(d*x + c) + (12*a*sin(d*x + c)^2 - 3*a*sin(d*x + c) - 2*a)/sin(d*x + c)^3)/d","A",0
503,1,69,0,0.785650," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, a \log\left(\sin\left(d x + c\right)\right) + 12 \, a \sin\left(d x + c\right) + \frac{24 \, a \sin\left(d x + c\right)^{3} + 12 \, a \sin\left(d x + c\right)^{2} - 4 \, a \sin\left(d x + c\right) - 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a*log(sin(d*x + c)) + 12*a*sin(d*x + c) + (24*a*sin(d*x + c)^3 + 12*a*sin(d*x + c)^2 - 4*a*sin(d*x + c) - 3*a)/sin(d*x + c)^4)/d","A",0
504,1,72,0,0.683274," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{60 \, a \log\left(\sin\left(d x + c\right)\right) - \frac{60 \, a \sin\left(d x + c\right)^{4} - 60 \, a \sin\left(d x + c\right)^{3} - 40 \, a \sin\left(d x + c\right)^{2} + 15 \, a \sin\left(d x + c\right) + 12 \, a}{\sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*a*log(sin(d*x + c)) - (60*a*sin(d*x + c)^4 - 60*a*sin(d*x + c)^3 - 40*a*sin(d*x + c)^2 + 15*a*sin(d*x + c) + 12*a)/sin(d*x + c)^5)/d","A",0
505,1,70,0,0.712350," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, a \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3} - 15 \, a \sin\left(d x + c\right)^{2} + 6 \, a \sin\left(d x + c\right) + 5 \, a}{30 \, d \sin\left(d x + c\right)^{6}}"," ",0,"-1/30*(30*a*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3 - 15*a*sin(d*x + c)^2 + 6*a*sin(d*x + c) + 5*a)/(d*sin(d*x + c)^6)","A",0
506,1,70,0,0.595085," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{105 \, a \sin\left(d x + c\right)^{5} + 70 \, a \sin\left(d x + c\right)^{4} - 105 \, a \sin\left(d x + c\right)^{3} - 84 \, a \sin\left(d x + c\right)^{2} + 35 \, a \sin\left(d x + c\right) + 30 \, a}{210 \, d \sin\left(d x + c\right)^{7}}"," ",0,"-1/210*(105*a*sin(d*x + c)^5 + 70*a*sin(d*x + c)^4 - 105*a*sin(d*x + c)^3 - 84*a*sin(d*x + c)^2 + 35*a*sin(d*x + c) + 30*a)/(d*sin(d*x + c)^7)","A",0
507,1,70,0,0.511866," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{280 \, a \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} - 336 \, a \sin\left(d x + c\right)^{3} - 280 \, a \sin\left(d x + c\right)^{2} + 120 \, a \sin\left(d x + c\right) + 105 \, a}{840 \, d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(280*a*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 - 336*a*sin(d*x + c)^3 - 280*a*sin(d*x + c)^2 + 120*a*sin(d*x + c) + 105*a)/(d*sin(d*x + c)^8)","A",0
508,1,70,0,0.691216," ","integrate(cos(d*x+c)^5*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{630 \, a \sin\left(d x + c\right)^{5} + 504 \, a \sin\left(d x + c\right)^{4} - 840 \, a \sin\left(d x + c\right)^{3} - 720 \, a \sin\left(d x + c\right)^{2} + 315 \, a \sin\left(d x + c\right) + 280 \, a}{2520 \, d \sin\left(d x + c\right)^{9}}"," ",0,"-1/2520*(630*a*sin(d*x + c)^5 + 504*a*sin(d*x + c)^4 - 840*a*sin(d*x + c)^3 - 720*a*sin(d*x + c)^2 + 315*a*sin(d*x + c) + 280*a)/(d*sin(d*x + c)^9)","A",0
509,1,70,0,0.449512," ","integrate(cos(d*x+c)^5*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{252 \, a \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} - 360 \, a \sin\left(d x + c\right)^{3} - 315 \, a \sin\left(d x + c\right)^{2} + 140 \, a \sin\left(d x + c\right) + 126 \, a}{1260 \, d \sin\left(d x + c\right)^{10}}"," ",0,"-1/1260*(252*a*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 - 360*a*sin(d*x + c)^3 - 315*a*sin(d*x + c)^2 + 140*a*sin(d*x + c) + 126*a)/(d*sin(d*x + c)^10)","A",0
510,1,70,0,0.507978," ","integrate(cos(d*x+c)^5*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2310 \, a \sin\left(d x + c\right)^{5} + 1980 \, a \sin\left(d x + c\right)^{4} - 3465 \, a \sin\left(d x + c\right)^{3} - 3080 \, a \sin\left(d x + c\right)^{2} + 1386 \, a \sin\left(d x + c\right) + 1260 \, a}{13860 \, d \sin\left(d x + c\right)^{11}}"," ",0,"-1/13860*(2310*a*sin(d*x + c)^5 + 1980*a*sin(d*x + c)^4 - 3465*a*sin(d*x + c)^3 - 3080*a*sin(d*x + c)^2 + 1386*a*sin(d*x + c) + 1260*a)/(d*sin(d*x + c)^11)","A",0
511,1,97,0,0.511325," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{252 \, a^{2} \sin\left(d x + c\right)^{10} + 560 \, a^{2} \sin\left(d x + c\right)^{9} - 315 \, a^{2} \sin\left(d x + c\right)^{8} - 1440 \, a^{2} \sin\left(d x + c\right)^{7} - 420 \, a^{2} \sin\left(d x + c\right)^{6} + 1008 \, a^{2} \sin\left(d x + c\right)^{5} + 630 \, a^{2} \sin\left(d x + c\right)^{4}}{2520 \, d}"," ",0,"1/2520*(252*a^2*sin(d*x + c)^10 + 560*a^2*sin(d*x + c)^9 - 315*a^2*sin(d*x + c)^8 - 1440*a^2*sin(d*x + c)^7 - 420*a^2*sin(d*x + c)^6 + 1008*a^2*sin(d*x + c)^5 + 630*a^2*sin(d*x + c)^4)/d","A",0
512,1,97,0,0.618966," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{140 \, a^{2} \sin\left(d x + c\right)^{9} + 315 \, a^{2} \sin\left(d x + c\right)^{8} - 180 \, a^{2} \sin\left(d x + c\right)^{7} - 840 \, a^{2} \sin\left(d x + c\right)^{6} - 252 \, a^{2} \sin\left(d x + c\right)^{5} + 630 \, a^{2} \sin\left(d x + c\right)^{4} + 420 \, a^{2} \sin\left(d x + c\right)^{3}}{1260 \, d}"," ",0,"1/1260*(140*a^2*sin(d*x + c)^9 + 315*a^2*sin(d*x + c)^8 - 180*a^2*sin(d*x + c)^7 - 840*a^2*sin(d*x + c)^6 - 252*a^2*sin(d*x + c)^5 + 630*a^2*sin(d*x + c)^4 + 420*a^2*sin(d*x + c)^3)/d","A",0
513,1,97,0,0.483778," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{105 \, a^{2} \sin\left(d x + c\right)^{8} + 240 \, a^{2} \sin\left(d x + c\right)^{7} - 140 \, a^{2} \sin\left(d x + c\right)^{6} - 672 \, a^{2} \sin\left(d x + c\right)^{5} - 210 \, a^{2} \sin\left(d x + c\right)^{4} + 560 \, a^{2} \sin\left(d x + c\right)^{3} + 420 \, a^{2} \sin\left(d x + c\right)^{2}}{840 \, d}"," ",0,"1/840*(105*a^2*sin(d*x + c)^8 + 240*a^2*sin(d*x + c)^7 - 140*a^2*sin(d*x + c)^6 - 672*a^2*sin(d*x + c)^5 - 210*a^2*sin(d*x + c)^4 + 560*a^2*sin(d*x + c)^3 + 420*a^2*sin(d*x + c)^2)/d","A",0
514,1,94,0,0.462663," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{10 \, a^{2} \sin\left(d x + c\right)^{6} + 24 \, a^{2} \sin\left(d x + c\right)^{5} - 15 \, a^{2} \sin\left(d x + c\right)^{4} - 80 \, a^{2} \sin\left(d x + c\right)^{3} - 30 \, a^{2} \sin\left(d x + c\right)^{2} + 60 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + 120 \, a^{2} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(10*a^2*sin(d*x + c)^6 + 24*a^2*sin(d*x + c)^5 - 15*a^2*sin(d*x + c)^4 - 80*a^2*sin(d*x + c)^3 - 30*a^2*sin(d*x + c)^2 + 60*a^2*log(sin(d*x + c)) + 120*a^2*sin(d*x + c))/d","A",0
515,1,94,0,0.691662," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, a^{2} \sin\left(d x + c\right)^{5} + 15 \, a^{2} \sin\left(d x + c\right)^{4} - 10 \, a^{2} \sin\left(d x + c\right)^{3} - 60 \, a^{2} \sin\left(d x + c\right)^{2} + 60 \, a^{2} \log\left(\sin\left(d x + c\right)\right) - 30 \, a^{2} \sin\left(d x + c\right) - \frac{30 \, a^{2}}{\sin\left(d x + c\right)}}{30 \, d}"," ",0,"1/30*(6*a^2*sin(d*x + c)^5 + 15*a^2*sin(d*x + c)^4 - 10*a^2*sin(d*x + c)^3 - 60*a^2*sin(d*x + c)^2 + 60*a^2*log(sin(d*x + c)) - 30*a^2*sin(d*x + c) - 30*a^2/sin(d*x + c))/d","A",0
516,1,93,0,0.558013," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} \sin\left(d x + c\right)^{4} + 8 \, a^{2} \sin\left(d x + c\right)^{3} - 6 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{2} \log\left(\sin\left(d x + c\right)\right) - 48 \, a^{2} \sin\left(d x + c\right) - \frac{6 \, {\left(4 \, a^{2} \sin\left(d x + c\right) + a^{2}\right)}}{\sin\left(d x + c\right)^{2}}}{12 \, d}"," ",0,"1/12*(3*a^2*sin(d*x + c)^4 + 8*a^2*sin(d*x + c)^3 - 6*a^2*sin(d*x + c)^2 - 12*a^2*log(sin(d*x + c)) - 48*a^2*sin(d*x + c) - 6*(4*a^2*sin(d*x + c) + a^2)/sin(d*x + c)^2)/d","A",0
517,1,93,0,0.406924," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \sin\left(d x + c\right)^{3} + 3 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{2} \log\left(\sin\left(d x + c\right)\right) - 3 \, a^{2} \sin\left(d x + c\right) + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2} - 3 \, a^{2} \sin\left(d x + c\right) - a^{2}}{\sin\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(a^2*sin(d*x + c)^3 + 3*a^2*sin(d*x + c)^2 - 12*a^2*log(sin(d*x + c)) - 3*a^2*sin(d*x + c) + (3*a^2*sin(d*x + c)^2 - 3*a^2*sin(d*x + c) - a^2)/sin(d*x + c)^3)/d","A",0
518,1,94,0,0.654848," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, a^{2} \sin\left(d x + c\right)^{2} - 12 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + 24 \, a^{2} \sin\left(d x + c\right) + \frac{48 \, a^{2} \sin\left(d x + c\right)^{3} + 6 \, a^{2} \sin\left(d x + c\right)^{2} - 8 \, a^{2} \sin\left(d x + c\right) - 3 \, a^{2}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(6*a^2*sin(d*x + c)^2 - 12*a^2*log(sin(d*x + c)) + 24*a^2*sin(d*x + c) + (48*a^2*sin(d*x + c)^3 + 6*a^2*sin(d*x + c)^2 - 8*a^2*sin(d*x + c) - 3*a^2)/sin(d*x + c)^4)/d","A",0
519,1,94,0,0.560919," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{60 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + 30 \, a^{2} \sin\left(d x + c\right) + \frac{30 \, a^{2} \sin\left(d x + c\right)^{4} + 60 \, a^{2} \sin\left(d x + c\right)^{3} + 10 \, a^{2} \sin\left(d x + c\right)^{2} - 15 \, a^{2} \sin\left(d x + c\right) - 6 \, a^{2}}{\sin\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"1/30*(60*a^2*log(sin(d*x + c)) + 30*a^2*sin(d*x + c) + (30*a^2*sin(d*x + c)^4 + 60*a^2*sin(d*x + c)^3 + 10*a^2*sin(d*x + c)^2 - 15*a^2*sin(d*x + c) - 6*a^2)/sin(d*x + c)^5)/d","A",0
520,1,97,0,0.660623," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{60 \, a^{2} \log\left(\sin\left(d x + c\right)\right) - \frac{120 \, a^{2} \sin\left(d x + c\right)^{5} - 30 \, a^{2} \sin\left(d x + c\right)^{4} - 80 \, a^{2} \sin\left(d x + c\right)^{3} - 15 \, a^{2} \sin\left(d x + c\right)^{2} + 24 \, a^{2} \sin\left(d x + c\right) + 10 \, a^{2}}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"1/60*(60*a^2*log(sin(d*x + c)) - (120*a^2*sin(d*x + c)^5 - 30*a^2*sin(d*x + c)^4 - 80*a^2*sin(d*x + c)^3 - 15*a^2*sin(d*x + c)^2 + 24*a^2*sin(d*x + c) + 10*a^2)/sin(d*x + c)^6)/d","A",0
521,1,110,0,0.656652," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{84 \, a^{3} \sin\left(d x + c\right)^{10} + 280 \, a^{3} \sin\left(d x + c\right)^{9} + 105 \, a^{3} \sin\left(d x + c\right)^{8} - 600 \, a^{3} \sin\left(d x + c\right)^{7} - 700 \, a^{3} \sin\left(d x + c\right)^{6} + 168 \, a^{3} \sin\left(d x + c\right)^{5} + 630 \, a^{3} \sin\left(d x + c\right)^{4} + 280 \, a^{3} \sin\left(d x + c\right)^{3}}{840 \, d}"," ",0,"1/840*(84*a^3*sin(d*x + c)^10 + 280*a^3*sin(d*x + c)^9 + 105*a^3*sin(d*x + c)^8 - 600*a^3*sin(d*x + c)^7 - 700*a^3*sin(d*x + c)^6 + 168*a^3*sin(d*x + c)^5 + 630*a^3*sin(d*x + c)^4 + 280*a^3*sin(d*x + c)^3)/d","A",0
522,1,110,0,0.520155," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{56 \, a^{3} \sin\left(d x + c\right)^{9} + 189 \, a^{3} \sin\left(d x + c\right)^{8} + 72 \, a^{3} \sin\left(d x + c\right)^{7} - 420 \, a^{3} \sin\left(d x + c\right)^{6} - 504 \, a^{3} \sin\left(d x + c\right)^{5} + 126 \, a^{3} \sin\left(d x + c\right)^{4} + 504 \, a^{3} \sin\left(d x + c\right)^{3} + 252 \, a^{3} \sin\left(d x + c\right)^{2}}{504 \, d}"," ",0,"1/504*(56*a^3*sin(d*x + c)^9 + 189*a^3*sin(d*x + c)^8 + 72*a^3*sin(d*x + c)^7 - 420*a^3*sin(d*x + c)^6 - 504*a^3*sin(d*x + c)^5 + 126*a^3*sin(d*x + c)^4 + 504*a^3*sin(d*x + c)^3 + 252*a^3*sin(d*x + c)^2)/d","A",0
523,1,107,0,0.514753," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{60 \, a^{3} \sin\left(d x + c\right)^{7} + 210 \, a^{3} \sin\left(d x + c\right)^{6} + 84 \, a^{3} \sin\left(d x + c\right)^{5} - 525 \, a^{3} \sin\left(d x + c\right)^{4} - 700 \, a^{3} \sin\left(d x + c\right)^{3} + 210 \, a^{3} \sin\left(d x + c\right)^{2} + 420 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 1260 \, a^{3} \sin\left(d x + c\right)}{420 \, d}"," ",0,"1/420*(60*a^3*sin(d*x + c)^7 + 210*a^3*sin(d*x + c)^6 + 84*a^3*sin(d*x + c)^5 - 525*a^3*sin(d*x + c)^4 - 700*a^3*sin(d*x + c)^3 + 210*a^3*sin(d*x + c)^2 + 420*a^3*log(sin(d*x + c)) + 1260*a^3*sin(d*x + c))/d","A",0
524,1,107,0,0.507939," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{10 \, a^{3} \sin\left(d x + c\right)^{6} + 36 \, a^{3} \sin\left(d x + c\right)^{5} + 15 \, a^{3} \sin\left(d x + c\right)^{4} - 100 \, a^{3} \sin\left(d x + c\right)^{3} - 150 \, a^{3} \sin\left(d x + c\right)^{2} + 180 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 60 \, a^{3} \sin\left(d x + c\right) - \frac{60 \, a^{3}}{\sin\left(d x + c\right)}}{60 \, d}"," ",0,"1/60*(10*a^3*sin(d*x + c)^6 + 36*a^3*sin(d*x + c)^5 + 15*a^3*sin(d*x + c)^4 - 100*a^3*sin(d*x + c)^3 - 150*a^3*sin(d*x + c)^2 + 180*a^3*log(sin(d*x + c)) + 60*a^3*sin(d*x + c) - 60*a^3/sin(d*x + c))/d","A",0
525,1,106,0,0.613114," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{12 \, a^{3} \sin\left(d x + c\right)^{5} + 45 \, a^{3} \sin\left(d x + c\right)^{4} + 20 \, a^{3} \sin\left(d x + c\right)^{3} - 150 \, a^{3} \sin\left(d x + c\right)^{2} + 60 \, a^{3} \log\left(\sin\left(d x + c\right)\right) - 300 \, a^{3} \sin\left(d x + c\right) - \frac{30 \, {\left(6 \, a^{3} \sin\left(d x + c\right) + a^{3}\right)}}{\sin\left(d x + c\right)^{2}}}{60 \, d}"," ",0,"1/60*(12*a^3*sin(d*x + c)^5 + 45*a^3*sin(d*x + c)^4 + 20*a^3*sin(d*x + c)^3 - 150*a^3*sin(d*x + c)^2 + 60*a^3*log(sin(d*x + c)) - 300*a^3*sin(d*x + c) - 30*(6*a^3*sin(d*x + c) + a^3)/sin(d*x + c)^2)/d","A",0
526,1,108,0,0.446737," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} \sin\left(d x + c\right)^{4} + 12 \, a^{3} \sin\left(d x + c\right)^{3} + 6 \, a^{3} \sin\left(d x + c\right)^{2} - 60 \, a^{3} \log\left(\sin\left(d x + c\right)\right) - 60 \, a^{3} \sin\left(d x + c\right) - \frac{2 \, {\left(6 \, a^{3} \sin\left(d x + c\right)^{2} + 9 \, a^{3} \sin\left(d x + c\right) + 2 \, a^{3}\right)}}{\sin\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"1/12*(3*a^3*sin(d*x + c)^4 + 12*a^3*sin(d*x + c)^3 + 6*a^3*sin(d*x + c)^2 - 60*a^3*log(sin(d*x + c)) - 60*a^3*sin(d*x + c) - 2*(6*a^3*sin(d*x + c)^2 + 9*a^3*sin(d*x + c) + 2*a^3)/sin(d*x + c)^3)/d","A",0
527,1,108,0,0.519475," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, a^{3} \sin\left(d x + c\right)^{3} + 18 \, a^{3} \sin\left(d x + c\right)^{2} - 60 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 12 \, a^{3} \sin\left(d x + c\right) + \frac{3 \, {\left(20 \, a^{3} \sin\left(d x + c\right)^{3} - 2 \, a^{3} \sin\left(d x + c\right)^{2} - 4 \, a^{3} \sin\left(d x + c\right) - a^{3}\right)}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(4*a^3*sin(d*x + c)^3 + 18*a^3*sin(d*x + c)^2 - 60*a^3*log(sin(d*x + c)) + 12*a^3*sin(d*x + c) + 3*(20*a^3*sin(d*x + c)^3 - 2*a^3*sin(d*x + c)^2 - 4*a^3*sin(d*x + c) - a^3)/sin(d*x + c)^4)/d","A",0
528,1,107,0,0.750085," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{30 \, a^{3} \sin\left(d x + c\right)^{2} + 60 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 180 \, a^{3} \sin\left(d x + c\right) + \frac{300 \, a^{3} \sin\left(d x + c\right)^{4} + 150 \, a^{3} \sin\left(d x + c\right)^{3} - 20 \, a^{3} \sin\left(d x + c\right)^{2} - 45 \, a^{3} \sin\left(d x + c\right) - 12 \, a^{3}}{\sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(30*a^3*sin(d*x + c)^2 + 60*a^3*log(sin(d*x + c)) + 180*a^3*sin(d*x + c) + (300*a^3*sin(d*x + c)^4 + 150*a^3*sin(d*x + c)^3 - 20*a^3*sin(d*x + c)^2 - 45*a^3*sin(d*x + c) - 12*a^3)/sin(d*x + c)^5)/d","A",0
529,1,108,0,0.525194," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{180 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + 60 \, a^{3} \sin\left(d x + c\right) - \frac{60 \, a^{3} \sin\left(d x + c\right)^{5} - 150 \, a^{3} \sin\left(d x + c\right)^{4} - 100 \, a^{3} \sin\left(d x + c\right)^{3} + 15 \, a^{3} \sin\left(d x + c\right)^{2} + 36 \, a^{3} \sin\left(d x + c\right) + 10 \, a^{3}}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"1/60*(180*a^3*log(sin(d*x + c)) + 60*a^3*sin(d*x + c) - (60*a^3*sin(d*x + c)^5 - 150*a^3*sin(d*x + c)^4 - 100*a^3*sin(d*x + c)^3 + 15*a^3*sin(d*x + c)^2 + 36*a^3*sin(d*x + c) + 10*a^3)/sin(d*x + c)^6)/d","A",0
530,1,119,0,0.791860," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, a^{4} \sin\left(d x + c\right)^{5} + 15 \, a^{4} \sin\left(d x + c\right)^{4} + 20 \, a^{4} \sin\left(d x + c\right)^{3} - 30 \, a^{4} \sin\left(d x + c\right)^{2} - 60 \, a^{4} \log\left(\sin\left(d x + c\right)\right) - 150 \, a^{4} \sin\left(d x + c\right) - \frac{5 \, {\left(12 \, a^{4} \sin\left(d x + c\right)^{2} + 6 \, a^{4} \sin\left(d x + c\right) + a^{4}\right)}}{\sin\left(d x + c\right)^{3}}}{15 \, d}"," ",0,"1/15*(3*a^4*sin(d*x + c)^5 + 15*a^4*sin(d*x + c)^4 + 20*a^4*sin(d*x + c)^3 - 30*a^4*sin(d*x + c)^2 - 60*a^4*log(sin(d*x + c)) - 150*a^4*sin(d*x + c) - 5*(12*a^4*sin(d*x + c)^2 + 6*a^4*sin(d*x + c) + a^4)/sin(d*x + c)^3)/d","A",0
531,1,120,0,0.716685," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{3 \, a^{4} \sin\left(d x + c\right)^{4} + 16 \, a^{4} \sin\left(d x + c\right)^{3} + 24 \, a^{4} \sin\left(d x + c\right)^{2} - 120 \, a^{4} \log\left(\sin\left(d x + c\right)\right) - 48 \, a^{4} \sin\left(d x + c\right) + \frac{48 \, a^{4} \sin\left(d x + c\right)^{3} - 24 \, a^{4} \sin\left(d x + c\right)^{2} - 16 \, a^{4} \sin\left(d x + c\right) - 3 \, a^{4}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(3*a^4*sin(d*x + c)^4 + 16*a^4*sin(d*x + c)^3 + 24*a^4*sin(d*x + c)^2 - 120*a^4*log(sin(d*x + c)) - 48*a^4*sin(d*x + c) + (48*a^4*sin(d*x + c)^3 - 24*a^4*sin(d*x + c)^2 - 16*a^4*sin(d*x + c) - 3*a^4)/sin(d*x + c)^4)/d","A",0
532,1,120,0,0.574490," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{5 \, a^{4} \sin\left(d x + c\right)^{3} + 30 \, a^{4} \sin\left(d x + c\right)^{2} - 60 \, a^{4} \log\left(\sin\left(d x + c\right)\right) + 60 \, a^{4} \sin\left(d x + c\right) + \frac{150 \, a^{4} \sin\left(d x + c\right)^{4} + 30 \, a^{4} \sin\left(d x + c\right)^{3} - 20 \, a^{4} \sin\left(d x + c\right)^{2} - 15 \, a^{4} \sin\left(d x + c\right) - 3 \, a^{4}}{\sin\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*(5*a^4*sin(d*x + c)^3 + 30*a^4*sin(d*x + c)^2 - 60*a^4*log(sin(d*x + c)) + 60*a^4*sin(d*x + c) + (150*a^4*sin(d*x + c)^4 + 30*a^4*sin(d*x + c)^3 - 20*a^4*sin(d*x + c)^2 - 15*a^4*sin(d*x + c) - 3*a^4)/sin(d*x + c)^5)/d","A",0
533,1,49,0,0.674781," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{60 \, \sin\left(d x + c\right)^{7} - 70 \, \sin\left(d x + c\right)^{6} - 84 \, \sin\left(d x + c\right)^{5} + 105 \, \sin\left(d x + c\right)^{4}}{420 \, a d}"," ",0,"1/420*(60*sin(d*x + c)^7 - 70*sin(d*x + c)^6 - 84*sin(d*x + c)^5 + 105*sin(d*x + c)^4)/(a*d)","A",0
534,1,49,0,0.578322," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{10 \, \sin\left(d x + c\right)^{6} - 12 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} + 20 \, \sin\left(d x + c\right)^{3}}{60 \, a d}"," ",0,"1/60*(10*sin(d*x + c)^6 - 12*sin(d*x + c)^5 - 15*sin(d*x + c)^4 + 20*sin(d*x + c)^3)/(a*d)","A",0
535,1,49,0,0.550432," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} - 20 \, \sin\left(d x + c\right)^{3} + 30 \, \sin\left(d x + c\right)^{2}}{60 \, a d}"," ",0,"1/60*(12*sin(d*x + c)^5 - 15*sin(d*x + c)^4 - 20*sin(d*x + c)^3 + 30*sin(d*x + c)^2)/(a*d)","A",0
536,1,51,0,0.833400," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} - 6 \, \sin\left(d x + c\right)}{a} + \frac{6 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{6 \, d}"," ",0,"1/6*((2*sin(d*x + c)^3 - 3*sin(d*x + c)^2 - 6*sin(d*x + c))/a + 6*log(sin(d*x + c))/a)/d","A",0
537,1,52,0,0.319636," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)}{a} - \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a} - \frac{2}{a \sin\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*((sin(d*x + c)^2 - 2*sin(d*x + c))/a - 2*log(sin(d*x + c))/a - 2/(a*sin(d*x + c)))/d","A",0
538,1,52,0,0.907115," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a} - \frac{2 \, \sin\left(d x + c\right)}{a} - \frac{2 \, \sin\left(d x + c\right) - 1}{a \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*log(sin(d*x + c))/a - 2*sin(d*x + c)/a - (2*sin(d*x + c) - 1)/(a*sin(d*x + c)^2))/d","A",0
539,1,50,0,0.765906," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{6 \, \log\left(\sin\left(d x + c\right)\right)}{a} + \frac{6 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 2}{a \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*log(sin(d*x + c))/a + (6*sin(d*x + c)^2 + 3*sin(d*x + c) - 2)/(a*sin(d*x + c)^3))/d","A",0
540,1,46,0,0.807413," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{12 \, \sin\left(d x + c\right)^{3} - 6 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) + 3}{12 \, a d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(12*sin(d*x + c)^3 - 6*sin(d*x + c)^2 - 4*sin(d*x + c) + 3)/(a*d*sin(d*x + c)^4)","A",0
541,1,46,0,0.774593," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, \sin\left(d x + c\right)^{3} - 20 \, \sin\left(d x + c\right)^{2} - 15 \, \sin\left(d x + c\right) + 12}{60 \, a d \sin\left(d x + c\right)^{5}}"," ",0,"-1/60*(30*sin(d*x + c)^3 - 20*sin(d*x + c)^2 - 15*sin(d*x + c) + 12)/(a*d*sin(d*x + c)^5)","A",0
542,1,46,0,0.817527," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{20 \, \sin\left(d x + c\right)^{3} - 15 \, \sin\left(d x + c\right)^{2} - 12 \, \sin\left(d x + c\right) + 10}{60 \, a d \sin\left(d x + c\right)^{6}}"," ",0,"-1/60*(20*sin(d*x + c)^3 - 15*sin(d*x + c)^2 - 12*sin(d*x + c) + 10)/(a*d*sin(d*x + c)^6)","A",0
543,1,46,0,1.003922," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{105 \, \sin\left(d x + c\right)^{3} - 84 \, \sin\left(d x + c\right)^{2} - 70 \, \sin\left(d x + c\right) + 60}{420 \, a d \sin\left(d x + c\right)^{7}}"," ",0,"-1/420*(105*sin(d*x + c)^3 - 84*sin(d*x + c)^2 - 70*sin(d*x + c) + 60)/(a*d*sin(d*x + c)^7)","A",0
544,1,39,0,0.718924," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{10 \, \sin\left(d x + c\right)^{6} - 24 \, \sin\left(d x + c\right)^{5} + 15 \, \sin\left(d x + c\right)^{4}}{60 \, a^{2} d}"," ",0,"1/60*(10*sin(d*x + c)^6 - 24*sin(d*x + c)^5 + 15*sin(d*x + c)^4)/(a^2*d)","A",0
545,1,39,0,0.569914," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} + 10 \, \sin\left(d x + c\right)^{3}}{30 \, a^{2} d}"," ",0,"1/30*(6*sin(d*x + c)^5 - 15*sin(d*x + c)^4 + 10*sin(d*x + c)^3)/(a^2*d)","A",0
546,1,39,0,0.809442," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, \sin\left(d x + c\right)^{4} - 8 \, \sin\left(d x + c\right)^{3} + 6 \, \sin\left(d x + c\right)^{2}}{12 \, a^{2} d}"," ",0,"1/12*(3*sin(d*x + c)^4 - 8*sin(d*x + c)^3 + 6*sin(d*x + c)^2)/(a^2*d)","A",0
547,1,39,0,0.510196," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right)}{a^{2}} + \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{2 \, d}"," ",0,"1/2*((sin(d*x + c)^2 - 4*sin(d*x + c))/a^2 + 2*log(sin(d*x + c))/a^2)/d","A",0
548,1,41,0,0.573313," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a^{2}} - \frac{\sin\left(d x + c\right)}{a^{2}} + \frac{1}{a^{2} \sin\left(d x + c\right)}}{d}"," ",0,"-(2*log(sin(d*x + c))/a^2 - sin(d*x + c)/a^2 + 1/(a^2*sin(d*x + c)))/d","A",0
549,1,40,0,0.848911," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a^{2}} + \frac{4 \, \sin\left(d x + c\right) - 1}{a^{2} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*log(sin(d*x + c))/a^2 + (4*sin(d*x + c) - 1)/(a^2*sin(d*x + c)^2))/d","A",0
550,1,36,0,0.306618," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, \sin\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) + 1}{3 \, a^{2} d \sin\left(d x + c\right)^{3}}"," ",0,"-1/3*(3*sin(d*x + c)^2 - 3*sin(d*x + c) + 1)/(a^2*d*sin(d*x + c)^3)","A",0
551,1,36,0,0.533312," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, \sin\left(d x + c\right)^{2} - 8 \, \sin\left(d x + c\right) + 3}{12 \, a^{2} d \sin\left(d x + c\right)^{4}}"," ",0,"-1/12*(6*sin(d*x + c)^2 - 8*sin(d*x + c) + 3)/(a^2*d*sin(d*x + c)^4)","A",0
552,1,36,0,0.409327," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{10 \, \sin\left(d x + c\right)^{2} - 15 \, \sin\left(d x + c\right) + 6}{30 \, a^{2} d \sin\left(d x + c\right)^{5}}"," ",0,"-1/30*(10*sin(d*x + c)^2 - 15*sin(d*x + c) + 6)/(a^2*d*sin(d*x + c)^5)","A",0
553,1,36,0,0.963163," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{15 \, \sin\left(d x + c\right)^{2} - 24 \, \sin\left(d x + c\right) + 10}{60 \, a^{2} d \sin\left(d x + c\right)^{6}}"," ",0,"-1/60*(15*sin(d*x + c)^2 - 24*sin(d*x + c) + 10)/(a^2*d*sin(d*x + c)^6)","A",0
554,1,73,0,0.423504," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{12 \, \sin\left(d x + c\right)^{5} - 45 \, \sin\left(d x + c\right)^{4} + 80 \, \sin\left(d x + c\right)^{3} - 120 \, \sin\left(d x + c\right)^{2} + 240 \, \sin\left(d x + c\right)}{a^{3}} - \frac{240 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}}}{60 \, d}"," ",0,"1/60*((12*sin(d*x + c)^5 - 45*sin(d*x + c)^4 + 80*sin(d*x + c)^3 - 120*sin(d*x + c)^2 + 240*sin(d*x + c))/a^3 - 240*log(sin(d*x + c) + 1)/a^3)/d","A",0
555,1,61,0,0.412046," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3} + 8 \, \sin\left(d x + c\right)^{2} - 16 \, \sin\left(d x + c\right)}{a^{3}} + \frac{16 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}}}{4 \, d}"," ",0,"1/4*((sin(d*x + c)^4 - 4*sin(d*x + c)^3 + 8*sin(d*x + c)^2 - 16*sin(d*x + c))/a^3 + 16*log(sin(d*x + c) + 1)/a^3)/d","A",0
556,1,53,0,0.595683," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, \sin\left(d x + c\right)^{3} - 9 \, \sin\left(d x + c\right)^{2} + 24 \, \sin\left(d x + c\right)}{a^{3}} - \frac{24 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}}}{6 \, d}"," ",0,"1/6*((2*sin(d*x + c)^3 - 9*sin(d*x + c)^2 + 24*sin(d*x + c))/a^3 - 24*log(sin(d*x + c) + 1)/a^3)/d","A",0
557,1,43,0,0.488190," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{4 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} - \frac{\log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{\sin\left(d x + c\right)}{a^{3}}}{d}"," ",0,"-(4*log(sin(d*x + c) + 1)/a^3 - log(sin(d*x + c))/a^3 - sin(d*x + c)/a^3)/d","A",0
558,1,44,0,0.867572," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{4 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} - \frac{3 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{1}{a^{3} \sin\left(d x + c\right)}}{d}"," ",0,"(4*log(sin(d*x + c) + 1)/a^3 - 3*log(sin(d*x + c))/a^3 - 1/(a^3*sin(d*x + c)))/d","A",0
559,1,55,0,0.798340," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{8 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} - \frac{8 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{6 \, \sin\left(d x + c\right) - 1}{a^{3} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(8*log(sin(d*x + c) + 1)/a^3 - 8*log(sin(d*x + c))/a^3 - (6*sin(d*x + c) - 1)/(a^3*sin(d*x + c)^2))/d","A",0
560,1,65,0,0.721231," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{24 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} - \frac{24 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{24 \, \sin\left(d x + c\right)^{2} - 9 \, \sin\left(d x + c\right) + 2}{a^{3} \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(24*log(sin(d*x + c) + 1)/a^3 - 24*log(sin(d*x + c))/a^3 - (24*sin(d*x + c)^2 - 9*sin(d*x + c) + 2)/(a^3*sin(d*x + c)^3))/d","A",0
561,1,75,0,0.673255," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{16 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} - \frac{16 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{16 \, \sin\left(d x + c\right)^{3} - 8 \, \sin\left(d x + c\right)^{2} + 4 \, \sin\left(d x + c\right) - 1}{a^{3} \sin\left(d x + c\right)^{4}}}{4 \, d}"," ",0,"-1/4*(16*log(sin(d*x + c) + 1)/a^3 - 16*log(sin(d*x + c))/a^3 - (16*sin(d*x + c)^3 - 8*sin(d*x + c)^2 + 4*sin(d*x + c) - 1)/(a^3*sin(d*x + c)^4))/d","A",0
562,1,85,0,0.872220," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{240 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3}} - \frac{240 \, \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{240 \, \sin\left(d x + c\right)^{4} - 120 \, \sin\left(d x + c\right)^{3} + 80 \, \sin\left(d x + c\right)^{2} - 45 \, \sin\left(d x + c\right) + 12}{a^{3} \sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(240*log(sin(d*x + c) + 1)/a^3 - 240*log(sin(d*x + c))/a^3 - (240*sin(d*x + c)^4 - 120*sin(d*x + c)^3 + 80*sin(d*x + c)^2 - 45*sin(d*x + c) + 12)/(a^3*sin(d*x + c)^5))/d","A",0
563,1,100,0,0.543401," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{\frac{192 \, \sin\left(d x + c\right)^{4} + 96 \, \sin\left(d x + c\right)^{3} - 32 \, \sin\left(d x + c\right)^{2} + 13 \, \sin\left(d x + c\right) - 3}{a^{4} \sin\left(d x + c\right)^{5} + a^{4} \sin\left(d x + c\right)^{4}} - \frac{192 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} + \frac{192 \, \log\left(\sin\left(d x + c\right)\right)}{a^{4}}}{12 \, d}"," ",0,"1/12*((192*sin(d*x + c)^4 + 96*sin(d*x + c)^3 - 32*sin(d*x + c)^2 + 13*sin(d*x + c) - 3)/(a^4*sin(d*x + c)^5 + a^4*sin(d*x + c)^4) - 192*log(sin(d*x + c) + 1)/a^4 + 192*log(sin(d*x + c))/a^4)/d","A",0
564,1,110,0,0.777372," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","-\frac{\frac{300 \, \sin\left(d x + c\right)^{5} + 150 \, \sin\left(d x + c\right)^{4} - 50 \, \sin\left(d x + c\right)^{3} + 25 \, \sin\left(d x + c\right)^{2} - 12 \, \sin\left(d x + c\right) + 3}{a^{4} \sin\left(d x + c\right)^{6} + a^{4} \sin\left(d x + c\right)^{5}} - \frac{300 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4}} + \frac{300 \, \log\left(\sin\left(d x + c\right)\right)}{a^{4}}}{15 \, d}"," ",0,"-1/15*((300*sin(d*x + c)^5 + 150*sin(d*x + c)^4 - 50*sin(d*x + c)^3 + 25*sin(d*x + c)^2 - 12*sin(d*x + c) + 3)/(a^4*sin(d*x + c)^6 + a^4*sin(d*x + c)^5) - 300*log(sin(d*x + c) + 1)/a^4 + 300*log(sin(d*x + c))/a^4)/d","A",0
565,1,161,0,0.926881," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{a^{3} \sin\left(d x + c\right)^{n + 8}}{n + 8} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{n + 7}}{n + 7} + \frac{a^{3} \sin\left(d x + c\right)^{n + 6}}{n + 6} - \frac{5 \, a^{3} \sin\left(d x + c\right)^{n + 5}}{n + 5} - \frac{5 \, a^{3} \sin\left(d x + c\right)^{n + 4}}{n + 4} + \frac{a^{3} \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a^{3} \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(a^3*sin(d*x + c)^(n + 8)/(n + 8) + 3*a^3*sin(d*x + c)^(n + 7)/(n + 7) + a^3*sin(d*x + c)^(n + 6)/(n + 6) - 5*a^3*sin(d*x + c)^(n + 5)/(n + 5) - 5*a^3*sin(d*x + c)^(n + 4)/(n + 4) + a^3*sin(d*x + c)^(n + 3)/(n + 3) + 3*a^3*sin(d*x + c)^(n + 2)/(n + 2) + a^3*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
566,1,143,0,0.967315," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{a^{2} \sin\left(d x + c\right)^{n + 7}}{n + 7} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{n + 6}}{n + 6} - \frac{a^{2} \sin\left(d x + c\right)^{n + 5}}{n + 5} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{n + 4}}{n + 4} - \frac{a^{2} \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a^{2} \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(a^2*sin(d*x + c)^(n + 7)/(n + 7) + 2*a^2*sin(d*x + c)^(n + 6)/(n + 6) - a^2*sin(d*x + c)^(n + 5)/(n + 5) - 4*a^2*sin(d*x + c)^(n + 4)/(n + 4) - a^2*sin(d*x + c)^(n + 3)/(n + 3) + 2*a^2*sin(d*x + c)^(n + 2)/(n + 2) + a^2*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
567,1,109,0,0.595402," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{a \sin\left(d x + c\right)^{n + 6}}{n + 6} + \frac{a \sin\left(d x + c\right)^{n + 5}}{n + 5} - \frac{2 \, a \sin\left(d x + c\right)^{n + 4}}{n + 4} - \frac{2 \, a \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{a \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(a*sin(d*x + c)^(n + 6)/(n + 6) + a*sin(d*x + c)^(n + 5)/(n + 5) - 2*a*sin(d*x + c)^(n + 4)/(n + 4) - 2*a*sin(d*x + c)^(n + 3)/(n + 3) + a*sin(d*x + c)^(n + 2)/(n + 2) + a*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
568,1,124,0,0.800648," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left({\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} \sin\left(d x + c\right)^{4} - {\left(n^{3} + 7 \, n^{2} + 14 \, n + 8\right)} \sin\left(d x + c\right)^{3} - {\left(n^{3} + 8 \, n^{2} + 19 \, n + 12\right)} \sin\left(d x + c\right)^{2} + {\left(n^{3} + 9 \, n^{2} + 26 \, n + 24\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{{\left(n^{4} + 10 \, n^{3} + 35 \, n^{2} + 50 \, n + 24\right)} a d}"," ",0,"((n^3 + 6*n^2 + 11*n + 6)*sin(d*x + c)^4 - (n^3 + 7*n^2 + 14*n + 8)*sin(d*x + c)^3 - (n^3 + 8*n^2 + 19*n + 12)*sin(d*x + c)^2 + (n^3 + 9*n^2 + 26*n + 24)*sin(d*x + c))*sin(d*x + c)^n/((n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*a*d)","A",0
569,1,81,0,0.920269," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left({\left(n^{2} + 3 \, n + 2\right)} \sin\left(d x + c\right)^{3} - 2 \, {\left(n^{2} + 4 \, n + 3\right)} \sin\left(d x + c\right)^{2} + {\left(n^{2} + 5 \, n + 6\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{{\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} a^{2} d}"," ",0,"((n^2 + 3*n + 2)*sin(d*x + c)^3 - 2*(n^2 + 4*n + 3)*sin(d*x + c)^2 + (n^2 + 5*n + 6)*sin(d*x + c))*sin(d*x + c)^n/((n^3 + 6*n^2 + 11*n + 6)*a^2*d)","A",0
570,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{{\left(a \sin\left(d x + c\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(a*sin(d*x + c) + a)^3, x)","F",0
571,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(a*sin(d*x + c) + a)^4, x)","F",0
572,1,86,0,0.375616," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{10240 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a - 693 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{7096320 \, d}"," ",0,"-1/7096320*(10240*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a - 693*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a)/d","A",0
573,1,76,0,0.422484," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{10240 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a + 63 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{645120 \, d}"," ",0,"1/645120*(10240*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a + 63*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a)/d","A",0
574,1,76,0,0.502795," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{1024 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a + 21 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{64512 \, d}"," ",0,"1/64512*(1024*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a + 21*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a)/d","A",0
575,1,63,0,0.349586," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3072 \, a \cos\left(d x + c\right)^{7} - 7 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a}{21504 \, d}"," ",0,"-1/21504*(3072*a*cos(d*x + c)^7 - 7*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a)/d","A",0
576,1,106,0,0.391757," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{32 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a}{960 \, d}"," ",0,"1/960*(32*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a)/d","A",0
577,1,121,0,0.468066," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a - 15 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a}{120 \, d}"," ",0,"1/120*(4*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a - 15*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a)/d","A",0
578,1,131,0,0.566319," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a + 3 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a}{24 \, d}"," ",0,"-1/24*(2*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a + 3*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a)/d","A",0
579,1,122,0,0.598094," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a - 2 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a}{12 \, d}"," ",0,"-1/12*((4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a - 2*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a)/d","A",0
580,1,136,0,0.614922," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{8 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a - 3 \, a {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(8*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a - 3*a*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
581,1,125,0,0.436799," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{16 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a + 15 \, a {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"-1/240*(16*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a + 15*a*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
582,1,137,0,0.426950," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a - 5 \, a {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"-1/480*(32*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a - 5*a*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
583,1,106,0,0.403141," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{7 \, a {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{96 \, a}{\tan\left(d x + c\right)^{7}}}{672 \, d}"," ",0,"1/672*(7*a*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) - 96*a/tan(d*x + c)^7)/d","A",0
584,1,126,0,0.370023," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{7 \, a {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{768 \, a}{\tan\left(d x + c\right)^{7}}}{5376 \, d}"," ",0,"-1/5376*(7*a*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 768*a/tan(d*x + c)^7)/d","A",0
585,1,138,0,0.351848," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{21 \, a {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{256 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a}{\tan\left(d x + c\right)^{9}}}{16128 \, d}"," ",0,"-1/16128*(21*a*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 256*(9*tan(d*x + c)^2 + 7)*a/tan(d*x + c)^9)/d","A",0
586,1,158,0,0.565227," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{63 \, a {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{2560 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a}{\tan\left(d x + c\right)^{9}}}{161280 \, d}"," ",0,"-1/161280*(63*a*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 2560*(9*tan(d*x + c)^2 + 7)*a/tan(d*x + c)^9)/d","A",0
587,1,168,0,0.333344," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{693 \, a {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{2560 \, {\left(99 \, \tan\left(d x + c\right)^{4} + 154 \, \tan\left(d x + c\right)^{2} + 63\right)} a}{\tan\left(d x + c\right)^{11}}}{1774080 \, d}"," ",0,"-1/1774080*(693*a*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 2560*(99*tan(d*x + c)^4 + 154*tan(d*x + c)^2 + 63)*a/tan(d*x + c)^11)/d","A",0
588,1,138,0,0.358807," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{81920 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a^{2} - 2772 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} - 1155 \, {\left(4 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 120 \, d x + 120 \, c + 9 \, \sin\left(8 \, d x + 8 \, c\right) - 48 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{28385280 \, d}"," ",0,"-1/28385280*(81920*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a^2 - 2772*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a^2 - 1155*(4*sin(4*d*x + 4*c)^3 + 120*d*x + 120*c + 9*sin(8*d*x + 8*c) - 48*sin(4*d*x + 4*c))*a^2)/d","A",0
589,1,116,0,0.409431," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{5120 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a^{2} - 56320 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{2} - 693 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{3548160 \, d}"," ",0,"-1/3548160*(5120*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a^2 - 56320*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^2 - 693*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a^2)/d","A",0
590,1,128,0,0.337461," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{20480 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{2} + 63 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} + 210 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{645120 \, d}"," ",0,"1/645120*(20480*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^2 + 63*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a^2 + 210*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^2)/d","A",0
591,1,93,0,0.978546," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4608 \, a^{2} \cos\left(d x + c\right)^{7} - 512 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{2} - 21 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2}}{32256 \, d}"," ",0,"-1/32256*(4608*a^2*cos(d*x + c)^7 - 512*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^2 - 21*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^2)/d","A",0
592,1,123,0,0.432650," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{480 \, a^{2} \cos\left(d x + c\right)^{7} - 112 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2}}{3360 \, d}"," ",0,"-1/3360*(480*a^2*cos(d*x + c)^7 - 112*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^2 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^2)/d","A",0
593,1,173,0,0.778433," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{64 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} - 120 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2}}{960 \, d}"," ",0,"1/960*(64*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^2 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^2 - 120*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^2)/d","A",0
594,1,191,0,0.812723," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} - 5 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} - 15 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2}}{60 \, d}"," ",0,"1/60*(2*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^2 - 5*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^2 - 15*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^2)/d","A",0
595,1,190,0,0.757161," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} + 3 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2} - 4 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{2}}{24 \, d}"," ",0,"-1/24*(4*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^2 + 3*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^2 - 4*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^2)/d","A",0
596,1,206,0,0.435838," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} - 16 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{2} + 3 \, a^{2} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"-1/48*(4*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^2 - 16*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^2 + 3*a^2*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
597,1,184,0,0.647161," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{20 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{2} - 8 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{2} - 15 \, a^{2} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{120 \, d}"," ",0,"1/120*(20*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^2 - 8*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^2 - 15*a^2*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
598,1,220,0,0.462233," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{64 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{2} - 5 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 30 \, a^{2} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"-1/480*(64*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^2 - 5*a^2*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 30*a^2*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
599,1,154,0,0.428012," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{112 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{2} - 35 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{240 \, a^{2}}{\tan\left(d x + c\right)^{7}}}{1680 \, d}"," ",0,"-1/1680*(112*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^2 - 35*a^2*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 240*a^2/tan(d*x + c)^7)/d","A",0
600,1,221,0,0.537760," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{7 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 56 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{1536 \, a^{2}}{\tan\left(d x + c\right)^{7}}}{5376 \, d}"," ",0,"-1/5376*(7*a^2*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) - 56*a^2*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 1536*a^2/tan(d*x + c)^7)/d","A",0
601,1,155,0,0.365060," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{21 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{1152 \, a^{2}}{\tan\left(d x + c\right)^{7}} + \frac{128 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a^{2}}{\tan\left(d x + c\right)^{9}}}{8064 \, d}"," ",0,"-1/8064*(21*a^2*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 1152*a^2/tan(d*x + c)^7 + 128*(9*tan(d*x + c)^2 + 7)*a^2/tan(d*x + c)^9)/d","A",0
602,1,273,0,0.321221," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{63 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 210 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{5120 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a^{2}}{\tan\left(d x + c\right)^{9}}}{161280 \, d}"," ",0,"-1/161280*(63*a^2*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 210*a^2*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 5120*(9*tan(d*x + c)^2 + 7)*a^2/tan(d*x + c)^9)/d","A",0
603,1,197,0,0.327729," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{693 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{14080 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a^{2}}{\tan\left(d x + c\right)^{9}} + \frac{1280 \, {\left(99 \, \tan\left(d x + c\right)^{4} + 154 \, \tan\left(d x + c\right)^{2} + 63\right)} a^{2}}{\tan\left(d x + c\right)^{11}}}{887040 \, d}"," ",0,"-1/887040*(693*a^2*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 14080*(9*tan(d*x + c)^2 + 7)*a^2/tan(d*x + c)^9 + 1280*(99*tan(d*x + c)^4 + 154*tan(d*x + c)^2 + 63)*a^2/tan(d*x + c)^11)/d","A",0
604,1,323,0,0.325083," ","integrate(cos(d*x+c)^6*csc(d*x+c)^13*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{1155 \, a^{2} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{11} - 85 \, \cos\left(d x + c\right)^{9} + 198 \, \cos\left(d x + c\right)^{7} + 198 \, \cos\left(d x + c\right)^{5} - 85 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{12} - 6 \, \cos\left(d x + c\right)^{10} + 15 \, \cos\left(d x + c\right)^{8} - 20 \, \cos\left(d x + c\right)^{6} + 15 \, \cos\left(d x + c\right)^{4} - 6 \, \cos\left(d x + c\right)^{2} + 1} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2772 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{20480 \, {\left(99 \, \tan\left(d x + c\right)^{4} + 154 \, \tan\left(d x + c\right)^{2} + 63\right)} a^{2}}{\tan\left(d x + c\right)^{11}}}{7096320 \, d}"," ",0,"-1/7096320*(1155*a^2*(2*(15*cos(d*x + c)^11 - 85*cos(d*x + c)^9 + 198*cos(d*x + c)^7 + 198*cos(d*x + c)^5 - 85*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^12 - 6*cos(d*x + c)^10 + 15*cos(d*x + c)^8 - 20*cos(d*x + c)^6 + 15*cos(d*x + c)^4 - 6*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 2772*a^2*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 20480*(99*tan(d*x + c)^4 + 154*tan(d*x + c)^2 + 63)*a^2/tan(d*x + c)^11)/d","A",0
605,1,184,0,0.340081," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{40960 \, {\left(231 \, \cos\left(d x + c\right)^{13} - 819 \, \cos\left(d x + c\right)^{11} + 1001 \, \cos\left(d x + c\right)^{9} - 429 \, \cos\left(d x + c\right)^{7}\right)} a^{3} - 532480 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a^{3} + 12012 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} + 15015 \, {\left(4 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 120 \, d x + 120 \, c + 9 \, \sin\left(8 \, d x + 8 \, c\right) - 48 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{123002880 \, d}"," ",0,"1/123002880*(40960*(231*cos(d*x + c)^13 - 819*cos(d*x + c)^11 + 1001*cos(d*x + c)^9 - 429*cos(d*x + c)^7)*a^3 - 532480*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a^3 + 12012*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a^3 + 15015*(4*sin(4*d*x + 4*c)^3 + 120*d*x + 120*c + 9*sin(8*d*x + 8*c) - 48*sin(4*d*x + 4*c))*a^3)/d","A",0
606,1,164,0,0.350703," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{122880 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a^{3} - 450560 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{3} - 8316 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 1155 \, {\left(4 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 120 \, d x + 120 \, c + 9 \, \sin\left(8 \, d x + 8 \, c\right) - 48 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{28385280 \, d}"," ",0,"-1/28385280*(122880*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a^3 - 450560*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^3 - 8316*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a^3 - 1155*(4*sin(4*d*x + 4*c)^3 + 120*d*x + 120*c + 9*sin(8*d*x + 8*c) - 48*sin(4*d*x + 4*c))*a^3)/d","A",0
607,1,164,0,0.322977," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{10240 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a^{3} - 337920 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{3} - 2079 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 2310 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{7096320 \, d}"," ",0,"-1/7096320*(10240*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a^3 - 337920*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^3 - 2079*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a^3 - 2310*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^3)/d","A",0
608,1,141,0,0.321524," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{30720 \, a^{3} \cos\left(d x + c\right)^{7} - 10240 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{3} - 21 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} - 210 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3}}{215040 \, d}"," ",0,"-1/215040*(30720*a^3*cos(d*x + c)^7 - 10240*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^3 - 21*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a^3 - 210*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^3)/d","A",0
609,1,171,0,0.451243," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{46080 \, a^{3} \cos\left(d x + c\right)^{7} - 3584 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 35 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} + 1680 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3}}{107520 \, d}"," ",0,"-1/107520*(46080*a^3*cos(d*x + c)^7 - 3584*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^3 - 35*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^3 + 1680*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^3)/d","A",0
610,1,186,0,0.412369," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{320 \, a^{3} \cos\left(d x + c\right)^{7} - 224 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} + 280 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3}}{2240 \, d}"," ",0,"-1/2240*(320*a^3*cos(d*x + c)^7 - 224*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^3 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^3 + 280*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^3)/d","A",0
611,1,239,0,0.489224," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{96 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 80 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{3} - 360 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3}}{960 \, d}"," ",0,"1/960*(96*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^3 - 80*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^3 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^3 - 360*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^3)/d","A",0
612,1,246,0,0.424010," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 30 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 45 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3} + 20 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{3}}{120 \, d}"," ",0,"1/120*(4*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^3 - 30*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^3 - 45*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^3 + 20*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^3)/d","A",0
613,1,268,0,0.410919," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} + 2 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3} - 8 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{3} + a^{3} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{16 \, d}"," ",0,"-1/16*(4*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^3 + 2*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^3 - 8*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^3 + a^3*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
614,1,250,0,0.418249," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{20 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 120 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{3} + 16 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{3} + 45 \, a^{3} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{240 \, d}"," ",0,"-1/240*(20*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^3 - 120*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^3 + 16*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^3 + 45*a^3*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
615,1,275,0,0.409605," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{80 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{3} - 96 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{3} + 5 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 90 \, a^{3} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"1/480*(80*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^3 - 96*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^3 + 5*a^3*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) - 90*a^3*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
616,1,233,0,0.416591," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{224 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{3} - 35 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 70 \, a^{3} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{160 \, a^{3}}{\tan\left(d x + c\right)^{7}}}{1120 \, d}"," ",0,"-1/1120*(224*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^3 - 35*a^3*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 70*a^3*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 160*a^3/tan(d*x + c)^7)/d","A",0
617,1,265,0,0.412816," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1792 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{3} + 35 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 840 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{11520 \, a^{3}}{\tan\left(d x + c\right)^{7}}}{26880 \, d}"," ",0,"-1/26880*(1792*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^3 + 35*a^3*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) - 840*a^3*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 11520*a^3/tan(d*x + c)^7)/d","A",0
618,1,246,0,0.426858," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{63 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 168 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{6912 \, a^{3}}{\tan\left(d x + c\right)^{7}} + \frac{256 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a^{3}}{\tan\left(d x + c\right)^{9}}}{16128 \, d}"," ",0,"-1/16128*(63*a^3*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) - 168*a^3*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 6912*a^3/tan(d*x + c)^7 + 256*(9*tan(d*x + c)^2 + 7)*a^3/tan(d*x + c)^9)/d","A",0
619,1,286,0,0.338700," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{21 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 210 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{7680 \, a^{3}}{\tan\left(d x + c\right)^{7}} + \frac{2560 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a^{3}}{\tan\left(d x + c\right)^{9}}}{53760 \, d}"," ",0,"-1/53760*(21*a^3*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 210*a^3*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 7680*a^3/tan(d*x + c)^7 + 2560*(9*tan(d*x + c)^2 + 7)*a^3/tan(d*x + c)^9)/d","A",0
620,1,308,0,0.492904," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2079 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2310 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{84480 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a^{3}}{\tan\left(d x + c\right)^{9}} + \frac{2560 \, {\left(99 \, \tan\left(d x + c\right)^{4} + 154 \, \tan\left(d x + c\right)^{2} + 63\right)} a^{3}}{\tan\left(d x + c\right)^{11}}}{1774080 \, d}"," ",0,"-1/1774080*(2079*a^3*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 2310*a^3*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 84480*(9*tan(d*x + c)^2 + 7)*a^3/tan(d*x + c)^9 + 2560*(99*tan(d*x + c)^4 + 154*tan(d*x + c)^2 + 63)*a^3/tan(d*x + c)^11)/d","A",0
621,1,348,0,0.397689," ","integrate(cos(d*x+c)^6*csc(d*x+c)^13*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{1155 \, a^{3} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{11} - 85 \, \cos\left(d x + c\right)^{9} + 198 \, \cos\left(d x + c\right)^{7} + 198 \, \cos\left(d x + c\right)^{5} - 85 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{12} - 6 \, \cos\left(d x + c\right)^{10} + 15 \, \cos\left(d x + c\right)^{8} - 20 \, \cos\left(d x + c\right)^{6} + 15 \, \cos\left(d x + c\right)^{4} - 6 \, \cos\left(d x + c\right)^{2} + 1} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 8316 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{112640 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a^{3}}{\tan\left(d x + c\right)^{9}} + \frac{30720 \, {\left(99 \, \tan\left(d x + c\right)^{4} + 154 \, \tan\left(d x + c\right)^{2} + 63\right)} a^{3}}{\tan\left(d x + c\right)^{11}}}{7096320 \, d}"," ",0,"-1/7096320*(1155*a^3*(2*(15*cos(d*x + c)^11 - 85*cos(d*x + c)^9 + 198*cos(d*x + c)^7 + 198*cos(d*x + c)^5 - 85*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^12 - 6*cos(d*x + c)^10 + 15*cos(d*x + c)^8 - 20*cos(d*x + c)^6 + 15*cos(d*x + c)^4 - 6*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 8316*a^3*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 112640*(9*tan(d*x + c)^2 + 7)*a^3/tan(d*x + c)^9 + 30720*(99*tan(d*x + c)^4 + 154*tan(d*x + c)^2 + 63)*a^3/tan(d*x + c)^11)/d","A",0
622,1,368,0,0.361173," ","integrate(cos(d*x+c)^6*csc(d*x+c)^14*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{15015 \, a^{3} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{11} - 85 \, \cos\left(d x + c\right)^{9} + 198 \, \cos\left(d x + c\right)^{7} + 198 \, \cos\left(d x + c\right)^{5} - 85 \, \cos\left(d x + c\right)^{3} + 15 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{12} - 6 \, \cos\left(d x + c\right)^{10} + 15 \, \cos\left(d x + c\right)^{8} - 20 \, \cos\left(d x + c\right)^{6} + 15 \, \cos\left(d x + c\right)^{4} - 6 \, \cos\left(d x + c\right)^{2} + 1} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 12012 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{133120 \, {\left(99 \, \tan\left(d x + c\right)^{4} + 154 \, \tan\left(d x + c\right)^{2} + 63\right)} a^{3}}{\tan\left(d x + c\right)^{11}} + \frac{10240 \, {\left(429 \, \tan\left(d x + c\right)^{6} + 1001 \, \tan\left(d x + c\right)^{4} + 819 \, \tan\left(d x + c\right)^{2} + 231\right)} a^{3}}{\tan\left(d x + c\right)^{13}}}{30750720 \, d}"," ",0,"-1/30750720*(15015*a^3*(2*(15*cos(d*x + c)^11 - 85*cos(d*x + c)^9 + 198*cos(d*x + c)^7 + 198*cos(d*x + c)^5 - 85*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^12 - 6*cos(d*x + c)^10 + 15*cos(d*x + c)^8 - 20*cos(d*x + c)^6 + 15*cos(d*x + c)^4 - 6*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 12012*a^3*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 133120*(99*tan(d*x + c)^4 + 154*tan(d*x + c)^2 + 63)*a^3/tan(d*x + c)^11 + 10240*(429*tan(d*x + c)^6 + 1001*tan(d*x + c)^4 + 819*tan(d*x + c)^2 + 231)*a^3/tan(d*x + c)^13)/d","A",0
623,1,294,0,0.410091," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{128 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{4} - 320 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{4} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{4} - 720 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{4} + 160 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{4}}{960 \, d}"," ",0,"1/960*(128*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^4 - 320*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^4 - 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a^4 - 720*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^4 + 160*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^4)/d","A",0
624,1,502,0,0.483856," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{945 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9216 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8190 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{36864 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{97650 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{129024 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{106470 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{451584 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{322560 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{106470 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{215040 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{97650 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{8190 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{945 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - 1024}{a + \frac{9 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{36 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{84 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{126 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{126 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{84 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{36 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{9 \, a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{a \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}}} - \frac{945 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{20160 \, d}"," ",0,"-1/20160*((945*sin(d*x + c)/(cos(d*x + c) + 1) - 9216*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8190*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 36864*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 97650*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 129024*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 106470*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 451584*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 322560*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 106470*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 215040*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 97650*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 8190*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 945*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 1024)/(a + 9*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 36*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 84*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 126*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 126*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 84*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 36*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 9*a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + a*sin(d*x + c)^18/(cos(d*x + c) + 1)^18) - 945*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
625,1,461,0,0.524408," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2048 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{805 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1792 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{11655 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14336 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{23485 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{8960 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{23485 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{11655 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{8960 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{805 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{105 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - 256}{a + \frac{8 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{56 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{56 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{8 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{2240 \, d}"," ",0,"1/2240*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 2048*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 805*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1792*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 11655*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14336*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 23485*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 8960*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 23485*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 11655*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 8960*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 805*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 105*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 256)/(a + 8*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 56*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 56*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 8*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
626,1,400,0,0.564483," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{672 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1540 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{1344 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1085 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6720 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{3360 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{1085 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{3360 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{1540 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{105 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - 96}{a + \frac{7 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{21 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{35 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{35 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{21 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{7 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{840 \, d}"," ",0,"-1/840*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 672*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1540*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1344*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1085*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6720*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 3360*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 1085*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 3360*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1540*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 105*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 96)/(a + 7*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 21*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 35*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 35*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 21*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 7*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
627,1,379,0,0.516411," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{235 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{480 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{390 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{480 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{390 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{240 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{235 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{240 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{15 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 48}{a + \frac{6 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{120 \, d}"," ",0,"1/120*((15*sin(d*x + c)/(cos(d*x + c) + 1) - 48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 235*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 480*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 390*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 480*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 390*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 240*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 235*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 240*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 15*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 48)/(a + 6*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
628,1,280,0,0.539530," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{80 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{9 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{96 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{9 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{48 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 32}{a + \frac{4 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{9 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{12 \, d}"," ",0,"-1/12*((15*sin(d*x + c)/(cos(d*x + c) + 1) - 80*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 9*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 96*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 9*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 48*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 32)/(a + 4*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 9*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
629,1,277,0,0.485446," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{16 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{24 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{9 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{24 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 3}{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} + \frac{18 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{6 \, d}"," ",0,"-1/6*((16*sin(d*x + c)/(cos(d*x + c) + 1) + 15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 24*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 9*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 24*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 3)/(a*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) + 18*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 6*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - 3*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
630,1,261,0,0.576417," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a} - \frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{18 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{17 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 1}{\frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{8 \, d}"," ",0,"-1/8*((4*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a - (4*sin(d*x + c)/(cos(d*x + c) + 1) - 18*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 17*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1)/(a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
631,1,240,0,0.525566," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a} - \frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{51 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 1}{\frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} - \frac{48 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{36 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{24 \, d}"," ",0,"-1/24*((15*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a - (3*sin(d*x + c)/(cos(d*x + c) + 1) + 14*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 51*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1)/(a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) - 48*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 36*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
632,1,217,0,0.484670," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{120 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a} - \frac{384 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{72 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{120 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{a \sin\left(d x + c\right)^{4}}}{192 \, d}"," ",0,"1/192*((120*sin(d*x + c)/(cos(d*x + c) + 1) - 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a - 384*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 72*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (8*sin(d*x + c)/(cos(d*x + c) + 1) + 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 120*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3)*(cos(d*x + c) + 1)^4/(a*sin(d*x + c)^4))/d","B",0
633,1,234,0,0.664856," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{20 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{40 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{10 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{20 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 2\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a \sin\left(d x + c\right)^{5}}}{320 \, d}"," ",0,"1/320*((20*sin(d*x + c)/(cos(d*x + c) + 1) + 40*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (5*sin(d*x + c)/(cos(d*x + c) + 1) + 10*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 20*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2)*(cos(d*x + c) + 1)^5/(a*sin(d*x + c)^5))/d","B",0
634,1,416,0,0.428653," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1232 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{700 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2016 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3395 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1120 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{7280 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{3395 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{1680 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{700 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{105 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - 176}{a^{2} + \frac{7 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{21 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{35 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{35 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{21 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{7 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{420 \, d}"," ",0,"1/420*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 1232*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 700*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2016*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3395*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1120*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 7280*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 3395*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 1680*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 700*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 105*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 176)/(a^2 + 7*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 21*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 35*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 35*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 21*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 7*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
635,1,353,0,0.479263," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{384 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{65 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{750 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{640 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{750 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{960 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{65 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{45 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 64}{a^{2} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{120 \, d}"," ",0,"-1/120*((45*sin(d*x + c)/(cos(d*x + c) + 1) - 384*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 65*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 750*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 640*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 750*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 960*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 65*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 45*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 64)/(a^2 + 6*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
636,1,310,0,0.421185," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{80 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{90 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{40 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{240 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{90 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{60 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{15 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 28}{a^{2} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{30 \, d}"," ",0,"1/30*((15*sin(d*x + c)/(cos(d*x + c) + 1) - 80*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 90*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 40*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 240*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 90*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 60*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 15*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 28)/(a^2 + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
637,1,188,0,0.406688," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 2\right)}}{a^{2} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{6 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{3 \, d}"," ",0,"-1/3*(2*(3*sin(d*x + c)/(cos(d*x + c) + 1) - 6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 2)/(a^2 + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 6*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 3*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
638,1,202,0,0.410095," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 1}{\frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{2 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{4 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{\sin\left(d x + c\right)}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"-1/2*((8*sin(d*x + c)/(cos(d*x + c) + 1) + 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)/(a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 2*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 2*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 4*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - sin(d*x + c)/(a^2*(cos(d*x + c) + 1)))/d","B",0
639,1,204,0,0.408591," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1}{\frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{2}} + \frac{32 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{4 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{8 \, d}"," ",0,"1/8*((8*sin(d*x + c)/(cos(d*x + c) + 1) + 15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)/(a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - (8*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^2 + 32*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 4*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
640,1,176,0,0.445633," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{48 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{24 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{{\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{a^{2} \sin\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"1/24*((9*sin(d*x + c)/(cos(d*x + c) + 1) - 6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 48*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 24*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + (6*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^3/(a^2*sin(d*x + c)^3))/d","B",0
641,1,194,0,0.331373," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{48 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a^{2}} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{{\left(\frac{16 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{48 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{a^{2} \sin\left(d x + c\right)^{4}}}{192 \, d}"," ",0,"1/192*((48*sin(d*x + c)/(cos(d*x + c) + 1) + 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a^2 - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + (16*sin(d*x + c)/(cos(d*x + c) + 1) - 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 48*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3)*(cos(d*x + c) + 1)^4/(a^2*sin(d*x + c)^4))/d","B",0
642,1,195,0,0.316379," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{90 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{2}} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{{\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{90 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a^{2} \sin\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*((90*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^2 - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (15*sin(d*x + c)/(cos(d*x + c) + 1) - 25*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 90*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3)*(cos(d*x + c) + 1)^5/(a^2*sin(d*x + c)^5))/d","B",0
643,1,274,0,0.322075," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{240 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{45 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{24 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}{a^{2}} - \frac{360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{{\left(\frac{24 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{45 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{40 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{240 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 5\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{6}}{a^{2} \sin\left(d x + c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*((240*sin(d*x + c)/(cos(d*x + c) + 1) - 15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 45*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 24*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)/a^2 - 360*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + (24*sin(d*x + c)/(cos(d*x + c) + 1) - 45*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 40*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 240*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5)*(cos(d*x + c) + 1)^6/(a^2*sin(d*x + c)^6))/d","B",0
644,1,373,0,0.426040," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{345 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3264 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1955 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{7680 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2250 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5440 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2250 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{480 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{1955 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{345 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 544}{a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{345 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{120 \, d}"," ",0,"1/120*((345*sin(d*x + c)/(cos(d*x + c) + 1) - 3264*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1955*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 7680*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2250*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5440*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2250*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 480*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 1955*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 345*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 544)/(a^3 + 6*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 345*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
645,1,290,0,1.467292," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{195 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1520 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{750 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2320 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{720 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{750 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{195 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 304}{a^{3} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{195 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{60 \, d}"," ",0,"-1/60*((195*sin(d*x + c)/(cos(d*x + c) + 1) - 1520*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 750*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2320*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 720*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 750*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 195*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 304)/(a^3 + 5*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 195*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
646,1,267,0,0.443766," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{88 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{23 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{72 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{23 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 24}{a^{3} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{4 \, d}"," ",0,"1/4*((15*sin(d*x + c)/(cos(d*x + c) + 1) - 88*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 23*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 72*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 23*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 24)/(a^3 + 4*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
647,1,161,0,0.433115," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 6}{a^{3} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} - \frac{7 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{\log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{d}"," ",0,"((sin(d*x + c)/(cos(d*x + c) + 1) - 6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 6)/(a^3 + 2*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) - 7*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
648,1,158,0,0.425785," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1}{\frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}} + \frac{12 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{\sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{2 \, d}"," ",0,"1/2*((4*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)/(a^3*sin(d*x + c)/(cos(d*x + c) + 1) + a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3) + 12*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 6*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + sin(d*x + c)/(a^3*(cos(d*x + c) + 1)))/d","B",0
649,1,138,0,0.408216," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{3}} + \frac{16 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{28 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{{\left(\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{2}}{a^{3} \sin\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"-1/8*((12*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^3 + 16*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 28*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - (12*sin(d*x + c)/(cos(d*x + c) + 1) - 1)*(cos(d*x + c) + 1)^2/(a^3*sin(d*x + c)^2))/d","B",0
650,1,153,0,0.321169," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{3}} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{{\left(\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{45 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{3}}{a^{3} \sin\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"1/24*((45*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^3 - 60*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + (9*sin(d*x + c)/(cos(d*x + c) + 1) - 45*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1)*(cos(d*x + c) + 1)^3/(a^3*sin(d*x + c)^3))/d","B",0
651,1,195,0,0.323319," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{104 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{32 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{\sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a^{3}} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{{\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{32 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{104 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{a^{3} \sin\left(d x + c\right)^{4}}}{64 \, d}"," ",0,"-1/64*((104*sin(d*x + c)/(cos(d*x + c) + 1) - 32*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a^3 - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - (8*sin(d*x + c)/(cos(d*x + c) + 1) - 32*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 104*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)*(cos(d*x + c) + 1)^4/(a^3*sin(d*x + c)^4))/d","B",0
652,1,234,0,0.318061," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{1380 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{480 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{170 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{45 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{1560 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{{\left(\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{170 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{480 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1380 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 6\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a^{3} \sin\left(d x + c\right)^{5}}}{960 \, d}"," ",0,"1/960*((1380*sin(d*x + c)/(cos(d*x + c) + 1) - 480*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 170*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 45*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 1560*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + (45*sin(d*x + c)/(cos(d*x + c) + 1) - 170*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 480*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1380*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6)*(cos(d*x + c) + 1)^5/(a^3*sin(d*x + c)^5))/d","B",0
653,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{3} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^3*sin(d*x + c)^n*cos(d*x + c)^6, x)","F",0
654,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^2*sin(d*x + c)^n*cos(d*x + c)^6, x)","F",0
655,0,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{6}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)*sin(d*x + c)^n*cos(d*x + c)^6, x)","F",0
656,1,94,0,0.316197," ","integrate(cos(d*x+c)^7*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{8580 \, a \sin\left(d x + c\right)^{14} + 9240 \, a \sin\left(d x + c\right)^{13} - 30030 \, a \sin\left(d x + c\right)^{12} - 32760 \, a \sin\left(d x + c\right)^{11} + 36036 \, a \sin\left(d x + c\right)^{10} + 40040 \, a \sin\left(d x + c\right)^{9} - 15015 \, a \sin\left(d x + c\right)^{8} - 17160 \, a \sin\left(d x + c\right)^{7}}{120120 \, d}"," ",0,"-1/120120*(8580*a*sin(d*x + c)^14 + 9240*a*sin(d*x + c)^13 - 30030*a*sin(d*x + c)^12 - 32760*a*sin(d*x + c)^11 + 36036*a*sin(d*x + c)^10 + 40040*a*sin(d*x + c)^9 - 15015*a*sin(d*x + c)^8 - 17160*a*sin(d*x + c)^7)/d","A",0
657,1,94,0,0.318001," ","integrate(cos(d*x+c)^7*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{9240 \, a \sin\left(d x + c\right)^{13} + 10010 \, a \sin\left(d x + c\right)^{12} - 32760 \, a \sin\left(d x + c\right)^{11} - 36036 \, a \sin\left(d x + c\right)^{10} + 40040 \, a \sin\left(d x + c\right)^{9} + 45045 \, a \sin\left(d x + c\right)^{8} - 17160 \, a \sin\left(d x + c\right)^{7} - 20020 \, a \sin\left(d x + c\right)^{6}}{120120 \, d}"," ",0,"-1/120120*(9240*a*sin(d*x + c)^13 + 10010*a*sin(d*x + c)^12 - 32760*a*sin(d*x + c)^11 - 36036*a*sin(d*x + c)^10 + 40040*a*sin(d*x + c)^9 + 45045*a*sin(d*x + c)^8 - 17160*a*sin(d*x + c)^7 - 20020*a*sin(d*x + c)^6)/d","A",0
658,1,94,0,0.309602," ","integrate(cos(d*x+c)^7*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{770 \, a \sin\left(d x + c\right)^{12} + 840 \, a \sin\left(d x + c\right)^{11} - 2772 \, a \sin\left(d x + c\right)^{10} - 3080 \, a \sin\left(d x + c\right)^{9} + 3465 \, a \sin\left(d x + c\right)^{8} + 3960 \, a \sin\left(d x + c\right)^{7} - 1540 \, a \sin\left(d x + c\right)^{6} - 1848 \, a \sin\left(d x + c\right)^{5}}{9240 \, d}"," ",0,"-1/9240*(770*a*sin(d*x + c)^12 + 840*a*sin(d*x + c)^11 - 2772*a*sin(d*x + c)^10 - 3080*a*sin(d*x + c)^9 + 3465*a*sin(d*x + c)^8 + 3960*a*sin(d*x + c)^7 - 1540*a*sin(d*x + c)^6 - 1848*a*sin(d*x + c)^5)/d","A",0
659,1,94,0,0.308676," ","integrate(cos(d*x+c)^7*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{840 \, a \sin\left(d x + c\right)^{11} + 924 \, a \sin\left(d x + c\right)^{10} - 3080 \, a \sin\left(d x + c\right)^{9} - 3465 \, a \sin\left(d x + c\right)^{8} + 3960 \, a \sin\left(d x + c\right)^{7} + 4620 \, a \sin\left(d x + c\right)^{6} - 1848 \, a \sin\left(d x + c\right)^{5} - 2310 \, a \sin\left(d x + c\right)^{4}}{9240 \, d}"," ",0,"-1/9240*(840*a*sin(d*x + c)^11 + 924*a*sin(d*x + c)^10 - 3080*a*sin(d*x + c)^9 - 3465*a*sin(d*x + c)^8 + 3960*a*sin(d*x + c)^7 + 4620*a*sin(d*x + c)^6 - 1848*a*sin(d*x + c)^5 - 2310*a*sin(d*x + c)^4)/d","A",0
660,1,94,0,0.314485," ","integrate(cos(d*x+c)^7*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{252 \, a \sin\left(d x + c\right)^{10} + 280 \, a \sin\left(d x + c\right)^{9} - 945 \, a \sin\left(d x + c\right)^{8} - 1080 \, a \sin\left(d x + c\right)^{7} + 1260 \, a \sin\left(d x + c\right)^{6} + 1512 \, a \sin\left(d x + c\right)^{5} - 630 \, a \sin\left(d x + c\right)^{4} - 840 \, a \sin\left(d x + c\right)^{3}}{2520 \, d}"," ",0,"-1/2520*(252*a*sin(d*x + c)^10 + 280*a*sin(d*x + c)^9 - 945*a*sin(d*x + c)^8 - 1080*a*sin(d*x + c)^7 + 1260*a*sin(d*x + c)^6 + 1512*a*sin(d*x + c)^5 - 630*a*sin(d*x + c)^4 - 840*a*sin(d*x + c)^3)/d","A",0
661,1,94,0,0.379956," ","integrate(cos(d*x+c)^7*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{280 \, a \sin\left(d x + c\right)^{9} + 315 \, a \sin\left(d x + c\right)^{8} - 1080 \, a \sin\left(d x + c\right)^{7} - 1260 \, a \sin\left(d x + c\right)^{6} + 1512 \, a \sin\left(d x + c\right)^{5} + 1890 \, a \sin\left(d x + c\right)^{4} - 840 \, a \sin\left(d x + c\right)^{3} - 1260 \, a \sin\left(d x + c\right)^{2}}{2520 \, d}"," ",0,"-1/2520*(280*a*sin(d*x + c)^9 + 315*a*sin(d*x + c)^8 - 1080*a*sin(d*x + c)^7 - 1260*a*sin(d*x + c)^6 + 1512*a*sin(d*x + c)^5 + 1890*a*sin(d*x + c)^4 - 840*a*sin(d*x + c)^3 - 1260*a*sin(d*x + c)^2)/d","A",0
662,1,91,0,0.343374," ","integrate(cos(d*x+c)^7*csc(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, a \sin\left(d x + c\right)^{7} + 70 \, a \sin\left(d x + c\right)^{6} - 252 \, a \sin\left(d x + c\right)^{5} - 315 \, a \sin\left(d x + c\right)^{4} + 420 \, a \sin\left(d x + c\right)^{3} + 630 \, a \sin\left(d x + c\right)^{2} - 420 \, a \log\left(\sin\left(d x + c\right)\right) - 420 \, a \sin\left(d x + c\right)}{420 \, d}"," ",0,"-1/420*(60*a*sin(d*x + c)^7 + 70*a*sin(d*x + c)^6 - 252*a*sin(d*x + c)^5 - 315*a*sin(d*x + c)^4 + 420*a*sin(d*x + c)^3 + 630*a*sin(d*x + c)^2 - 420*a*log(sin(d*x + c)) - 420*a*sin(d*x + c))/d","A",0
663,1,91,0,0.363649," ","integrate(cos(d*x+c)^7*csc(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{10 \, a \sin\left(d x + c\right)^{6} + 12 \, a \sin\left(d x + c\right)^{5} - 45 \, a \sin\left(d x + c\right)^{4} - 60 \, a \sin\left(d x + c\right)^{3} + 90 \, a \sin\left(d x + c\right)^{2} - 60 \, a \log\left(\sin\left(d x + c\right)\right) + 180 \, a \sin\left(d x + c\right) + \frac{60 \, a}{\sin\left(d x + c\right)}}{60 \, d}"," ",0,"-1/60*(10*a*sin(d*x + c)^6 + 12*a*sin(d*x + c)^5 - 45*a*sin(d*x + c)^4 - 60*a*sin(d*x + c)^3 + 90*a*sin(d*x + c)^2 - 60*a*log(sin(d*x + c)) + 180*a*sin(d*x + c) + 60*a/sin(d*x + c))/d","A",0
664,1,90,0,0.356550," ","integrate(cos(d*x+c)^7*csc(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, a \sin\left(d x + c\right)^{5} + 5 \, a \sin\left(d x + c\right)^{4} - 20 \, a \sin\left(d x + c\right)^{3} - 30 \, a \sin\left(d x + c\right)^{2} + 60 \, a \log\left(\sin\left(d x + c\right)\right) + 60 \, a \sin\left(d x + c\right) + \frac{10 \, {\left(2 \, a \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right)^{2}}}{20 \, d}"," ",0,"-1/20*(4*a*sin(d*x + c)^5 + 5*a*sin(d*x + c)^4 - 20*a*sin(d*x + c)^3 - 30*a*sin(d*x + c)^2 + 60*a*log(sin(d*x + c)) + 60*a*sin(d*x + c) + 10*(2*a*sin(d*x + c) + a)/sin(d*x + c)^2)/d","A",0
665,1,92,0,0.331349," ","integrate(cos(d*x+c)^7*csc(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, a \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 18 \, a \sin\left(d x + c\right)^{2} + 36 \, a \log\left(\sin\left(d x + c\right)\right) - 36 \, a \sin\left(d x + c\right) - \frac{2 \, {\left(18 \, a \sin\left(d x + c\right)^{2} - 3 \, a \sin\left(d x + c\right) - 2 \, a\right)}}{\sin\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(3*a*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 18*a*sin(d*x + c)^2 + 36*a*log(sin(d*x + c)) - 36*a*sin(d*x + c) - 2*(18*a*sin(d*x + c)^2 - 3*a*sin(d*x + c) - 2*a)/sin(d*x + c)^3)/d","A",0
666,1,92,0,0.350983," ","integrate(cos(d*x+c)^7*csc(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, a \sin\left(d x + c\right)^{3} + 6 \, a \sin\left(d x + c\right)^{2} - 36 \, a \log\left(\sin\left(d x + c\right)\right) - 36 \, a \sin\left(d x + c\right) - \frac{36 \, a \sin\left(d x + c\right)^{3} + 18 \, a \sin\left(d x + c\right)^{2} - 4 \, a \sin\left(d x + c\right) - 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"-1/12*(4*a*sin(d*x + c)^3 + 6*a*sin(d*x + c)^2 - 36*a*log(sin(d*x + c)) - 36*a*sin(d*x + c) - (36*a*sin(d*x + c)^3 + 18*a*sin(d*x + c)^2 - 4*a*sin(d*x + c) - 3*a)/sin(d*x + c)^4)/d","A",0
667,1,91,0,0.337869," ","integrate(cos(d*x+c)^7*csc(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{10 \, a \sin\left(d x + c\right)^{2} - 60 \, a \log\left(\sin\left(d x + c\right)\right) + 20 \, a \sin\left(d x + c\right) + \frac{60 \, a \sin\left(d x + c\right)^{4} - 30 \, a \sin\left(d x + c\right)^{3} - 20 \, a \sin\left(d x + c\right)^{2} + 5 \, a \sin\left(d x + c\right) + 4 \, a}{\sin\left(d x + c\right)^{5}}}{20 \, d}"," ",0,"-1/20*(10*a*sin(d*x + c)^2 - 60*a*log(sin(d*x + c)) + 20*a*sin(d*x + c) + (60*a*sin(d*x + c)^4 - 30*a*sin(d*x + c)^3 - 20*a*sin(d*x + c)^2 + 5*a*sin(d*x + c) + 4*a)/sin(d*x + c)^5)/d","A",0
668,1,91,0,0.315948," ","integrate(cos(d*x+c)^7*csc(d*x+c)^7*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{60 \, a \log\left(\sin\left(d x + c\right)\right) + 60 \, a \sin\left(d x + c\right) + \frac{180 \, a \sin\left(d x + c\right)^{5} + 90 \, a \sin\left(d x + c\right)^{4} - 60 \, a \sin\left(d x + c\right)^{3} - 45 \, a \sin\left(d x + c\right)^{2} + 12 \, a \sin\left(d x + c\right) + 10 \, a}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*a*log(sin(d*x + c)) + 60*a*sin(d*x + c) + (180*a*sin(d*x + c)^5 + 90*a*sin(d*x + c)^4 - 60*a*sin(d*x + c)^3 - 45*a*sin(d*x + c)^2 + 12*a*sin(d*x + c) + 10*a)/sin(d*x + c)^6)/d","A",0
669,1,94,0,0.317299," ","integrate(cos(d*x+c)^7*csc(d*x+c)^8*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{420 \, a \log\left(\sin\left(d x + c\right)\right) - \frac{420 \, a \sin\left(d x + c\right)^{6} - 630 \, a \sin\left(d x + c\right)^{5} - 420 \, a \sin\left(d x + c\right)^{4} + 315 \, a \sin\left(d x + c\right)^{3} + 252 \, a \sin\left(d x + c\right)^{2} - 70 \, a \sin\left(d x + c\right) - 60 \, a}{\sin\left(d x + c\right)^{7}}}{420 \, d}"," ",0,"-1/420*(420*a*log(sin(d*x + c)) - (420*a*sin(d*x + c)^6 - 630*a*sin(d*x + c)^5 - 420*a*sin(d*x + c)^4 + 315*a*sin(d*x + c)^3 + 252*a*sin(d*x + c)^2 - 70*a*sin(d*x + c) - 60*a)/sin(d*x + c)^7)/d","A",0
670,1,92,0,0.325774," ","integrate(cos(d*x+c)^7*csc(d*x+c)^9*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{280 \, a \sin\left(d x + c\right)^{7} + 140 \, a \sin\left(d x + c\right)^{6} - 280 \, a \sin\left(d x + c\right)^{5} - 210 \, a \sin\left(d x + c\right)^{4} + 168 \, a \sin\left(d x + c\right)^{3} + 140 \, a \sin\left(d x + c\right)^{2} - 40 \, a \sin\left(d x + c\right) - 35 \, a}{280 \, d \sin\left(d x + c\right)^{8}}"," ",0,"1/280*(280*a*sin(d*x + c)^7 + 140*a*sin(d*x + c)^6 - 280*a*sin(d*x + c)^5 - 210*a*sin(d*x + c)^4 + 168*a*sin(d*x + c)^3 + 140*a*sin(d*x + c)^2 - 40*a*sin(d*x + c) - 35*a)/(d*sin(d*x + c)^8)","A",0
671,1,92,0,0.350650," ","integrate(cos(d*x+c)^7*csc(d*x+c)^10*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{1260 \, a \sin\left(d x + c\right)^{7} + 840 \, a \sin\left(d x + c\right)^{6} - 1890 \, a \sin\left(d x + c\right)^{5} - 1512 \, a \sin\left(d x + c\right)^{4} + 1260 \, a \sin\left(d x + c\right)^{3} + 1080 \, a \sin\left(d x + c\right)^{2} - 315 \, a \sin\left(d x + c\right) - 280 \, a}{2520 \, d \sin\left(d x + c\right)^{9}}"," ",0,"1/2520*(1260*a*sin(d*x + c)^7 + 840*a*sin(d*x + c)^6 - 1890*a*sin(d*x + c)^5 - 1512*a*sin(d*x + c)^4 + 1260*a*sin(d*x + c)^3 + 1080*a*sin(d*x + c)^2 - 315*a*sin(d*x + c) - 280*a)/(d*sin(d*x + c)^9)","A",0
672,1,92,0,0.370162," ","integrate(cos(d*x+c)^7*csc(d*x+c)^11*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{840 \, a \sin\left(d x + c\right)^{7} + 630 \, a \sin\left(d x + c\right)^{6} - 1512 \, a \sin\left(d x + c\right)^{5} - 1260 \, a \sin\left(d x + c\right)^{4} + 1080 \, a \sin\left(d x + c\right)^{3} + 945 \, a \sin\left(d x + c\right)^{2} - 280 \, a \sin\left(d x + c\right) - 252 \, a}{2520 \, d \sin\left(d x + c\right)^{10}}"," ",0,"1/2520*(840*a*sin(d*x + c)^7 + 630*a*sin(d*x + c)^6 - 1512*a*sin(d*x + c)^5 - 1260*a*sin(d*x + c)^4 + 1080*a*sin(d*x + c)^3 + 945*a*sin(d*x + c)^2 - 280*a*sin(d*x + c) - 252*a)/(d*sin(d*x + c)^10)","A",0
673,1,92,0,0.332620," ","integrate(cos(d*x+c)^7*csc(d*x+c)^12*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2310 \, a \sin\left(d x + c\right)^{7} + 1848 \, a \sin\left(d x + c\right)^{6} - 4620 \, a \sin\left(d x + c\right)^{5} - 3960 \, a \sin\left(d x + c\right)^{4} + 3465 \, a \sin\left(d x + c\right)^{3} + 3080 \, a \sin\left(d x + c\right)^{2} - 924 \, a \sin\left(d x + c\right) - 840 \, a}{9240 \, d \sin\left(d x + c\right)^{11}}"," ",0,"1/9240*(2310*a*sin(d*x + c)^7 + 1848*a*sin(d*x + c)^6 - 4620*a*sin(d*x + c)^5 - 3960*a*sin(d*x + c)^4 + 3465*a*sin(d*x + c)^3 + 3080*a*sin(d*x + c)^2 - 924*a*sin(d*x + c) - 840*a)/(d*sin(d*x + c)^11)","A",0
674,1,92,0,0.352223," ","integrate(cos(d*x+c)^7*csc(d*x+c)^13*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{1848 \, a \sin\left(d x + c\right)^{7} + 1540 \, a \sin\left(d x + c\right)^{6} - 3960 \, a \sin\left(d x + c\right)^{5} - 3465 \, a \sin\left(d x + c\right)^{4} + 3080 \, a \sin\left(d x + c\right)^{3} + 2772 \, a \sin\left(d x + c\right)^{2} - 840 \, a \sin\left(d x + c\right) - 770 \, a}{9240 \, d \sin\left(d x + c\right)^{12}}"," ",0,"1/9240*(1848*a*sin(d*x + c)^7 + 1540*a*sin(d*x + c)^6 - 3960*a*sin(d*x + c)^5 - 3465*a*sin(d*x + c)^4 + 3080*a*sin(d*x + c)^3 + 2772*a*sin(d*x + c)^2 - 840*a*sin(d*x + c) - 770*a)/(d*sin(d*x + c)^12)","A",0
675,1,92,0,0.364703," ","integrate(cos(d*x+c)^7*csc(d*x+c)^14*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{20020 \, a \sin\left(d x + c\right)^{7} + 17160 \, a \sin\left(d x + c\right)^{6} - 45045 \, a \sin\left(d x + c\right)^{5} - 40040 \, a \sin\left(d x + c\right)^{4} + 36036 \, a \sin\left(d x + c\right)^{3} + 32760 \, a \sin\left(d x + c\right)^{2} - 10010 \, a \sin\left(d x + c\right) - 9240 \, a}{120120 \, d \sin\left(d x + c\right)^{13}}"," ",0,"1/120120*(20020*a*sin(d*x + c)^7 + 17160*a*sin(d*x + c)^6 - 45045*a*sin(d*x + c)^5 - 40040*a*sin(d*x + c)^4 + 36036*a*sin(d*x + c)^3 + 32760*a*sin(d*x + c)^2 - 10010*a*sin(d*x + c) - 9240*a)/(d*sin(d*x + c)^13)","A",0
676,1,92,0,0.346531," ","integrate(cos(d*x+c)^7*csc(d*x+c)^15*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{17160 \, a \sin\left(d x + c\right)^{7} + 15015 \, a \sin\left(d x + c\right)^{6} - 40040 \, a \sin\left(d x + c\right)^{5} - 36036 \, a \sin\left(d x + c\right)^{4} + 32760 \, a \sin\left(d x + c\right)^{3} + 30030 \, a \sin\left(d x + c\right)^{2} - 9240 \, a \sin\left(d x + c\right) - 8580 \, a}{120120 \, d \sin\left(d x + c\right)^{14}}"," ",0,"1/120120*(17160*a*sin(d*x + c)^7 + 15015*a*sin(d*x + c)^6 - 40040*a*sin(d*x + c)^5 - 36036*a*sin(d*x + c)^4 + 32760*a*sin(d*x + c)^3 + 30030*a*sin(d*x + c)^2 - 9240*a*sin(d*x + c) - 8580*a)/(d*sin(d*x + c)^14)","A",0
677,1,69,0,0.376455," ","integrate(cos(d*x+c)^7*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2310 \, \sin\left(d x + c\right)^{12} - 2520 \, \sin\left(d x + c\right)^{11} - 5544 \, \sin\left(d x + c\right)^{10} + 6160 \, \sin\left(d x + c\right)^{9} + 3465 \, \sin\left(d x + c\right)^{8} - 3960 \, \sin\left(d x + c\right)^{7}}{27720 \, a d}"," ",0,"-1/27720*(2310*sin(d*x + c)^12 - 2520*sin(d*x + c)^11 - 5544*sin(d*x + c)^10 + 6160*sin(d*x + c)^9 + 3465*sin(d*x + c)^8 - 3960*sin(d*x + c)^7)/(a*d)","A",0
678,1,69,0,0.418153," ","integrate(cos(d*x+c)^7*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{1260 \, \sin\left(d x + c\right)^{11} - 1386 \, \sin\left(d x + c\right)^{10} - 3080 \, \sin\left(d x + c\right)^{9} + 3465 \, \sin\left(d x + c\right)^{8} + 1980 \, \sin\left(d x + c\right)^{7} - 2310 \, \sin\left(d x + c\right)^{6}}{13860 \, a d}"," ",0,"-1/13860*(1260*sin(d*x + c)^11 - 1386*sin(d*x + c)^10 - 3080*sin(d*x + c)^9 + 3465*sin(d*x + c)^8 + 1980*sin(d*x + c)^7 - 2310*sin(d*x + c)^6)/(a*d)","A",0
679,1,69,0,0.369509," ","integrate(cos(d*x+c)^7*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{126 \, \sin\left(d x + c\right)^{10} - 140 \, \sin\left(d x + c\right)^{9} - 315 \, \sin\left(d x + c\right)^{8} + 360 \, \sin\left(d x + c\right)^{7} + 210 \, \sin\left(d x + c\right)^{6} - 252 \, \sin\left(d x + c\right)^{5}}{1260 \, a d}"," ",0,"-1/1260*(126*sin(d*x + c)^10 - 140*sin(d*x + c)^9 - 315*sin(d*x + c)^8 + 360*sin(d*x + c)^7 + 210*sin(d*x + c)^6 - 252*sin(d*x + c)^5)/(a*d)","A",0
680,1,69,0,0.328331," ","integrate(cos(d*x+c)^7*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{280 \, \sin\left(d x + c\right)^{9} - 315 \, \sin\left(d x + c\right)^{8} - 720 \, \sin\left(d x + c\right)^{7} + 840 \, \sin\left(d x + c\right)^{6} + 504 \, \sin\left(d x + c\right)^{5} - 630 \, \sin\left(d x + c\right)^{4}}{2520 \, a d}"," ",0,"-1/2520*(280*sin(d*x + c)^9 - 315*sin(d*x + c)^8 - 720*sin(d*x + c)^7 + 840*sin(d*x + c)^6 + 504*sin(d*x + c)^5 - 630*sin(d*x + c)^4)/(a*d)","A",0
681,1,69,0,0.326583," ","integrate(cos(d*x+c)^7*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{105 \, \sin\left(d x + c\right)^{8} - 120 \, \sin\left(d x + c\right)^{7} - 280 \, \sin\left(d x + c\right)^{6} + 336 \, \sin\left(d x + c\right)^{5} + 210 \, \sin\left(d x + c\right)^{4} - 280 \, \sin\left(d x + c\right)^{3}}{840 \, a d}"," ",0,"-1/840*(105*sin(d*x + c)^8 - 120*sin(d*x + c)^7 - 280*sin(d*x + c)^6 + 336*sin(d*x + c)^5 + 210*sin(d*x + c)^4 - 280*sin(d*x + c)^3)/(a*d)","A",0
682,1,69,0,0.325759," ","integrate(cos(d*x+c)^7*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, \sin\left(d x + c\right)^{7} - 35 \, \sin\left(d x + c\right)^{6} - 84 \, \sin\left(d x + c\right)^{5} + 105 \, \sin\left(d x + c\right)^{4} + 70 \, \sin\left(d x + c\right)^{3} - 105 \, \sin\left(d x + c\right)^{2}}{210 \, a d}"," ",0,"-1/210*(30*sin(d*x + c)^7 - 35*sin(d*x + c)^6 - 84*sin(d*x + c)^5 + 105*sin(d*x + c)^4 + 70*sin(d*x + c)^3 - 105*sin(d*x + c)^2)/(a*d)","A",0
683,1,67,0,0.325574," ","integrate(cos(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, \sin\left(d x + c\right)^{6} - 6 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} + 20 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)^{2} - 30 \, \sin\left(d x + c\right)}{30 \, a d}"," ",0,"-1/30*(5*sin(d*x + c)^6 - 6*sin(d*x + c)^5 - 15*sin(d*x + c)^4 + 20*sin(d*x + c)^3 + 15*sin(d*x + c)^2 - 30*sin(d*x + c))/(a*d)","A",0
684,1,71,0,0.365749," ","integrate(cos(d*x+c)^7*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{12 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} - 40 \, \sin\left(d x + c\right)^{3} + 60 \, \sin\left(d x + c\right)^{2} + 60 \, \sin\left(d x + c\right)}{a} - \frac{60 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{60 \, d}"," ",0,"-1/60*((12*sin(d*x + c)^5 - 15*sin(d*x + c)^4 - 40*sin(d*x + c)^3 + 60*sin(d*x + c)^2 + 60*sin(d*x + c))/a - 60*log(sin(d*x + c))/a)/d","A",0
685,1,74,0,0.354180," ","integrate(cos(d*x+c)^7*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{3 \, \sin\left(d x + c\right)^{4} - 4 \, \sin\left(d x + c\right)^{3} - 12 \, \sin\left(d x + c\right)^{2} + 24 \, \sin\left(d x + c\right)}{a} + \frac{12 \, \log\left(\sin\left(d x + c\right)\right)}{a} + \frac{12}{a \sin\left(d x + c\right)}}{12 \, d}"," ",0,"-1/12*((3*sin(d*x + c)^4 - 4*sin(d*x + c)^3 - 12*sin(d*x + c)^2 + 24*sin(d*x + c))/a + 12*log(sin(d*x + c))/a + 12/(a*sin(d*x + c)))/d","A",0
686,1,74,0,0.362898," ","integrate(cos(d*x+c)^7*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} - 12 \, \sin\left(d x + c\right)}{a} + \frac{12 \, \log\left(\sin\left(d x + c\right)\right)}{a} - \frac{3 \, {\left(2 \, \sin\left(d x + c\right) - 1\right)}}{a \sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"-1/6*((2*sin(d*x + c)^3 - 3*sin(d*x + c)^2 - 12*sin(d*x + c))/a + 12*log(sin(d*x + c))/a - 3*(2*sin(d*x + c) - 1)/(a*sin(d*x + c)^2))/d","A",0
687,1,73,0,0.316618," ","integrate(cos(d*x+c)^7*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{3 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)}}{a} - \frac{12 \, \log\left(\sin\left(d x + c\right)\right)}{a} - \frac{12 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 2}{a \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(3*(sin(d*x + c)^2 - 2*sin(d*x + c))/a - 12*log(sin(d*x + c))/a - (12*sin(d*x + c)^2 + 3*sin(d*x + c) - 2)/(a*sin(d*x + c)^3))/d","A",0
688,1,72,0,0.329290," ","integrate(cos(d*x+c)^7*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{12 \, \log\left(\sin\left(d x + c\right)\right)}{a} - \frac{12 \, \sin\left(d x + c\right)}{a} - \frac{24 \, \sin\left(d x + c\right)^{3} - 12 \, \sin\left(d x + c\right)^{2} - 4 \, \sin\left(d x + c\right) + 3}{a \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*log(sin(d*x + c))/a - 12*sin(d*x + c)/a - (24*sin(d*x + c)^3 - 12*sin(d*x + c)^2 - 4*sin(d*x + c) + 3)/(a*sin(d*x + c)^4))/d","A",0
689,1,70,0,0.360592," ","integrate(cos(d*x+c)^7*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{60 \, \log\left(\sin\left(d x + c\right)\right)}{a} + \frac{60 \, \sin\left(d x + c\right)^{4} + 60 \, \sin\left(d x + c\right)^{3} - 40 \, \sin\left(d x + c\right)^{2} - 15 \, \sin\left(d x + c\right) + 12}{a \sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"-1/60*(60*log(sin(d*x + c))/a + (60*sin(d*x + c)^4 + 60*sin(d*x + c)^3 - 40*sin(d*x + c)^2 - 15*sin(d*x + c) + 12)/(a*sin(d*x + c)^5))/d","A",0
690,1,66,0,0.341786," ","integrate(cos(d*x+c)^7*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{30 \, \sin\left(d x + c\right)^{5} - 15 \, \sin\left(d x + c\right)^{4} - 20 \, \sin\left(d x + c\right)^{3} + 15 \, \sin\left(d x + c\right)^{2} + 6 \, \sin\left(d x + c\right) - 5}{30 \, a d \sin\left(d x + c\right)^{6}}"," ",0,"1/30*(30*sin(d*x + c)^5 - 15*sin(d*x + c)^4 - 20*sin(d*x + c)^3 + 15*sin(d*x + c)^2 + 6*sin(d*x + c) - 5)/(a*d*sin(d*x + c)^6)","A",0
691,1,66,0,0.377990," ","integrate(cos(d*x+c)^7*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{105 \, \sin\left(d x + c\right)^{5} - 70 \, \sin\left(d x + c\right)^{4} - 105 \, \sin\left(d x + c\right)^{3} + 84 \, \sin\left(d x + c\right)^{2} + 35 \, \sin\left(d x + c\right) - 30}{210 \, a d \sin\left(d x + c\right)^{7}}"," ",0,"1/210*(105*sin(d*x + c)^5 - 70*sin(d*x + c)^4 - 105*sin(d*x + c)^3 + 84*sin(d*x + c)^2 + 35*sin(d*x + c) - 30)/(a*d*sin(d*x + c)^7)","A",0
692,1,66,0,0.326809," ","integrate(cos(d*x+c)^7*csc(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{280 \, \sin\left(d x + c\right)^{5} - 210 \, \sin\left(d x + c\right)^{4} - 336 \, \sin\left(d x + c\right)^{3} + 280 \, \sin\left(d x + c\right)^{2} + 120 \, \sin\left(d x + c\right) - 105}{840 \, a d \sin\left(d x + c\right)^{8}}"," ",0,"1/840*(280*sin(d*x + c)^5 - 210*sin(d*x + c)^4 - 336*sin(d*x + c)^3 + 280*sin(d*x + c)^2 + 120*sin(d*x + c) - 105)/(a*d*sin(d*x + c)^8)","A",0
693,1,66,0,0.308394," ","integrate(cos(d*x+c)^7*csc(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{630 \, \sin\left(d x + c\right)^{5} - 504 \, \sin\left(d x + c\right)^{4} - 840 \, \sin\left(d x + c\right)^{3} + 720 \, \sin\left(d x + c\right)^{2} + 315 \, \sin\left(d x + c\right) - 280}{2520 \, a d \sin\left(d x + c\right)^{9}}"," ",0,"1/2520*(630*sin(d*x + c)^5 - 504*sin(d*x + c)^4 - 840*sin(d*x + c)^3 + 720*sin(d*x + c)^2 + 315*sin(d*x + c) - 280)/(a*d*sin(d*x + c)^9)","A",0
694,1,66,0,0.319798," ","integrate(cos(d*x+c)^7*csc(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{252 \, \sin\left(d x + c\right)^{5} - 210 \, \sin\left(d x + c\right)^{4} - 360 \, \sin\left(d x + c\right)^{3} + 315 \, \sin\left(d x + c\right)^{2} + 140 \, \sin\left(d x + c\right) - 126}{1260 \, a d \sin\left(d x + c\right)^{10}}"," ",0,"1/1260*(252*sin(d*x + c)^5 - 210*sin(d*x + c)^4 - 360*sin(d*x + c)^3 + 315*sin(d*x + c)^2 + 140*sin(d*x + c) - 126)/(a*d*sin(d*x + c)^10)","A",0
695,1,66,0,0.319335," ","integrate(cos(d*x+c)^7*csc(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2310 \, \sin\left(d x + c\right)^{5} - 1980 \, \sin\left(d x + c\right)^{4} - 3465 \, \sin\left(d x + c\right)^{3} + 3080 \, \sin\left(d x + c\right)^{2} + 1386 \, \sin\left(d x + c\right) - 1260}{13860 \, a d \sin\left(d x + c\right)^{11}}"," ",0,"1/13860*(2310*sin(d*x + c)^5 - 1980*sin(d*x + c)^4 - 3465*sin(d*x + c)^3 + 3080*sin(d*x + c)^2 + 1386*sin(d*x + c) - 1260)/(a*d*sin(d*x + c)^11)","A",0
696,1,66,0,0.316193," ","integrate(cos(d*x+c)^7*csc(d*x+c)^13/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3960 \, \sin\left(d x + c\right)^{5} - 3465 \, \sin\left(d x + c\right)^{4} - 6160 \, \sin\left(d x + c\right)^{3} + 5544 \, \sin\left(d x + c\right)^{2} + 2520 \, \sin\left(d x + c\right) - 2310}{27720 \, a d \sin\left(d x + c\right)^{12}}"," ",0,"1/27720*(3960*sin(d*x + c)^5 - 3465*sin(d*x + c)^4 - 6160*sin(d*x + c)^3 + 5544*sin(d*x + c)^2 + 2520*sin(d*x + c) - 2310)/(a*d*sin(d*x + c)^12)","A",0
697,1,165,0,0.353896," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{a^{3} \sin\left(d x + c\right)^{n + 10}}{n + 10} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{n + 9}}{n + 9} - \frac{8 \, a^{3} \sin\left(d x + c\right)^{n + 7}}{n + 7} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{n + 6}}{n + 6} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{n + 5}}{n + 5} + \frac{8 \, a^{3} \sin\left(d x + c\right)^{n + 4}}{n + 4} - \frac{3 \, a^{3} \sin\left(d x + c\right)^{n + 2}}{n + 2} - \frac{a^{3} \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"-(a^3*sin(d*x + c)^(n + 10)/(n + 10) + 3*a^3*sin(d*x + c)^(n + 9)/(n + 9) - 8*a^3*sin(d*x + c)^(n + 7)/(n + 7) - 6*a^3*sin(d*x + c)^(n + 6)/(n + 6) + 6*a^3*sin(d*x + c)^(n + 5)/(n + 5) + 8*a^3*sin(d*x + c)^(n + 4)/(n + 4) - 3*a^3*sin(d*x + c)^(n + 2)/(n + 2) - a^3*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
698,1,165,0,0.321741," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{a^{2} \sin\left(d x + c\right)^{n + 9}}{n + 9} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{n + 8}}{n + 8} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{n + 7}}{n + 7} - \frac{6 \, a^{2} \sin\left(d x + c\right)^{n + 6}}{n + 6} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{n + 4}}{n + 4} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{n + 3}}{n + 3} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{n + 2}}{n + 2} - \frac{a^{2} \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"-(a^2*sin(d*x + c)^(n + 9)/(n + 9) + 2*a^2*sin(d*x + c)^(n + 8)/(n + 8) - 2*a^2*sin(d*x + c)^(n + 7)/(n + 7) - 6*a^2*sin(d*x + c)^(n + 6)/(n + 6) + 6*a^2*sin(d*x + c)^(n + 4)/(n + 4) + 2*a^2*sin(d*x + c)^(n + 3)/(n + 3) - 2*a^2*sin(d*x + c)^(n + 2)/(n + 2) - a^2*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
699,1,148,0,0.319609," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{a \sin\left(d x + c\right)^{n + 8}}{n + 8} + \frac{a \sin\left(d x + c\right)^{n + 7}}{n + 7} - \frac{3 \, a \sin\left(d x + c\right)^{n + 6}}{n + 6} - \frac{3 \, a \sin\left(d x + c\right)^{n + 5}}{n + 5} + \frac{3 \, a \sin\left(d x + c\right)^{n + 4}}{n + 4} + \frac{3 \, a \sin\left(d x + c\right)^{n + 3}}{n + 3} - \frac{a \sin\left(d x + c\right)^{n + 2}}{n + 2} - \frac{a \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"-(a*sin(d*x + c)^(n + 8)/(n + 8) + a*sin(d*x + c)^(n + 7)/(n + 7) - 3*a*sin(d*x + c)^(n + 6)/(n + 6) - 3*a*sin(d*x + c)^(n + 5)/(n + 5) + 3*a*sin(d*x + c)^(n + 4)/(n + 4) + 3*a*sin(d*x + c)^(n + 3)/(n + 3) - a*sin(d*x + c)^(n + 2)/(n + 2) - a*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
700,1,241,0,0.368488," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left({\left(n^{5} + 15 \, n^{4} + 85 \, n^{3} + 225 \, n^{2} + 274 \, n + 120\right)} \sin\left(d x + c\right)^{6} - {\left(n^{5} + 16 \, n^{4} + 95 \, n^{3} + 260 \, n^{2} + 324 \, n + 144\right)} \sin\left(d x + c\right)^{5} - 2 \, {\left(n^{5} + 17 \, n^{4} + 107 \, n^{3} + 307 \, n^{2} + 396 \, n + 180\right)} \sin\left(d x + c\right)^{4} + 2 \, {\left(n^{5} + 18 \, n^{4} + 121 \, n^{3} + 372 \, n^{2} + 508 \, n + 240\right)} \sin\left(d x + c\right)^{3} + {\left(n^{5} + 19 \, n^{4} + 137 \, n^{3} + 461 \, n^{2} + 702 \, n + 360\right)} \sin\left(d x + c\right)^{2} - {\left(n^{5} + 20 \, n^{4} + 155 \, n^{3} + 580 \, n^{2} + 1044 \, n + 720\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{{\left(n^{6} + 21 \, n^{5} + 175 \, n^{4} + 735 \, n^{3} + 1624 \, n^{2} + 1764 \, n + 720\right)} a d}"," ",0,"-((n^5 + 15*n^4 + 85*n^3 + 225*n^2 + 274*n + 120)*sin(d*x + c)^6 - (n^5 + 16*n^4 + 95*n^3 + 260*n^2 + 324*n + 144)*sin(d*x + c)^5 - 2*(n^5 + 17*n^4 + 107*n^3 + 307*n^2 + 396*n + 180)*sin(d*x + c)^4 + 2*(n^5 + 18*n^4 + 121*n^3 + 372*n^2 + 508*n + 240)*sin(d*x + c)^3 + (n^5 + 19*n^4 + 137*n^3 + 461*n^2 + 702*n + 360)*sin(d*x + c)^2 - (n^5 + 20*n^4 + 155*n^3 + 580*n^2 + 1044*n + 720)*sin(d*x + c))*sin(d*x + c)^n/((n^6 + 21*n^5 + 175*n^4 + 735*n^3 + 1624*n^2 + 1764*n + 720)*a*d)","A",0
701,1,126,0,0.366977," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left({\left(n^{3} + 7 \, n^{2} + 14 \, n + 8\right)} \sin\left(d x + c\right)^{5} - 2 \, {\left(n^{3} + 8 \, n^{2} + 17 \, n + 10\right)} \sin\left(d x + c\right)^{4} + 2 \, {\left(n^{3} + 10 \, n^{2} + 29 \, n + 20\right)} \sin\left(d x + c\right)^{2} - {\left(n^{3} + 11 \, n^{2} + 38 \, n + 40\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{{\left(n^{4} + 12 \, n^{3} + 49 \, n^{2} + 78 \, n + 40\right)} a^{2} d}"," ",0,"-((n^3 + 7*n^2 + 14*n + 8)*sin(d*x + c)^5 - 2*(n^3 + 8*n^2 + 17*n + 10)*sin(d*x + c)^4 + 2*(n^3 + 10*n^2 + 29*n + 20)*sin(d*x + c)^2 - (n^3 + 11*n^2 + 38*n + 40)*sin(d*x + c))*sin(d*x + c)^n/((n^4 + 12*n^3 + 49*n^2 + 78*n + 40)*a^2*d)","A",0
702,1,126,0,0.368411," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left({\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} \sin\left(d x + c\right)^{4} - 3 \, {\left(n^{3} + 7 \, n^{2} + 14 \, n + 8\right)} \sin\left(d x + c\right)^{3} + 3 \, {\left(n^{3} + 8 \, n^{2} + 19 \, n + 12\right)} \sin\left(d x + c\right)^{2} - {\left(n^{3} + 9 \, n^{2} + 26 \, n + 24\right)} \sin\left(d x + c\right)\right)} \sin\left(d x + c\right)^{n}}{{\left(n^{4} + 10 \, n^{3} + 35 \, n^{2} + 50 \, n + 24\right)} a^{3} d}"," ",0,"-((n^3 + 6*n^2 + 11*n + 6)*sin(d*x + c)^4 - 3*(n^3 + 7*n^2 + 14*n + 8)*sin(d*x + c)^3 + 3*(n^3 + 8*n^2 + 19*n + 12)*sin(d*x + c)^2 - (n^3 + 9*n^2 + 26*n + 24)*sin(d*x + c))*sin(d*x + c)^n/((n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*a^3*d)","A",0
703,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{{\left(a \sin\left(d x + c\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^7/(a*sin(d*x + c) + a)^4, x)","F",0
704,0,0,0,0.000000," ","integrate(cos(d*x+c)^7*sin(d*x+c)^n/(a+a*sin(d*x+c))^5,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{7}}{{\left(a \sin\left(d x + c\right) + a\right)}^{5}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^7/(a*sin(d*x + c) + a)^5, x)","F",0
705,1,705,0,0.443922," ","integrate(cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{3465 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{98304 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{40425 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{540672 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{215523 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1982464 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{5794173 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{9732096 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{19523658 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{4866048 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{35058870 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{3784704 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{35058870 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{11354112 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{19523658 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} + \frac{5677056 \, \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{5794173 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{3784704 \, \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} - \frac{215523 \, \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} - \frac{40425 \, \sin\left(d x + c\right)^{21}}{{\left(\cos\left(d x + c\right) + 1\right)}^{21}} - \frac{3465 \, \sin\left(d x + c\right)^{23}}{{\left(\cos\left(d x + c\right) + 1\right)}^{23}} - 8192}{a + \frac{12 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{66 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{220 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{495 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{792 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{924 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{792 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{495 \, a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{220 \, a \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{66 \, a \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} + \frac{12 \, a \sin\left(d x + c\right)^{22}}{{\left(\cos\left(d x + c\right) + 1\right)}^{22}} + \frac{a \sin\left(d x + c\right)^{24}}{{\left(\cos\left(d x + c\right) + 1\right)}^{24}}} - \frac{3465 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{354816 \, d}"," ",0,"1/354816*((3465*sin(d*x + c)/(cos(d*x + c) + 1) - 98304*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 40425*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 540672*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 215523*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1982464*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 5794173*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 9732096*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 19523658*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 4866048*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 35058870*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 3784704*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 35058870*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 11354112*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 19523658*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 + 5677056*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + 5794173*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 3784704*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 - 215523*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 - 40425*sin(d*x + c)^21/(cos(d*x + c) + 1)^21 - 3465*sin(d*x + c)^23/(cos(d*x + c) + 1)^23 - 8192)/(a + 12*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 66*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 220*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 495*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 792*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 924*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 792*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 495*a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + 220*a*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + 66*a*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 + 12*a*sin(d*x + c)^22/(cos(d*x + c) + 1)^22 + a*sin(d*x + c)^24/(cos(d*x + c) + 1)^24) - 3465*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
706,1,624,0,0.439457," ","integrate(cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{10395 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{112640 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{110880 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{563200 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2302839 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3041280 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{4790016 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{15206400 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{5828130 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{21288960 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{26019840 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{5828130 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{11827200 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{4790016 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{4730880 \, \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{2302839 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{110880 \, \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} - \frac{10395 \, \sin\left(d x + c\right)^{21}}{{\left(\cos\left(d x + c\right) + 1\right)}^{21}} - 10240}{a + \frac{11 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{55 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{165 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{330 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{462 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{462 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{330 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{165 \, a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{55 \, a \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{11 \, a \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} + \frac{a \sin\left(d x + c\right)^{22}}{{\left(\cos\left(d x + c\right) + 1\right)}^{22}}} - \frac{10395 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{443520 \, d}"," ",0,"-1/443520*((10395*sin(d*x + c)/(cos(d*x + c) + 1) - 112640*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 110880*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 563200*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2302839*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3041280*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 4790016*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 15206400*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 5828130*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 21288960*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 26019840*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 5828130*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 11827200*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 4790016*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 4730880*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + 2302839*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 110880*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 - 10395*sin(d*x + c)^21/(cos(d*x + c) + 1)^21 - 10240)/(a + 11*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 55*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 165*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 330*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 462*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 462*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 330*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 165*a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + 55*a*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + 11*a*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 + a*sin(d*x + c)^22/(cos(d*x + c) + 1)^22) - 10395*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
707,1,583,0,0.441836," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{945 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{25600 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{9135 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{46080 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{218484 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{414720 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{653940 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{1183770 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{322560 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{1183770 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{537600 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{653940 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} + \frac{107520 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{218484 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{161280 \, \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{9135 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{945 \, \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} - 2560}{a + \frac{10 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{45 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{120 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{210 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{252 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{210 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{120 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{45 \, a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{10 \, a \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{a \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}}} - \frac{945 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{40320 \, d}"," ",0,"1/40320*((945*sin(d*x + c)/(cos(d*x + c) + 1) - 25600*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 9135*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 46080*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 218484*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 414720*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 653940*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 1183770*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 322560*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1183770*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 537600*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 653940*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 + 107520*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 218484*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 161280*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 9135*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 945*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 - 2560)/(a + 10*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 45*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 120*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 210*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 252*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 210*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 120*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 45*a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + 10*a*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + a*sin(d*x + c)^20/(cos(d*x + c) + 1)^20) - 945*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
708,1,522,0,0.432284," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2304 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8022 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6912 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10458 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{48384 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{18270 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{48384 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{80640 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{18270 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{26880 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{10458 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{16128 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{8022 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{315 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - 256}{a + \frac{9 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{36 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{84 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{126 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{126 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{84 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{36 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{9 \, a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{a \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}}} - \frac{315 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{4032 \, d}"," ",0,"-1/4032*((315*sin(d*x + c)/(cos(d*x + c) + 1) - 2304*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8022*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6912*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10458*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 48384*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 18270*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 48384*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 80640*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 18270*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 26880*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 10458*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 16128*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 8022*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 315*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 256)/(a + 9*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 36*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 84*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 126*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 126*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 84*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 36*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 9*a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + a*sin(d*x + c)^18/(cos(d*x + c) + 1)^18) - 315*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
709,1,501,0,0.426698," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{384 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2779 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{8064 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6265 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{8064 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{12355 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{13440 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{12355 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{13440 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6265 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{2688 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{2779 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{2688 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{105 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - 384}{a + \frac{8 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{56 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{56 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{8 \, a \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{1344 \, d}"," ",0,"1/1344*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 384*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2779*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 8064*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6265*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 8064*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 12355*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 13440*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 12355*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 13440*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6265*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 2688*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 2779*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 2688*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 105*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 384)/(a + 8*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 56*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 56*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 8*a*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a*sin(d*x + c)^16/(cos(d*x + c) + 1)^16) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
710,1,402,0,0.425200," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{165 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1488 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{25 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{3360 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{450 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{3680 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{450 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{2160 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{25 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{720 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{165 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 368}{a + \frac{6 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} + \frac{75 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{120 \, d}"," ",0,"-1/120*((165*sin(d*x + c)/(cos(d*x + c) + 1) - 1488*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 25*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 3360*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 450*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3680*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 450*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 2160*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 25*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 720*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 165*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 368)/(a + 6*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) + 75*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
711,1,379,0,0.428557," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{184 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{285 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{560 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{450 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1120 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{300 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{720 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{360 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{105 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 30}{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{10 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{5 \, a \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{a \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}} + \frac{225 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{30 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{60 \, d}"," ",0,"-1/60*((184*sin(d*x + c)/(cos(d*x + c) + 1) + 285*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 560*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 450*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1120*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 300*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 720*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 360*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 105*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 30)/(a*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 10*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 5*a*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + a*sin(d*x + c)^11/(cos(d*x + c) + 1)^11) + 225*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 60*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - 30*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
712,1,383,0,0.424774," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{124 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{102 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{322 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{78 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{348 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{42 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{147 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{42 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 3}{\frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{4 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} - \frac{3 \, {\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{a} + \frac{90 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{24 \, d}"," ",0,"1/24*((12*sin(d*x + c)/(cos(d*x + c) + 1) - 124*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 102*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 322*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 78*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 348*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 42*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 147*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 42*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 3)/(a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 4*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) - 3*(4*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a + 90*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 60*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
713,1,362,0,0.428529," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{27 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a} - \frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{121 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{102 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{201 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{80 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{147 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{3 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - 1}{\frac{a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{a \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}} - \frac{120 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{24 \, d}"," ",0,"-1/24*((27*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a - (3*sin(d*x + c)/(cos(d*x + c) + 1) + 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 121*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 102*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 201*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 80*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 147*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 1)/(a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + a*sin(d*x + c)^9/(cos(d*x + c) + 1)^9) - 120*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 60*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
714,1,340,0,0.417043," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{216 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{48 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a} + \frac{\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{42 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{200 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{477 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{616 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{432 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{24 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 3}{\frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{960 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{192 \, d}"," ",0,"1/192*((216*sin(d*x + c)/(cos(d*x + c) + 1) - 48*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a + (8*sin(d*x + c)/(cos(d*x + c) + 1) + 42*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 200*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 477*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 616*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 432*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 24*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3)/(a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 960*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 360*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
715,1,319,0,0.432745," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{660 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{240 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{70 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a} + \frac{\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{64 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{225 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{590 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2160 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{660 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 6}{\frac{a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} - \frac{1920 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{1800 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{960 \, d}"," ",0,"1/960*((660*sin(d*x + c)/(cos(d*x + c) + 1) + 240*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 70*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a + (15*sin(d*x + c)/(cos(d*x + c) + 1) + 64*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 225*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 590*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2160*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 660*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6)/(a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) - 1920*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a - 1800*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
716,1,298,0,0.454161," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{1320 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{225 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{140 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{45 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{12 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}{a} - \frac{3840 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{600 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{45 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{140 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{225 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1320 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 5\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{6}}{a \sin\left(d x + c\right)^{6}}}{1920 \, d}"," ",0,"-1/1920*((1320*sin(d*x + c)/(cos(d*x + c) + 1) - 225*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 140*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 45*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 12*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)/a - 3840*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a + 600*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (12*sin(d*x + c)/(cos(d*x + c) + 1) + 45*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 140*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 225*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1320*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5)*(cos(d*x + c) + 1)^6/(a*sin(d*x + c)^6))/d","B",0
717,1,315,0,0.360807," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{315 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{63 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{63 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{7 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a} - \frac{840 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{7 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{21 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{63 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{63 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{315 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{105 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{7}}{a \sin\left(d x + c\right)^{7}}}{2688 \, d}"," ",0,"-1/2688*((105*sin(d*x + c)/(cos(d*x + c) + 1) + 315*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 63*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 63*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 7*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a - 840*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (7*sin(d*x + c)/(cos(d*x + c) + 1) + 21*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 63*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 63*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 315*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 105*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3)*(cos(d*x + c) + 1)^7/(a*sin(d*x + c)^7))/d","B",0
718,1,354,0,0.325506," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{1680 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{336 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1008 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{168 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{336 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{112 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{48 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{21 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}}{a} - \frac{1680 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{48 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{112 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{336 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{168 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1008 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{336 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1680 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 21\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{8}}{a \sin\left(d x + c\right)^{8}}}{43008 \, d}"," ",0,"1/43008*((1680*sin(d*x + c)/(cos(d*x + c) + 1) + 336*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1008*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 168*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 336*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 112*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 48*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 21*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)/a - 1680*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (48*sin(d*x + c)/(cos(d*x + c) + 1) + 112*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 336*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 168*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1008*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 336*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 1680*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 21)*(cos(d*x + c) + 1)^8/(a*sin(d*x + c)^8))/d","B",0
719,1,355,0,0.332956," ","integrate(cos(d*x+c)^8*csc(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{1512 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1008 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{672 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{504 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{336 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{108 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{63 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{28 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a} - \frac{5040 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{63 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{108 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{336 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{504 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{672 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1008 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{1512 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - 28\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{9}}{a \sin\left(d x + c\right)^{9}}}{129024 \, d}"," ",0,"-1/129024*((1512*sin(d*x + c)/(cos(d*x + c) + 1) + 1008*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 672*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 504*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 336*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 108*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 63*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 28*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a - 5040*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (63*sin(d*x + c)/(cos(d*x + c) + 1) + 108*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 336*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 504*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 672*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1008*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 1512*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 28)*(cos(d*x + c) + 1)^9/(a*sin(d*x + c)^9))/d","B",0
720,1,394,0,0.357022," ","integrate(cos(d*x+c)^8*csc(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\frac{15120 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1260 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6720 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2520 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{630 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1080 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{280 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{126 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}}{a} - \frac{15120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} + \frac{{\left(\frac{280 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{315 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1080 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{630 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2520 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{6720 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{1260 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{15120 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 126\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{10}}{a \sin\left(d x + c\right)^{10}}}{1290240 \, d}"," ",0,"1/1290240*((15120*sin(d*x + c)/(cos(d*x + c) + 1) + 1260*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6720*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2520*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 630*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1080*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 315*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 280*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 126*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)/a - 15120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a + (280*sin(d*x + c)/(cos(d*x + c) + 1) + 315*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1080*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 630*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2520*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 6720*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 1260*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 15120*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 126)*(cos(d*x + c) + 1)^10/(a*sin(d*x + c)^10))/d","B",0
721,1,475,0,0.330637," ","integrate(cos(d*x+c)^8*csc(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{69300 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{13860 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{23100 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{27720 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6930 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6930 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{4950 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3465 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{770 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{1386 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{630 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{a} - \frac{166320 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{{\left(\frac{1386 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{770 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3465 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{4950 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6930 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6930 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{27720 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{23100 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{13860 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{69300 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - 630\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{11}}{a \sin\left(d x + c\right)^{11}}}{14192640 \, d}"," ",0,"-1/14192640*((69300*sin(d*x + c)/(cos(d*x + c) + 1) + 13860*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 23100*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 27720*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6930*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6930*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 4950*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3465*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 770*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 1386*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 630*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/a - 166320*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - (1386*sin(d*x + c)/(cos(d*x + c) + 1) + 770*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 3465*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4950*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6930*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6930*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 27720*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 23100*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 13860*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 69300*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 630)*(cos(d*x + c) + 1)^11/(a*sin(d*x + c)^11))/d","B",0
722,1,648,0,0.491583," ","integrate(cos(d*x+c)^8*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{10395 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{191488 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{110880 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{957440 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{535689 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{506880 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6564096 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{2534400 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{8364510 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{20579328 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{12536832 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{8364510 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{8279040 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{6564096 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{2365440 \, \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} - \frac{535689 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{110880 \, \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} - \frac{10395 \, \sin\left(d x + c\right)^{21}}{{\left(\cos\left(d x + c\right) + 1\right)}^{21}} - 17408}{a^{2} + \frac{11 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{55 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{165 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{330 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{462 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{462 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{330 \, a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{165 \, a^{2} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{55 \, a^{2} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{11 \, a^{2} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}} + \frac{a^{2} \sin\left(d x + c\right)^{22}}{{\left(\cos\left(d x + c\right) + 1\right)}^{22}}} - \frac{10395 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{221760 \, d}"," ",0,"1/221760*((10395*sin(d*x + c)/(cos(d*x + c) + 1) - 191488*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 110880*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 957440*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 535689*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 506880*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6564096*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 2534400*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 8364510*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 20579328*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 12536832*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 8364510*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 8279040*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 6564096*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 2365440*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 - 535689*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 110880*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 - 10395*sin(d*x + c)^21/(cos(d*x + c) + 1)^21 - 17408)/(a^2 + 11*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 55*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 165*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 330*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 462*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 462*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 330*a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 165*a^2*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + 55*a^2*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + 11*a^2*sin(d*x + c)^20/(cos(d*x + c) + 1)^20 + a^2*sin(d*x + c)^22/(cos(d*x + c) + 1)^22) - 10395*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
723,1,605,0,0.439680," ","integrate(cos(d*x+c)^8*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{2835 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{40960 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{27405 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{184320 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{139356 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{368640 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{618660 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{1290240 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{1609650 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{516096 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{1609650 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + \frac{430080 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{618660 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{860160 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{139356 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{27405 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - \frac{2835 \, \sin\left(d x + c\right)^{19}}{{\left(\cos\left(d x + c\right) + 1\right)}^{19}} - 4096}{a^{2} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{45 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{120 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{210 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{252 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{210 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{120 \, a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{45 \, a^{2} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}} + \frac{a^{2} \sin\left(d x + c\right)^{20}}{{\left(\cos\left(d x + c\right) + 1\right)}^{20}}} - \frac{2835 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{40320 \, d}"," ",0,"-1/40320*((2835*sin(d*x + c)/(cos(d*x + c) + 1) - 40960*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 27405*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 184320*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 139356*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 368640*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 618660*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 1290240*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1609650*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 516096*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 1609650*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 430080*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 618660*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 860160*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 139356*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 27405*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 2835*sin(d*x + c)^19/(cos(d*x + c) + 1)^19 - 4096)/(a^2 + 10*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 45*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 120*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 210*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 252*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 210*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 120*a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 45*a^2*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + 10*a^2*sin(d*x + c)^18/(cos(d*x + c) + 1)^18 + a^2*sin(d*x + c)^20/(cos(d*x + c) + 1)^20) - 2835*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
724,1,542,0,0.432637," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{945 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{14976 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8190 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{19584 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{97650 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{8064 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{106470 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{330624 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{120960 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{106470 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{147840 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{97650 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{40320 \, \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} - \frac{8190 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - \frac{945 \, \sin\left(d x + c\right)^{17}}{{\left(\cos\left(d x + c\right) + 1\right)}^{17}} - 1664}{a^{2} + \frac{9 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{36 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{84 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{126 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{126 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{84 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{36 \, a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{9 \, a^{2} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}} + \frac{a^{2} \sin\left(d x + c\right)^{18}}{{\left(\cos\left(d x + c\right) + 1\right)}^{18}}} - \frac{945 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{10080 \, d}"," ",0,"1/10080*((945*sin(d*x + c)/(cos(d*x + c) + 1) - 14976*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8190*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 19584*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 97650*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 8064*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 106470*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 330624*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 120960*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 106470*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 147840*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 97650*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 40320*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 - 8190*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 945*sin(d*x + c)^17/(cos(d*x + c) + 1)^17 - 1664)/(a^2 + 9*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 36*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 84*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 126*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 126*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 84*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 36*a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + 9*a^2*sin(d*x + c)^16/(cos(d*x + c) + 1)^16 + a^2*sin(d*x + c)^18/(cos(d*x + c) + 1)^18) - 945*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
725,1,479,0,0.441470," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{1155 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{12288 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{9065 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{10752 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{38605 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{86016 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{79135 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{53760 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{79135 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{38605 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{53760 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{9065 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{1155 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - 1536}{a^{2} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{56 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{56 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a^{2} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}} - \frac{1155 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{6720 \, d}"," ",0,"-1/6720*((1155*sin(d*x + c)/(cos(d*x + c) + 1) - 12288*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 9065*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 10752*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 38605*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 86016*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 79135*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 53760*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 79135*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 38605*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 53760*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 9065*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 1155*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 1536)/(a^2 + 8*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 56*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 56*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 8*a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a^2*sin(d*x + c)^16/(cos(d*x + c) + 1)^16) - 1155*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
726,1,436,0,0.458671," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{672 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1540 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1176 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1085 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6720 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{840 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{1085 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{3360 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{1540 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{840 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{105 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - 216}{a^{2} + \frac{7 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{21 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{35 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{35 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{21 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{7 \, a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{a^{2} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{420 \, d}"," ",0,"1/420*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 672*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1540*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1176*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1085*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6720*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 840*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 1085*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 3360*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1540*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 840*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 105*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 216)/(a^2 + 7*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 21*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 35*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 35*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 21*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 7*a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + a^2*sin(d*x + c)^14/(cos(d*x + c) + 1)^14) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
727,1,333,0,0.429300," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{75 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{280 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{30 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{320 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{360 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{30 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{60 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{75 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 68}{a^{2} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{30 \, d}"," ",0,"-1/30*((75*sin(d*x + c)/(cos(d*x + c) + 1) - 280*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 30*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 320*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 360*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 30*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 60*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 75*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 68)/(a^2 + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 10*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 30*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
728,1,348,0,0.435500," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{64 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{21 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{160 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{57 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{192 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{96 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{9 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 6}{\frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}} + \frac{27 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{24 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{6 \, \sin\left(d x + c\right)}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}}{12 \, d}"," ",0,"-1/12*((64*sin(d*x + c)/(cos(d*x + c) + 1) + 21*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 160*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 57*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 192*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 96*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 9*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6)/(a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 4*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9) + 27*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 24*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 6*sin(d*x + c)/(a^2*(cos(d*x + c) + 1)))/d","B",0
729,1,330,0,0.441154," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{24 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{120 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{9 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{72 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{45 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{24 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 3}{\frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{3 \, {\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{a^{2}} + \frac{144 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{24 \, d}"," ",0,"1/24*((24*sin(d*x + c)/(cos(d*x + c) + 1) + 7*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 120*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 9*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 72*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 45*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 24*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3)/(a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 3*(8*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^2 + 144*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
730,1,306,0,0.445372," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{108 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{19 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{102 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{27 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 1}{\frac{a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} - \frac{\frac{3 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{2}} - \frac{24 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{72 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{24 \, d}"," ",0,"1/24*((6*sin(d*x + c)/(cos(d*x + c) + 1) + sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 108*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 19*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 102*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 27*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 1)/(a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) - (3*sin(d*x + c)/(cos(d*x + c) + 1) + 6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^2 - 24*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 72*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
731,1,263,0,0.431750," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{16 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{224 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{384 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{240 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 3}{\frac{a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{\frac{240 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a^{2}} - \frac{768 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{216 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{192 \, d}"," ",0,"1/192*((16*sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 224*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 384*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 240*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 3)/(a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + (240*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a^2 - 768*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 216*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
732,1,258,0,0.434267," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{270 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{120 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{2}} - \frac{960 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{{\left(\frac{15 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{120 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{270 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a^{2} \sin\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*((270*sin(d*x + c)/(cos(d*x + c) + 1) - 120*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^2 - 960*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + 360*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (15*sin(d*x + c)/(cos(d*x + c) + 1) - 5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 120*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 270*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3)*(cos(d*x + c) + 1)^5/(a^2*sin(d*x + c)^5))/d","B",0
733,1,275,0,0.332751," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{240 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{255 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{120 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{24 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{5 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}{a^{2}} - \frac{840 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{{\left(\frac{24 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{120 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{255 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{240 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 5\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{6}}{a^{2} \sin\left(d x + c\right)^{6}}}{1920 \, d}"," ",0,"-1/1920*((240*sin(d*x + c)/(cos(d*x + c) + 1) + 255*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 120*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 24*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)/a^2 - 840*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (24*sin(d*x + c)/(cos(d*x + c) + 1) - 15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 120*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 255*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 240*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5)*(cos(d*x + c) + 1)^6/(a^2*sin(d*x + c)^6))/d","B",0
734,1,314,0,0.332859," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{1155 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{210 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{525 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{210 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{70 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{2}} - \frac{1680 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{{\left(\frac{70 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{63 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{210 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{525 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{210 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1155 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 15\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{7}}{a^{2} \sin\left(d x + c\right)^{7}}}{13440 \, d}"," ",0,"1/13440*((1155*sin(d*x + c)/(cos(d*x + c) + 1) + 210*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 525*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 210*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 70*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^2 - 1680*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + (70*sin(d*x + c)/(cos(d*x + c) + 1) - 63*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 210*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 525*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 210*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1155*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 15)*(cos(d*x + c) + 1)^7/(a^2*sin(d*x + c)^7))/d","B",0
735,1,355,0,0.331595," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{10080 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1680 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3360 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2520 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{672 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{560 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{480 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{105 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}}{a^{2}} - \frac{18480 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{{\left(\frac{480 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{560 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{672 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2520 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3360 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1680 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{10080 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 105\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{8}}{a^{2} \sin\left(d x + c\right)^{8}}}{215040 \, d}"," ",0,"-1/215040*((10080*sin(d*x + c)/(cos(d*x + c) + 1) + 1680*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 3360*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2520*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 672*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 560*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 480*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 105*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)/a^2 - 18480*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (480*sin(d*x + c)/(cos(d*x + c) + 1) - 560*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 672*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2520*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3360*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1680*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 10080*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 105)*(cos(d*x + c) + 1)^8/(a^2*sin(d*x + c)^8))/d","B",0
736,1,314,0,0.340139," ","integrate(cos(d*x+c)^8*csc(d*x+c)^10/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{11340 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3360 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2520 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{1008 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{450 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{70 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}}{a^{2}} - \frac{15120 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{{\left(\frac{315 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{450 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1008 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2520 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{3360 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{11340 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - 70\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{9}}{a^{2} \sin\left(d x + c\right)^{9}}}{322560 \, d}"," ",0,"1/322560*((11340*sin(d*x + c)/(cos(d*x + c) + 1) - 3360*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2520*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1008*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 450*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 315*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 70*sin(d*x + c)^9/(cos(d*x + c) + 1)^9)/a^2 - 15120*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + (315*sin(d*x + c)/(cos(d*x + c) + 1) - 450*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1008*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2520*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 3360*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 11340*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 70)*(cos(d*x + c) + 1)^9/(a^2*sin(d*x + c)^9))/d","B",0
737,1,435,0,0.428998," ","integrate(cos(d*x+c)^8*csc(d*x+c)^11/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{30240 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1260 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6720 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{7560 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4032 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{630 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{720 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{945 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{560 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{126 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}}{a^{2}} - \frac{45360 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{{\left(\frac{560 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{945 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{720 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{630 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4032 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{7560 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6720 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{1260 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{30240 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - 126\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{10}}{a^{2} \sin\left(d x + c\right)^{10}}}{1290240 \, d}"," ",0,"-1/1290240*((30240*sin(d*x + c)/(cos(d*x + c) + 1) - 1260*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6720*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 7560*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4032*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 630*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 720*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 945*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 560*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 126*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)/a^2 - 45360*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - (560*sin(d*x + c)/(cos(d*x + c) + 1) - 945*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 720*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 630*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4032*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 7560*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6720*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 1260*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 30240*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 126)*(cos(d*x + c) + 1)^10/(a^2*sin(d*x + c)^10))/d","B",0
738,1,474,0,0.332271," ","integrate(cos(d*x+c)^8*csc(d*x+c)^12/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{131670 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{13860 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{25410 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{27720 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{18711 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{6930 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1485 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3465 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{2695 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{1386 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{315 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}}{a^{2}} - \frac{166320 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} + \frac{{\left(\frac{1386 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2695 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3465 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1485 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6930 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{18711 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{27720 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{25410 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{13860 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{131670 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - 315\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{11}}{a^{2} \sin\left(d x + c\right)^{11}}}{7096320 \, d}"," ",0,"1/7096320*((131670*sin(d*x + c)/(cos(d*x + c) + 1) - 13860*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 25410*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 27720*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 18711*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 6930*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1485*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3465*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 2695*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 1386*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 315*sin(d*x + c)^11/(cos(d*x + c) + 1)^11)/a^2 - 166320*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 + (1386*sin(d*x + c)/(cos(d*x + c) + 1) - 2695*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3465*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1485*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6930*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 18711*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 27720*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 25410*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 13860*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 131670*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 315)*(cos(d*x + c) + 1)^11/(a^2*sin(d*x + c)^11))/d","B",0
739,1,499,0,0.431587," ","integrate(cos(d*x+c)^8*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{3045 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{38912 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{23345 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{109312 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{51275 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{14336 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{179095 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{170240 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{179095 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{286720 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{51275 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{26880 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{23345 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{3045 \, \sin\left(d x + c\right)^{15}}{{\left(\cos\left(d x + c\right) + 1\right)}^{15}} - 4864}{a^{3} + \frac{8 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{56 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{70 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{56 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{28 \, a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{8 \, a^{3} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}} + \frac{a^{3} \sin\left(d x + c\right)^{16}}{{\left(\cos\left(d x + c\right) + 1\right)}^{16}}} - \frac{3045 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{6720 \, d}"," ",0,"1/6720*((3045*sin(d*x + c)/(cos(d*x + c) + 1) - 38912*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 23345*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 109312*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 51275*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 14336*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 179095*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 170240*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 179095*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 286720*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 51275*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 26880*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 23345*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 3045*sin(d*x + c)^15/(cos(d*x + c) + 1)^15 - 4864)/(a^3 + 8*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 56*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 70*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 56*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 28*a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 8*a^3*sin(d*x + c)^14/(cos(d*x + c) + 1)^14 + a^3*sin(d*x + c)^16/(cos(d*x + c) + 1)^16) - 3045*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
740,1,416,0,0.465571," ","integrate(cos(d*x+c)^8*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{1120 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{252 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1344 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2499 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{448 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{5152 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{2499 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2016 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{252 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{105 \, \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - 160}{a^{3} + \frac{7 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{21 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{35 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{35 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{21 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{7 \, a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + \frac{a^{3} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{168 \, d}"," ",0,"-1/168*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 1120*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 252*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1344*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2499*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 448*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 5152*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 2499*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2016*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 252*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 105*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - 160)/(a^3 + 7*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 21*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 35*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 35*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 21*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 7*a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + a^3*sin(d*x + c)^14/(cos(d*x + c) + 1)^14) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
741,1,393,0,0.469303," ","integrate(cos(d*x+c)^8*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{105 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{816 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{365 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{480 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{1110 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1760 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1110 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{2160 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{365 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{240 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{105 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 176}{a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{120 \, d}"," ",0,"1/120*((105*sin(d*x + c)/(cos(d*x + c) + 1) - 816*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 365*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 480*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1110*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1760*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1110*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 2160*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 365*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 240*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 105*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 176)/(a^3 + 6*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 15*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 6*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
742,1,269,0,0.599980," ","integrate(cos(d*x+c)^8*csc(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{11 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{16 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{19 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{19 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{16 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{11 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{3} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{4 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{13 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{4 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{4 \, d}"," ",0,"-1/4*((11*sin(d*x + c)/(cos(d*x + c) + 1) - 16*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 19*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 19*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 16*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 11*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/(a^3 + 4*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 4*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 13*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 4*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
743,1,285,0,0.431791," ","integrate(cos(d*x+c)^8*csc(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{32 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{72 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{9 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{24 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 3}{\frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} - \frac{6 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{18 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{3 \, \sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{6 \, d}"," ",0,"-1/6*((32*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 72*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 9*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 24*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 21*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 3)/(a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) - 6*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + 18*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 3*sin(d*x + c)/(a^3*(cos(d*x + c) + 1)))/d","B",0
744,1,267,0,0.571316," ","integrate(cos(d*x+c)^8*csc(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{46 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{16 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{47 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{20 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 1}{\frac{a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} - \frac{\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}}{a^{3}} + \frac{40 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{20 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{8 \, d}"," ",0,"1/8*((12*sin(d*x + c)/(cos(d*x + c) + 1) + 46*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 16*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 47*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 20*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1)/(a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) - (12*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^3 + 40*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + 20*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
745,1,242,0,0.427036," ","integrate(cos(d*x+c)^8*csc(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{9 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{34 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{39 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{33 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 1}{\frac{a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{\frac{33 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{\sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}}}{a^{3}} - \frac{144 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{12 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{24 \, d}"," ",0,"1/24*((9*sin(d*x + c)/(cos(d*x + c) + 1) - 34*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 39*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 33*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1)/(a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + (33*sin(d*x + c)/(cos(d*x + c) + 1) - 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + sin(d*x + c)^3/(cos(d*x + c) + 1)^3)/a^3 - 144*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + 12*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
746,1,218,0,0.502525," ","integrate(cos(d*x+c)^8*csc(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{\sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}}{a^{3}} - \frac{128 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{104 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{{\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{24 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - 1\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{4}}{a^{3} \sin\left(d x + c\right)^{4}}}{64 \, d}"," ",0,"-1/64*((8*sin(d*x + c)/(cos(d*x + c) + 1) - 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - sin(d*x + c)^4/(cos(d*x + c) + 1)^4)/a^3 - 128*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + 104*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - (8*sin(d*x + c)/(cos(d*x + c) + 1) - 24*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1)*(cos(d*x + c) + 1)^4/(a^3*sin(d*x + c)^4))/d","B",0
747,1,235,0,0.403968," ","integrate(cos(d*x+c)^8*csc(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{420 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{120 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{130 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{45 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}}{a^{3}} - \frac{840 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{{\left(\frac{45 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{130 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{120 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{420 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - 6\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{5}}{a^{3} \sin\left(d x + c\right)^{5}}}{960 \, d}"," ",0,"-1/960*((420*sin(d*x + c)/(cos(d*x + c) + 1) + 120*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 130*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 45*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6*sin(d*x + c)^5/(cos(d*x + c) + 1)^5)/a^3 - 840*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - (45*sin(d*x + c)/(cos(d*x + c) + 1) - 130*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 120*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 420*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6)*(cos(d*x + c) + 1)^5/(a^3*sin(d*x + c)^5))/d","B",0
748,1,274,0,0.326303," ","integrate(cos(d*x+c)^8*csc(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{600 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{15 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{140 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{105 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}}{a^{3}} - \frac{840 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{{\left(\frac{36 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{105 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{140 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{600 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - 5\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{6}}{a^{3} \sin\left(d x + c\right)^{6}}}{1920 \, d}"," ",0,"1/1920*((600*sin(d*x + c)/(cos(d*x + c) + 1) - 15*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 140*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 105*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)/a^3 - 840*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + (36*sin(d*x + c)/(cos(d*x + c) + 1) - 105*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 140*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 600*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 5)*(cos(d*x + c) + 1)^6/(a^3*sin(d*x + c)^6))/d","B",0
749,1,315,0,0.326981," ","integrate(cos(d*x+c)^8*csc(d*x+c)^8/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{609 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{63 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{91 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{105 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{21 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{3 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}}{a^{3}} - \frac{840 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{{\left(\frac{21 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{63 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{105 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{91 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{63 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{609 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - 3\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{7}}{a^{3} \sin\left(d x + c\right)^{7}}}{2688 \, d}"," ",0,"-1/2688*((609*sin(d*x + c)/(cos(d*x + c) + 1) - 63*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 91*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 105*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 21*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7)/a^3 - 840*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - (21*sin(d*x + c)/(cos(d*x + c) + 1) - 63*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 105*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 91*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 63*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 609*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 3)*(cos(d*x + c) + 1)^7/(a^3*sin(d*x + c)^7))/d","B",0
750,1,354,0,0.333641," ","integrate(cos(d*x+c)^8*csc(d*x+c)^9/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{\frac{38640 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6720 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3920 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5880 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4368 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2240 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{720 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{105 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}}{a^{3}} - \frac{48720 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} + \frac{{\left(\frac{720 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2240 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4368 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5880 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{3920 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{6720 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{38640 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 105\right)} {\left(\cos\left(d x + c\right) + 1\right)}^{8}}{a^{3} \sin\left(d x + c\right)^{8}}}{215040 \, d}"," ",0,"1/215040*((38640*sin(d*x + c)/(cos(d*x + c) + 1) - 6720*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 3920*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5880*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4368*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2240*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 720*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 105*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)/a^3 - 48720*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 + (720*sin(d*x + c)/(cos(d*x + c) + 1) - 2240*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4368*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5880*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3920*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 6720*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 38640*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 105)*(cos(d*x + c) + 1)^8/(a^3*sin(d*x + c)^8))/d","B",0
751,1,75,0,0.440629," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a + 3 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a}{6 \, d}"," ",0,"-1/6*(2*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a + 3*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a)/d","A",0
752,1,62,0,0.417867," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a - 2 \, a {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{2 \, d}"," ",0,"-1/2*((3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a - 2*a*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
753,1,39,0,0.422093," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} a - a {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*a - a*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
754,1,32,0,0.413837," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} a - \frac{a}{\cos\left(d x + c\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*a - a/cos(d*x + c))/d","A",0
755,1,48,0,0.337911," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2 \, a \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 2*a*tan(d*x + c))/d","A",0
756,1,59,0,0.449769," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 2 \, a {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)}}{2 \, d}"," ",0,"1/2*(a*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 2*a*(1/tan(d*x + c) - tan(d*x + c)))/d","A",0
757,1,84,0,0.318471," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 4 \, a {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*(a*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 4*a*(1/tan(d*x + c) - tan(d*x + c)))/d","A",0
758,1,98,0,0.312034," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 4 \, a {\left(\frac{6 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} - 3 \, \tan\left(d x + c\right)\right)}}{12 \, d}"," ",0,"1/12*(3*a*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 4*a*((6*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 - 3*tan(d*x + c)))/d","A",0
759,1,98,0,0.619962," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a^{2} + 3 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{2} - 3 \, a^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{3 \, d}"," ",0,"-1/3*((cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^2 + 3*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^2 - 3*a^2*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
760,1,84,0,0.524644," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{2} + 2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} - 4 \, a^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{2 \, d}"," ",0,"-1/2*((3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^2 + 2*(d*x + c - tan(d*x + c))*a^2 - 4*a^2*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
761,1,57,0,1.070632," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} - a^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - \frac{a^{2}}{\cos\left(d x + c\right)}}{d}"," ",0,"-(2*(d*x + c - tan(d*x + c))*a^2 - a^2*(1/cos(d*x + c) + cos(d*x + c)) - a^2/cos(d*x + c))/d","A",0
762,1,65,0,0.307145," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 4 \, a^{2} \tan\left(d x + c\right) + \frac{2 \, a^{2}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(a^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 4*a^2*tan(d*x + c) + 2*a^2/cos(d*x + c))/d","A",0
763,1,72,0,0.482635," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - a^{2} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + a^{2} \tan\left(d x + c\right)}{d}"," ",0,"(a^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - a^2*(1/tan(d*x + c) - tan(d*x + c)) + a^2*tan(d*x + c))/d","A",0
764,1,124,0,0.330301," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2 \, a^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 8 \, a^{2} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*(a^2*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 2*a^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 8*a^2*(1/tan(d*x + c) - tan(d*x + c)))/d","A",0
765,1,162,0,0.414962," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{8 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a^{3} + {\left(15 \, d x + 15 \, c - \frac{9 \, \tan\left(d x + c\right)^{3} + 7 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 8 \, \tan\left(d x + c\right)\right)} a^{3} + 12 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{3} - 8 \, a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{8 \, d}"," ",0,"-1/8*(8*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^3 + (15*d*x + 15*c - (9*tan(d*x + c)^3 + 7*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 8*tan(d*x + c))*a^3 + 12*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^3 - 8*a^3*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
766,1,117,0,0.422093," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a^{3} + 9 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{3} + 6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} - 18 \, a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"-1/6*(2*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a^3 + 9*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^3 + 6*(d*x + c - tan(d*x + c))*a^3 - 18*a^3*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
767,1,97,0,0.424905," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{3} + 6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} - 6 \, a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - \frac{2 \, a^{3}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*((3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^3 + 6*(d*x + c - tan(d*x + c))*a^3 - 6*a^3*(1/cos(d*x + c) + cos(d*x + c)) - 2*a^3/cos(d*x + c))/d","A",0
768,1,84,0,0.430773," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} - a^{3} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 6 \, a^{3} \tan\left(d x + c\right) - \frac{6 \, a^{3}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c - tan(d*x + c))*a^3 - a^3*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 6*a^3*tan(d*x + c) - 6*a^3/cos(d*x + c))/d","A",0
769,1,88,0,0.328924," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 2 \, a^{3} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + 6 \, a^{3} \tan\left(d x + c\right) + \frac{2 \, a^{3}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(3*a^3*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 2*a^3*(1/tan(d*x + c) - tan(d*x + c)) + 6*a^3*tan(d*x + c) + 2*a^3/cos(d*x + c))/d","A",0
770,1,135,0,0.341206," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 12 \, a^{3} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + 4 \, a^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(a^3*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 6*a^3*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 12*a^3*(1/tan(d*x + c) - tan(d*x + c)) + 4*a^3*tan(d*x + c))/d","A",0
771,1,160,0,0.334000," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{9 \, a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 36 \, a^{3} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} - 4 \, a^{3} {\left(\frac{6 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} - 3 \, \tan\left(d x + c\right)\right)}}{12 \, d}"," ",0,"1/12*(9*a^3*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 6*a^3*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 36*a^3*(1/tan(d*x + c) - tan(d*x + c)) - 4*a^3*((6*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 - 3*tan(d*x + c)))/d","A",0
772,1,236,0,0.426658," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{13 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{6 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 8}{a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{2 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}\right)}}{3 \, d}"," ",0,"2/3*((13*sin(d*x + c)/(cos(d*x + c) + 1) + 2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 6*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 8)/(a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) + a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 2*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
773,1,154,0,0.423418," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{6 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 2}{a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{3 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}\right)}}{3 \, d}"," ",0,"-2/3*((sin(d*x + c)/(cos(d*x + c) + 1) - 6*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2)/(a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + 3*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
774,1,90,0,0.317973," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{2 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + 1\right)}}{3 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d}"," ",0,"4/3*(2*sin(d*x + c)/(cos(d*x + c) + 1) + 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d)","A",0
775,1,110,0,0.319787," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{2 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{3 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}\right)} d}"," ",0,"2/3*(2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4)*d)","B",0
776,1,136,0,0.323581," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{5 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{3 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 4\right)}}{a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}}} + \frac{3 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{3 \, d}"," ",0,"1/3*(2*(5*sin(d*x + c)/(cos(d*x + c) + 1) - 3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 4)/(a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4) + 3*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","A",0
777,1,215,0,0.334945," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{22 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{8 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{30 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 3}{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}}} + \frac{6 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{3 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{6 \, d}"," ",0,"-1/6*((22*sin(d*x + c)/(cos(d*x + c) + 1) + 8*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 30*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3)/(a*sin(d*x + c)/(cos(d*x + c) + 1) + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5) + 6*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - 3*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
778,1,421,0,0.431448," ","integrate(sec(d*x+c)^2*sin(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{211 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{268 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{212 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{84 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{174 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{300 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{300 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{180 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{45 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 64}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{7 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{6 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{7 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{45 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{5 \, d}"," ",0,"-1/5*((211*sin(d*x + c)/(cos(d*x + c) + 1) + 268*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 212*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 84*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 174*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 300*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 300*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 180*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 45*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 64)/(a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 7*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 6*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 7*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 45*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
779,1,335,0,0.432589," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{\frac{97 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{108 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{27 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{40 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{85 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{60 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 28}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{6 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{15 \, d}"," ",0,"4/15*((97*sin(d*x + c)/(cos(d*x + c) + 1) + 108*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 27*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 40*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 85*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 60*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 28)/(a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 6*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 4*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 6*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 4*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
780,1,249,0,0.427752," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\frac{49 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{70 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{60 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 16}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{15 \, d}"," ",0,"-2/15*((49*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 70*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 60*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 16)/(a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
781,1,164,0,0.333060," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + 1\right)}}{5 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d}"," ",0,"4/5*(4*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d)","B",0
782,1,184,0,0.334073," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 1\right)}}{15 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d}"," ",0,"8/15*(4*sin(d*x + c)/(cos(d*x + c) + 1) + 5*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d)","B",0
783,1,204,0,0.330318," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{20 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{20 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 1\right)}}{15 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}\right)} d}"," ",0,"2/15*(4*sin(d*x + c)/(cos(d*x + c) + 1) + 20*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 20*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6)*d)","B",0
784,1,250,0,0.333988," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(\frac{37 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{10 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{30 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{15 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 13\right)}}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{5 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}}} + \frac{15 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{15 \, d}"," ",0,"1/15*(4*(37*sin(d*x + c)/(cos(d*x + c) + 1) + 35*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 10*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 30*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 15*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 13)/(a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 5*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 5*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 4*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6) + 15*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
785,1,309,0,0.335752," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{244 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{571 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{320 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{475 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{660 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{255 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 15}{\frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{5 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}}} + \frac{60 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{15 \, \sin\left(d x + c\right)}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}}{30 \, d}"," ",0,"-1/30*((244*sin(d*x + c)/(cos(d*x + c) + 1) + 571*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 320*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 475*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 660*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 255*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 15)/(a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 5*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 5*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 4*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7) + 60*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 15*sin(d*x + c)/(a^2*(cos(d*x + c) + 1)))/d","B",0
786,1,354,0,0.339963," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{20 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{567 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1448 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{985 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{820 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1355 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{520 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - 5}{\frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{5 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} - \frac{5 \, {\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{a^{2}} + \frac{180 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{40 \, d}"," ",0,"1/40*((20*sin(d*x + c)/(cos(d*x + c) + 1) + 567*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1448*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 985*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 820*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1355*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 520*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 5)/(a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 5*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 4*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) - 5*(8*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^2 + 180*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
787,1,421,0,0.439264," ","integrate(sec(d*x+c)^2*sin(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{951 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2010 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1980 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{574 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{966 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1890 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{1540 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{630 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{105 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 176}{a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{15 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{20 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{20 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{15 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{35 \, d}"," ",0,"2/35*((951*sin(d*x + c)/(cos(d*x + c) + 1) + 2010*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1980*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 574*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 966*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1890*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 1540*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 630*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 105*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 176)/(a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 15*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 20*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 14*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 20*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 15*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 6*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
788,1,335,0,0.429169," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\frac{711 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1274 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{469 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1260 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{1435 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{630 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{105 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 136}{a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{105 \, d}"," ",0,"-2/105*((711*sin(d*x + c)/(cos(d*x + c) + 1) + 1274*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 469*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1260*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1435*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 630*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 105*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 136)/(a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 14*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
789,1,230,0,0.337819," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{16 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 1\right)}}{35 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"16/35*(6*sin(d*x + c)/(cos(d*x + c) + 1) + 14*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 14*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
790,1,250,0,0.335172," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{18 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{42 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{42 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{35 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 3\right)}}{35 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"4/35*(18*sin(d*x + c)/(cos(d*x + c) + 1) + 42*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 42*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 35*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 3)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 14*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
791,1,270,0,0.338148," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{28 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{21 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 1\right)}}{21 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"4/21*(6*sin(d*x + c)/(cos(d*x + c) + 1) + 14*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 28*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 21*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 14*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
792,1,290,0,0.340877," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{21 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{56 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{105 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{70 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{35 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 1\right)}}{35 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"-2/35*(6*sin(d*x + c)/(cos(d*x + c) + 1) - 21*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 56*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 105*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 70*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 35*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 14*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
793,1,336,0,0.345273," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{1011 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1939 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1379 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{525 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{1715 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{1155 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{315 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 221\right)}}{a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{105 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{105 \, d}"," ",0,"1/105*(2*(1011*sin(d*x + c)/(cos(d*x + c) + 1) + 1939*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1379*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 525*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 1715*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 1155*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 315*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 221)/(a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 14*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 6*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 105*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
794,1,395,0,0.340660," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{934 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3854 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{6566 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3556 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3710 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{7070 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{4270 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{1015 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 35}{\frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{14 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{14 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}} + \frac{210 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{35 \, \sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{70 \, d}"," ",0,"-1/70*((934*sin(d*x + c)/(cos(d*x + c) + 1) + 3854*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 6566*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3556*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3710*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 7070*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 4270*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 1015*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 35)/(a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 6*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 14*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 14*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 14*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 14*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 6*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9) + 210*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 35*sin(d*x + c)/(a^3*(cos(d*x + c) + 1)))/d","B",0
795,1,96,0,0.415979," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} - 9 \, \cos\left(d x + c\right)\right)} a + {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a}{6 \, d}"," ",0,"1/6*(2*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*a + (2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a)/d","A",0
796,1,87,0,0.421527," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a - 2 \, a {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*((2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a - 2*a*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
797,1,65,0,0.417315," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a - a {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a - a*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
798,1,55,0,0.420386," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a - \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a - (3*cos(d*x + c)^2 - 1)*a/cos(d*x + c)^3)/d","A",0
799,1,39,0,0.315356," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \tan\left(d x + c\right)^{3} - \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(a*tan(d*x + c)^3 - (3*cos(d*x + c)^2 - 1)*a/cos(d*x + c)^3)/d","A",0
800,1,26,0,0.319975," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a \tan\left(d x + c\right)^{3} + \frac{a}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(a*tan(d*x + c)^3 + a/cos(d*x + c)^3)/d","A",0
801,1,73,0,0.318714," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a + a {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 + 3*tan(d*x + c))*a + a*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)))/d","A",0
802,1,83,0,0.321033," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} - \frac{3}{\tan\left(d x + c\right)} + 6 \, \tan\left(d x + c\right)\right)} a + a {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 - 3/tan(d*x + c) + 6*tan(d*x + c))*a + a*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)))/d","A",0
803,1,106,0,0.321191," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} - \frac{3}{\tan\left(d x + c\right)} + 6 \, \tan\left(d x + c\right)\right)} a + a {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3}} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(4*(tan(d*x + c)^3 - 3/tan(d*x + c) + 6*tan(d*x + c))*a + a*(2*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 - 2)/(cos(d*x + c)^5 - cos(d*x + c)^3) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)))/d","A",0
804,1,120,0,0.425334," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{2} + 2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} - 4 \, a^{2} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*((2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^2 + 2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2 - 4*a^2*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
805,1,95,0,0.424387," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} - a^{2} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)} - \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{2}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2 - a^2*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) - (3*cos(d*x + c)^2 - 1)*a^2/cos(d*x + c)^3)/d","A",0
806,1,71,0,0.416093," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{2} - \frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{2}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(a^2*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^2 - 2*(3*cos(d*x + c)^2 - 1)*a^2/cos(d*x + c)^3)/d","A",0
807,1,56,0,0.320514," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, a^{2} \tan\left(d x + c\right)^{3} - \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{2}}{\cos\left(d x + c\right)^{3}} + \frac{a^{2}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(2*a^2*tan(d*x + c)^3 - (3*cos(d*x + c)^2 - 1)*a^2/cos(d*x + c)^3 + a^2/cos(d*x + c)^3)/d","A",0
808,1,90,0,0.323422," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} + a^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{2 \, a^{2}}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(4*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 + a^2*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 2*a^2/cos(d*x + c)^3)/d","A",0
809,1,107,0,0.332529," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(\tan\left(d x + c\right)^{3} - \frac{3}{\tan\left(d x + c\right)} + 6 \, \tan\left(d x + c\right)\right)} a^{2} + {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{2} + a^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{3 \, d}"," ",0,"1/3*((tan(d*x + c)^3 - 3/tan(d*x + c) + 6*tan(d*x + c))*a^2 + (tan(d*x + c)^3 + 3*tan(d*x + c))*a^2 + a^2*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)))/d","A",0
810,1,160,0,0.330802," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{8 \, {\left(\tan\left(d x + c\right)^{3} - \frac{3}{\tan\left(d x + c\right)} + 6 \, \tan\left(d x + c\right)\right)} a^{2} + a^{2} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3}} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2 \, a^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(8*(tan(d*x + c)^3 - 3/tan(d*x + c) + 6*tan(d*x + c))*a^2 + a^2*(2*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 - 2)/(cos(d*x + c)^5 - cos(d*x + c)^3) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 2*a^2*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)))/d","A",0
811,1,165,0,0.415346," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} - 9 \, \cos\left(d x + c\right)\right)} a^{3} + 3 \, {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{3} + 2 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3} - 6 \, a^{3} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*(2*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*a^3 + 3*(2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^3 + 2*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3 - 6*a^3*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
812,1,145,0,0.425591," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{{\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{3} + 6 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3} - 6 \, a^{3} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)} - \frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{3}}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*((2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^3 + 6*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3 - 6*a^3*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) - 2*(3*cos(d*x + c)^2 - 1)*a^3/cos(d*x + c)^3)/d","A",0
813,1,107,0,0.424392," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3} \tan\left(d x + c\right)^{3} + 3 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3} - a^{3} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)} - \frac{3 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{3}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(a^3*tan(d*x + c)^3 + 3*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3 - a^3*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) - 3*(3*cos(d*x + c)^2 - 1)*a^3/cos(d*x + c)^3)/d","A",0
814,1,84,0,0.421087," ","integrate(sec(d*x+c)^4*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, a^{3} \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{3} - \frac{3 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{3}}{\cos\left(d x + c\right)^{3}} + \frac{a^{3}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*a^3*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^3 - 3*(3*cos(d*x + c)^2 - 1)*a^3/cos(d*x + c)^3 + a^3/cos(d*x + c)^3)/d","A",0
815,1,103,0,0.328440," ","integrate(csc(d*x+c)*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, a^{3} \tan\left(d x + c\right)^{3} + 6 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} + a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{6 \, a^{3}}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(2*a^3*tan(d*x + c)^3 + 6*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 + a^3*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 6*a^3/cos(d*x + c)^3)/d","A",0
816,1,123,0,0.323561," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\tan\left(d x + c\right)^{3} - \frac{3}{\tan\left(d x + c\right)} + 6 \, \tan\left(d x + c\right)\right)} a^{3} + 6 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} + 3 \, a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{2 \, a^{3}}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(2*(tan(d*x + c)^3 - 3/tan(d*x + c) + 6*tan(d*x + c))*a^3 + 6*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 + 3*a^3*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 2*a^3/cos(d*x + c)^3)/d","A",0
817,1,182,0,0.331059," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{12 \, {\left(\tan\left(d x + c\right)^{3} - \frac{3}{\tan\left(d x + c\right)} + 6 \, \tan\left(d x + c\right)\right)} a^{3} + 4 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} a^{3} + a^{3} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3}} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 6 \, a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(12*(tan(d*x + c)^3 - 3/tan(d*x + c) + 6*tan(d*x + c))*a^3 + 4*(tan(d*x + c)^3 + 3*tan(d*x + c))*a^3 + a^3*(2*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 - 2)/(cos(d*x + c)^5 - cos(d*x + c)^3) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 6*a^3*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)))/d","A",0
818,1,205,0,0.335779," ","integrate(csc(d*x+c)^4*sec(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{12 \, {\left(\tan\left(d x + c\right)^{3} - \frac{3}{\tan\left(d x + c\right)} + 6 \, \tan\left(d x + c\right)\right)} a^{3} + 4 \, {\left(\tan\left(d x + c\right)^{3} - \frac{9 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} + 9 \, \tan\left(d x + c\right)\right)} a^{3} + 3 \, a^{3} {\left(\frac{2 \, {\left(15 \, \cos\left(d x + c\right)^{4} - 10 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{5} - \cos\left(d x + c\right)^{3}} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2 \, a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} + 1\right)}}{\cos\left(d x + c\right)^{3}} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(12*(tan(d*x + c)^3 - 3/tan(d*x + c) + 6*tan(d*x + c))*a^3 + 4*(tan(d*x + c)^3 - (9*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 + 9*tan(d*x + c))*a^3 + 3*a^3*(2*(15*cos(d*x + c)^4 - 10*cos(d*x + c)^2 - 2)/(cos(d*x + c)^5 - cos(d*x + c)^3) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 2*a^3*(2*(3*cos(d*x + c)^2 + 1)/cos(d*x + c)^3 - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)))/d","A",0
819,1,238,0,0.432370," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{32 \, {\left(\cos\left(d x + c\right)^{3} - \frac{9 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} - 9 \, \cos\left(d x + c\right)\right)} a^{4} + {\left(8 \, \tan\left(d x + c\right)^{3} + 105 \, d x + 105 \, c - \frac{3 \, {\left(13 \, \tan\left(d x + c\right)^{3} + 11 \, \tan\left(d x + c\right)\right)}}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 72 \, \tan\left(d x + c\right)\right)} a^{4} + 24 \, {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{4} + 8 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{4} - 32 \, a^{4} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)}}{24 \, d}"," ",0,"1/24*(32*(cos(d*x + c)^3 - (9*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 - 9*cos(d*x + c))*a^4 + (8*tan(d*x + c)^3 + 105*d*x + 105*c - 3*(13*tan(d*x + c)^3 + 11*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 72*tan(d*x + c))*a^4 + 24*(2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^4 + 8*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^4 - 32*a^4*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)))/d","A",0
820,1,158,0,0.421771," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2*(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{2 \, a^{4} \tan\left(d x + c\right)^{3} + {\left(2 \, \tan\left(d x + c\right)^{3} + 15 \, d x + 15 \, c - \frac{3 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 12 \, \tan\left(d x + c\right)\right)} a^{4} + 12 \, {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} a^{4} - 8 \, a^{4} {\left(\frac{6 \, \cos\left(d x + c\right)^{2} - 1}{\cos\left(d x + c\right)^{3}} + 3 \, \cos\left(d x + c\right)\right)} - \frac{8 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} a^{4}}{\cos\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(2*a^4*tan(d*x + c)^3 + (2*tan(d*x + c)^3 + 15*d*x + 15*c - 3*tan(d*x + c)/(tan(d*x + c)^2 + 1) - 12*tan(d*x + c))*a^4 + 12*(tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*a^4 - 8*a^4*((6*cos(d*x + c)^2 - 1)/cos(d*x + c)^3 + 3*cos(d*x + c)) - 8*(3*cos(d*x + c)^2 - 1)*a^4/cos(d*x + c)^3)/d","A",0
821,1,400,0,0.421581," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(\frac{\frac{81 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{78 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{172 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{26 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{22 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{70 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{20 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{30 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{15 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 48}{a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{2 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{4 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}\right)}}{15 \, d}"," ",0,"-2/15*((81*sin(d*x + c)/(cos(d*x + c) + 1) - 78*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 172*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 26*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 22*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 70*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 20*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 30*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 15*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 48)/(a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 2*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 4*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
822,1,318,0,0.426635," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{46 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{13 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{100 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{35 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{30 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 8}{a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{15 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}\right)}}{15 \, d}"," ",0,"2/15*((sin(d*x + c)/(cos(d*x + c) + 1) - 46*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 13*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 100*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 35*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 30*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8)/(a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 15*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
823,1,214,0,0.326377," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{16 \, {\left(\frac{2 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + 1\right)}}{15 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"-16/15*(2*sin(d*x + c)/(cos(d*x + c) + 1) - 2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
824,1,234,0,0.336693," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, {\left(\frac{2 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{15 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 1\right)}}{15 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"-4/15*(2*sin(d*x + c)/(cos(d*x + c) + 1) - 2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 15*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
825,1,254,0,0.344780," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{2 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 1\right)}}{15 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"4/15*(2*sin(d*x + c)/(cos(d*x + c) + 1) - 2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
826,1,274,0,0.332851," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{5 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{10 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 3\right)}}{15 \, {\left(a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}\right)} d}"," ",0,"2/15*(6*sin(d*x + c)/(cos(d*x + c) + 1) + 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 5*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 10*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 3)/((a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8)*d)","B",0
827,1,320,0,0.337567," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{31 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{31 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{73 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{25 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{65 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{15 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{15 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 23\right)}}{a + \frac{2 \, a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{6 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{6 \, a \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{2 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}}} + \frac{15 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a}}{15 \, d}"," ",0,"1/15*(2*(31*sin(d*x + c)/(cos(d*x + c) + 1) - 31*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 73*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 25*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 65*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 15*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 15*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 23)/(a + 2*a*sin(d*x + c)/(cos(d*x + c) + 1) - 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 6*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 6*a*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 2*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8) + 15*log(sin(d*x + c)/(cos(d*x + c) + 1))/a)/d","B",0
828,1,379,0,0.335320," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\frac{122 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{26 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{454 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{252 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{510 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{330 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{210 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{195 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 15}{\frac{a \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2 \, a \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2 \, a \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{6 \, a \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{6 \, a \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{2 \, a \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{2 \, a \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{a \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}}} + \frac{30 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a} - \frac{15 \, \sin\left(d x + c\right)}{a {\left(\cos\left(d x + c\right) + 1\right)}}}{30 \, d}"," ",0,"-1/30*((122*sin(d*x + c)/(cos(d*x + c) + 1) - 26*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 454*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 252*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 510*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 330*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 210*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 195*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 15)/(a*sin(d*x + c)/(cos(d*x + c) + 1) + 2*a*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2*a*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 6*a*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 6*a*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 2*a*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 2*a*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - a*sin(d*x + c)^9/(cos(d*x + c) + 1)^9) + 30*log(sin(d*x + c)/(cos(d*x + c) + 1))/a - 15*sin(d*x + c)/(a*(cos(d*x + c) + 1)))/d","B",0
829,1,507,0,0.434766," ","integrate(sec(d*x+c)^4*sin(d*x+c)^7/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(\frac{\frac{759 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{444 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1249 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1816 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{454 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{616 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1274 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{560 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{385 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{420 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{105 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + 216}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{11 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{11 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} + \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{105 \, d}"," ",0,"-4/105*((759*sin(d*x + c)/(cos(d*x + c) + 1) + 444*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1249*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1816*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 454*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 616*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1274*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 560*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 385*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 420*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 105*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 216)/(a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 4*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 11*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 8*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 11*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 4*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 4*a^2*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) + 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
830,1,421,0,0.427931," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{279 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{132 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1048 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{364 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{1554 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{980 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{280 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{420 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{105 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 96}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{105 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}\right)}}{105 \, d}"," ",0,"2/105*((279*sin(d*x + c)/(cos(d*x + c) + 1) - 132*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1048*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 364*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1554*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 980*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 280*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 420*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 105*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 96)/(a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 105*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
831,1,296,0,0.338860," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{16 \, {\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + 1\right)}}{21 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d}"," ",0,"-16/21*(4*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 1)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d)","B",0
832,1,316,0,0.339742," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{32 \, {\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{21 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 1\right)}}{105 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d}"," ",0,"-32/105*(4*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 21*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d)","B",0
833,1,336,0,0.338555," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{4 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{91 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{84 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{105 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 1\right)}}{105 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d}"," ",0,"4/105*(4*sin(d*x + c)/(cos(d*x + c) + 1) + 3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 91*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 84*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 105*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d)","B",0
834,1,356,0,0.340236," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{12 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{9 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{11 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{7 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{42 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{35 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{35 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 3\right)}}{105 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d}"," ",0,"8/105*(12*sin(d*x + c)/(cos(d*x + c) + 1) + 9*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 11*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 7*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 42*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 35*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 35*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 3)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d)","B",0
835,1,376,0,0.334847," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{36 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{132 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{68 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{14 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{84 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{140 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{140 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{105 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 9\right)}}{105 \, {\left(a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}\right)} d}"," ",0,"2/105*(36*sin(d*x + c)/(cos(d*x + c) + 1) + 132*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 68*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 14*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 84*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 140*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 140*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 105*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 9)/((a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10)*d)","B",0
836,1,422,0,0.338187," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{554 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{258 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1108 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{1204 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{504 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{1470 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{420 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{210 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 191\right)}}{a^{2} + \frac{4 \, a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}}} + \frac{105 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{105 \, d}"," ",0,"1/105*(2*(554*sin(d*x + c)/(cos(d*x + c) + 1) + 258*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1108*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 1204*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 504*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1470*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 420*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 315*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 210*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 191)/(a^2 + 4*a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 3*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 8*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 14*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 8*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 4*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10) + 105*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
837,1,481,0,0.337511," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{\frac{1828 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{3847 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1656 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{12734 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{7952 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{9702 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{12600 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{315 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{5460 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2205 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 105}{\frac{a^{2} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{a^{2} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}}} + \frac{420 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}} - \frac{105 \, \sin\left(d x + c\right)}{a^{2} {\left(\cos\left(d x + c\right) + 1\right)}}}{210 \, d}"," ",0,"-1/210*((1828*sin(d*x + c)/(cos(d*x + c) + 1) + 3847*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1656*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 12734*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 7952*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 9702*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 12600*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 315*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 5460*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2205*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 105)/(a^2*sin(d*x + c)/(cos(d*x + c) + 1) + 4*a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 3*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 8*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 14*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 14*a^2*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 8*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 3*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 4*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - a^2*sin(d*x + c)^11/(cos(d*x + c) + 1)^11) + 420*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2 - 105*sin(d*x + c)/(a^2*(cos(d*x + c) + 1)))/d","B",0
838,1,526,0,0.342657," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{\frac{420 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{15173 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{38432 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{894 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{95344 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{77182 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{61992 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{101115 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{11340 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{33495 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{14280 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - 105}{\frac{a^{2} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{4 \, a^{2} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{3 \, a^{2} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{8 \, a^{2} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{14 \, a^{2} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{14 \, a^{2} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{8 \, a^{2} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{3 \, a^{2} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{4 \, a^{2} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{2} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} - \frac{105 \, {\left(\frac{8 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} - \frac{\sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}}\right)}}{a^{2}} + \frac{4620 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{2}}}{840 \, d}"," ",0,"1/840*((420*sin(d*x + c)/(cos(d*x + c) + 1) + 15173*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 38432*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 894*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 95344*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 77182*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 61992*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 101115*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 11340*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 33495*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 14280*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 105)/(a^2*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 4*a^2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 3*a^2*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 8*a^2*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 14*a^2*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 14*a^2*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 8*a^2*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 3*a^2*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 4*a^2*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^2*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) - 105*(8*sin(d*x + c)/(cos(d*x + c) + 1) - sin(d*x + c)^2/(cos(d*x + c) + 1)^2)/a^2 + 4620*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^2)/d","B",0
839,1,487,0,0.437613," ","integrate(sec(d*x+c)^4*sin(d*x+c)^7/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{\frac{1893 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{2526 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{2939 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{9936 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{3546 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{11172 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{9702 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} - \frac{3675 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{1890 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{315 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + 368}{a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} + \frac{315 \, \arctan\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}\right)}}{315 \, d}"," ",0,"2/315*((1893*sin(d*x + c)/(cos(d*x + c) + 1) + 2526*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 2939*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 9936*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 3546*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 11172*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 9702*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 - 3675*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 1890*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 315*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 368)/(a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) + 315*arctan(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
840,1,362,0,0.343022," ","integrate(sec(d*x+c)^4*sin(d*x+c)^6/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{32 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + 1\right)}}{63 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"-32/63*(6*sin(d*x + c)/(cos(d*x + c) + 1) + 12*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 1)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
841,1,382,0,0.342567," ","integrate(sec(d*x+c)^4*sin(d*x+c)^5/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{16 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{42 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + 1\right)}}{63 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"-16/63*(6*sin(d*x + c)/(cos(d*x + c) + 1) + 12*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 42*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
842,1,402,0,0.335468," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{16 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{162 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{126 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} - \frac{126 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + 1\right)}}{315 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"-16/315*(6*sin(d*x + c)/(cos(d*x + c) + 1) + 12*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 162*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 126*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 - 126*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 1)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
843,1,422,0,0.342197," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{18 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{18 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{84 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{54 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{45 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + 1\right)}}{45 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"4/45*(6*sin(d*x + c)/(cos(d*x + c) + 1) + 12*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 18*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 18*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 84*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 54*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 45*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 1)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
844,1,442,0,0.343249," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{66 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{132 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{232 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{18 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{108 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{84 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{504 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{315 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{210 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 11\right)}}{315 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"4/315*(66*sin(d*x + c)/(cos(d*x + c) + 1) + 132*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 232*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 18*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 108*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 84*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 504*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 315*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 210*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 11)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
845,1,442,0,0.339963," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, {\left(\frac{6 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{75 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{128 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{162 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{42 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{189 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{126 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{63 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 1\right)}}{63 \, {\left(a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}\right)} d}"," ",0,"2/63*(6*sin(d*x + c)/(cos(d*x + c) + 1) + 75*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 128*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 162*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 42*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 189*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 126*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 63*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 1)/((a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12)*d)","B",0
846,1,508,0,0.342752," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(\frac{3063 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{4866 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} - \frac{1289 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{11736 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{10566 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{5292 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{13482 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{6300 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2625 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{3150 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{945 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + 668\right)}}{a^{3} + \frac{6 \, a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}}} + \frac{315 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}}}{315 \, d}"," ",0,"1/315*(2*(3063*sin(d*x + c)/(cos(d*x + c) + 1) + 4866*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 - 1289*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 11736*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 10566*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 5292*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 13482*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 6300*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2625*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 3150*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 945*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 668)/(a^3 + 6*a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 12*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 2*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 27*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 36*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 36*a^3*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 27*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 - 2*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 12*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 6*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12) + 315*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3)/d","B",0
847,1,567,0,0.346732," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{\frac{\frac{8786 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{35076 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{43062 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{41753 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{152172 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{99072 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{93324 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{157689 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{44730 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{50820 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{42210 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{10395 \, \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} + 315}{\frac{a^{3} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{6 \, a^{3} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{12 \, a^{3} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2 \, a^{3} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{27 \, a^{3} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{36 \, a^{3} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{36 \, a^{3} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{27 \, a^{3} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} - \frac{2 \, a^{3} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{12 \, a^{3} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{6 \, a^{3} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{a^{3} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}}} + \frac{1890 \, \log\left(\frac{\sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1}\right)}{a^{3}} - \frac{315 \, \sin\left(d x + c\right)}{a^{3} {\left(\cos\left(d x + c\right) + 1\right)}}}{630 \, d}"," ",0,"-1/630*((8786*sin(d*x + c)/(cos(d*x + c) + 1) + 35076*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 43062*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 41753*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 152172*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 99072*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 93324*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 157689*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 44730*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 50820*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 42210*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 10395*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 + 315)/(a^3*sin(d*x + c)/(cos(d*x + c) + 1) + 6*a^3*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 12*a^3*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2*a^3*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 27*a^3*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 36*a^3*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 36*a^3*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 27*a^3*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 - 2*a^3*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 12*a^3*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 6*a^3*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - a^3*sin(d*x + c)^13/(cos(d*x + c) + 1)^13) + 1890*log(sin(d*x + c)/(cos(d*x + c) + 1))/a^3 - 315*sin(d*x + c)/(a^3*(cos(d*x + c) + 1)))/d","B",0
848,1,488,0,0.351464," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{32 \, {\left(\frac{16 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{50 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{64 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{22 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{517 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{726 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{1650 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{924 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{693 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + 2\right)}}{3465 \, {\left(a^{4} + \frac{8 \, a^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{25 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{32 \, a^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{11 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{88 \, a^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{99 \, a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{99 \, a^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{88 \, a^{4} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{11 \, a^{4} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{32 \, a^{4} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{25 \, a^{4} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{8 \, a^{4} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{a^{4} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}\right)} d}"," ",0,"32/3465*(16*sin(d*x + c)/(cos(d*x + c) + 1) + 50*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 64*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 22*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 517*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 726*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 1650*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 924*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 693*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 2)/((a^4 + 8*a^4*sin(d*x + c)/(cos(d*x + c) + 1) + 25*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 32*a^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 11*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 88*a^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 99*a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 99*a^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 88*a^4*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 11*a^4*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 32*a^4*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 25*a^4*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 8*a^4*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - a^4*sin(d*x + c)^14/(cos(d*x + c) + 1)^14)*d)","B",0
849,1,508,0,0.345065," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{4 \, {\left(\frac{488 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{1525 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{1952 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{2794 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{176 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} + \frac{4818 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{5280 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{10857 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{5544 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{3465 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + 61\right)}}{3465 \, {\left(a^{4} + \frac{8 \, a^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{25 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{32 \, a^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{11 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{88 \, a^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{99 \, a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{99 \, a^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{88 \, a^{4} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{11 \, a^{4} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{32 \, a^{4} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{25 \, a^{4} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{8 \, a^{4} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{a^{4} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}\right)} d}"," ",0,"4/3465*(488*sin(d*x + c)/(cos(d*x + c) + 1) + 1525*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 1952*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 2794*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 176*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 + 4818*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 5280*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 10857*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 5544*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 3465*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 61)/((a^4 + 8*a^4*sin(d*x + c)/(cos(d*x + c) + 1) + 25*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 32*a^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 11*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 88*a^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 99*a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 99*a^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 88*a^4*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 11*a^4*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 32*a^4*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 25*a^4*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 8*a^4*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - a^4*sin(d*x + c)^14/(cos(d*x + c) + 1)^14)*d)","B",0
850,1,528,0,0.346963," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+a*sin(d*x+c))^4,x, algorithm=""maxima"")","\frac{8 \, {\left(\frac{16 \, \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{50 \, \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{141 \, \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} + \frac{132 \, \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} + \frac{132 \, \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{44 \, \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{110 \, \sin\left(d x + c\right)^{7}}{{\left(\cos\left(d x + c\right) + 1\right)}^{7}} + \frac{154 \, \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{308 \, \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{154 \, \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} + \frac{77 \, \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} + 2\right)}}{231 \, {\left(a^{4} + \frac{8 \, a^{4} \sin\left(d x + c\right)}{\cos\left(d x + c\right) + 1} + \frac{25 \, a^{4} \sin\left(d x + c\right)^{2}}{{\left(\cos\left(d x + c\right) + 1\right)}^{2}} + \frac{32 \, a^{4} \sin\left(d x + c\right)^{3}}{{\left(\cos\left(d x + c\right) + 1\right)}^{3}} - \frac{11 \, a^{4} \sin\left(d x + c\right)^{4}}{{\left(\cos\left(d x + c\right) + 1\right)}^{4}} - \frac{88 \, a^{4} \sin\left(d x + c\right)^{5}}{{\left(\cos\left(d x + c\right) + 1\right)}^{5}} - \frac{99 \, a^{4} \sin\left(d x + c\right)^{6}}{{\left(\cos\left(d x + c\right) + 1\right)}^{6}} + \frac{99 \, a^{4} \sin\left(d x + c\right)^{8}}{{\left(\cos\left(d x + c\right) + 1\right)}^{8}} + \frac{88 \, a^{4} \sin\left(d x + c\right)^{9}}{{\left(\cos\left(d x + c\right) + 1\right)}^{9}} + \frac{11 \, a^{4} \sin\left(d x + c\right)^{10}}{{\left(\cos\left(d x + c\right) + 1\right)}^{10}} - \frac{32 \, a^{4} \sin\left(d x + c\right)^{11}}{{\left(\cos\left(d x + c\right) + 1\right)}^{11}} - \frac{25 \, a^{4} \sin\left(d x + c\right)^{12}}{{\left(\cos\left(d x + c\right) + 1\right)}^{12}} - \frac{8 \, a^{4} \sin\left(d x + c\right)^{13}}{{\left(\cos\left(d x + c\right) + 1\right)}^{13}} - \frac{a^{4} \sin\left(d x + c\right)^{14}}{{\left(\cos\left(d x + c\right) + 1\right)}^{14}}\right)} d}"," ",0,"8/231*(16*sin(d*x + c)/(cos(d*x + c) + 1) + 50*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 141*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 + 132*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 + 132*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 44*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 110*sin(d*x + c)^7/(cos(d*x + c) + 1)^7 + 154*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 308*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 154*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 + 77*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 + 2)/((a^4 + 8*a^4*sin(d*x + c)/(cos(d*x + c) + 1) + 25*a^4*sin(d*x + c)^2/(cos(d*x + c) + 1)^2 + 32*a^4*sin(d*x + c)^3/(cos(d*x + c) + 1)^3 - 11*a^4*sin(d*x + c)^4/(cos(d*x + c) + 1)^4 - 88*a^4*sin(d*x + c)^5/(cos(d*x + c) + 1)^5 - 99*a^4*sin(d*x + c)^6/(cos(d*x + c) + 1)^6 + 99*a^4*sin(d*x + c)^8/(cos(d*x + c) + 1)^8 + 88*a^4*sin(d*x + c)^9/(cos(d*x + c) + 1)^9 + 11*a^4*sin(d*x + c)^10/(cos(d*x + c) + 1)^10 - 32*a^4*sin(d*x + c)^11/(cos(d*x + c) + 1)^11 - 25*a^4*sin(d*x + c)^12/(cos(d*x + c) + 1)^12 - 8*a^4*sin(d*x + c)^13/(cos(d*x + c) + 1)^13 - a^4*sin(d*x + c)^14/(cos(d*x + c) + 1)^14)*d)","B",0
851,1,106,0,0.317683," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{8 \, a \sin\left(d x + c\right)^{2} + 9 \, a \log\left(\sin\left(d x + c\right) + 1\right) + 39 \, a \log\left(\sin\left(d x + c\right) - 1\right) + 16 \, a \sin\left(d x + c\right) - \frac{2 \, {\left(9 \, a \sin\left(d x + c\right)^{2} + 3 \, a \sin\left(d x + c\right) - 10 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"-1/16*(8*a*sin(d*x + c)^2 + 9*a*log(sin(d*x + c) + 1) + 39*a*log(sin(d*x + c) - 1) + 16*a*sin(d*x + c) - 2*(9*a*sin(d*x + c)^2 + 3*a*sin(d*x + c) - 10*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
852,1,95,0,0.311857," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{7 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 23 \, a \log\left(\sin\left(d x + c\right) - 1\right) - 16 \, a \sin\left(d x + c\right) + \frac{2 \, {\left(9 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - 6 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"1/16*(7*a*log(sin(d*x + c) + 1) - 23*a*log(sin(d*x + c) - 1) - 16*a*sin(d*x + c) + 2*(9*a*sin(d*x + c)^2 - a*sin(d*x + c) - 6*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
853,1,86,0,0.313461," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, a \log\left(\sin\left(d x + c\right) + 1\right) + 11 \, a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(5 \, a \sin\left(d x + c\right)^{2} + 3 \, a \sin\left(d x + c\right) - 6 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"-1/16*(5*a*log(sin(d*x + c) + 1) + 11*a*log(sin(d*x + c) - 1) - 2*(5*a*sin(d*x + c)^2 + 3*a*sin(d*x + c) - 6*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
854,1,86,0,0.311028," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, a \log\left(\sin\left(d x + c\right) - 1\right) + \frac{2 \, {\left(5 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - 2 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"1/16*(3*a*log(sin(d*x + c) + 1) - 3*a*log(sin(d*x + c) - 1) + 2*(5*a*sin(d*x + c)^2 - a*sin(d*x + c) - 2*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
855,1,84,0,0.310326," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(d x + c\right) + 1\right) - a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(a \sin\left(d x + c\right)^{2} + 3 \, a \sin\left(d x + c\right) - 2 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"-1/16*(a*log(sin(d*x + c) + 1) - a*log(sin(d*x + c) - 1) - 2*(a*sin(d*x + c)^2 + 3*a*sin(d*x + c) - 2*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
856,1,84,0,0.311601," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(d x + c\right) + 1\right) - a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) + 2 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"-1/16*(a*log(sin(d*x + c) + 1) - a*log(sin(d*x + c) - 1) - 2*(a*sin(d*x + c)^2 - a*sin(d*x + c) + 2*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
857,1,95,0,0.317054," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, a \log\left(\sin\left(d x + c\right) + 1\right) + 11 \, a \log\left(\sin\left(d x + c\right) - 1\right) - 16 \, a \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, {\left(3 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) - 6 \, a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"-1/16*(5*a*log(sin(d*x + c) + 1) + 11*a*log(sin(d*x + c) - 1) - 16*a*log(sin(d*x + c)) + 2*(3*a*sin(d*x + c)^2 + a*sin(d*x + c) - 6*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
858,1,114,0,0.347227," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{7 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 23 \, a \log\left(\sin\left(d x + c\right) - 1\right) + 16 \, a \log\left(\sin\left(d x + c\right)\right) - \frac{2 \, {\left(15 \, a \sin\left(d x + c\right)^{3} - 11 \, a \sin\left(d x + c\right)^{2} - 14 \, a \sin\left(d x + c\right) + 8 \, a\right)}}{\sin\left(d x + c\right)^{4} - \sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} + \sin\left(d x + c\right)}}{16 \, d}"," ",0,"1/16*(7*a*log(sin(d*x + c) + 1) - 23*a*log(sin(d*x + c) - 1) + 16*a*log(sin(d*x + c)) - 2*(15*a*sin(d*x + c)^3 - 11*a*sin(d*x + c)^2 - 14*a*sin(d*x + c) + 8*a)/(sin(d*x + c)^4 - sin(d*x + c)^3 - sin(d*x + c)^2 + sin(d*x + c)))/d","A",0
859,1,127,0,0.313173," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{9 \, a \log\left(\sin\left(d x + c\right) + 1\right) + 39 \, a \log\left(\sin\left(d x + c\right) - 1\right) - 48 \, a \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, {\left(15 \, a \sin\left(d x + c\right)^{4} - 3 \, a \sin\left(d x + c\right)^{3} - 22 \, a \sin\left(d x + c\right)^{2} + 4 \, a \sin\left(d x + c\right) + 4 \, a\right)}}{\sin\left(d x + c\right)^{5} - \sin\left(d x + c\right)^{4} - \sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"-1/16*(9*a*log(sin(d*x + c) + 1) + 39*a*log(sin(d*x + c) - 1) - 48*a*log(sin(d*x + c)) + 2*(15*a*sin(d*x + c)^4 - 3*a*sin(d*x + c)^3 - 22*a*sin(d*x + c)^2 + 4*a*sin(d*x + c) + 4*a)/(sin(d*x + c)^5 - sin(d*x + c)^4 - sin(d*x + c)^3 + sin(d*x + c)^2))/d","A",0
860,1,138,0,0.365942," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{33 \, a \log\left(\sin\left(d x + c\right) + 1\right) - 177 \, a \log\left(\sin\left(d x + c\right) - 1\right) + 144 \, a \log\left(\sin\left(d x + c\right)\right) - \frac{2 \, {\left(105 \, a \sin\left(d x + c\right)^{5} - 69 \, a \sin\left(d x + c\right)^{4} - 106 \, a \sin\left(d x + c\right)^{3} + 52 \, a \sin\left(d x + c\right)^{2} + 4 \, a \sin\left(d x + c\right) + 8 \, a\right)}}{\sin\left(d x + c\right)^{6} - \sin\left(d x + c\right)^{5} - \sin\left(d x + c\right)^{4} + \sin\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(33*a*log(sin(d*x + c) + 1) - 177*a*log(sin(d*x + c) - 1) + 144*a*log(sin(d*x + c)) - 2*(105*a*sin(d*x + c)^5 - 69*a*sin(d*x + c)^4 - 106*a*sin(d*x + c)^3 + 52*a*sin(d*x + c)^2 + 4*a*sin(d*x + c) + 8*a)/(sin(d*x + c)^6 - sin(d*x + c)^5 - sin(d*x + c)^4 + sin(d*x + c)^3))/d","A",0
861,1,96,0,0.420889," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, a^{2} \sin\left(d x + c\right)^{2} + a^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 31 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) + 16 \, a^{2} \sin\left(d x + c\right) - \frac{2 \, {\left(9 \, a^{2} \sin\left(d x + c\right) - 8 \, a^{2}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"-1/8*(4*a^2*sin(d*x + c)^2 + a^2*log(sin(d*x + c) + 1) + 31*a^2*log(sin(d*x + c) - 1) + 16*a^2*sin(d*x + c) - 2*(9*a^2*sin(d*x + c) - 8*a^2)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
862,1,83,0,0.313813," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 17 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - 8 \, a^{2} \sin\left(d x + c\right) + \frac{2 \, {\left(7 \, a^{2} \sin\left(d x + c\right) - 6 \, a^{2}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"1/8*(a^2*log(sin(d*x + c) + 1) - 17*a^2*log(sin(d*x + c) - 1) - 8*a^2*sin(d*x + c) + 2*(7*a^2*sin(d*x + c) - 6*a^2)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
863,1,72,0,0.315766," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 7 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(5 \, a^{2} \sin\left(d x + c\right) - 4 \, a^{2}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"-1/8*(a^2*log(sin(d*x + c) + 1) + 7*a^2*log(sin(d*x + c) - 1) - 2*(5*a^2*sin(d*x + c) - 4*a^2)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
864,1,72,0,0.309921," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - a^{2} \log\left(\sin\left(d x + c\right) - 1\right) + \frac{2 \, {\left(3 \, a^{2} \sin\left(d x + c\right) - 2 \, a^{2}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"1/8*(a^2*log(sin(d*x + c) + 1) - a^2*log(sin(d*x + c) - 1) + 2*(3*a^2*sin(d*x + c) - 2*a^2)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
865,1,64,0,0.312149," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, a^{2} \sin\left(d x + c\right)}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"-1/8*(a^2*log(sin(d*x + c) + 1) - a^2*log(sin(d*x + c) - 1) - 2*a^2*sin(d*x + c)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
866,1,84,0,0.480393," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 7 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - 8 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, {\left(3 \, a^{2} \sin\left(d x + c\right) - 4 \, a^{2}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"-1/8*(a^2*log(sin(d*x + c) + 1) + 7*a^2*log(sin(d*x + c) - 1) - 8*a^2*log(sin(d*x + c)) + 2*(3*a^2*sin(d*x + c) - 4*a^2)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
867,1,104,0,0.314791," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 17 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) + 16 \, a^{2} \log\left(\sin\left(d x + c\right)\right) - \frac{2 \, {\left(9 \, a^{2} \sin\left(d x + c\right)^{2} - 14 \, a^{2} \sin\left(d x + c\right) + 4 \, a^{2}\right)}}{\sin\left(d x + c\right)^{3} - 2 \, \sin\left(d x + c\right)^{2} + \sin\left(d x + c\right)}}{8 \, d}"," ",0,"1/8*(a^2*log(sin(d*x + c) + 1) - 17*a^2*log(sin(d*x + c) - 1) + 16*a^2*log(sin(d*x + c)) - 2*(9*a^2*sin(d*x + c)^2 - 14*a^2*sin(d*x + c) + 4*a^2)/(sin(d*x + c)^3 - 2*sin(d*x + c)^2 + sin(d*x + c)))/d","A",0
868,1,119,0,0.310076," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a^{2} \log\left(\sin\left(d x + c\right) + 1\right) + 31 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - 32 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, {\left(15 \, a^{2} \sin\left(d x + c\right)^{3} - 22 \, a^{2} \sin\left(d x + c\right)^{2} + 4 \, a^{2} \sin\left(d x + c\right) + 2 \, a^{2}\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"-1/8*(a^2*log(sin(d*x + c) + 1) + 31*a^2*log(sin(d*x + c) - 1) - 32*a^2*log(sin(d*x + c)) + 2*(15*a^2*sin(d*x + c)^3 - 22*a^2*sin(d*x + c)^2 + 4*a^2*sin(d*x + c) + 2*a^2)/(sin(d*x + c)^4 - 2*sin(d*x + c)^3 + sin(d*x + c)^2))/d","A",0
869,1,133,0,0.446725," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 147 \, a^{2} \log\left(\sin\left(d x + c\right) - 1\right) + 144 \, a^{2} \log\left(\sin\left(d x + c\right)\right) - \frac{2 \, {\left(75 \, a^{2} \sin\left(d x + c\right)^{4} - 114 \, a^{2} \sin\left(d x + c\right)^{3} + 28 \, a^{2} \sin\left(d x + c\right)^{2} + 4 \, a^{2} \sin\left(d x + c\right) + 4 \, a^{2}\right)}}{\sin\left(d x + c\right)^{5} - 2 \, \sin\left(d x + c\right)^{4} + \sin\left(d x + c\right)^{3}}}{24 \, d}"," ",0,"1/24*(3*a^2*log(sin(d*x + c) + 1) - 147*a^2*log(sin(d*x + c) - 1) + 144*a^2*log(sin(d*x + c)) - 2*(75*a^2*sin(d*x + c)^4 - 114*a^2*sin(d*x + c)^3 + 28*a^2*sin(d*x + c)^2 + 4*a^2*sin(d*x + c) + 4*a^2)/(sin(d*x + c)^5 - 2*sin(d*x + c)^4 + sin(d*x + c)^3))/d","A",0
870,1,96,0,0.430260," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, a^{3} \sin\left(d x + c\right)^{3} + 9 \, a^{3} \sin\left(d x + c\right)^{2} + 60 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + 36 \, a^{3} \sin\left(d x + c\right) - \frac{3 \, {\left(10 \, a^{3} \sin\left(d x + c\right) - 9 \, a^{3}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{6 \, d}"," ",0,"-1/6*(2*a^3*sin(d*x + c)^3 + 9*a^3*sin(d*x + c)^2 + 60*a^3*log(sin(d*x + c) - 1) + 36*a^3*sin(d*x + c) - 3*(10*a^3*sin(d*x + c) - 9*a^3)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
871,1,82,0,0.311044," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{a^{3} \sin\left(d x + c\right)^{2} + 12 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, a^{3} \sin\left(d x + c\right) - \frac{8 \, a^{3} \sin\left(d x + c\right) - 7 \, a^{3}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{2 \, d}"," ",0,"-1/2*(a^3*sin(d*x + c)^2 + 12*a^3*log(sin(d*x + c) - 1) + 6*a^3*sin(d*x + c) - (8*a^3*sin(d*x + c) - 7*a^3)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
872,1,70,0,0.354478," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{6 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + 2 \, a^{3} \sin\left(d x + c\right) - \frac{6 \, a^{3} \sin\left(d x + c\right) - 5 \, a^{3}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{2 \, d}"," ",0,"-1/2*(6*a^3*log(sin(d*x + c) - 1) + 2*a^3*sin(d*x + c) - (6*a^3*sin(d*x + c) - 5*a^3)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
873,1,59,0,0.305976," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{4 \, a^{3} \sin\left(d x + c\right) - 3 \, a^{3}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{2 \, d}"," ",0,"-1/2*(2*a^3*log(sin(d*x + c) - 1) - (4*a^3*sin(d*x + c) - 3*a^3)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
874,1,42,0,0.330324," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{2 \, a^{3} \sin\left(d x + c\right) - a^{3}}{2 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)} d}"," ",0,"1/2*(2*a^3*sin(d*x + c) - a^3)/((sin(d*x + c)^2 - 2*sin(d*x + c) + 1)*d)","A",0
875,1,70,0,0.484834," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) - 2 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, a^{3} \sin\left(d x + c\right) - 3 \, a^{3}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{2 \, d}"," ",0,"-1/2*(2*a^3*log(sin(d*x + c) - 1) - 2*a^3*log(sin(d*x + c)) + (2*a^3*sin(d*x + c) - 3*a^3)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
876,1,90,0,0.318357," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{6 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) - 6 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + \frac{6 \, a^{3} \sin\left(d x + c\right)^{2} - 9 \, a^{3} \sin\left(d x + c\right) + 2 \, a^{3}}{\sin\left(d x + c\right)^{3} - 2 \, \sin\left(d x + c\right)^{2} + \sin\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(6*a^3*log(sin(d*x + c) - 1) - 6*a^3*log(sin(d*x + c)) + (6*a^3*sin(d*x + c)^2 - 9*a^3*sin(d*x + c) + 2*a^3)/(sin(d*x + c)^3 - 2*sin(d*x + c)^2 + sin(d*x + c)))/d","A",0
877,1,103,0,0.318061," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+a*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{12 \, a^{3} \log\left(\sin\left(d x + c\right) - 1\right) - 12 \, a^{3} \log\left(\sin\left(d x + c\right)\right) + \frac{12 \, a^{3} \sin\left(d x + c\right)^{3} - 18 \, a^{3} \sin\left(d x + c\right)^{2} + 4 \, a^{3} \sin\left(d x + c\right) + a^{3}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(12*a^3*log(sin(d*x + c) - 1) - 12*a^3*log(sin(d*x + c)) + (12*a^3*sin(d*x + c)^3 - 18*a^3*sin(d*x + c)^2 + 4*a^3*sin(d*x + c) + a^3)/(sin(d*x + c)^4 - 2*sin(d*x + c)^3 + sin(d*x + c)^2))/d","A",0
878,1,209,0,0.326869," ","integrate(sec(d*x+c)^7*sin(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(2295 \, \sin\left(d x + c\right)^{6} + 375 \, \sin\left(d x + c\right)^{5} - 5480 \, \sin\left(d x + c\right)^{4} - 680 \, \sin\left(d x + c\right)^{3} + 4473 \, \sin\left(d x + c\right)^{2} + 313 \, \sin\left(d x + c\right) - 1232\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{128 \, {\left(2 \, \sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} + 30 \, \sin\left(d x + c\right)\right)}}{a} + \frac{5385 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{1545 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(2295*sin(d*x + c)^6 + 375*sin(d*x + c)^5 - 5480*sin(d*x + c)^4 - 680*sin(d*x + c)^3 + 4473*sin(d*x + c)^2 + 313*sin(d*x + c) - 1232)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 128*(2*sin(d*x + c)^3 - 3*sin(d*x + c)^2 + 30*sin(d*x + c))/a + 5385*log(sin(d*x + c) + 1)/a - 1545*log(sin(d*x + c) - 1)/a)/d","A",0
879,1,197,0,0.395291," ","integrate(sec(d*x+c)^7*sin(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(975 \, \sin\left(d x + c\right)^{6} - 945 \, \sin\left(d x + c\right)^{5} - 3240 \, \sin\left(d x + c\right)^{4} + 1560 \, \sin\left(d x + c\right)^{3} + 3489 \, \sin\left(d x + c\right)^{2} - 671 \, \sin\left(d x + c\right) - 1232\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} + \frac{384 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)}}{a} + \frac{2865 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{975 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"1/768*(2*(975*sin(d*x + c)^6 - 945*sin(d*x + c)^5 - 3240*sin(d*x + c)^4 + 1560*sin(d*x + c)^3 + 3489*sin(d*x + c)^2 - 671*sin(d*x + c) - 1232)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) + 384*(sin(d*x + c)^2 - 2*sin(d*x + c))/a + 2865*log(sin(d*x + c) + 1)/a + 975*log(sin(d*x + c) - 1)/a)/d","A",0
880,1,186,0,0.333685," ","integrate(sec(d*x+c)^7*sin(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(975 \, \sin\left(d x + c\right)^{6} + 207 \, \sin\left(d x + c\right)^{5} - 2088 \, \sin\left(d x + c\right)^{4} - 360 \, \sin\left(d x + c\right)^{3} + 1569 \, \sin\left(d x + c\right)^{2} + 161 \, \sin\left(d x + c\right) - 400\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} + \frac{1329 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{561 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{768 \, \sin\left(d x + c\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(975*sin(d*x + c)^6 + 207*sin(d*x + c)^5 - 2088*sin(d*x + c)^4 - 360*sin(d*x + c)^3 + 1569*sin(d*x + c)^2 + 161*sin(d*x + c) - 400)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) + 1329*log(sin(d*x + c) + 1)/a - 561*log(sin(d*x + c) - 1)/a - 768*sin(d*x + c)/a)/d","A",0
881,1,175,0,0.323057," ","integrate(sec(d*x+c)^7*sin(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(279 \, \sin\left(d x + c\right)^{6} - 489 \, \sin\left(d x + c\right)^{5} - 1000 \, \sin\left(d x + c\right)^{4} + 728 \, \sin\left(d x + c\right)^{3} + 1113 \, \sin\left(d x + c\right)^{2} - 295 \, \sin\left(d x + c\right) - 400\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} + \frac{489 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{279 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"1/768*(2*(279*sin(d*x + c)^6 - 489*sin(d*x + c)^5 - 1000*sin(d*x + c)^4 + 728*sin(d*x + c)^3 + 1113*sin(d*x + c)^2 - 295*sin(d*x + c) - 400)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) + 489*log(sin(d*x + c) + 1)/a + 279*log(sin(d*x + c) - 1)/a)/d","A",0
882,1,175,0,0.321886," ","integrate(sec(d*x+c)^7*sin(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(279 \, \sin\left(d x + c\right)^{6} + 87 \, \sin\left(d x + c\right)^{5} - 424 \, \sin\left(d x + c\right)^{4} - 136 \, \sin\left(d x + c\right)^{3} + 249 \, \sin\left(d x + c\right)^{2} + 57 \, \sin\left(d x + c\right) - 48\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} + \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(279*sin(d*x + c)^6 + 87*sin(d*x + c)^5 - 424*sin(d*x + c)^4 - 136*sin(d*x + c)^3 + 249*sin(d*x + c)^2 + 57*sin(d*x + c) - 48)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) + 105*log(sin(d*x + c) + 1)/a - 105*log(sin(d*x + c) - 1)/a)/d","A",0
883,1,175,0,0.320672," ","integrate(sec(d*x+c)^7*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{6} - 177 \, \sin\left(d x + c\right)^{5} - 104 \, \sin\left(d x + c\right)^{4} + 184 \, \sin\left(d x + c\right)^{3} + 129 \, \sin\left(d x + c\right)^{2} - 63 \, \sin\left(d x + c\right) - 48\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"1/768*(2*(15*sin(d*x + c)^6 - 177*sin(d*x + c)^5 - 104*sin(d*x + c)^4 + 184*sin(d*x + c)^3 + 129*sin(d*x + c)^2 - 63*sin(d*x + c) - 48)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 15*log(sin(d*x + c) + 1)/a + 15*log(sin(d*x + c) - 1)/a)/d","A",0
884,1,173,0,0.318053," ","integrate(sec(d*x+c)^7*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{6} + 15 \, \sin\left(d x + c\right)^{5} + 88 \, \sin\left(d x + c\right)^{4} - 8 \, \sin\left(d x + c\right)^{3} - 63 \, \sin\left(d x + c\right)^{2} + \sin\left(d x + c\right) + 16\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(15*sin(d*x + c)^6 + 15*sin(d*x + c)^5 + 88*sin(d*x + c)^4 - 8*sin(d*x + c)^3 - 63*sin(d*x + c)^2 + sin(d*x + c) + 16)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 15*log(sin(d*x + c) + 1)/a + 15*log(sin(d*x + c) - 1)/a)/d","A",0
885,1,175,0,0.361546," ","integrate(sec(d*x+c)^7*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(9 \, \sin\left(d x + c\right)^{6} + 9 \, \sin\left(d x + c\right)^{5} - 24 \, \sin\left(d x + c\right)^{4} + 72 \, \sin\left(d x + c\right)^{3} + 39 \, \sin\left(d x + c\right)^{2} - 25 \, \sin\left(d x + c\right) - 16\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{9 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{9 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(9*sin(d*x + c)^6 + 9*sin(d*x + c)^5 - 24*sin(d*x + c)^4 + 72*sin(d*x + c)^3 + 39*sin(d*x + c)^2 - 25*sin(d*x + c) - 16)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 9*log(sin(d*x + c) + 1)/a + 9*log(sin(d*x + c) - 1)/a)/d","A",0
886,1,175,0,0.319995," ","integrate(sec(d*x+c)^7*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(9 \, \sin\left(d x + c\right)^{6} + 9 \, \sin\left(d x + c\right)^{5} - 24 \, \sin\left(d x + c\right)^{4} - 24 \, \sin\left(d x + c\right)^{3} - 57 \, \sin\left(d x + c\right)^{2} + 7 \, \sin\left(d x + c\right) + 16\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{9 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{9 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"1/768*(2*(9*sin(d*x + c)^6 + 9*sin(d*x + c)^5 - 24*sin(d*x + c)^4 - 24*sin(d*x + c)^3 - 57*sin(d*x + c)^2 + 7*sin(d*x + c) + 16)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 9*log(sin(d*x + c) + 1)/a + 9*log(sin(d*x + c) - 1)/a)/d","A",0
887,1,175,0,0.314066," ","integrate(sec(d*x+c)^7*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{6} + 15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{4} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)^{2} - 31 \, \sin\left(d x + c\right) - 16\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"1/768*(2*(15*sin(d*x + c)^6 + 15*sin(d*x + c)^5 - 40*sin(d*x + c)^4 - 40*sin(d*x + c)^3 + 33*sin(d*x + c)^2 - 31*sin(d*x + c) - 16)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 15*log(sin(d*x + c) + 1)/a + 15*log(sin(d*x + c) - 1)/a)/d","A",0
888,1,175,0,0.313413," ","integrate(sec(d*x+c)^7*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{6} + 15 \, \sin\left(d x + c\right)^{5} - 40 \, \sin\left(d x + c\right)^{4} - 40 \, \sin\left(d x + c\right)^{3} + 33 \, \sin\left(d x + c\right)^{2} + 33 \, \sin\left(d x + c\right) + 48\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(15*sin(d*x + c)^6 + 15*sin(d*x + c)^5 - 40*sin(d*x + c)^4 - 40*sin(d*x + c)^3 + 33*sin(d*x + c)^2 + 33*sin(d*x + c) + 48)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 15*log(sin(d*x + c) + 1)/a + 15*log(sin(d*x + c) - 1)/a)/d","A",0
889,1,175,0,0.312913," ","integrate(sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{6} + 105 \, \sin\left(d x + c\right)^{5} - 280 \, \sin\left(d x + c\right)^{4} - 280 \, \sin\left(d x + c\right)^{3} + 231 \, \sin\left(d x + c\right)^{2} + 231 \, \sin\left(d x + c\right) - 48\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(105*sin(d*x + c)^6 + 105*sin(d*x + c)^5 - 280*sin(d*x + c)^4 - 280*sin(d*x + c)^3 + 231*sin(d*x + c)^2 + 231*sin(d*x + c) - 48)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 105*log(sin(d*x + c) + 1)/a + 105*log(sin(d*x + c) - 1)/a)/d","A",0
890,1,187,0,0.330320," ","integrate(csc(d*x+c)*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{6} - 87 \, \sin\left(d x + c\right)^{5} - 472 \, \sin\left(d x + c\right)^{4} + 200 \, \sin\left(d x + c\right)^{3} + 711 \, \sin\left(d x + c\right)^{2} - 121 \, \sin\left(d x + c\right) - 400\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a} - \frac{489 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{279 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} + \frac{768 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{768 \, d}"," ",0,"1/768*(2*(105*sin(d*x + c)^6 - 87*sin(d*x + c)^5 - 472*sin(d*x + c)^4 + 200*sin(d*x + c)^3 + 711*sin(d*x + c)^2 - 121*sin(d*x + c) - 400)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a) - 489*log(sin(d*x + c) + 1)/a - 279*log(sin(d*x + c) - 1)/a + 768*log(sin(d*x + c))/a)/d","A",0
891,1,205,0,0.323535," ","integrate(csc(d*x+c)^2*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(945 \, \sin\left(d x + c\right)^{7} + 753 \, \sin\left(d x + c\right)^{6} - 2712 \, \sin\left(d x + c\right)^{5} - 2040 \, \sin\left(d x + c\right)^{4} + 2559 \, \sin\left(d x + c\right)^{3} + 1727 \, \sin\left(d x + c\right)^{2} - 784 \, \sin\left(d x + c\right) - 384\right)}}{a \sin\left(d x + c\right)^{8} + a \sin\left(d x + c\right)^{7} - 3 \, a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} + 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} - a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right)} - \frac{1329 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{561 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} + \frac{768 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(945*sin(d*x + c)^7 + 753*sin(d*x + c)^6 - 2712*sin(d*x + c)^5 - 2040*sin(d*x + c)^4 + 2559*sin(d*x + c)^3 + 1727*sin(d*x + c)^2 - 784*sin(d*x + c) - 384)/(a*sin(d*x + c)^8 + a*sin(d*x + c)^7 - 3*a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 + 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 - a*sin(d*x + c)^2 - a*sin(d*x + c)) - 1329*log(sin(d*x + c) + 1)/a + 561*log(sin(d*x + c) - 1)/a + 768*log(sin(d*x + c))/a)/d","A",0
892,1,217,0,0.336477," ","integrate(csc(d*x+c)^3*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(945 \, \sin\left(d x + c\right)^{8} - 15 \, \sin\left(d x + c\right)^{7} - 3480 \, \sin\left(d x + c\right)^{6} - 120 \, \sin\left(d x + c\right)^{5} + 4479 \, \sin\left(d x + c\right)^{4} + 319 \, \sin\left(d x + c\right)^{3} - 2192 \, \sin\left(d x + c\right)^{2} - 192 \, \sin\left(d x + c\right) + 192\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 3 \, a \sin\left(d x + c\right)^{7} - 3 \, a \sin\left(d x + c\right)^{6} + 3 \, a \sin\left(d x + c\right)^{5} + 3 \, a \sin\left(d x + c\right)^{4} - a \sin\left(d x + c\right)^{3} - a \sin\left(d x + c\right)^{2}} - \frac{2865 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{975 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} + \frac{3840 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{768 \, d}"," ",0,"1/768*(2*(945*sin(d*x + c)^8 - 15*sin(d*x + c)^7 - 3480*sin(d*x + c)^6 - 120*sin(d*x + c)^5 + 4479*sin(d*x + c)^4 + 319*sin(d*x + c)^3 - 2192*sin(d*x + c)^2 - 192*sin(d*x + c) + 192)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 3*a*sin(d*x + c)^7 - 3*a*sin(d*x + c)^6 + 3*a*sin(d*x + c)^5 + 3*a*sin(d*x + c)^4 - a*sin(d*x + c)^3 - a*sin(d*x + c)^2) - 2865*log(sin(d*x + c) + 1)/a - 975*log(sin(d*x + c) - 1)/a + 3840*log(sin(d*x + c))/a)/d","A",0
893,1,227,0,0.328337," ","integrate(csc(d*x+c)^4*sec(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3465 \, \sin\left(d x + c\right)^{9} + 2505 \, \sin\left(d x + c\right)^{8} - 10200 \, \sin\left(d x + c\right)^{7} - 6840 \, \sin\left(d x + c\right)^{6} + 10023 \, \sin\left(d x + c\right)^{5} + 5863 \, \sin\left(d x + c\right)^{4} - 3344 \, \sin\left(d x + c\right)^{3} - 1344 \, \sin\left(d x + c\right)^{2} + 64 \, \sin\left(d x + c\right) - 128\right)}}{a \sin\left(d x + c\right)^{10} + a \sin\left(d x + c\right)^{9} - 3 \, a \sin\left(d x + c\right)^{8} - 3 \, a \sin\left(d x + c\right)^{7} + 3 \, a \sin\left(d x + c\right)^{6} + 3 \, a \sin\left(d x + c\right)^{5} - a \sin\left(d x + c\right)^{4} - a \sin\left(d x + c\right)^{3}} - \frac{5385 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{1545 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} + \frac{3840 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{768 \, d}"," ",0,"-1/768*(2*(3465*sin(d*x + c)^9 + 2505*sin(d*x + c)^8 - 10200*sin(d*x + c)^7 - 6840*sin(d*x + c)^6 + 10023*sin(d*x + c)^5 + 5863*sin(d*x + c)^4 - 3344*sin(d*x + c)^3 - 1344*sin(d*x + c)^2 + 64*sin(d*x + c) - 128)/(a*sin(d*x + c)^10 + a*sin(d*x + c)^9 - 3*a*sin(d*x + c)^8 - 3*a*sin(d*x + c)^7 + 3*a*sin(d*x + c)^6 + 3*a*sin(d*x + c)^5 - a*sin(d*x + c)^4 - a*sin(d*x + c)^3) - 5385*log(sin(d*x + c) + 1)/a + 1545*log(sin(d*x + c) - 1)/a + 3840*log(sin(d*x + c))/a)/d","A",0
894,1,91,0,0.318753," ","integrate(sec(d*x+c)^8*sin(d*x+c)^3*(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 7 \, \tan\left(d x + c\right)^{5}\right)} a^{2} + \frac{{\left(35 \, \cos\left(d x + c\right)^{4} - 42 \, \cos\left(d x + c\right)^{2} + 15\right)} a^{2}}{\cos\left(d x + c\right)^{7}} - \frac{3 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} a^{2}}{\cos\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*(6*(5*tan(d*x + c)^7 + 7*tan(d*x + c)^5)*a^2 + (35*cos(d*x + c)^4 - 42*cos(d*x + c)^2 + 15)*a^2/cos(d*x + c)^7 - 3*(7*cos(d*x + c)^2 - 5)*a^2/cos(d*x + c)^7)/d","A",0
895,1,236,0,0.336872," ","integrate(sec(d*x+c)^9*sin(d*x+c)^12/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(4215 \, \sin\left(d x + c\right)^{8} - 5385 \, \sin\left(d x + c\right)^{7} - 18655 \, \sin\left(d x + c\right)^{6} + 13345 \, \sin\left(d x + c\right)^{5} + 30113 \, \sin\left(d x + c\right)^{4} - 11487 \, \sin\left(d x + c\right)^{3} - 21257 \, \sin\left(d x + c\right)^{2} + 3383 \, \sin\left(d x + c\right) + 5568\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} + \frac{1280 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right)\right)}}{a} + \frac{11145 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{4215 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{2560 \, d}"," ",0,"-1/2560*(2*(4215*sin(d*x + c)^8 - 5385*sin(d*x + c)^7 - 18655*sin(d*x + c)^6 + 13345*sin(d*x + c)^5 + 30113*sin(d*x + c)^4 - 11487*sin(d*x + c)^3 - 21257*sin(d*x + c)^2 + 3383*sin(d*x + c) + 5568)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) + 1280*(sin(d*x + c)^2 - 2*sin(d*x + c))/a + 11145*log(sin(d*x + c) + 1)/a + 4215*log(sin(d*x + c) - 1)/a)/d","A",0
896,1,225,0,0.381437," ","integrate(sec(d*x+c)^9*sin(d*x+c)^11/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(12645 \, \sin\left(d x + c\right)^{8} + 3045 \, \sin\left(d x + c\right)^{7} - 36765 \, \sin\left(d x + c\right)^{6} - 7965 \, \sin\left(d x + c\right)^{5} + 42339 \, \sin\left(d x + c\right)^{4} + 7139 \, \sin\left(d x + c\right)^{3} - 22171 \, \sin\left(d x + c\right)^{2} - 2171 \, \sin\left(d x + c\right) + 4384\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} + \frac{14235 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{6555 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{7680 \, \sin\left(d x + c\right)}{a}}{7680 \, d}"," ",0,"1/7680*(2*(12645*sin(d*x + c)^8 + 3045*sin(d*x + c)^7 - 36765*sin(d*x + c)^6 - 7965*sin(d*x + c)^5 + 42339*sin(d*x + c)^4 + 7139*sin(d*x + c)^3 - 22171*sin(d*x + c)^2 - 2171*sin(d*x + c) + 4384)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) + 14235*log(sin(d*x + c) + 1)/a - 6555*log(sin(d*x + c) - 1)/a - 7680*sin(d*x + c)/a)/d","A",0
897,1,214,0,0.534527," ","integrate(sec(d*x+c)^9*sin(d*x+c)^10/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(2895 \, \sin\left(d x + c\right)^{8} - 6705 \, \sin\left(d x + c\right)^{7} - 13815 \, \sin\left(d x + c\right)^{6} + 14985 \, \sin\left(d x + c\right)^{5} + 23049 \, \sin\left(d x + c\right)^{4} - 12151 \, \sin\left(d x + c\right)^{3} - 16561 \, \sin\left(d x + c\right)^{2} + 3439 \, \sin\left(d x + c\right) + 4384\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} + \frac{4785 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{2895 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{7680 \, d}"," ",0,"-1/7680*(2*(2895*sin(d*x + c)^8 - 6705*sin(d*x + c)^7 - 13815*sin(d*x + c)^6 + 14985*sin(d*x + c)^5 + 23049*sin(d*x + c)^4 - 12151*sin(d*x + c)^3 - 16561*sin(d*x + c)^2 + 3439*sin(d*x + c) + 4384)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) + 4785*log(sin(d*x + c) + 1)/a + 2895*log(sin(d*x + c) - 1)/a)/d","A",0
898,1,214,0,0.524545," ","integrate(sec(d*x+c)^9*sin(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(965 \, \sin\left(d x + c\right)^{8} + 325 \, \sin\left(d x + c\right)^{7} - 2045 \, \sin\left(d x + c\right)^{6} - 765 \, \sin\left(d x + c\right)^{5} + 1923 \, \sin\left(d x + c\right)^{4} + 643 \, \sin\left(d x + c\right)^{3} - 827 \, \sin\left(d x + c\right)^{2} - 187 \, \sin\left(d x + c\right) + 128\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} + \frac{315 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{315 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{2560 \, d}"," ",0,"1/2560*(2*(965*sin(d*x + c)^8 + 325*sin(d*x + c)^7 - 2045*sin(d*x + c)^6 - 765*sin(d*x + c)^5 + 1923*sin(d*x + c)^4 + 643*sin(d*x + c)^3 - 827*sin(d*x + c)^2 - 187*sin(d*x + c) + 128)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) + 315*log(sin(d*x + c) + 1)/a - 315*log(sin(d*x + c) - 1)/a)/d","A",0
899,1,214,0,0.341558," ","integrate(sec(d*x+c)^9*sin(d*x+c)^8/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{8} - 1815 \, \sin\left(d x + c\right)^{7} - 1025 \, \sin\left(d x + c\right)^{6} + 2815 \, \sin\left(d x + c\right)^{5} + 1919 \, \sin\left(d x + c\right)^{4} - 1921 \, \sin\left(d x + c\right)^{3} - 1431 \, \sin\left(d x + c\right)^{2} + 489 \, \sin\left(d x + c\right) + 384\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{7680 \, d}"," ",0,"-1/7680*(2*(105*sin(d*x + c)^8 - 1815*sin(d*x + c)^7 - 1025*sin(d*x + c)^6 + 2815*sin(d*x + c)^5 + 1919*sin(d*x + c)^4 - 1921*sin(d*x + c)^3 - 1431*sin(d*x + c)^2 + 489*sin(d*x + c) + 384)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 105*log(sin(d*x + c) + 1)/a + 105*log(sin(d*x + c) - 1)/a)/d","A",0
900,1,214,0,0.406593," ","integrate(sec(d*x+c)^9*sin(d*x+c)^7/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{8} + 105 \, \sin\left(d x + c\right)^{7} + 895 \, \sin\left(d x + c\right)^{6} - 65 \, \sin\left(d x + c\right)^{5} - 961 \, \sin\left(d x + c\right)^{4} - \sin\left(d x + c\right)^{3} + 489 \, \sin\left(d x + c\right)^{2} + 9 \, \sin\left(d x + c\right) - 96\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{7680 \, d}"," ",0,"1/7680*(2*(105*sin(d*x + c)^8 + 105*sin(d*x + c)^7 + 895*sin(d*x + c)^6 - 65*sin(d*x + c)^5 - 961*sin(d*x + c)^4 - sin(d*x + c)^3 + 489*sin(d*x + c)^2 + 9*sin(d*x + c) - 96)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 105*log(sin(d*x + c) + 1)/a + 105*log(sin(d*x + c) - 1)/a)/d","A",0
901,1,214,0,0.327059," ","integrate(sec(d*x+c)^9*sin(d*x+c)^6/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{8} + 15 \, \sin\left(d x + c\right)^{7} - 55 \, \sin\left(d x + c\right)^{6} + 265 \, \sin\left(d x + c\right)^{5} + 137 \, \sin\left(d x + c\right)^{4} - 183 \, \sin\left(d x + c\right)^{3} - 113 \, \sin\left(d x + c\right)^{2} + 47 \, \sin\left(d x + c\right) + 32\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{2560 \, d}"," ",0,"1/2560*(2*(15*sin(d*x + c)^8 + 15*sin(d*x + c)^7 - 55*sin(d*x + c)^6 + 265*sin(d*x + c)^5 + 137*sin(d*x + c)^4 - 183*sin(d*x + c)^3 - 113*sin(d*x + c)^2 + 47*sin(d*x + c) + 32)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 15*log(sin(d*x + c) + 1)/a + 15*log(sin(d*x + c) - 1)/a)/d","A",0
902,1,214,0,0.483030," ","integrate(sec(d*x+c)^9*sin(d*x+c)^5/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(45 \, \sin\left(d x + c\right)^{8} + 45 \, \sin\left(d x + c\right)^{7} - 165 \, \sin\left(d x + c\right)^{6} - 165 \, \sin\left(d x + c\right)^{5} - 549 \, \sin\left(d x + c\right)^{4} + 91 \, \sin\left(d x + c\right)^{3} + 301 \, \sin\left(d x + c\right)^{2} - 19 \, \sin\left(d x + c\right) - 64\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{45 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{45 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{7680 \, d}"," ",0,"-1/7680*(2*(45*sin(d*x + c)^8 + 45*sin(d*x + c)^7 - 165*sin(d*x + c)^6 - 165*sin(d*x + c)^5 - 549*sin(d*x + c)^4 + 91*sin(d*x + c)^3 + 301*sin(d*x + c)^2 - 19*sin(d*x + c) - 64)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 45*log(sin(d*x + c) + 1)/a + 45*log(sin(d*x + c) - 1)/a)/d","A",0
903,1,214,0,0.428412," ","integrate(sec(d*x+c)^9*sin(d*x+c)^4/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(45 \, \sin\left(d x + c\right)^{8} + 45 \, \sin\left(d x + c\right)^{7} - 165 \, \sin\left(d x + c\right)^{6} - 165 \, \sin\left(d x + c\right)^{5} + 219 \, \sin\left(d x + c\right)^{4} - 421 \, \sin\left(d x + c\right)^{3} - 211 \, \sin\left(d x + c\right)^{2} + 109 \, \sin\left(d x + c\right) + 64\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{45 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{45 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{7680 \, d}"," ",0,"-1/7680*(2*(45*sin(d*x + c)^8 + 45*sin(d*x + c)^7 - 165*sin(d*x + c)^6 - 165*sin(d*x + c)^5 + 219*sin(d*x + c)^4 - 421*sin(d*x + c)^3 - 211*sin(d*x + c)^2 + 109*sin(d*x + c) + 64)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 45*log(sin(d*x + c) + 1)/a + 45*log(sin(d*x + c) - 1)/a)/d","A",0
904,1,214,0,0.336339," ","integrate(sec(d*x+c)^9*sin(d*x+c)^3/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(15 \, \sin\left(d x + c\right)^{8} + 15 \, \sin\left(d x + c\right)^{7} - 55 \, \sin\left(d x + c\right)^{6} - 55 \, \sin\left(d x + c\right)^{5} + 73 \, \sin\left(d x + c\right)^{4} + 73 \, \sin\left(d x + c\right)^{3} + 143 \, \sin\left(d x + c\right)^{2} - 17 \, \sin\left(d x + c\right) - 32\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{15 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{15 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{2560 \, d}"," ",0,"1/2560*(2*(15*sin(d*x + c)^8 + 15*sin(d*x + c)^7 - 55*sin(d*x + c)^6 - 55*sin(d*x + c)^5 + 73*sin(d*x + c)^4 + 73*sin(d*x + c)^3 + 143*sin(d*x + c)^2 - 17*sin(d*x + c) - 32)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 15*log(sin(d*x + c) + 1)/a + 15*log(sin(d*x + c) - 1)/a)/d","A",0
905,1,214,0,0.488538," ","integrate(sec(d*x+c)^9*sin(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{8} + 105 \, \sin\left(d x + c\right)^{7} - 385 \, \sin\left(d x + c\right)^{6} - 385 \, \sin\left(d x + c\right)^{5} + 511 \, \sin\left(d x + c\right)^{4} + 511 \, \sin\left(d x + c\right)^{3} - 279 \, \sin\left(d x + c\right)^{2} + 201 \, \sin\left(d x + c\right) + 96\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{7680 \, d}"," ",0,"1/7680*(2*(105*sin(d*x + c)^8 + 105*sin(d*x + c)^7 - 385*sin(d*x + c)^6 - 385*sin(d*x + c)^5 + 511*sin(d*x + c)^4 + 511*sin(d*x + c)^3 - 279*sin(d*x + c)^2 + 201*sin(d*x + c) + 96)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 105*log(sin(d*x + c) + 1)/a + 105*log(sin(d*x + c) - 1)/a)/d","A",0
906,1,214,0,0.337638," ","integrate(sec(d*x+c)^9*sin(d*x+c)/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(105 \, \sin\left(d x + c\right)^{8} + 105 \, \sin\left(d x + c\right)^{7} - 385 \, \sin\left(d x + c\right)^{6} - 385 \, \sin\left(d x + c\right)^{5} + 511 \, \sin\left(d x + c\right)^{4} + 511 \, \sin\left(d x + c\right)^{3} - 279 \, \sin\left(d x + c\right)^{2} - 279 \, \sin\left(d x + c\right) - 384\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{105 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{105 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{7680 \, d}"," ",0,"-1/7680*(2*(105*sin(d*x + c)^8 + 105*sin(d*x + c)^7 - 385*sin(d*x + c)^6 - 385*sin(d*x + c)^5 + 511*sin(d*x + c)^4 + 511*sin(d*x + c)^3 - 279*sin(d*x + c)^2 - 279*sin(d*x + c) - 384)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 105*log(sin(d*x + c) + 1)/a + 105*log(sin(d*x + c) - 1)/a)/d","A",0
907,1,214,0,0.404553," ","integrate(sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(315 \, \sin\left(d x + c\right)^{8} + 315 \, \sin\left(d x + c\right)^{7} - 1155 \, \sin\left(d x + c\right)^{6} - 1155 \, \sin\left(d x + c\right)^{5} + 1533 \, \sin\left(d x + c\right)^{4} + 1533 \, \sin\left(d x + c\right)^{3} - 837 \, \sin\left(d x + c\right)^{2} - 837 \, \sin\left(d x + c\right) + 128\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{315 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{315 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a}}{2560 \, d}"," ",0,"-1/2560*(2*(315*sin(d*x + c)^8 + 315*sin(d*x + c)^7 - 1155*sin(d*x + c)^6 - 1155*sin(d*x + c)^5 + 1533*sin(d*x + c)^4 + 1533*sin(d*x + c)^3 - 837*sin(d*x + c)^2 - 837*sin(d*x + c) + 128)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 315*log(sin(d*x + c) + 1)/a + 315*log(sin(d*x + c) - 1)/a)/d","A",0
908,1,226,0,0.494216," ","integrate(csc(d*x+c)*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(945 \, \sin\left(d x + c\right)^{8} - 975 \, \sin\left(d x + c\right)^{7} - 5385 \, \sin\left(d x + c\right)^{6} + 3255 \, \sin\left(d x + c\right)^{5} + 11319 \, \sin\left(d x + c\right)^{4} - 3721 \, \sin\left(d x + c\right)^{3} - 10831 \, \sin\left(d x + c\right)^{2} + 1489 \, \sin\left(d x + c\right) + 4384\right)}}{a \sin\left(d x + c\right)^{9} + a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} - 4 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} + 6 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} - 4 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a} - \frac{4785 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{2895 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} + \frac{7680 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{7680 \, d}"," ",0,"1/7680*(2*(945*sin(d*x + c)^8 - 975*sin(d*x + c)^7 - 5385*sin(d*x + c)^6 + 3255*sin(d*x + c)^5 + 11319*sin(d*x + c)^4 - 3721*sin(d*x + c)^3 - 10831*sin(d*x + c)^2 + 1489*sin(d*x + c) + 4384)/(a*sin(d*x + c)^9 + a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 - 4*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 + 6*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 - 4*a*sin(d*x + c)^2 + a*sin(d*x + c) + a) - 4785*log(sin(d*x + c) + 1)/a - 2895*log(sin(d*x + c) - 1)/a + 7680*log(sin(d*x + c))/a)/d","A",0
909,1,245,0,0.351286," ","integrate(csc(d*x+c)^2*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(10395 \, \sin\left(d x + c\right)^{9} + 8475 \, \sin\left(d x + c\right)^{8} - 40035 \, \sin\left(d x + c\right)^{7} - 31395 \, \sin\left(d x + c\right)^{6} + 57309 \, \sin\left(d x + c\right)^{5} + 42269 \, \sin\left(d x + c\right)^{4} - 35941 \, \sin\left(d x + c\right)^{3} - 23621 \, \sin\left(d x + c\right)^{2} + 8224 \, \sin\left(d x + c\right) + 3840\right)}}{a \sin\left(d x + c\right)^{10} + a \sin\left(d x + c\right)^{9} - 4 \, a \sin\left(d x + c\right)^{8} - 4 \, a \sin\left(d x + c\right)^{7} + 6 \, a \sin\left(d x + c\right)^{6} + 6 \, a \sin\left(d x + c\right)^{5} - 4 \, a \sin\left(d x + c\right)^{4} - 4 \, a \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right)} - \frac{14235 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{6555 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} + \frac{7680 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{7680 \, d}"," ",0,"-1/7680*(2*(10395*sin(d*x + c)^9 + 8475*sin(d*x + c)^8 - 40035*sin(d*x + c)^7 - 31395*sin(d*x + c)^6 + 57309*sin(d*x + c)^5 + 42269*sin(d*x + c)^4 - 35941*sin(d*x + c)^3 - 23621*sin(d*x + c)^2 + 8224*sin(d*x + c) + 3840)/(a*sin(d*x + c)^10 + a*sin(d*x + c)^9 - 4*a*sin(d*x + c)^8 - 4*a*sin(d*x + c)^7 + 6*a*sin(d*x + c)^6 + 6*a*sin(d*x + c)^5 - 4*a*sin(d*x + c)^4 - 4*a*sin(d*x + c)^3 + a*sin(d*x + c)^2 + a*sin(d*x + c)) - 14235*log(sin(d*x + c) + 1)/a + 6555*log(sin(d*x + c) - 1)/a + 7680*log(sin(d*x + c))/a)/d","A",0
910,1,257,0,0.326354," ","integrate(csc(d*x+c)^3*sec(d*x+c)^9/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(3465 \, \sin\left(d x + c\right)^{10} - 375 \, \sin\left(d x + c\right)^{9} - 16545 \, \sin\left(d x + c\right)^{8} + 735 \, \sin\left(d x + c\right)^{7} + 30303 \, \sin\left(d x + c\right)^{6} + 223 \, \sin\left(d x + c\right)^{5} - 25847 \, \sin\left(d x + c\right)^{4} - 1207 \, \sin\left(d x + c\right)^{3} + 9408 \, \sin\left(d x + c\right)^{2} + 640 \, \sin\left(d x + c\right) - 640\right)}}{a \sin\left(d x + c\right)^{11} + a \sin\left(d x + c\right)^{10} - 4 \, a \sin\left(d x + c\right)^{9} - 4 \, a \sin\left(d x + c\right)^{8} + 6 \, a \sin\left(d x + c\right)^{7} + 6 \, a \sin\left(d x + c\right)^{6} - 4 \, a \sin\left(d x + c\right)^{5} - 4 \, a \sin\left(d x + c\right)^{4} + a \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2}} - \frac{11145 \, \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{4215 \, \log\left(\sin\left(d x + c\right) - 1\right)}{a} + \frac{15360 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{2560 \, d}"," ",0,"1/2560*(2*(3465*sin(d*x + c)^10 - 375*sin(d*x + c)^9 - 16545*sin(d*x + c)^8 + 735*sin(d*x + c)^7 + 30303*sin(d*x + c)^6 + 223*sin(d*x + c)^5 - 25847*sin(d*x + c)^4 - 1207*sin(d*x + c)^3 + 9408*sin(d*x + c)^2 + 640*sin(d*x + c) - 640)/(a*sin(d*x + c)^11 + a*sin(d*x + c)^10 - 4*a*sin(d*x + c)^9 - 4*a*sin(d*x + c)^8 + 6*a*sin(d*x + c)^7 + 6*a*sin(d*x + c)^6 - 4*a*sin(d*x + c)^5 - 4*a*sin(d*x + c)^4 + a*sin(d*x + c)^3 + a*sin(d*x + c)^2) - 11145*log(sin(d*x + c) + 1)/a - 4215*log(sin(d*x + c) - 1)/a + 15360*log(sin(d*x + c))/a)/d","A",0
911,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m,x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
912,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\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)\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e), x)","F",0
913,1,486,0,1.295796," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^4*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(d^{2} {\left(n + 1\right)} \sin\left(f x + e\right)^{2} + c d n \sin\left(f x + e\right) - c^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{4}}{{\left(n^{2} + 3 \, n + 2\right)} d^{2}} + \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n + 1} a^{4}}{d {\left(n + 1\right)}} + \frac{6 \, {\left({\left(n^{2} + 3 \, n + 2\right)} d^{3} \sin\left(f x + e\right)^{3} + {\left(n^{2} + n\right)} c d^{2} \sin\left(f x + e\right)^{2} - 2 \, c^{2} d n \sin\left(f x + e\right) + 2 \, c^{3}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{4}}{{\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} d^{3}} + \frac{4 \, {\left({\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} d^{4} \sin\left(f x + e\right)^{4} + {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} c d^{3} \sin\left(f x + e\right)^{3} - 3 \, {\left(n^{2} + n\right)} c^{2} d^{2} \sin\left(f x + e\right)^{2} + 6 \, c^{3} d n \sin\left(f x + e\right) - 6 \, c^{4}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{4}}{{\left(n^{4} + 10 \, n^{3} + 35 \, n^{2} + 50 \, n + 24\right)} d^{4}} + \frac{{\left({\left(n^{4} + 10 \, n^{3} + 35 \, n^{2} + 50 \, n + 24\right)} d^{5} \sin\left(f x + e\right)^{5} + {\left(n^{4} + 6 \, n^{3} + 11 \, n^{2} + 6 \, n\right)} c d^{4} \sin\left(f x + e\right)^{4} - 4 \, {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} c^{2} d^{3} \sin\left(f x + e\right)^{3} + 12 \, {\left(n^{2} + n\right)} c^{3} d^{2} \sin\left(f x + e\right)^{2} - 24 \, c^{4} d n \sin\left(f x + e\right) + 24 \, c^{5}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{4}}{{\left(n^{5} + 15 \, n^{4} + 85 \, n^{3} + 225 \, n^{2} + 274 \, n + 120\right)} d^{5}}}{f}"," ",0,"(4*(d^2*(n + 1)*sin(f*x + e)^2 + c*d*n*sin(f*x + e) - c^2)*(d*sin(f*x + e) + c)^n*a^4/((n^2 + 3*n + 2)*d^2) + (d*sin(f*x + e) + c)^(n + 1)*a^4/(d*(n + 1)) + 6*((n^2 + 3*n + 2)*d^3*sin(f*x + e)^3 + (n^2 + n)*c*d^2*sin(f*x + e)^2 - 2*c^2*d*n*sin(f*x + e) + 2*c^3)*(d*sin(f*x + e) + c)^n*a^4/((n^3 + 6*n^2 + 11*n + 6)*d^3) + 4*((n^3 + 6*n^2 + 11*n + 6)*d^4*sin(f*x + e)^4 + (n^3 + 3*n^2 + 2*n)*c*d^3*sin(f*x + e)^3 - 3*(n^2 + n)*c^2*d^2*sin(f*x + e)^2 + 6*c^3*d*n*sin(f*x + e) - 6*c^4)*(d*sin(f*x + e) + c)^n*a^4/((n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*d^4) + ((n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*d^5*sin(f*x + e)^5 + (n^4 + 6*n^3 + 11*n^2 + 6*n)*c*d^4*sin(f*x + e)^4 - 4*(n^3 + 3*n^2 + 2*n)*c^2*d^3*sin(f*x + e)^3 + 12*(n^2 + n)*c^3*d^2*sin(f*x + e)^2 - 24*c^4*d*n*sin(f*x + e) + 24*c^5)*(d*sin(f*x + e) + c)^n*a^4/((n^5 + 15*n^4 + 85*n^3 + 225*n^2 + 274*n + 120)*d^5))/f","B",0
914,1,313,0,0.661289," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(d^{2} {\left(n + 1\right)} \sin\left(f x + e\right)^{2} + c d n \sin\left(f x + e\right) - c^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{3}}{{\left(n^{2} + 3 \, n + 2\right)} d^{2}} + \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n + 1} a^{3}}{d {\left(n + 1\right)}} + \frac{3 \, {\left({\left(n^{2} + 3 \, n + 2\right)} d^{3} \sin\left(f x + e\right)^{3} + {\left(n^{2} + n\right)} c d^{2} \sin\left(f x + e\right)^{2} - 2 \, c^{2} d n \sin\left(f x + e\right) + 2 \, c^{3}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{3}}{{\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} d^{3}} + \frac{{\left({\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} d^{4} \sin\left(f x + e\right)^{4} + {\left(n^{3} + 3 \, n^{2} + 2 \, n\right)} c d^{3} \sin\left(f x + e\right)^{3} - 3 \, {\left(n^{2} + n\right)} c^{2} d^{2} \sin\left(f x + e\right)^{2} + 6 \, c^{3} d n \sin\left(f x + e\right) - 6 \, c^{4}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{3}}{{\left(n^{4} + 10 \, n^{3} + 35 \, n^{2} + 50 \, n + 24\right)} d^{4}}}{f}"," ",0,"(3*(d^2*(n + 1)*sin(f*x + e)^2 + c*d*n*sin(f*x + e) - c^2)*(d*sin(f*x + e) + c)^n*a^3/((n^2 + 3*n + 2)*d^2) + (d*sin(f*x + e) + c)^(n + 1)*a^3/(d*(n + 1)) + 3*((n^2 + 3*n + 2)*d^3*sin(f*x + e)^3 + (n^2 + n)*c*d^2*sin(f*x + e)^2 - 2*c^2*d*n*sin(f*x + e) + 2*c^3)*(d*sin(f*x + e) + c)^n*a^3/((n^3 + 6*n^2 + 11*n + 6)*d^3) + ((n^3 + 6*n^2 + 11*n + 6)*d^4*sin(f*x + e)^4 + (n^3 + 3*n^2 + 2*n)*c*d^3*sin(f*x + e)^3 - 3*(n^2 + n)*c^2*d^2*sin(f*x + e)^2 + 6*c^3*d*n*sin(f*x + e) - 6*c^4)*(d*sin(f*x + e) + c)^n*a^3/((n^4 + 10*n^3 + 35*n^2 + 50*n + 24)*d^4))/f","B",0
915,1,183,0,0.710704," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(d^{2} {\left(n + 1\right)} \sin\left(f x + e\right)^{2} + c d n \sin\left(f x + e\right) - c^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{2}}{{\left(n^{2} + 3 \, n + 2\right)} d^{2}} + \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n + 1} a^{2}}{d {\left(n + 1\right)}} + \frac{{\left({\left(n^{2} + 3 \, n + 2\right)} d^{3} \sin\left(f x + e\right)^{3} + {\left(n^{2} + n\right)} c d^{2} \sin\left(f x + e\right)^{2} - 2 \, c^{2} d n \sin\left(f x + e\right) + 2 \, c^{3}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a^{2}}{{\left(n^{3} + 6 \, n^{2} + 11 \, n + 6\right)} d^{3}}}{f}"," ",0,"(2*(d^2*(n + 1)*sin(f*x + e)^2 + c*d*n*sin(f*x + e) - c^2)*(d*sin(f*x + e) + c)^n*a^2/((n^2 + 3*n + 2)*d^2) + (d*sin(f*x + e) + c)^(n + 1)*a^2/(d*(n + 1)) + ((n^2 + 3*n + 2)*d^3*sin(f*x + e)^3 + (n^2 + n)*c*d^2*sin(f*x + e)^2 - 2*c^2*d*n*sin(f*x + e) + 2*c^3)*(d*sin(f*x + e) + c)^n*a^2/((n^3 + 6*n^2 + 11*n + 6)*d^3))/f","A",0
916,1,87,0,0.693487," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\frac{\frac{{\left(d^{2} {\left(n + 1\right)} \sin\left(f x + e\right)^{2} + c d n \sin\left(f x + e\right) - c^{2}\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} a}{{\left(n^{2} + 3 \, n + 2\right)} d^{2}} + \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n + 1} a}{d {\left(n + 1\right)}}}{f}"," ",0,"((d^2*(n + 1)*sin(f*x + e)^2 + c*d*n*sin(f*x + e) - c^2)*(d*sin(f*x + e) + c)^n*a/((n^2 + 3*n + 2)*d^2) + (d*sin(f*x + e) + c)^(n + 1)*a/(d*(n + 1)))/f","A",0
917,0,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)/(a*sin(f*x + e) + a), x)","F",0
918,0,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)/(a*sin(f*x + e) + a)^2, x)","F",0
919,0,0,0,0.000000," ","integrate(cos(f*x+e)*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)/(a*sin(f*x + e) + a)^3, x)","F",0
920,1,457,0,0.698208," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^4,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(a^{m} {\left(m + 1\right)} \sin\left(f x + e\right)^{2} + a^{m} m \sin\left(f x + e\right) - a^{m}\right)} c^{3} d {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{2} + 3 \, m + 2} + \frac{6 \, {\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(f x + e\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 2 \, a^{m} m \sin\left(f x + e\right) + 2 \, a^{m}\right)} c^{2} d^{2} {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} + \frac{4 \, {\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} a^{m} \sin\left(f x + e\right)^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} - 3 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} + 6 \, a^{m} m \sin\left(f x + e\right) - 6 \, a^{m}\right)} c d^{3} {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24} + \frac{{\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} a^{m} \sin\left(f x + e\right)^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(f x + e\right)^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} + 12 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 24 \, a^{m} m \sin\left(f x + e\right) + 24 \, a^{m}\right)} d^{4} {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} c^{4}}{a {\left(m + 1\right)}}}{f}"," ",0,"(4*(a^m*(m + 1)*sin(f*x + e)^2 + a^m*m*sin(f*x + e) - a^m)*c^3*d*(sin(f*x + e) + 1)^m/(m^2 + 3*m + 2) + 6*((m^2 + 3*m + 2)*a^m*sin(f*x + e)^3 + (m^2 + m)*a^m*sin(f*x + e)^2 - 2*a^m*m*sin(f*x + e) + 2*a^m)*c^2*d^2*(sin(f*x + e) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) + 4*((m^3 + 6*m^2 + 11*m + 6)*a^m*sin(f*x + e)^4 + (m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 - 3*(m^2 + m)*a^m*sin(f*x + e)^2 + 6*a^m*m*sin(f*x + e) - 6*a^m)*c*d^3*(sin(f*x + e) + 1)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24) + ((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*a^m*sin(f*x + e)^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(f*x + e)^4 - 4*(m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 + 12*(m^2 + m)*a^m*sin(f*x + e)^2 - 24*a^m*m*sin(f*x + e) + 24*a^m)*d^4*(sin(f*x + e) + 1)^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120) + (a*sin(f*x + e) + a)^(m + 1)*c^4/(a*(m + 1)))/f","B",0
921,1,294,0,0.750971," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(a^{m} {\left(m + 1\right)} \sin\left(f x + e\right)^{2} + a^{m} m \sin\left(f x + e\right) - a^{m}\right)} c^{2} d {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{2} + 3 \, m + 2} + \frac{3 \, {\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(f x + e\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 2 \, a^{m} m \sin\left(f x + e\right) + 2 \, a^{m}\right)} c d^{2} {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} + \frac{{\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} a^{m} \sin\left(f x + e\right)^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} - 3 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} + 6 \, a^{m} m \sin\left(f x + e\right) - 6 \, a^{m}\right)} d^{3} {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} c^{3}}{a {\left(m + 1\right)}}}{f}"," ",0,"(3*(a^m*(m + 1)*sin(f*x + e)^2 + a^m*m*sin(f*x + e) - a^m)*c^2*d*(sin(f*x + e) + 1)^m/(m^2 + 3*m + 2) + 3*((m^2 + 3*m + 2)*a^m*sin(f*x + e)^3 + (m^2 + m)*a^m*sin(f*x + e)^2 - 2*a^m*m*sin(f*x + e) + 2*a^m)*c*d^2*(sin(f*x + e) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) + ((m^3 + 6*m^2 + 11*m + 6)*a^m*sin(f*x + e)^4 + (m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 - 3*(m^2 + m)*a^m*sin(f*x + e)^2 + 6*a^m*m*sin(f*x + e) - 6*a^m)*d^3*(sin(f*x + e) + 1)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24) + (a*sin(f*x + e) + a)^(m + 1)*c^3/(a*(m + 1)))/f","B",0
922,1,171,0,0.669185," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a^{m} {\left(m + 1\right)} \sin\left(f x + e\right)^{2} + a^{m} m \sin\left(f x + e\right) - a^{m}\right)} c d {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{2} + 3 \, m + 2} + \frac{{\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(f x + e\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 2 \, a^{m} m \sin\left(f x + e\right) + 2 \, a^{m}\right)} d^{2} {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} c^{2}}{a {\left(m + 1\right)}}}{f}"," ",0,"(2*(a^m*(m + 1)*sin(f*x + e)^2 + a^m*m*sin(f*x + e) - a^m)*c*d*(sin(f*x + e) + 1)^m/(m^2 + 3*m + 2) + ((m^2 + 3*m + 2)*a^m*sin(f*x + e)^3 + (m^2 + m)*a^m*sin(f*x + e)^2 - 2*a^m*m*sin(f*x + e) + 2*a^m)*d^2*(sin(f*x + e) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) + (a*sin(f*x + e) + a)^(m + 1)*c^2/(a*(m + 1)))/f","A",0
923,1,83,0,0.833005," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{{\left(a^{m} {\left(m + 1\right)} \sin\left(f x + e\right)^{2} + a^{m} m \sin\left(f x + e\right) - a^{m}\right)} d {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{2} + 3 \, m + 2} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} c}{a {\left(m + 1\right)}}}{f}"," ",0,"((a^m*(m + 1)*sin(f*x + e)^2 + a^m*m*sin(f*x + e) - a^m)*d*(sin(f*x + e) + 1)^m/(m^2 + 3*m + 2) + (a*sin(f*x + e) + a)^(m + 1)*c/(a*(m + 1)))/f","A",0
924,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)/(d*sin(f*x + e) + c), x)","F",0
925,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)}{{\left(d \sin\left(f x + e\right) + c\right)}^{2}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)/(d*sin(f*x + e) + c)^2, x)","F",0
926,0,0,0,0.000000," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m/(c+d*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)}{{\left(d \sin\left(f x + e\right) + c\right)}^{3}}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*cos(f*x + e)/(d*sin(f*x + e) + c)^3, x)","F",0
927,0,0,0,0.000000," ","integrate(cos(d*x+c)*sin(d*x+c)^n*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*sin(d*x + c)^n*cos(d*x + c), x)","F",0
928,1,159,0,0.909291," ","integrate(cos(d*x+c)*sin(d*x+c)^4*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} a^{m} \sin\left(d x + c\right)^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(d x + c\right)^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(d x + c\right)^{3} + 12 \, {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} - 24 \, a^{m} m \sin\left(d x + c\right) + 24 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{{\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} d}"," ",0,"((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*a^m*sin(d*x + c)^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(d*x + c)^4 - 4*(m^3 + 3*m^2 + 2*m)*a^m*sin(d*x + c)^3 + 12*(m^2 + m)*a^m*sin(d*x + c)^2 - 24*a^m*m*sin(d*x + c) + 24*a^m)*(sin(d*x + c) + 1)^m/((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*d)","A",0
929,1,119,0,0.691463," ","integrate(cos(d*x+c)*sin(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} a^{m} \sin\left(d x + c\right)^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(d x + c\right)^{3} - 3 \, {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} + 6 \, a^{m} m \sin\left(d x + c\right) - 6 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{{\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} d}"," ",0,"((m^3 + 6*m^2 + 11*m + 6)*a^m*sin(d*x + c)^4 + (m^3 + 3*m^2 + 2*m)*a^m*sin(d*x + c)^3 - 3*(m^2 + m)*a^m*sin(d*x + c)^2 + 6*a^m*m*sin(d*x + c) - 6*a^m)*(sin(d*x + c) + 1)^m/((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*d)","A",0
930,1,84,0,0.637260," ","integrate(cos(d*x+c)*sin(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(d x + c\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(d x + c\right)^{2} - 2 \, a^{m} m \sin\left(d x + c\right) + 2 \, a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{{\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} d}"," ",0,"((m^2 + 3*m + 2)*a^m*sin(d*x + c)^3 + (m^2 + m)*a^m*sin(d*x + c)^2 - 2*a^m*m*sin(d*x + c) + 2*a^m)*(sin(d*x + c) + 1)^m/((m^3 + 6*m^2 + 11*m + 6)*d)","A",0
931,1,56,0,0.910509," ","integrate(cos(d*x+c)*sin(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\frac{{\left(a^{m} {\left(m + 1\right)} \sin\left(d x + c\right)^{2} + a^{m} m \sin\left(d x + c\right) - a^{m}\right)} {\left(\sin\left(d x + c\right) + 1\right)}^{m}}{{\left(m^{2} + 3 \, m + 2\right)} d}"," ",0,"(a^m*(m + 1)*sin(d*x + c)^2 + a^m*m*sin(d*x + c) - a^m)*(sin(d*x + c) + 1)^m/((m^2 + 3*m + 2)*d)","A",0
932,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c), x)","F",0
933,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)^2*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c)^2, x)","F",0
934,0,0,0,0.000000," ","integrate(cos(d*x+c)*csc(d*x+c)^3*(a+a*sin(d*x+c))^m,x, algorithm=""maxima"")","\int {\left(a \sin\left(d x + c\right) + a\right)}^{m} \cos\left(d x + c\right) \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((a*sin(d*x + c) + a)^m*cos(d*x + c)*csc(d*x + c)^3, x)","F",0
935,1,74,0,0.336349," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{32 \, a c \cos\left(f x + e\right)^{3} + 32 \, a d \cos\left(f x + e\right)^{3} - 24 \, {\left(2 \, f x + 2 \, e + \sin\left(2 \, f x + 2 \, e\right)\right)} a c - 3 \, {\left(4 \, f x + 4 \, e - \sin\left(4 \, f x + 4 \, e\right)\right)} a d}{96 \, f}"," ",0,"-1/96*(32*a*c*cos(f*x + e)^3 + 32*a*d*cos(f*x + e)^3 - 24*(2*f*x + 2*e + sin(2*f*x + 2*e))*a*c - 3*(4*f*x + 4*e - sin(4*f*x + 4*e))*a*d)/f","A",0
936,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*(d*sin(f*x + e) + c)), x)","F",0
937,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((a*sin(f*x + e) + a)^(3/2)*sqrt(d*sin(f*x + e) + c)), x)","F",0
938,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
939,-1,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^3*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
940,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
941,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
942,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(a*sin(f*x + e) + a), x)","F",0
943,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(a*sin(f*x + e) + a)^2, x)","F",0
944,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(a*sin(f*x + e) + a)^3, x)","F",0
945,-1,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
946,-1,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
947,-1,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
948,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a), x)","F",0
949,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a)^2, x)","F",0
950,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{3}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a)^3, x)","F",0
951,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{4}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a)^4, x)","F",0
952,0,0,0,0.000000," ","integrate(cos(f*x+e)^4*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^5,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{4}}{{\left(a \sin\left(f x + e\right) + a\right)}^{5}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^4/(a*sin(f*x + e) + a)^5, x)","F",0
953,1,134,0,0.356420," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{280 \, B a \sin\left(d x + c\right)^{9} + 315 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{8} + 360 \, {\left(A - 3 \, B\right)} a \sin\left(d x + c\right)^{7} - 1260 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{6} - 1512 \, {\left(A - B\right)} a \sin\left(d x + c\right)^{5} + 1890 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{4} + 840 \, {\left(3 \, A - B\right)} a \sin\left(d x + c\right)^{3} - 1260 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{2} - 2520 \, A a \sin\left(d x + c\right)}{2520 \, d}"," ",0,"-1/2520*(280*B*a*sin(d*x + c)^9 + 315*(A + B)*a*sin(d*x + c)^8 + 360*(A - 3*B)*a*sin(d*x + c)^7 - 1260*(A + B)*a*sin(d*x + c)^6 - 1512*(A - B)*a*sin(d*x + c)^5 + 1890*(A + B)*a*sin(d*x + c)^4 + 840*(3*A - B)*a*sin(d*x + c)^3 - 1260*(A + B)*a*sin(d*x + c)^2 - 2520*A*a*sin(d*x + c))/d","A",0
954,1,104,0,0.346191," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{30 \, B a \sin\left(d x + c\right)^{7} + 35 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{6} + 42 \, {\left(A - 2 \, B\right)} a \sin\left(d x + c\right)^{5} - 105 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{4} - 70 \, {\left(2 \, A - B\right)} a \sin\left(d x + c\right)^{3} + 105 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{2} + 210 \, A a \sin\left(d x + c\right)}{210 \, d}"," ",0,"1/210*(30*B*a*sin(d*x + c)^7 + 35*(A + B)*a*sin(d*x + c)^6 + 42*(A - 2*B)*a*sin(d*x + c)^5 - 105*(A + B)*a*sin(d*x + c)^4 - 70*(2*A - B)*a*sin(d*x + c)^3 + 105*(A + B)*a*sin(d*x + c)^2 + 210*A*a*sin(d*x + c))/d","A",0
955,1,72,0,0.350892," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{12 \, B a \sin\left(d x + c\right)^{5} + 15 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{4} + 20 \, {\left(A - B\right)} a \sin\left(d x + c\right)^{3} - 30 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{2} - 60 \, A a \sin\left(d x + c\right)}{60 \, d}"," ",0,"-1/60*(12*B*a*sin(d*x + c)^5 + 15*(A + B)*a*sin(d*x + c)^4 + 20*(A - B)*a*sin(d*x + c)^3 - 30*(A + B)*a*sin(d*x + c)^2 - 60*A*a*sin(d*x + c))/d","A",0
956,1,42,0,0.345844," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B a \sin\left(d x + c\right)^{3} + 3 \, {\left(A + B\right)} a \sin\left(d x + c\right)^{2} + 6 \, A a \sin\left(d x + c\right)}{6 \, d}"," ",0,"1/6*(2*B*a*sin(d*x + c)^3 + 3*(A + B)*a*sin(d*x + c)^2 + 6*A*a*sin(d*x + c))/d","A",0
957,1,29,0,0.358254," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\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
958,1,55,0,0.344500," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(A - B\right)} a \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A - B\right)} a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(A + B\right)} a}{\sin\left(d x + c\right) - 1}}{4 \, d}"," ",0,"1/4*((A - B)*a*log(sin(d*x + c) + 1) - (A - B)*a*log(sin(d*x + c) - 1) - 2*(A + B)*a/(sin(d*x + c) - 1))/d","A",0
959,1,115,0,0.345352," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, A - B\right)} a \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A - B\right)} a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left({\left(3 \, A - B\right)} a \sin\left(d x + c\right)^{2} - {\left(3 \, A - B\right)} a \sin\left(d x + c\right) - 2 \, {\left(A + B\right)} a\right)}}{\sin\left(d x + c\right)^{3} - \sin\left(d x + c\right)^{2} - \sin\left(d x + c\right) + 1}}{16 \, d}"," ",0,"1/16*((3*A - B)*a*log(sin(d*x + c) + 1) - (3*A - B)*a*log(sin(d*x + c) - 1) - 2*((3*A - B)*a*sin(d*x + c)^2 - (3*A - B)*a*sin(d*x + c) - 2*(A + B)*a)/(sin(d*x + c)^3 - sin(d*x + c)^2 - sin(d*x + c) + 1))/d","A",0
960,1,171,0,0.351781," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, A - B\right)} a \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A - B\right)} a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(5 \, A - B\right)} a \sin\left(d x + c\right)^{4} - 3 \, {\left(5 \, A - B\right)} a \sin\left(d x + c\right)^{3} - 5 \, {\left(5 \, A - B\right)} a \sin\left(d x + c\right)^{2} + 5 \, {\left(5 \, A - B\right)} a \sin\left(d x + c\right) + 8 \, {\left(A + B\right)} a\right)}}{\sin\left(d x + c\right)^{5} - \sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{3} + 2 \, \sin\left(d x + c\right)^{2} + \sin\left(d x + c\right) - 1}}{96 \, d}"," ",0,"1/96*(3*(5*A - B)*a*log(sin(d*x + c) + 1) - 3*(5*A - B)*a*log(sin(d*x + c) - 1) - 2*(3*(5*A - B)*a*sin(d*x + c)^4 - 3*(5*A - B)*a*sin(d*x + c)^3 - 5*(5*A - B)*a*sin(d*x + c)^2 + 5*(5*A - B)*a*sin(d*x + c) + 8*(A + B)*a)/(sin(d*x + c)^5 - sin(d*x + c)^4 - 2*sin(d*x + c)^3 + 2*sin(d*x + c)^2 + sin(d*x + c) - 1))/d","A",0
961,1,124,0,0.338607," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3072 \, A a \cos\left(d x + c\right)^{7} + 3072 \, B a \cos\left(d x + c\right)^{7} + 112 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 7 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a}{21504 \, d}"," ",0,"-1/21504*(3072*A*a*cos(d*x + c)^7 + 3072*B*a*cos(d*x + c)^7 + 112*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a - 7*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*B*a)/d","A",0
962,1,98,0,0.403456," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{192 \, A a \cos\left(d x + c\right)^{5} + 192 \, B a \cos\left(d x + c\right)^{5} - 30 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a}{960 \, d}"," ",0,"-1/960*(192*A*a*cos(d*x + c)^5 + 192*B*a*cos(d*x + c)^5 - 30*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a - 5*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*B*a)/d","A",0
963,1,74,0,0.378881," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, A a \cos\left(d x + c\right)^{3} + 32 \, B a \cos\left(d x + c\right)^{3} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a - 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} B a}{96 \, d}"," ",0,"-1/96*(32*A*a*cos(d*x + c)^3 + 32*B*a*cos(d*x + c)^3 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a - 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*B*a)/d","A",0
964,1,56,0,0.430059," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} B a - A a \tan\left(d x + c\right) - \frac{A a}{\cos\left(d x + c\right)} - \frac{B a}{\cos\left(d x + c\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*B*a - A*a*tan(d*x + c) - A*a/cos(d*x + c) - B*a/cos(d*x + c))/d","A",0
965,1,59,0,0.320965," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{B a \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a + \frac{A a}{\cos\left(d x + c\right)^{3}} + \frac{B a}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(B*a*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*tan(d*x + c))*A*a + A*a/cos(d*x + c)^3 + B*a/cos(d*x + c)^3)/d","A",0
966,1,86,0,0.365651," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a + {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} B a + \frac{3 \, A a}{\cos\left(d x + c\right)^{5}} + \frac{3 \, B a}{\cos\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*((3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a + (3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*B*a + 3*A*a/cos(d*x + c)^5 + 3*B*a/cos(d*x + c)^5)/d","A",0
967,1,107,0,0.326533," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} A a + {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} B a + \frac{15 \, A a}{\cos\left(d x + c\right)^{7}} + \frac{15 \, B a}{\cos\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*(3*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*A*a + (15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*B*a + 15*A*a/cos(d*x + c)^7 + 15*B*a/cos(d*x + c)^7)/d","A",0
968,1,126,0,0.327531," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(35 \, \tan\left(d x + c\right)^{9} + 180 \, \tan\left(d x + c\right)^{7} + 378 \, \tan\left(d x + c\right)^{5} + 420 \, \tan\left(d x + c\right)^{3} + 315 \, \tan\left(d x + c\right)\right)} A a + {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} B a + \frac{35 \, A a}{\cos\left(d x + c\right)^{9}} + \frac{35 \, B a}{\cos\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"1/315*((35*tan(d*x + c)^9 + 180*tan(d*x + c)^7 + 378*tan(d*x + c)^5 + 420*tan(d*x + c)^3 + 315*tan(d*x + c))*A*a + (35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*B*a + 35*A*a/cos(d*x + c)^9 + 35*B*a/cos(d*x + c)^9)/d","A",0
969,1,168,0,0.309504," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{126 \, B a^{2} \sin\left(d x + c\right)^{10} + 140 \, {\left(A + 2 \, B\right)} a^{2} \sin\left(d x + c\right)^{9} + 315 \, {\left(A - B\right)} a^{2} \sin\left(d x + c\right)^{8} - 360 \, {\left(A + 3 \, B\right)} a^{2} \sin\left(d x + c\right)^{7} - 1260 \, A a^{2} \sin\left(d x + c\right)^{6} + 1512 \, B a^{2} \sin\left(d x + c\right)^{5} + 630 \, {\left(3 \, A + B\right)} a^{2} \sin\left(d x + c\right)^{4} + 840 \, {\left(A - B\right)} a^{2} \sin\left(d x + c\right)^{3} - 630 \, {\left(2 \, A + B\right)} a^{2} \sin\left(d x + c\right)^{2} - 1260 \, A a^{2} \sin\left(d x + c\right)}{1260 \, d}"," ",0,"-1/1260*(126*B*a^2*sin(d*x + c)^10 + 140*(A + 2*B)*a^2*sin(d*x + c)^9 + 315*(A - B)*a^2*sin(d*x + c)^8 - 360*(A + 3*B)*a^2*sin(d*x + c)^7 - 1260*A*a^2*sin(d*x + c)^6 + 1512*B*a^2*sin(d*x + c)^5 + 630*(3*A + B)*a^2*sin(d*x + c)^4 + 840*(A - B)*a^2*sin(d*x + c)^3 - 630*(2*A + B)*a^2*sin(d*x + c)^2 - 1260*A*a^2*sin(d*x + c))/d","A",0
970,1,142,0,0.314229," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{105 \, B a^{2} \sin\left(d x + c\right)^{8} + 120 \, {\left(A + 2 \, B\right)} a^{2} \sin\left(d x + c\right)^{7} + 140 \, {\left(2 \, A - B\right)} a^{2} \sin\left(d x + c\right)^{6} - 168 \, {\left(A + 4 \, B\right)} a^{2} \sin\left(d x + c\right)^{5} - 210 \, {\left(4 \, A + B\right)} a^{2} \sin\left(d x + c\right)^{4} - 280 \, {\left(A - 2 \, B\right)} a^{2} \sin\left(d x + c\right)^{3} + 420 \, {\left(2 \, A + B\right)} a^{2} \sin\left(d x + c\right)^{2} + 840 \, A a^{2} \sin\left(d x + c\right)}{840 \, d}"," ",0,"1/840*(105*B*a^2*sin(d*x + c)^8 + 120*(A + 2*B)*a^2*sin(d*x + c)^7 + 140*(2*A - B)*a^2*sin(d*x + c)^6 - 168*(A + 4*B)*a^2*sin(d*x + c)^5 - 210*(4*A + B)*a^2*sin(d*x + c)^4 - 280*(A - 2*B)*a^2*sin(d*x + c)^3 + 420*(2*A + B)*a^2*sin(d*x + c)^2 + 840*A*a^2*sin(d*x + c))/d","A",0
971,1,96,0,0.311785," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, B a^{2} \sin\left(d x + c\right)^{6} + 6 \, {\left(A + 2 \, B\right)} a^{2} \sin\left(d x + c\right)^{5} + 15 \, A a^{2} \sin\left(d x + c\right)^{4} - 20 \, B a^{2} \sin\left(d x + c\right)^{3} - 15 \, {\left(2 \, A + B\right)} a^{2} \sin\left(d x + c\right)^{2} - 30 \, A a^{2} \sin\left(d x + c\right)}{30 \, d}"," ",0,"-1/30*(5*B*a^2*sin(d*x + c)^6 + 6*(A + 2*B)*a^2*sin(d*x + c)^5 + 15*A*a^2*sin(d*x + c)^4 - 20*B*a^2*sin(d*x + c)^3 - 15*(2*A + B)*a^2*sin(d*x + c)^2 - 30*A*a^2*sin(d*x + c))/d","A",0
972,1,68,0,0.312212," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, B a^{2} \sin\left(d x + c\right)^{4} + 4 \, {\left(A + 2 \, B\right)} a^{2} \sin\left(d x + c\right)^{3} + 6 \, {\left(2 \, A + B\right)} a^{2} \sin\left(d x + c\right)^{2} + 12 \, A a^{2} \sin\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(3*B*a^2*sin(d*x + c)^4 + 4*(A + 2*B)*a^2*sin(d*x + c)^3 + 6*(2*A + B)*a^2*sin(d*x + c)^2 + 12*A*a^2*sin(d*x + c))/d","A",0
973,1,52,0,0.311440," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{B a^{2} \sin\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*sin(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
974,1,37,0,0.350284," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{B a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{{\left(A + B\right)} a^{2}}{\sin\left(d x + c\right) - 1}}{d}"," ",0,"(B*a^2*log(sin(d*x + c) - 1) - (A + B)*a^2/(sin(d*x + c) - 1))/d","A",0
975,1,87,0,0.492198," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(A - B\right)} a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A - B\right)} a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left({\left(A - B\right)} a^{2} \sin\left(d x + c\right) - 2 \, A a^{2}\right)}}{\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1}}{8 \, d}"," ",0,"1/8*((A - B)*a^2*log(sin(d*x + c) + 1) - (A - B)*a^2*log(sin(d*x + c) - 1) - 2*((A - B)*a^2*sin(d*x + c) - 2*A*a^2)/(sin(d*x + c)^2 - 2*sin(d*x + c) + 1))/d","A",0
976,1,148,0,0.433300," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(2 \, A - B\right)} a^{2} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(2 \, A - B\right)} a^{2} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(2 \, A - B\right)} a^{2} \sin\left(d x + c\right)^{3} - 6 \, {\left(2 \, A - B\right)} a^{2} \sin\left(d x + c\right)^{2} + {\left(2 \, A - B\right)} a^{2} \sin\left(d x + c\right) + 2 \, {\left(4 \, A + B\right)} a^{2}\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{3} + 2 \, \sin\left(d x + c\right) - 1}}{48 \, d}"," ",0,"1/48*(3*(2*A - B)*a^2*log(sin(d*x + c) + 1) - 3*(2*A - B)*a^2*log(sin(d*x + c) - 1) - 2*(3*(2*A - B)*a^2*sin(d*x + c)^3 - 6*(2*A - B)*a^2*sin(d*x + c)^2 + (2*A - B)*a^2*sin(d*x + c) + 2*(4*A + B)*a^2)/(sin(d*x + c)^4 - 2*sin(d*x + c)^3 + 2*sin(d*x + c) - 1))/d","A",0
977,1,208,0,0.335990," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{18432 \, A a^{2} \cos\left(d x + c\right)^{7} + 9216 \, B a^{2} \cos\left(d x + c\right)^{7} - 21 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} A a^{2} + 336 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 1024 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} B a^{2} - 42 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{2}}{64512 \, d}"," ",0,"-1/64512*(18432*A*a^2*cos(d*x + c)^7 + 9216*B*a^2*cos(d*x + c)^7 - 21*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*A*a^2 + 336*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^2 - 1024*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*B*a^2 - 42*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*B*a^2)/d","A",0
978,1,171,0,0.452061," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2688 \, A a^{2} \cos\left(d x + c\right)^{5} + 1344 \, B a^{2} \cos\left(d x + c\right)^{5} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} A a^{2} - 210 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 192 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} B a^{2} - 70 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{2}}{6720 \, d}"," ",0,"-1/6720*(2688*A*a^2*cos(d*x + c)^5 + 1344*B*a^2*cos(d*x + c)^5 - 35*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*A*a^2 - 210*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^2 - 192*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*B*a^2 - 70*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*B*a^2)/d","A",0
979,1,134,0,0.331731," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{320 \, A a^{2} \cos\left(d x + c\right)^{3} + 160 \, B a^{2} \cos\left(d x + c\right)^{3} - 15 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} A a^{2} - 120 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{2} - 32 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} B a^{2} - 30 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{2}}{480 \, d}"," ",0,"-1/480*(320*A*a^2*cos(d*x + c)^3 + 160*B*a^2*cos(d*x + c)^3 - 15*(4*d*x + 4*c - sin(4*d*x + 4*c))*A*a^2 - 120*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^2 - 32*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*B*a^2 - 30*(4*d*x + 4*c - sin(4*d*x + 4*c))*B*a^2)/d","A",0
980,1,104,0,0.497787," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} A a^{2} + 2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} B a^{2} - B a^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - A a^{2} \tan\left(d x + c\right) - \frac{2 \, A a^{2}}{\cos\left(d x + c\right)} - \frac{B a^{2}}{\cos\left(d x + c\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*A*a^2 + 2*(d*x + c - tan(d*x + c))*B*a^2 - B*a^2*(1/cos(d*x + c) + cos(d*x + c)) - A*a^2*tan(d*x + c) - 2*A*a^2/cos(d*x + c) - B*a^2/cos(d*x + c))/d","A",0
981,1,108,0,0.440777," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{A a^{2} \tan\left(d x + c\right)^{3} + 2 \, B a^{2} \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{2} - \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} B a^{2}}{\cos\left(d x + c\right)^{3}} + \frac{2 \, A a^{2}}{\cos\left(d x + c\right)^{3}} + \frac{B a^{2}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(A*a^2*tan(d*x + c)^3 + 2*B*a^2*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^2 - (3*cos(d*x + c)^2 - 1)*B*a^2/cos(d*x + c)^3 + 2*A*a^2/cos(d*x + c)^3 + B*a^2/cos(d*x + c)^3)/d","A",0
982,1,147,0,0.483153," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{2} + {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} A a^{2} + 2 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} B a^{2} - \frac{{\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} B a^{2}}{\cos\left(d x + c\right)^{5}} + \frac{6 \, A a^{2}}{\cos\left(d x + c\right)^{5}} + \frac{3 \, B a^{2}}{\cos\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*((3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^2 + (3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*A*a^2 + 2*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*B*a^2 - (5*cos(d*x + c)^2 - 3)*B*a^2/cos(d*x + c)^5 + 6*A*a^2/cos(d*x + c)^5 + 3*B*a^2/cos(d*x + c)^5)/d","A",0
983,1,178,0,0.343046," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} A a^{2} + 3 \, {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} A a^{2} + 2 \, {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} B a^{2} - \frac{3 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} B a^{2}}{\cos\left(d x + c\right)^{7}} + \frac{30 \, A a^{2}}{\cos\left(d x + c\right)^{7}} + \frac{15 \, B a^{2}}{\cos\left(d x + c\right)^{7}}}{105 \, d}"," ",0,"1/105*((15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*A*a^2 + 3*(5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*A*a^2 + 2*(15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*B*a^2 - 3*(7*cos(d*x + c)^2 - 5)*B*a^2/cos(d*x + c)^7 + 30*A*a^2/cos(d*x + c)^7 + 15*B*a^2/cos(d*x + c)^7)/d","A",0
984,1,207,0,0.470714," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(35 \, \tan\left(d x + c\right)^{9} + 180 \, \tan\left(d x + c\right)^{7} + 378 \, \tan\left(d x + c\right)^{5} + 420 \, \tan\left(d x + c\right)^{3} + 315 \, \tan\left(d x + c\right)\right)} A a^{2} + {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} A a^{2} + 2 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} B a^{2} - \frac{5 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 7\right)} B a^{2}}{\cos\left(d x + c\right)^{9}} + \frac{70 \, A a^{2}}{\cos\left(d x + c\right)^{9}} + \frac{35 \, B a^{2}}{\cos\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"1/315*((35*tan(d*x + c)^9 + 180*tan(d*x + c)^7 + 378*tan(d*x + c)^5 + 420*tan(d*x + c)^3 + 315*tan(d*x + c))*A*a^2 + (35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*A*a^2 + 2*(35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*B*a^2 - 5*(9*cos(d*x + c)^2 - 7)*B*a^2/cos(d*x + c)^9 + 70*A*a^2/cos(d*x + c)^9 + 35*B*a^2/cos(d*x + c)^9)/d","A",0
985,1,238,0,0.705804," ","integrate(sec(d*x+c)^12*(a+a*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(315 \, \tan\left(d x + c\right)^{11} + 1540 \, \tan\left(d x + c\right)^{9} + 2970 \, \tan\left(d x + c\right)^{7} + 2772 \, \tan\left(d x + c\right)^{5} + 1155 \, \tan\left(d x + c\right)^{3}\right)} A a^{2} + 5 \, {\left(63 \, \tan\left(d x + c\right)^{11} + 385 \, \tan\left(d x + c\right)^{9} + 990 \, \tan\left(d x + c\right)^{7} + 1386 \, \tan\left(d x + c\right)^{5} + 1155 \, \tan\left(d x + c\right)^{3} + 693 \, \tan\left(d x + c\right)\right)} A a^{2} + 2 \, {\left(315 \, \tan\left(d x + c\right)^{11} + 1540 \, \tan\left(d x + c\right)^{9} + 2970 \, \tan\left(d x + c\right)^{7} + 2772 \, \tan\left(d x + c\right)^{5} + 1155 \, \tan\left(d x + c\right)^{3}\right)} B a^{2} - \frac{35 \, {\left(11 \, \cos\left(d x + c\right)^{2} - 9\right)} B a^{2}}{\cos\left(d x + c\right)^{11}} + \frac{630 \, A a^{2}}{\cos\left(d x + c\right)^{11}} + \frac{315 \, B a^{2}}{\cos\left(d x + c\right)^{11}}}{3465 \, d}"," ",0,"1/3465*((315*tan(d*x + c)^11 + 1540*tan(d*x + c)^9 + 2970*tan(d*x + c)^7 + 2772*tan(d*x + c)^5 + 1155*tan(d*x + c)^3)*A*a^2 + 5*(63*tan(d*x + c)^11 + 385*tan(d*x + c)^9 + 990*tan(d*x + c)^7 + 1386*tan(d*x + c)^5 + 1155*tan(d*x + c)^3 + 693*tan(d*x + c))*A*a^2 + 2*(315*tan(d*x + c)^11 + 1540*tan(d*x + c)^9 + 2970*tan(d*x + c)^7 + 2772*tan(d*x + c)^5 + 1155*tan(d*x + c)^3)*B*a^2 - 35*(11*cos(d*x + c)^2 - 9)*B*a^2/cos(d*x + c)^11 + 630*A*a^2/cos(d*x + c)^11 + 315*B*a^2/cos(d*x + c)^11)/d","A",0
986,1,182,0,0.509268," ","integrate(cos(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{210 \, B a^{3} \sin\left(d x + c\right)^{11} + 231 \, {\left(A + 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{10} + 770 \, A a^{3} \sin\left(d x + c\right)^{9} - 2310 \, B a^{3} \sin\left(d x + c\right)^{8} - 660 \, {\left(4 \, A + 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{7} - 2310 \, {\left(A - B\right)} a^{3} \sin\left(d x + c\right)^{6} + 924 \, {\left(3 \, A + 4 \, B\right)} a^{3} \sin\left(d x + c\right)^{5} + 4620 \, A a^{3} \sin\left(d x + c\right)^{4} - 2310 \, B a^{3} \sin\left(d x + c\right)^{3} - 1155 \, {\left(3 \, A + B\right)} a^{3} \sin\left(d x + c\right)^{2} - 2310 \, A a^{3} \sin\left(d x + c\right)}{2310 \, d}"," ",0,"-1/2310*(210*B*a^3*sin(d*x + c)^11 + 231*(A + 3*B)*a^3*sin(d*x + c)^10 + 770*A*a^3*sin(d*x + c)^9 - 2310*B*a^3*sin(d*x + c)^8 - 660*(4*A + 3*B)*a^3*sin(d*x + c)^7 - 2310*(A - B)*a^3*sin(d*x + c)^6 + 924*(3*A + 4*B)*a^3*sin(d*x + c)^5 + 4620*A*a^3*sin(d*x + c)^4 - 2310*B*a^3*sin(d*x + c)^3 - 1155*(3*A + B)*a^3*sin(d*x + c)^2 - 2310*A*a^3*sin(d*x + c))/d","A",0
987,1,158,0,0.365367," ","integrate(cos(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{56 \, B a^{3} \sin\left(d x + c\right)^{9} + 63 \, {\left(A + 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{8} + 72 \, {\left(3 \, A + B\right)} a^{3} \sin\left(d x + c\right)^{7} + 84 \, {\left(A - 5 \, B\right)} a^{3} \sin\left(d x + c\right)^{6} - 504 \, {\left(A + B\right)} a^{3} \sin\left(d x + c\right)^{5} - 126 \, {\left(5 \, A - B\right)} a^{3} \sin\left(d x + c\right)^{4} + 168 \, {\left(A + 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{3} + 252 \, {\left(3 \, A + B\right)} a^{3} \sin\left(d x + c\right)^{2} + 504 \, A a^{3} \sin\left(d x + c\right)}{504 \, d}"," ",0,"1/504*(56*B*a^3*sin(d*x + c)^9 + 63*(A + 3*B)*a^3*sin(d*x + c)^8 + 72*(3*A + B)*a^3*sin(d*x + c)^7 + 84*(A - 5*B)*a^3*sin(d*x + c)^6 - 504*(A + B)*a^3*sin(d*x + c)^5 - 126*(5*A - B)*a^3*sin(d*x + c)^4 + 168*(A + 3*B)*a^3*sin(d*x + c)^3 + 252*(3*A + B)*a^3*sin(d*x + c)^2 + 504*A*a^3*sin(d*x + c))/d","A",0
988,1,126,0,0.442935," ","integrate(cos(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, B a^{3} \sin\left(d x + c\right)^{7} + 35 \, {\left(A + 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{6} + 42 \, {\left(3 \, A + 2 \, B\right)} a^{3} \sin\left(d x + c\right)^{5} + 105 \, {\left(A - B\right)} a^{3} \sin\left(d x + c\right)^{4} - 70 \, {\left(2 \, A + 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{3} - 105 \, {\left(3 \, A + B\right)} a^{3} \sin\left(d x + c\right)^{2} - 210 \, A a^{3} \sin\left(d x + c\right)}{210 \, d}"," ",0,"-1/210*(30*B*a^3*sin(d*x + c)^7 + 35*(A + 3*B)*a^3*sin(d*x + c)^6 + 42*(3*A + 2*B)*a^3*sin(d*x + c)^5 + 105*(A - B)*a^3*sin(d*x + c)^4 - 70*(2*A + 3*B)*a^3*sin(d*x + c)^3 - 105*(3*A + B)*a^3*sin(d*x + c)^2 - 210*A*a^3*sin(d*x + c))/d","A",0
989,1,84,0,0.308886," ","integrate(cos(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, B a^{3} \sin\left(d x + c\right)^{5} + 5 \, {\left(A + 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{4} + 20 \, {\left(A + B\right)} a^{3} \sin\left(d x + c\right)^{3} + 10 \, {\left(3 \, A + B\right)} a^{3} \sin\left(d x + c\right)^{2} + 20 \, A a^{3} \sin\left(d x + c\right)}{20 \, d}"," ",0,"1/20*(4*B*a^3*sin(d*x + c)^5 + 5*(A + 3*B)*a^3*sin(d*x + c)^4 + 20*(A + B)*a^3*sin(d*x + c)^3 + 10*(3*A + B)*a^3*sin(d*x + c)^2 + 20*A*a^3*sin(d*x + c))/d","A",0
990,1,73,0,0.352817," ","integrate(sec(d*x+c)*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, B a^{3} \sin\left(d x + c\right)^{3} + 3 \, {\left(A + 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{2} + 24 \, {\left(A + B\right)} a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + 6 \, {\left(3 \, A + 4 \, B\right)} a^{3} \sin\left(d x + c\right)}{6 \, d}"," ",0,"-1/6*(2*B*a^3*sin(d*x + c)^3 + 3*(A + 3*B)*a^3*sin(d*x + c)^2 + 24*(A + B)*a^3*log(sin(d*x + c) - 1) + 6*(3*A + 4*B)*a^3*sin(d*x + c))/d","A",0
991,1,52,0,0.306244," ","integrate(sec(d*x+c)^3*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(A + 3 \, B\right)} a^{3} \log\left(\sin\left(d x + c\right) - 1\right) + B a^{3} \sin\left(d x + c\right) - \frac{2 \, {\left(A + B\right)} a^{3}}{\sin\left(d x + c\right) - 1}}{d}"," ",0,"((A + 3*B)*a^3*log(sin(d*x + c) - 1) + B*a^3*sin(d*x + c) - 2*(A + B)*a^3/(sin(d*x + c) - 1))/d","A",0
992,1,47,0,0.304507," ","integrate(sec(d*x+c)^5*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B a^{3} \sin\left(d x + c\right) + {\left(A - B\right)} a^{3}}{2 \, {\left(\sin\left(d x + c\right)^{2} - 2 \, \sin\left(d x + c\right) + 1\right)} d}"," ",0,"1/2*(2*B*a^3*sin(d*x + c) + (A - B)*a^3)/((sin(d*x + c)^2 - 2*sin(d*x + c) + 1)*d)","A",0
993,1,123,0,0.307229," ","integrate(sec(d*x+c)^7*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(A - B\right)} a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(A - B\right)} a^{3} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(A - B\right)} a^{3} \sin\left(d x + c\right)^{2} - 9 \, {\left(A - B\right)} a^{3} \sin\left(d x + c\right) + 2 \, {\left(5 \, A - B\right)} a^{3}\right)}}{\sin\left(d x + c\right)^{3} - 3 \, \sin\left(d x + c\right)^{2} + 3 \, \sin\left(d x + c\right) - 1}}{48 \, d}"," ",0,"1/48*(3*(A - B)*a^3*log(sin(d*x + c) + 1) - 3*(A - B)*a^3*log(sin(d*x + c) - 1) - 2*(3*(A - B)*a^3*sin(d*x + c)^2 - 9*(A - B)*a^3*sin(d*x + c) + 2*(5*A - B)*a^3)/(sin(d*x + c)^3 - 3*sin(d*x + c)^2 + 3*sin(d*x + c) - 1))/d","A",0
994,1,185,0,0.318385," ","integrate(sec(d*x+c)^9*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, A - 3 \, B\right)} a^{3} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A - 3 \, B\right)} a^{3} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(5 \, A - 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{4} - 9 \, {\left(5 \, A - 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{3} + 7 \, {\left(5 \, A - 3 \, B\right)} a^{3} \sin\left(d x + c\right)^{2} + 3 \, {\left(5 \, A - 3 \, B\right)} a^{3} \sin\left(d x + c\right) - 32 \, A a^{3}\right)}}{\sin\left(d x + c\right)^{5} - 3 \, \sin\left(d x + c\right)^{4} + 2 \, \sin\left(d x + c\right)^{3} + 2 \, \sin\left(d x + c\right)^{2} - 3 \, \sin\left(d x + c\right) + 1}}{192 \, d}"," ",0,"1/192*(3*(5*A - 3*B)*a^3*log(sin(d*x + c) + 1) - 3*(5*A - 3*B)*a^3*log(sin(d*x + c) - 1) - 2*(3*(5*A - 3*B)*a^3*sin(d*x + c)^4 - 9*(5*A - 3*B)*a^3*sin(d*x + c)^3 + 7*(5*A - 3*B)*a^3*sin(d*x + c)^2 + 3*(5*A - 3*B)*a^3*sin(d*x + c) - 32*A*a^3)/(sin(d*x + c)^5 - 3*sin(d*x + c)^4 + 2*sin(d*x + c)^3 + 2*sin(d*x + c)^2 - 3*sin(d*x + c) + 1))/d","A",0
995,1,284,0,0.335824," ","integrate(cos(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{276480 \, A a^{3} \cos\left(d x + c\right)^{7} + 92160 \, B a^{3} \cos\left(d x + c\right)^{7} - 10240 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} A a^{3} - 630 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} A a^{3} + 3360 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 30720 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} B a^{3} - 63 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{3} - 630 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{3}}{645120 \, d}"," ",0,"-1/645120*(276480*A*a^3*cos(d*x + c)^7 + 92160*B*a^3*cos(d*x + c)^7 - 10240*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*A*a^3 - 630*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*A*a^3 + 3360*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*A*a^3 - 30720*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*B*a^3 - 63*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*B*a^3 - 630*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*B*a^3)/d","A",0
996,1,232,0,0.324957," ","integrate(cos(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{21504 \, A a^{3} \cos\left(d x + c\right)^{5} + 7168 \, B a^{3} \cos\left(d x + c\right)^{5} - 1024 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} A a^{3} - 560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} A a^{3} - 1120 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 3072 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} B a^{3} - 560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{3} - 35 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{3}}{35840 \, d}"," ",0,"-1/35840*(21504*A*a^3*cos(d*x + c)^5 + 7168*B*a^3*cos(d*x + c)^5 - 1024*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*A*a^3 - 560*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*A*a^3 - 1120*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*A*a^3 - 3072*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*B*a^3 - 560*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*B*a^3 - 35*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*B*a^3)/d","A",0
997,1,199,0,0.319494," ","integrate(cos(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{960 \, A a^{3} \cos\left(d x + c\right)^{3} + 320 \, B a^{3} \cos\left(d x + c\right)^{3} - 64 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} A a^{3} - 90 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} A a^{3} - 240 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} A a^{3} - 192 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} B a^{3} + 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{3} - 90 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} B a^{3}}{960 \, d}"," ",0,"-1/960*(960*A*a^3*cos(d*x + c)^3 + 320*B*a^3*cos(d*x + c)^3 - 64*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*A*a^3 - 90*(4*d*x + 4*c - sin(4*d*x + 4*c))*A*a^3 - 240*(2*d*x + 2*c + sin(2*d*x + 2*c))*A*a^3 - 192*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*B*a^3 + 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*B*a^3 - 90*(4*d*x + 4*c - sin(4*d*x + 4*c))*B*a^3)/d","A",0
998,1,167,0,0.414085," ","integrate(sec(d*x+c)^2*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} A a^{3} + {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} B a^{3} + 6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} B a^{3} - 2 \, A a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - 6 \, B a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - 2 \, A a^{3} \tan\left(d x + c\right) - \frac{6 \, A a^{3}}{\cos\left(d x + c\right)} - \frac{2 \, B a^{3}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(6*(d*x + c - tan(d*x + c))*A*a^3 + (3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*B*a^3 + 6*(d*x + c - tan(d*x + c))*B*a^3 - 2*A*a^3*(1/cos(d*x + c) + cos(d*x + c)) - 6*B*a^3*(1/cos(d*x + c) + cos(d*x + c)) - 2*A*a^3*tan(d*x + c) - 6*A*a^3/cos(d*x + c) - 2*B*a^3/cos(d*x + c))/d","A",0
999,1,164,0,0.421110," ","integrate(sec(d*x+c)^4*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, A a^{3} \tan\left(d x + c\right)^{3} + 3 \, B a^{3} \tan\left(d x + c\right)^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, \tan\left(d x + c\right)\right)} A a^{3} + {\left(\tan\left(d x + c\right)^{3} + 3 \, d x + 3 \, c - 3 \, \tan\left(d x + c\right)\right)} B a^{3} - \frac{{\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} A a^{3}}{\cos\left(d x + c\right)^{3}} - \frac{3 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 1\right)} B a^{3}}{\cos\left(d x + c\right)^{3}} + \frac{3 \, A a^{3}}{\cos\left(d x + c\right)^{3}} + \frac{B a^{3}}{\cos\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(3*A*a^3*tan(d*x + c)^3 + 3*B*a^3*tan(d*x + c)^3 + (tan(d*x + c)^3 + 3*tan(d*x + c))*A*a^3 + (tan(d*x + c)^3 + 3*d*x + 3*c - 3*tan(d*x + c))*B*a^3 - (3*cos(d*x + c)^2 - 1)*A*a^3/cos(d*x + c)^3 - 3*(3*cos(d*x + c)^2 - 1)*B*a^3/cos(d*x + c)^3 + 3*A*a^3/cos(d*x + c)^3 + B*a^3/cos(d*x + c)^3)/d","B",0
1000,1,188,0,0.334415," ","integrate(sec(d*x+c)^6*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, B a^{3} \tan\left(d x + c\right)^{5} + {\left(3 \, \tan\left(d x + c\right)^{5} + 10 \, \tan\left(d x + c\right)^{3} + 15 \, \tan\left(d x + c\right)\right)} A a^{3} + 3 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} A a^{3} + 3 \, {\left(3 \, \tan\left(d x + c\right)^{5} + 5 \, \tan\left(d x + c\right)^{3}\right)} B a^{3} - \frac{{\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} A a^{3}}{\cos\left(d x + c\right)^{5}} - \frac{3 \, {\left(5 \, \cos\left(d x + c\right)^{2} - 3\right)} B a^{3}}{\cos\left(d x + c\right)^{5}} + \frac{9 \, A a^{3}}{\cos\left(d x + c\right)^{5}} + \frac{3 \, B a^{3}}{\cos\left(d x + c\right)^{5}}}{15 \, d}"," ",0,"1/15*(3*B*a^3*tan(d*x + c)^5 + (3*tan(d*x + c)^5 + 10*tan(d*x + c)^3 + 15*tan(d*x + c))*A*a^3 + 3*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*A*a^3 + 3*(3*tan(d*x + c)^5 + 5*tan(d*x + c)^3)*B*a^3 - (5*cos(d*x + c)^2 - 3)*A*a^3/cos(d*x + c)^5 - 3*(5*cos(d*x + c)^2 - 3)*B*a^3/cos(d*x + c)^5 + 9*A*a^3/cos(d*x + c)^5 + 3*B*a^3/cos(d*x + c)^5)/d","A",0
1001,1,228,0,0.370090," ","integrate(sec(d*x+c)^8*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} A a^{3} + {\left(5 \, \tan\left(d x + c\right)^{7} + 21 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3} + 35 \, \tan\left(d x + c\right)\right)} A a^{3} + {\left(15 \, \tan\left(d x + c\right)^{7} + 42 \, \tan\left(d x + c\right)^{5} + 35 \, \tan\left(d x + c\right)^{3}\right)} B a^{3} + {\left(5 \, \tan\left(d x + c\right)^{7} + 7 \, \tan\left(d x + c\right)^{5}\right)} B a^{3} - \frac{{\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} A a^{3}}{\cos\left(d x + c\right)^{7}} - \frac{3 \, {\left(7 \, \cos\left(d x + c\right)^{2} - 5\right)} B a^{3}}{\cos\left(d x + c\right)^{7}} + \frac{15 \, A a^{3}}{\cos\left(d x + c\right)^{7}} + \frac{5 \, B a^{3}}{\cos\left(d x + c\right)^{7}}}{35 \, d}"," ",0,"1/35*((15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*A*a^3 + (5*tan(d*x + c)^7 + 21*tan(d*x + c)^5 + 35*tan(d*x + c)^3 + 35*tan(d*x + c))*A*a^3 + (15*tan(d*x + c)^7 + 42*tan(d*x + c)^5 + 35*tan(d*x + c)^3)*B*a^3 + (5*tan(d*x + c)^7 + 7*tan(d*x + c)^5)*B*a^3 - (7*cos(d*x + c)^2 - 5)*A*a^3/cos(d*x + c)^7 - 3*(7*cos(d*x + c)^2 - 5)*B*a^3/cos(d*x + c)^7 + 15*A*a^3/cos(d*x + c)^7 + 5*B*a^3/cos(d*x + c)^7)/d","B",0
1002,1,270,0,0.354988," ","integrate(sec(d*x+c)^10*(a+a*sin(d*x+c))^3*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(35 \, \tan\left(d x + c\right)^{9} + 180 \, \tan\left(d x + c\right)^{7} + 378 \, \tan\left(d x + c\right)^{5} + 420 \, \tan\left(d x + c\right)^{3} + 315 \, \tan\left(d x + c\right)\right)} A a^{3} + 3 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} A a^{3} + 3 \, {\left(35 \, \tan\left(d x + c\right)^{9} + 135 \, \tan\left(d x + c\right)^{7} + 189 \, \tan\left(d x + c\right)^{5} + 105 \, \tan\left(d x + c\right)^{3}\right)} B a^{3} + {\left(35 \, \tan\left(d x + c\right)^{9} + 90 \, \tan\left(d x + c\right)^{7} + 63 \, \tan\left(d x + c\right)^{5}\right)} B a^{3} - \frac{5 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 7\right)} A a^{3}}{\cos\left(d x + c\right)^{9}} - \frac{15 \, {\left(9 \, \cos\left(d x + c\right)^{2} - 7\right)} B a^{3}}{\cos\left(d x + c\right)^{9}} + \frac{105 \, A a^{3}}{\cos\left(d x + c\right)^{9}} + \frac{35 \, B a^{3}}{\cos\left(d x + c\right)^{9}}}{315 \, d}"," ",0,"1/315*((35*tan(d*x + c)^9 + 180*tan(d*x + c)^7 + 378*tan(d*x + c)^5 + 420*tan(d*x + c)^3 + 315*tan(d*x + c))*A*a^3 + 3*(35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*A*a^3 + 3*(35*tan(d*x + c)^9 + 135*tan(d*x + c)^7 + 189*tan(d*x + c)^5 + 105*tan(d*x + c)^3)*B*a^3 + (35*tan(d*x + c)^9 + 90*tan(d*x + c)^7 + 63*tan(d*x + c)^5)*B*a^3 - 5*(9*cos(d*x + c)^2 - 7)*A*a^3/cos(d*x + c)^9 - 15*(9*cos(d*x + c)^2 - 7)*B*a^3/cos(d*x + c)^9 + 105*A*a^3/cos(d*x + c)^9 + 35*B*a^3/cos(d*x + c)^9)/d","B",0
1003,1,104,0,0.319952," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, B \sin\left(d x + c\right)^{7} + 35 \, {\left(A - B\right)} \sin\left(d x + c\right)^{6} - 42 \, {\left(A + 2 \, B\right)} \sin\left(d x + c\right)^{5} - 105 \, {\left(A - B\right)} \sin\left(d x + c\right)^{4} + 70 \, {\left(2 \, A + B\right)} \sin\left(d x + c\right)^{3} + 105 \, {\left(A - B\right)} \sin\left(d x + c\right)^{2} - 210 \, A \sin\left(d x + c\right)}{210 \, a d}"," ",0,"-1/210*(30*B*sin(d*x + c)^7 + 35*(A - B)*sin(d*x + c)^6 - 42*(A + 2*B)*sin(d*x + c)^5 - 105*(A - B)*sin(d*x + c)^4 + 70*(2*A + B)*sin(d*x + c)^3 + 105*(A - B)*sin(d*x + c)^2 - 210*A*sin(d*x + c))/(a*d)","A",0
1004,1,72,0,0.323916," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, B \sin\left(d x + c\right)^{5} + 15 \, {\left(A - B\right)} \sin\left(d x + c\right)^{4} - 20 \, {\left(A + B\right)} \sin\left(d x + c\right)^{3} - 30 \, {\left(A - B\right)} \sin\left(d x + c\right)^{2} + 60 \, A \sin\left(d x + c\right)}{60 \, a d}"," ",0,"1/60*(12*B*sin(d*x + c)^5 + 15*(A - B)*sin(d*x + c)^4 - 20*(A + B)*sin(d*x + c)^3 - 30*(A - B)*sin(d*x + c)^2 + 60*A*sin(d*x + c))/(a*d)","A",0
1005,1,44,0,0.333987," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, B \sin\left(d x + c\right)^{3} + 3 \, {\left(A - B\right)} \sin\left(d x + c\right)^{2} - 6 \, A \sin\left(d x + c\right)}{6 \, a d}"," ",0,"-1/6*(2*B*sin(d*x + c)^3 + 3*(A - B)*sin(d*x + c)^2 - 6*A*sin(d*x + c))/(a*d)","A",0
1006,1,34,0,0.321167," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{{\left(A - B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a} + \frac{B \sin\left(d x + c\right)}{a}}{d}"," ",0,"((A - B)*log(sin(d*x + c) + 1)/a + B*sin(d*x + c)/a)/d","A",0
1007,1,58,0,0.320596," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{{\left(A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{{\left(A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{2 \, {\left(A - B\right)}}{a \sin\left(d x + c\right) + a}}{4 \, d}"," ",0,"1/4*((A + B)*log(sin(d*x + c) + 1)/a - (A + B)*log(sin(d*x + c) - 1)/a - 2*(A - B)/(a*sin(d*x + c) + a))/d","A",0
1008,1,113,0,0.330643," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{{\left(3 \, A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{{\left(3 \, A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{2 \, {\left({\left(3 \, A + B\right)} \sin\left(d x + c\right)^{2} + {\left(3 \, A + B\right)} \sin\left(d x + c\right) - 2 \, A + 2 \, B\right)}}{a \sin\left(d x + c\right)^{3} + a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a}}{16 \, d}"," ",0,"1/16*((3*A + B)*log(sin(d*x + c) + 1)/a - (3*A + B)*log(sin(d*x + c) - 1)/a - 2*((3*A + B)*sin(d*x + c)^2 + (3*A + B)*sin(d*x + c) - 2*A + 2*B)/(a*sin(d*x + c)^3 + a*sin(d*x + c)^2 - a*sin(d*x + c) - a))/d","A",0
1009,1,165,0,0.345965," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{3 \, {\left(5 \, A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{3 \, {\left(5 \, A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{2 \, {\left(3 \, {\left(5 \, A + B\right)} \sin\left(d x + c\right)^{4} + 3 \, {\left(5 \, A + B\right)} \sin\left(d x + c\right)^{3} - 5 \, {\left(5 \, A + B\right)} \sin\left(d x + c\right)^{2} - 5 \, {\left(5 \, A + B\right)} \sin\left(d x + c\right) + 8 \, A - 8 \, B\right)}}{a \sin\left(d x + c\right)^{5} + a \sin\left(d x + c\right)^{4} - 2 \, a \sin\left(d x + c\right)^{3} - 2 \, a \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) + a}}{96 \, d}"," ",0,"1/96*(3*(5*A + B)*log(sin(d*x + c) + 1)/a - 3*(5*A + B)*log(sin(d*x + c) - 1)/a - 2*(3*(5*A + B)*sin(d*x + c)^4 + 3*(5*A + B)*sin(d*x + c)^3 - 5*(5*A + B)*sin(d*x + c)^2 - 5*(5*A + B)*sin(d*x + c) + 8*A - 8*B)/(a*sin(d*x + c)^5 + a*sin(d*x + c)^4 - 2*a*sin(d*x + c)^3 - 2*a*sin(d*x + c)^2 + a*sin(d*x + c) + a))/d","A",0
1010,1,220,0,0.341972," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{15 \, {\left(7 \, A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a} - \frac{15 \, {\left(7 \, A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a} - \frac{2 \, {\left(15 \, {\left(7 \, A + B\right)} \sin\left(d x + c\right)^{6} + 15 \, {\left(7 \, A + B\right)} \sin\left(d x + c\right)^{5} - 40 \, {\left(7 \, A + B\right)} \sin\left(d x + c\right)^{4} - 40 \, {\left(7 \, A + B\right)} \sin\left(d x + c\right)^{3} + 33 \, {\left(7 \, A + B\right)} \sin\left(d x + c\right)^{2} + 33 \, {\left(7 \, A + B\right)} \sin\left(d x + c\right) - 48 \, A + 48 \, B\right)}}{a \sin\left(d x + c\right)^{7} + a \sin\left(d x + c\right)^{6} - 3 \, a \sin\left(d x + c\right)^{5} - 3 \, a \sin\left(d x + c\right)^{4} + 3 \, a \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - a \sin\left(d x + c\right) - a}}{768 \, d}"," ",0,"1/768*(15*(7*A + B)*log(sin(d*x + c) + 1)/a - 15*(7*A + B)*log(sin(d*x + c) - 1)/a - 2*(15*(7*A + B)*sin(d*x + c)^6 + 15*(7*A + B)*sin(d*x + c)^5 - 40*(7*A + B)*sin(d*x + c)^4 - 40*(7*A + B)*sin(d*x + c)^3 + 33*(7*A + B)*sin(d*x + c)^2 + 33*(7*A + B)*sin(d*x + c) - 48*A + 48*B)/(a*sin(d*x + c)^7 + a*sin(d*x + c)^6 - 3*a*sin(d*x + c)^5 - 3*a*sin(d*x + c)^4 + 3*a*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - a*sin(d*x + c) - a))/d","A",0
1011,1,83,0,0.340021," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{5 \, B \sin\left(d x + c\right)^{6} + 6 \, {\left(A - 2 \, B\right)} \sin\left(d x + c\right)^{5} - 15 \, A \sin\left(d x + c\right)^{4} + 20 \, B \sin\left(d x + c\right)^{3} + 15 \, {\left(2 \, A - B\right)} \sin\left(d x + c\right)^{2} - 30 \, A \sin\left(d x + c\right)}{30 \, a^{2} d}"," ",0,"-1/30*(5*B*sin(d*x + c)^6 + 6*(A - 2*B)*sin(d*x + c)^5 - 15*A*sin(d*x + c)^4 + 20*B*sin(d*x + c)^3 + 15*(2*A - B)*sin(d*x + c)^2 - 30*A*sin(d*x + c))/(a^2*d)","A",0
1012,1,61,0,0.323379," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, B \sin\left(d x + c\right)^{4} + 4 \, {\left(A - 2 \, B\right)} \sin\left(d x + c\right)^{3} - 6 \, {\left(2 \, A - B\right)} \sin\left(d x + c\right)^{2} + 12 \, A \sin\left(d x + c\right)}{12 \, a^{2} d}"," ",0,"1/12*(3*B*sin(d*x + c)^4 + 4*(A - 2*B)*sin(d*x + c)^3 - 6*(2*A - B)*sin(d*x + c)^2 + 12*A*sin(d*x + c))/(a^2*d)","A",0
1013,1,54,0,0.321842," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{4 \, {\left(A - B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} - \frac{B \sin\left(d x + c\right)^{2} + 2 \, {\left(A - 2 \, B\right)} \sin\left(d x + c\right)}{a^{2}}}{2 \, d}"," ",0,"1/2*(4*(A - B)*log(sin(d*x + c) + 1)/a^2 - (B*sin(d*x + c)^2 + 2*(A - 2*B)*sin(d*x + c))/a^2)/d","A",0
1014,1,43,0,0.398523," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{A - B}{a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{B \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}}}{d}"," ",0,"-((A - B)/(a^2*sin(d*x + c) + a^2) - B*log(sin(d*x + c) + 1)/a^2)/d","A",0
1015,1,84,0,0.426371," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left({\left(A + B\right)} \sin\left(d x + c\right) + 2 \, A\right)}}{a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{{\left(A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{{\left(A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{8 \, d}"," ",0,"-1/8*(2*((A + B)*sin(d*x + c) + 2*A)/(a^2*sin(d*x + c)^2 + 2*a^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^2)/d","A",0
1016,1,139,0,0.419396," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(3 \, {\left(2 \, A + B\right)} \sin\left(d x + c\right)^{3} + 6 \, {\left(2 \, A + B\right)} \sin\left(d x + c\right)^{2} + {\left(2 \, A + B\right)} \sin\left(d x + c\right) - 8 \, A + 2 \, B\right)}}{a^{2} \sin\left(d x + c\right)^{4} + 2 \, a^{2} \sin\left(d x + c\right)^{3} - 2 \, a^{2} \sin\left(d x + c\right) - a^{2}} - \frac{3 \, {\left(2 \, A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{3 \, {\left(2 \, A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{48 \, d}"," ",0,"-1/48*(2*(3*(2*A + B)*sin(d*x + c)^3 + 6*(2*A + B)*sin(d*x + c)^2 + (2*A + B)*sin(d*x + c) - 8*A + 2*B)/(a^2*sin(d*x + c)^4 + 2*a^2*sin(d*x + c)^3 - 2*a^2*sin(d*x + c) - a^2) - 3*(2*A + B)*log(sin(d*x + c) + 1)/a^2 + 3*(2*A + B)*log(sin(d*x + c) - 1)/a^2)/d","A",0
1017,1,207,0,0.340242," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(15 \, {\left(3 \, A + B\right)} \sin\left(d x + c\right)^{5} + 30 \, {\left(3 \, A + B\right)} \sin\left(d x + c\right)^{4} - 10 \, {\left(3 \, A + B\right)} \sin\left(d x + c\right)^{3} - 50 \, {\left(3 \, A + B\right)} \sin\left(d x + c\right)^{2} - 17 \, {\left(3 \, A + B\right)} \sin\left(d x + c\right) + 48 \, A - 16 \, B\right)}}{a^{2} \sin\left(d x + c\right)^{6} + 2 \, a^{2} \sin\left(d x + c\right)^{5} - a^{2} \sin\left(d x + c\right)^{4} - 4 \, a^{2} \sin\left(d x + c\right)^{3} - a^{2} \sin\left(d x + c\right)^{2} + 2 \, a^{2} \sin\left(d x + c\right) + a^{2}} - \frac{15 \, {\left(3 \, A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{15 \, {\left(3 \, A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{384 \, d}"," ",0,"-1/384*(2*(15*(3*A + B)*sin(d*x + c)^5 + 30*(3*A + B)*sin(d*x + c)^4 - 10*(3*A + B)*sin(d*x + c)^3 - 50*(3*A + B)*sin(d*x + c)^2 - 17*(3*A + B)*sin(d*x + c) + 48*A - 16*B)/(a^2*sin(d*x + c)^6 + 2*a^2*sin(d*x + c)^5 - a^2*sin(d*x + c)^4 - 4*a^2*sin(d*x + c)^3 - a^2*sin(d*x + c)^2 + 2*a^2*sin(d*x + c) + a^2) - 15*(3*A + B)*log(sin(d*x + c) + 1)/a^2 + 15*(3*A + B)*log(sin(d*x + c) - 1)/a^2)/d","A",0
1018,1,252,0,0.353156," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+a*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(105 \, {\left(4 \, A + B\right)} \sin\left(d x + c\right)^{7} + 210 \, {\left(4 \, A + B\right)} \sin\left(d x + c\right)^{6} - 175 \, {\left(4 \, A + B\right)} \sin\left(d x + c\right)^{5} - 560 \, {\left(4 \, A + B\right)} \sin\left(d x + c\right)^{4} - 49 \, {\left(4 \, A + B\right)} \sin\left(d x + c\right)^{3} + 462 \, {\left(4 \, A + B\right)} \sin\left(d x + c\right)^{2} + 183 \, {\left(4 \, A + B\right)} \sin\left(d x + c\right) - 384 \, A + 144 \, B\right)}}{a^{2} \sin\left(d x + c\right)^{8} + 2 \, a^{2} \sin\left(d x + c\right)^{7} - 2 \, a^{2} \sin\left(d x + c\right)^{6} - 6 \, a^{2} \sin\left(d x + c\right)^{5} + 6 \, a^{2} \sin\left(d x + c\right)^{3} + 2 \, a^{2} \sin\left(d x + c\right)^{2} - 2 \, a^{2} \sin\left(d x + c\right) - a^{2}} - \frac{105 \, {\left(4 \, A + B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2}} + \frac{105 \, {\left(4 \, A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2}}}{3840 \, d}"," ",0,"-1/3840*(2*(105*(4*A + B)*sin(d*x + c)^7 + 210*(4*A + B)*sin(d*x + c)^6 - 175*(4*A + B)*sin(d*x + c)^5 - 560*(4*A + B)*sin(d*x + c)^4 - 49*(4*A + B)*sin(d*x + c)^3 + 462*(4*A + B)*sin(d*x + c)^2 + 183*(4*A + B)*sin(d*x + c) - 384*A + 144*B)/(a^2*sin(d*x + c)^8 + 2*a^2*sin(d*x + c)^7 - 2*a^2*sin(d*x + c)^6 - 6*a^2*sin(d*x + c)^5 + 6*a^2*sin(d*x + c)^3 + 2*a^2*sin(d*x + c)^2 - 2*a^2*sin(d*x + c) - a^2) - 105*(4*A + B)*log(sin(d*x + c) + 1)/a^2 + 105*(4*A + B)*log(sin(d*x + c) - 1)/a^2)/d","A",0
1019,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m, x)","F",0
1020,1,1207,0,0.426859," ","integrate(cos(f*x+e)^7*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{{\left({\left(m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720\right)} a^{m} \sin\left(f x + e\right)^{7} + {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} a^{m} \sin\left(f x + e\right)^{6} - 6 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} a^{m} \sin\left(f x + e\right)^{5} + 30 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(f x + e\right)^{4} - 120 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} + 360 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 720 \, a^{m} m \sin\left(f x + e\right) + 720 \, a^{m}\right)} A {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040} - \frac{3 \, {\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} a^{m} \sin\left(f x + e\right)^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(f x + e\right)^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} + 12 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 24 \, a^{m} m \sin\left(f x + e\right) + 24 \, a^{m}\right)} A {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120} + \frac{3 \, {\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(f x + e\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 2 \, a^{m} m \sin\left(f x + e\right) + 2 \, a^{m}\right)} A {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} + \frac{{\left({\left(m^{7} + 28 \, m^{6} + 322 \, m^{5} + 1960 \, m^{4} + 6769 \, m^{3} + 13132 \, m^{2} + 13068 \, m + 5040\right)} a^{m} \sin\left(f x + e\right)^{8} + {\left(m^{7} + 21 \, m^{6} + 175 \, m^{5} + 735 \, m^{4} + 1624 \, m^{3} + 1764 \, m^{2} + 720 \, m\right)} a^{m} \sin\left(f x + e\right)^{7} - 7 \, {\left(m^{6} + 15 \, m^{5} + 85 \, m^{4} + 225 \, m^{3} + 274 \, m^{2} + 120 \, m\right)} a^{m} \sin\left(f x + e\right)^{6} + 42 \, {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} a^{m} \sin\left(f x + e\right)^{5} - 210 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(f x + e\right)^{4} + 840 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} - 2520 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} + 5040 \, a^{m} m \sin\left(f x + e\right) - 5040 \, a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{8} + 36 \, m^{7} + 546 \, m^{6} + 4536 \, m^{5} + 22449 \, m^{4} + 67284 \, m^{3} + 118124 \, m^{2} + 109584 \, m + 40320} - \frac{3 \, {\left({\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} a^{m} \sin\left(f x + e\right)^{6} + {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} a^{m} \sin\left(f x + e\right)^{5} - 5 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(f x + e\right)^{4} + 20 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} - 60 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} + 120 \, a^{m} m \sin\left(f x + e\right) - 120 \, a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720} + \frac{3 \, {\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} a^{m} \sin\left(f x + e\right)^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} - 3 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} + 6 \, a^{m} m \sin\left(f x + e\right) - 6 \, a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24} - \frac{{\left(a^{m} {\left(m + 1\right)} \sin\left(f x + e\right)^{2} + a^{m} m \sin\left(f x + e\right) - a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{2} + 3 \, m + 2} - \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} A}{a {\left(m + 1\right)}}}{f}"," ",0,"-(((m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720)*a^m*sin(f*x + e)^7 + (m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*a^m*sin(f*x + e)^6 - 6*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*a^m*sin(f*x + e)^5 + 30*(m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(f*x + e)^4 - 120*(m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 + 360*(m^2 + m)*a^m*sin(f*x + e)^2 - 720*a^m*m*sin(f*x + e) + 720*a^m)*A*(sin(f*x + e) + 1)^m/(m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040) - 3*((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*a^m*sin(f*x + e)^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(f*x + e)^4 - 4*(m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 + 12*(m^2 + m)*a^m*sin(f*x + e)^2 - 24*a^m*m*sin(f*x + e) + 24*a^m)*A*(sin(f*x + e) + 1)^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120) + 3*((m^2 + 3*m + 2)*a^m*sin(f*x + e)^3 + (m^2 + m)*a^m*sin(f*x + e)^2 - 2*a^m*m*sin(f*x + e) + 2*a^m)*A*(sin(f*x + e) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) + ((m^7 + 28*m^6 + 322*m^5 + 1960*m^4 + 6769*m^3 + 13132*m^2 + 13068*m + 5040)*a^m*sin(f*x + e)^8 + (m^7 + 21*m^6 + 175*m^5 + 735*m^4 + 1624*m^3 + 1764*m^2 + 720*m)*a^m*sin(f*x + e)^7 - 7*(m^6 + 15*m^5 + 85*m^4 + 225*m^3 + 274*m^2 + 120*m)*a^m*sin(f*x + e)^6 + 42*(m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*a^m*sin(f*x + e)^5 - 210*(m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(f*x + e)^4 + 840*(m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 - 2520*(m^2 + m)*a^m*sin(f*x + e)^2 + 5040*a^m*m*sin(f*x + e) - 5040*a^m)*B*(sin(f*x + e) + 1)^m/(m^8 + 36*m^7 + 546*m^6 + 4536*m^5 + 22449*m^4 + 67284*m^3 + 118124*m^2 + 109584*m + 40320) - 3*((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*a^m*sin(f*x + e)^6 + (m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*a^m*sin(f*x + e)^5 - 5*(m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(f*x + e)^4 + 20*(m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 - 60*(m^2 + m)*a^m*sin(f*x + e)^2 + 120*a^m*m*sin(f*x + e) - 120*a^m)*B*(sin(f*x + e) + 1)^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720) + 3*((m^3 + 6*m^2 + 11*m + 6)*a^m*sin(f*x + e)^4 + (m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 - 3*(m^2 + m)*a^m*sin(f*x + e)^2 + 6*a^m*m*sin(f*x + e) - 6*a^m)*B*(sin(f*x + e) + 1)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24) - (a^m*(m + 1)*sin(f*x + e)^2 + a^m*m*sin(f*x + e) - a^m)*B*(sin(f*x + e) + 1)^m/(m^2 + 3*m + 2) - (a*sin(f*x + e) + a)^(m + 1)*A/(a*(m + 1)))/f","B",0
1021,1,643,0,0.421424," ","integrate(cos(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{{\left({\left(m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24\right)} a^{m} \sin\left(f x + e\right)^{5} + {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(f x + e\right)^{4} - 4 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} + 12 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 24 \, a^{m} m \sin\left(f x + e\right) + 24 \, a^{m}\right)} A {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120} - \frac{2 \, {\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(f x + e\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 2 \, a^{m} m \sin\left(f x + e\right) + 2 \, a^{m}\right)} A {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} + \frac{{\left({\left(m^{5} + 15 \, m^{4} + 85 \, m^{3} + 225 \, m^{2} + 274 \, m + 120\right)} a^{m} \sin\left(f x + e\right)^{6} + {\left(m^{5} + 10 \, m^{4} + 35 \, m^{3} + 50 \, m^{2} + 24 \, m\right)} a^{m} \sin\left(f x + e\right)^{5} - 5 \, {\left(m^{4} + 6 \, m^{3} + 11 \, m^{2} + 6 \, m\right)} a^{m} \sin\left(f x + e\right)^{4} + 20 \, {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} - 60 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} + 120 \, a^{m} m \sin\left(f x + e\right) - 120 \, a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{6} + 21 \, m^{5} + 175 \, m^{4} + 735 \, m^{3} + 1624 \, m^{2} + 1764 \, m + 720} - \frac{2 \, {\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} a^{m} \sin\left(f x + e\right)^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} - 3 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} + 6 \, a^{m} m \sin\left(f x + e\right) - 6 \, a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24} + \frac{{\left(a^{m} {\left(m + 1\right)} \sin\left(f x + e\right)^{2} + a^{m} m \sin\left(f x + e\right) - a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{2} + 3 \, m + 2} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} A}{a {\left(m + 1\right)}}}{f}"," ",0,"(((m^4 + 10*m^3 + 35*m^2 + 50*m + 24)*a^m*sin(f*x + e)^5 + (m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(f*x + e)^4 - 4*(m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 + 12*(m^2 + m)*a^m*sin(f*x + e)^2 - 24*a^m*m*sin(f*x + e) + 24*a^m)*A*(sin(f*x + e) + 1)^m/(m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120) - 2*((m^2 + 3*m + 2)*a^m*sin(f*x + e)^3 + (m^2 + m)*a^m*sin(f*x + e)^2 - 2*a^m*m*sin(f*x + e) + 2*a^m)*A*(sin(f*x + e) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) + ((m^5 + 15*m^4 + 85*m^3 + 225*m^2 + 274*m + 120)*a^m*sin(f*x + e)^6 + (m^5 + 10*m^4 + 35*m^3 + 50*m^2 + 24*m)*a^m*sin(f*x + e)^5 - 5*(m^4 + 6*m^3 + 11*m^2 + 6*m)*a^m*sin(f*x + e)^4 + 20*(m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 - 60*(m^2 + m)*a^m*sin(f*x + e)^2 + 120*a^m*m*sin(f*x + e) - 120*a^m)*B*(sin(f*x + e) + 1)^m/(m^6 + 21*m^5 + 175*m^4 + 735*m^3 + 1624*m^2 + 1764*m + 720) - 2*((m^3 + 6*m^2 + 11*m + 6)*a^m*sin(f*x + e)^4 + (m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 - 3*(m^2 + m)*a^m*sin(f*x + e)^2 + 6*a^m*m*sin(f*x + e) - 6*a^m)*B*(sin(f*x + e) + 1)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24) + (a^m*(m + 1)*sin(f*x + e)^2 + a^m*m*sin(f*x + e) - a^m)*B*(sin(f*x + e) + 1)^m/(m^2 + 3*m + 2) + (a*sin(f*x + e) + a)^(m + 1)*A/(a*(m + 1)))/f","B",0
1022,1,285,0,0.399837," ","integrate(cos(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{\frac{{\left({\left(m^{2} + 3 \, m + 2\right)} a^{m} \sin\left(f x + e\right)^{3} + {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} - 2 \, a^{m} m \sin\left(f x + e\right) + 2 \, a^{m}\right)} A {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{3} + 6 \, m^{2} + 11 \, m + 6} + \frac{{\left({\left(m^{3} + 6 \, m^{2} + 11 \, m + 6\right)} a^{m} \sin\left(f x + e\right)^{4} + {\left(m^{3} + 3 \, m^{2} + 2 \, m\right)} a^{m} \sin\left(f x + e\right)^{3} - 3 \, {\left(m^{2} + m\right)} a^{m} \sin\left(f x + e\right)^{2} + 6 \, a^{m} m \sin\left(f x + e\right) - 6 \, a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{4} + 10 \, m^{3} + 35 \, m^{2} + 50 \, m + 24} - \frac{{\left(a^{m} {\left(m + 1\right)} \sin\left(f x + e\right)^{2} + a^{m} m \sin\left(f x + e\right) - a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{2} + 3 \, m + 2} - \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} A}{a {\left(m + 1\right)}}}{f}"," ",0,"-(((m^2 + 3*m + 2)*a^m*sin(f*x + e)^3 + (m^2 + m)*a^m*sin(f*x + e)^2 - 2*a^m*m*sin(f*x + e) + 2*a^m)*A*(sin(f*x + e) + 1)^m/(m^3 + 6*m^2 + 11*m + 6) + ((m^3 + 6*m^2 + 11*m + 6)*a^m*sin(f*x + e)^4 + (m^3 + 3*m^2 + 2*m)*a^m*sin(f*x + e)^3 - 3*(m^2 + m)*a^m*sin(f*x + e)^2 + 6*a^m*m*sin(f*x + e) - 6*a^m)*B*(sin(f*x + e) + 1)^m/(m^4 + 10*m^3 + 35*m^2 + 50*m + 24) - (a^m*(m + 1)*sin(f*x + e)^2 + a^m*m*sin(f*x + e) - a^m)*B*(sin(f*x + e) + 1)^m/(m^2 + 3*m + 2) - (a*sin(f*x + e) + a)^(m + 1)*A/(a*(m + 1)))/f","B",0
1023,1,83,0,0.404944," ","integrate(cos(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\frac{\frac{{\left(a^{m} {\left(m + 1\right)} \sin\left(f x + e\right)^{2} + a^{m} m \sin\left(f x + e\right) - a^{m}\right)} B {\left(\sin\left(f x + e\right) + 1\right)}^{m}}{m^{2} + 3 \, m + 2} + \frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m + 1} A}{a {\left(m + 1\right)}}}{f}"," ",0,"((a^m*(m + 1)*sin(f*x + e)^2 + a^m*m*sin(f*x + e) - a^m)*B*(sin(f*x + e) + 1)^m/(m^2 + 3*m + 2) + (a*sin(f*x + e) + a)^(m + 1)*A/(a*(m + 1)))/f","A",0
1024,0,0,0,0.000000," ","integrate(sec(f*x+e)*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e), x)","F",0
1025,0,0,0,0.000000," ","integrate(sec(f*x+e)^3*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{3}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^3, x)","F",0
1026,0,0,0,0.000000," ","integrate(sec(f*x+e)^5*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{5}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^5, x)","F",0
1027,-1,0,0,0.000000," ","integrate(cos(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1028,-1,0,0,0.000000," ","integrate(cos(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1029,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
1030,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^2, x)","F",0
1031,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{4}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^4, x)","F",0
1032,0,0,0,0.000000," ","integrate(sec(f*x+e)^6*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \sec\left(f x + e\right)^{6}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*sec(f*x + e)^6, x)","F",0
1033,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-p),x, algorithm=""maxima"")","\int {\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 - 4}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 4), x)","F",0
1034,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-p),x, algorithm=""maxima"")","\int {\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 - 3}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 3), x)","F",0
1035,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-p),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 2), x)","F",0
1036,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-p),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p - 1), x)","F",0
1037,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^p),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p/(-c*sin(f*x + e) + c)^p, x)","F",0
1038,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-p),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p + 1), x)","F",0
1039,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-p),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^p*(-c*sin(f*x + e) + c)^(-p + 2), x)","F",0
1040,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(A*m-A*(1+m+p)*sin(f*x+e)),x, algorithm=""maxima"")","-\int {\left(A {\left(m + p + 1\right)} \sin\left(f x + e\right) - A m\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"-integrate((A*(m + p + 1)*sin(f*x + e) - A*m)*(g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m, x)","F",0
1041,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a-a*sin(f*x+e))^m*(A*m+A*(1+m+p)*sin(f*x+e)),x, algorithm=""maxima"")","\int {\left(A {\left(m + p + 1\right)} \sin\left(f x + e\right) + A m\right)} \left(g \cos\left(f x + e\right)\right)^{p} {\left(-a \sin\left(f x + e\right) + a\right)}^{m}\,{d x}"," ",0,"integrate((A*(m + p + 1)*sin(f*x + e) + A*m)*(g*cos(f*x + e))^p*(-a*sin(f*x + e) + a)^m, x)","F",0
1042,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
1043,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(a \sin\left(f x + e\right) + a\right)}^{2} \left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)^2*(g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n, x)","F",0
1044,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(a+a*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((a*sin(f*x + e) + a)*(g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n, x)","F",0
1045,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a), x)","F",0
1046,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{p} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{{\left(a \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a)^2, x)","F",0
1047,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^3,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1048,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^p*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^4,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1049,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^p*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
1050,1,65,0,0.302800," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{64 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b}{960 \, d}"," ",0,"1/960*(64*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a - 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*b)/d","A",0
1051,1,52,0,0.304437," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{15 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a + 32 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} b}{480 \, d}"," ",0,"1/480*(15*(4*d*x + 4*c - sin(4*d*x + 4*c))*a + 32*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*b)/d","A",0
1052,1,39,0,0.370268," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{32 \, a \cos\left(d x + c\right)^{3} - 3 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} b}{96 \, d}"," ",0,"-1/96*(32*a*cos(d*x + c)^3 - 3*(4*d*x + 4*c - sin(4*d*x + 4*c))*b)/d","A",0
1053,1,57,0,0.362182," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b + 2 \, a {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"1/4*((2*d*x + 2*c + sin(2*d*x + 2*c))*b + 2*a*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
1054,1,54,0,0.495055," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a - b {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c + 1/tan(d*x + c))*a - b*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
1055,1,66,0,0.504874," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} b - a {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(4*(d*x + c + 1/tan(d*x + c))*b - a*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)))/d","A",0
1056,1,61,0,0.384460," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{4 \, a}{\tan\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"1/12*(3*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) - 4*a/tan(d*x + c)^3)/d","A",0
1057,1,80,0,0.312329," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, a {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{16 \, b}{\tan\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"-1/48*(3*a*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 16*b/tan(d*x + c)^3)/d","A",0
1058,1,92,0,0.405543," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{15 \, b {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{16 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a}{\tan\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"-1/240*(15*b*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 16*(5*tan(d*x + c)^2 + 3)*a/tan(d*x + c)^5)/d","A",0
1059,1,104,0,0.401801," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{224 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{2} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b - 32 \, {\left(15 \, \cos\left(d x + c\right)^{7} - 42 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3}\right)} b^{2}}{3360 \, d}"," ",0,"1/3360*(224*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^2 - 35*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a*b - 32*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*b^2)/d","A",0
1060,1,92,0,0.385765," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{30 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} + 128 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a b - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{960 \, d}"," ",0,"1/960*(30*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^2 + 128*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a*b - 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*b^2)/d","A",0
1061,1,68,0,0.375158," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{80 \, a^{2} \cos\left(d x + c\right)^{3} - 15 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a b - 16 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} b^{2}}{240 \, d}"," ",0,"-1/240*(80*a^2*cos(d*x + c)^3 - 15*(4*d*x + 4*c - sin(4*d*x + 4*c))*a*b - 16*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*b^2)/d","A",0
1062,1,74,0,0.308101," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, b^{2} \cos\left(d x + c\right)^{3} - 3 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b - 3 \, a^{2} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"-1/6*(2*b^2*cos(d*x + c)^3 - 3*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b - 3*a^2*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
1063,1,79,0,0.420000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} - {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b^{2} - 4 \, a b {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(4*(d*x + c + 1/tan(d*x + c))*a^2 - (2*d*x + 2*c + sin(2*d*x + 2*c))*b^2 - 4*a*b*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
1064,1,103,0,0.416183," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{8 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a b - a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 2 \, b^{2} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(8*(d*x + c + 1/tan(d*x + c))*a*b - a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) - 2*b^2*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
1065,1,82,0,0.521821," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{6 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} b^{2} - 3 \, a b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{2 \, a^{2}}{\tan\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c + 1/tan(d*x + c))*b^2 - 3*a*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 2*a^2/tan(d*x + c)^3)/d","A",0
1066,1,129,0,0.406588," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, a^{2} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 12 \, b^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{32 \, a b}{\tan\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"-1/48*(3*a^2*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 12*b^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 32*a*b/tan(d*x + c)^3)/d","A",0
1067,1,108,0,0.378838," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{15 \, a b {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{40 \, b^{2}}{\tan\left(d x + c\right)^{3}} + \frac{8 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{2}}{\tan\left(d x + c\right)^{5}}}{120 \, d}"," ",0,"-1/120*(15*a*b*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 40*b^2/tan(d*x + c)^3 + 8*(5*tan(d*x + c)^2 + 3)*a^2/tan(d*x + c)^5)/d","A",0
1068,1,186,0,0.329777," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{5 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 30 \, b^{2} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{64 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a b}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(5*a^2*(2*(3*cos(d*x + c)^5 - 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 30*b^2*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 64*(5*tan(d*x + c)^2 + 3)*a*b/tan(d*x + c)^5)/d","A",0
1069,1,131,0,0.326759," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{210 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} + 1344 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a^{2} b - 105 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{2} - 64 \, {\left(15 \, \cos\left(d x + c\right)^{7} - 42 \, \cos\left(d x + c\right)^{5} + 35 \, \cos\left(d x + c\right)^{3}\right)} b^{3}}{6720 \, d}"," ",0,"1/6720*(210*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^3 + 1344*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a^2*b - 105*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*a*b^2 - 64*(15*cos(d*x + c)^7 - 42*cos(d*x + c)^5 + 35*cos(d*x + c)^3)*b^3)/d","A",0
1070,1,108,0,0.319088," ","integrate(cos(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{320 \, a^{3} \cos\left(d x + c\right)^{3} - 90 \, {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} b - 192 \, {\left(3 \, \cos\left(d x + c\right)^{5} - 5 \, \cos\left(d x + c\right)^{3}\right)} a b^{2} + 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 12 \, d x - 12 \, c + 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{3}}{960 \, d}"," ",0,"-1/960*(320*a^3*cos(d*x + c)^3 - 90*(4*d*x + 4*c - sin(4*d*x + 4*c))*a^2*b - 192*(3*cos(d*x + c)^5 - 5*cos(d*x + c)^3)*a*b^2 + 5*(4*sin(2*d*x + 2*c)^3 - 12*d*x - 12*c + 3*sin(4*d*x + 4*c))*b^3)/d","A",0
1071,1,101,0,0.401223," ","integrate(cos(d*x+c)^2*csc(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{32 \, a b^{2} \cos\left(d x + c\right)^{3} - 24 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b - {\left(4 \, d x + 4 \, c - \sin\left(4 \, d x + 4 \, c\right)\right)} b^{3} - 16 \, a^{3} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{32 \, d}"," ",0,"-1/32*(32*a*b^2*cos(d*x + c)^3 - 24*(2*d*x + 2*c + sin(2*d*x + 2*c))*a^2*b - (4*d*x + 4*c - sin(4*d*x + 4*c))*b^3 - 16*a^3*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
1072,1,95,0,0.413516," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{4 \, b^{3} \cos\left(d x + c\right)^{3} + 12 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{3} - 9 \, {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{2} - 18 \, a^{2} b {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"-1/12*(4*b^3*cos(d*x + c)^3 + 12*(d*x + c + 1/tan(d*x + c))*a^3 - 9*(2*d*x + 2*c + sin(2*d*x + 2*c))*a*b^2 - 18*a^2*b*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
1073,1,128,0,0.502538," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{12 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a^{2} b - {\left(2 \, d x + 2 \, c + \sin\left(2 \, d x + 2 \, c\right)\right)} b^{3} - a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 6 \, a b^{2} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(12*(d*x + c + 1/tan(d*x + c))*a^2*b - (2*d*x + 2*c + sin(2*d*x + 2*c))*b^3 - a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) - 6*a*b^2*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)))/d","A",0
1074,1,119,0,0.418571," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{36 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} a b^{2} - 9 \, a^{2} b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 6 \, b^{3} {\left(2 \, \cos\left(d x + c\right) - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{4 \, a^{3}}{\tan\left(d x + c\right)^{3}}}{12 \, d}"," ",0,"-1/12*(36*(d*x + c + 1/tan(d*x + c))*a*b^2 - 9*a^2*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) - 6*b^3*(2*cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 4*a^3/tan(d*x + c)^3)/d","A",0
1075,1,149,0,0.420474," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{16 \, {\left(d x + c + \frac{1}{\tan\left(d x + c\right)}\right)} b^{3} + a^{3} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 12 \, a b^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{16 \, a^{2} b}{\tan\left(d x + c\right)^{3}}}{16 \, d}"," ",0,"-1/16*(16*(d*x + c + 1/tan(d*x + c))*b^3 + a^3*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 12*a*b^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 16*a^2*b/tan(d*x + c)^3)/d","A",0
1076,1,157,0,0.334304," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{45 \, a^{2} b {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 60 \, b^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + \log\left(\cos\left(d x + c\right) + 1\right) - \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{240 \, a b^{2}}{\tan\left(d x + c\right)^{3}} + \frac{16 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{3}}{\tan\left(d x + c\right)^{5}}}{240 \, d}"," ",0,"-1/240*(45*a^2*b*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 60*b^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) + log(cos(d*x + c) + 1) - log(cos(d*x + c) - 1)) + 240*a*b^2/tan(d*x + c)^3 + 16*(5*tan(d*x + c)^2 + 3)*a^3/tan(d*x + c)^5)/d","A",0
1077,1,202,0,0.396482," ","integrate(cos(d*x+c)^2*csc(d*x+c)^7*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{5 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 90 \, a b^{2} {\left(\frac{2 \, {\left(\cos\left(d x + c\right)^{3} + \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{160 \, b^{3}}{\tan\left(d x + c\right)^{3}} + \frac{96 \, {\left(5 \, \tan\left(d x + c\right)^{2} + 3\right)} a^{2} b}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"-1/480*(5*a^3*(2*(3*cos(d*x + c)^5 - 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 90*a*b^2*(2*(cos(d*x + c)^3 + cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 160*b^3/tan(d*x + c)^3 + 96*(5*tan(d*x + c)^2 + 3)*a^2*b/tan(d*x + c)^5)/d","A",0
1078,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1079,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1080,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1081,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1082,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1083,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1084,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1085,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1086,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1087,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1088,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1089,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1090,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1091,0,0,0,0.000000," ","integrate(cos(f*x+e)^2/(a+b*sin(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(cos(f*x + e)^2/((b*sin(f*x + e) + a)^(5/2)*sqrt(d*sin(f*x + e))), x)","F",0
1092,1,71,0,0.308430," ","integrate(cos(d*x+c)^4*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{315 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a - 1024 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} b}{322560 \, d}"," ",0,"1/322560*(315*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a - 1024*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*b)/d","A",0
1093,1,61,0,0.376213," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{1024 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a + 35 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b}{35840 \, d}"," ",0,"1/35840*(1024*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a + 35*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*b)/d","A",0
1094,1,65,0,0.385123," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a + 192 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} b}{6720 \, d}"," ",0,"1/6720*(35*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a + 192*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*b)/d","A",0
1095,1,52,0,0.304431," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{192 \, a \cos\left(d x + c\right)^{5} - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b}{960 \, d}"," ",0,"-1/960*(192*a*cos(d*x + c)^5 - 5*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*b)/d","A",0
1096,1,81,0,0.402330," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a + 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b}{96 \, d}"," ",0,"1/96*(16*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a + 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b)/d","A",0
1097,1,91,0,0.503675," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a - {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} b}{6 \, d}"," ",0,"-1/6*(3*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a - (2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*b)/d","A",0
1098,1,101,0,0.446083," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} b - a {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{4 \, d}"," ",0,"-1/4*(2*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*b - a*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1099,1,92,0,0.482565," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a + 3 \, b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(4*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a + 3*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1100,1,107,0,0.455144," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} b - 3 \, a {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*b - 3*a*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1101,1,86,0,0.315057," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{5 \, b {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{16 \, a}{\tan\left(d x + c\right)^{5}}}{80 \, d}"," ",0,"-1/80*(5*b*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) + 16*a/tan(d*x + c)^5)/d","A",0
1102,1,106,0,0.320000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{5 \, a {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{96 \, b}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(5*a*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 96*b/tan(d*x + c)^5)/d","A",0
1103,1,118,0,0.391438," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{35 \, b {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{96 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a}{\tan\left(d x + c\right)^{7}}}{3360 \, d}"," ",0,"1/3360*(35*b*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 96*(7*tan(d*x + c)^2 + 5)*a/tan(d*x + c)^7)/d","A",0
1104,1,138,0,0.385323," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{35 \, a {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{256 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} b}{\tan\left(d x + c\right)^{7}}}{8960 \, d}"," ",0,"1/8960*(35*a*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 256*(7*tan(d*x + c)^2 + 5)*b/tan(d*x + c)^7)/d","A",0
1105,1,100,0,0.317900," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{4608 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{2} + 315 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b - 512 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} b^{2}}{161280 \, d}"," ",0,"1/161280*(4608*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^2 + 315*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a*b - 512*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*b^2)/d","A",0
1106,1,101,0,0.345685," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} + 6144 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a b + 105 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{107520 \, d}"," ",0,"1/107520*(560*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^2 + 6144*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a*b + 105*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*b^2)/d","A",0
1107,1,81,0,0.384451," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{672 \, a^{2} \cos\left(d x + c\right)^{5} - 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b - 96 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} b^{2}}{3360 \, d}"," ",0,"-1/3360*(672*a^2*cos(d*x + c)^5 - 35*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a*b - 96*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*b^2)/d","A",0
1108,1,97,0,0.386955," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{48 \, b^{2} \cos\left(d x + c\right)^{5} - 40 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b}{240 \, d}"," ",0,"-1/240*(48*b^2*cos(d*x + c)^5 - 40*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^2 - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a*b)/d","A",0
1109,1,127,0,0.493753," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{48 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2} - 32 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a b - 3 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b^{2}}{96 \, d}"," ",0,"-1/96*(48*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^2 - 32*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a*b - 3*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b^2)/d","A",0
1110,1,150,0,0.479180," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{12 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a b - 2 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} b^{2} - 3 \, a^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"-1/12*(12*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a*b - 2*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*b^2 - 3*a^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1111,1,138,0,0.557229," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} - 3 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} b^{2} + 3 \, a b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{6 \, d}"," ",0,"1/6*(2*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2 - 3*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*b^2 + 3*a*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1112,1,166,0,0.414649," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a b - 3 \, a^{2} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 12 \, b^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(32*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a*b - 3*a^2*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) + 12*b^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1113,1,123,0,0.413878," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{40 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} b^{2} - 15 \, a b {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{24 \, a^{2}}{\tan\left(d x + c\right)^{5}}}{120 \, d}"," ",0,"1/120*(40*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*b^2 - 15*a*b*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 24*a^2/tan(d*x + c)^5)/d","A",0
1114,1,180,0,0.405809," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{5 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 30 \, b^{2} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{192 \, a b}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(5*a^2*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 30*b^2*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 192*a*b/tan(d*x + c)^5)/d","A",0
1115,1,134,0,0.326508," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{35 \, a b {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{336 \, b^{2}}{\tan\left(d x + c\right)^{5}} - \frac{48 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{2}}{\tan\left(d x + c\right)^{7}}}{1680 \, d}"," ",0,"1/1680*(35*a*b*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 336*b^2/tan(d*x + c)^5 - 48*(7*tan(d*x + c)^2 + 5)*a^2/tan(d*x + c)^7)/d","A",0
1116,1,140,0,0.451910," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{1680 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{3} + 27648 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a^{2} b + 945 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b^{2} - 1024 \, {\left(35 \, \cos\left(d x + c\right)^{9} - 90 \, \cos\left(d x + c\right)^{7} + 63 \, \cos\left(d x + c\right)^{5}\right)} b^{3}}{322560 \, d}"," ",0,"1/322560*(1680*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^3 + 27648*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a^2*b + 945*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*a*b^2 - 1024*(35*cos(d*x + c)^9 - 90*cos(d*x + c)^7 + 63*cos(d*x + c)^5)*b^3)/d","A",0
1117,1,117,0,0.399411," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{7168 \, a^{3} \cos\left(d x + c\right)^{5} - 560 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} b - 3072 \, {\left(5 \, \cos\left(d x + c\right)^{7} - 7 \, \cos\left(d x + c\right)^{5}\right)} a b^{2} - 35 \, {\left(24 \, d x + 24 \, c + \sin\left(8 \, d x + 8 \, c\right) - 8 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{3}}{35840 \, d}"," ",0,"-1/35840*(7168*a^3*cos(d*x + c)^5 - 560*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*a^2*b - 3072*(5*cos(d*x + c)^7 - 7*cos(d*x + c)^5)*a*b^2 - 35*(24*d*x + 24*c + sin(8*d*x + 8*c) - 8*sin(4*d*x + 4*c))*b^3)/d","A",0
1118,1,137,0,0.425469," ","integrate(cos(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{576 \, a b^{2} \cos\left(d x + c\right)^{5} - 160 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{3} - 90 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a^{2} b - 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 12 \, d x + 12 \, c - 3 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{3}}{960 \, d}"," ",0,"-1/960*(576*a*b^2*cos(d*x + c)^5 - 160*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^3 - 90*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a^2*b - 5*(4*sin(2*d*x + 2*c)^3 + 12*d*x + 12*c - 3*sin(4*d*x + 4*c))*b^3)/d","A",0
1119,1,143,0,0.510584," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{32 \, b^{3} \cos\left(d x + c\right)^{5} + 80 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{3} - 80 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} b - 15 \, {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b^{2}}{160 \, d}"," ",0,"-1/160*(32*b^3*cos(d*x + c)^5 + 80*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^3 - 80*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a^2*b - 15*(12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*a*b^2)/d","A",0
1120,1,186,0,0.463349," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{48 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2} b - 16 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a b^{2} - {\left(12 \, d x + 12 \, c + \sin\left(4 \, d x + 4 \, c\right) + 8 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b^{3} - 8 \, a^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{32 \, d}"," ",0,"-1/32*(48*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a^2*b - 16*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*a*b^2 - (12*d*x + 12*c + sin(4*d*x + 4*c) + 8*sin(2*d*x + 2*c))*b^3 - 8*a^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1121,1,187,0,0.471234," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{4 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{3} - 18 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a b^{2} + 2 \, {\left(2 \, \cos\left(d x + c\right)^{3} + 6 \, \cos\left(d x + c\right) - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} b^{3} + 9 \, a^{2} b {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{12 \, d}"," ",0,"1/12*(4*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^3 - 18*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*a*b^2 + 2*(2*cos(d*x + c)^3 + 6*cos(d*x + c) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1))*b^3 + 9*a^2*b*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1122,1,212,0,0.653568," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{16 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a^{2} b - 8 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} + 2}{\tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} b^{3} - a^{3} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 12 \, a b^{2} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{16 \, d}"," ",0,"1/16*(16*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a^2*b - 8*(3*d*x + 3*c + (3*tan(d*x + c)^2 + 2)/(tan(d*x + c)^3 + tan(d*x + c)))*b^3 - a^3*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) + 12*a*b^2*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)))/d","A",0
1123,1,182,0,0.493232," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{80 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} a b^{2} - 15 \, a^{2} b {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 20 \, b^{3} {\left(\frac{2 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} - 4 \, \cos\left(d x + c\right) + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{16 \, a^{3}}{\tan\left(d x + c\right)^{5}}}{80 \, d}"," ",0,"1/80*(80*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*a*b^2 - 15*a^2*b*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) + 20*b^3*(2*cos(d*x + c)/(cos(d*x + c)^2 - 1) - 4*cos(d*x + c) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 16*a^3/tan(d*x + c)^5)/d","A",0
1124,1,217,0,0.422002," ","integrate(cos(d*x+c)^4*csc(d*x+c)^7*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{160 \, {\left(3 \, d x + 3 \, c + \frac{3 \, \tan\left(d x + c\right)^{2} - 1}{\tan\left(d x + c\right)^{3}}\right)} b^{3} + 5 \, a^{3} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 90 \, a b^{2} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{288 \, a^{2} b}{\tan\left(d x + c\right)^{5}}}{480 \, d}"," ",0,"1/480*(160*(3*d*x + 3*c + (3*tan(d*x + c)^2 - 1)/tan(d*x + c)^3)*b^3 + 5*a^3*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 90*a*b^2*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 288*a^2*b/tan(d*x + c)^5)/d","A",0
1125,1,208,0,0.330227," ","integrate(cos(d*x+c)^4*csc(d*x+c)^8*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{35 \, a^{2} b {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 70 \, b^{3} {\left(\frac{2 \, {\left(5 \, \cos\left(d x + c\right)^{3} - 3 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} + 3 \, \log\left(\cos\left(d x + c\right) + 1\right) - 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{672 \, a b^{2}}{\tan\left(d x + c\right)^{5}} - \frac{32 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{3}}{\tan\left(d x + c\right)^{7}}}{1120 \, d}"," ",0,"1/1120*(35*a^2*b*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 70*b^3*(2*(5*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) + 3*log(cos(d*x + c) + 1) - 3*log(cos(d*x + c) - 1)) - 672*a*b^2/tan(d*x + c)^5 - 32*(7*tan(d*x + c)^2 + 5)*a^3/tan(d*x + c)^7)/d","A",0
1126,1,248,0,0.329252," ","integrate(cos(d*x+c)^4*csc(d*x+c)^9*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{35 \, a^{3} {\left(\frac{2 \, {\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)}}{\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} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 280 \, a b^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - \frac{1792 \, b^{3}}{\tan\left(d x + c\right)^{5}} - \frac{768 \, {\left(7 \, \tan\left(d x + c\right)^{2} + 5\right)} a^{2} b}{\tan\left(d x + c\right)^{7}}}{8960 \, d}"," ",0,"1/8960*(35*a^3*(2*(3*cos(d*x + c)^7 - 11*cos(d*x + c)^5 - 11*cos(d*x + c)^3 + 3*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 280*a*b^2*(2*(3*cos(d*x + c)^5 + 8*cos(d*x + c)^3 - 3*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 1792*b^3/tan(d*x + c)^5 - 768*(7*tan(d*x + c)^2 + 5)*a^2*b/tan(d*x + c)^7)/d","A",0
1127,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1128,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1129,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1130,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1131,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1132,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1133,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1134,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1135,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1136,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1137,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1138,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1139,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1140,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1141,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1142,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1143,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c)^2, x)","F",0
1144,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
1145,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{3} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^3*cot(d*x + c), x)","F",0
1146,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right)^{2} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)^2*cot(d*x + c)^2, x)","F",0
1147,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cos\left(d x + c\right) \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cos(d*x + c)*cot(d*x + c)^3, x)","F",0
1148,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cot(d*x + c)^4, x)","F",0
1149,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cot\left(d x + c\right)^{4} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cot(d*x + c)^4*csc(d*x + c), x)","F",0
1150,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \sqrt{b \sin\left(d x + c\right) + a} \cot\left(d x + c\right)^{4} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate(sqrt(b*sin(d*x + c) + a)*cot(d*x + c)^4*csc(d*x + c)^2, x)","F",0
1151,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*sin(d*x + c)^2, x)","F",0
1152,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
1153,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{3} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^3*cot(d*x + c), x)","F",0
1154,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right)^{2} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)^2*cot(d*x + c)^2, x)","F",0
1155,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cos\left(d x + c\right) \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cos(d*x + c)*cot(d*x + c)^3, x)","F",0
1156,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cot(d*x + c)^4, x)","F",0
1157,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{4} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cot(d*x + c)^4*csc(d*x + c), x)","F",0
1158,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^2*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{4} \csc\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cot(d*x + c)^4*csc(d*x + c)^2, x)","F",0
1159,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)^3*(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} \cot\left(d x + c\right)^{4} \csc\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(3/2)*cot(d*x + c)^4*csc(d*x + c)^3, x)","F",0
1160,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{4} \sin\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^4*sin(d*x + c), x)","F",0
1161,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{3} \cot\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^3*cot(d*x + c), x)","F",0
1162,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right)^{2} \cot\left(d x + c\right)^{2}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)^2*cot(d*x + c)^2, x)","F",0
1163,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cos\left(d x + c\right) \cot\left(d x + c\right)^{3}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cos(d*x + c)*cot(d*x + c)^3, x)","F",0
1164,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cot(d*x + c)^4, x)","F",0
1165,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)*(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}} \cot\left(d x + c\right)^{4} \csc\left(d x + c\right)\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^(5/2)*cot(d*x + c)^4*csc(d*x + c), x)","F",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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1168,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^3/sqrt(b*sin(d*x + c) + a), x)","F",0
1169,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
1170,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1171,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3} \cot\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3*cot(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1172,0,0,0,0.000000," ","integrate(cos(d*x+c)^2*cot(d*x+c)^2/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{2} \cot\left(d x + c\right)^{2}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)^2*cot(d*x + c)^2/sqrt(b*sin(d*x + c) + a), x)","F",0
1173,0,0,0,0.000000," ","integrate(cos(d*x+c)*cot(d*x+c)^3/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right) \cot\left(d x + c\right)^{3}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cos(d*x + c)*cot(d*x + c)^3/sqrt(b*sin(d*x + c) + a), x)","F",0
1174,0,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{4}}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^4/sqrt(b*sin(d*x + c) + a), x)","F",0
1175,0,0,0,0.000000," ","integrate(cot(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \frac{\cot\left(d x + c\right)^{4} \csc\left(d x + c\right)}{\sqrt{b \sin\left(d x + c\right) + a}}\,{d x}"," ",0,"integrate(cot(d*x + c)^4*csc(d*x + c)/sqrt(b*sin(d*x + c) + a), x)","F",0
1176,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{3}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^3/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1177,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1178,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/(b*sin(d*x + c) + a)^(3/2), x)","F",0
1179,-1,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1181,-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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1182,-1,0,0,0.000000," ","integrate(cot(d*x+c)^4/(a+b*sin(d*x+c))^(3/2),x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1183,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{3}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^3/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1184,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)^{2}}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^2/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1185,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{4} \sin\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)/(b*sin(d*x + c) + a)^(5/2), x)","F",0
1186,0,0,0,0.000000," ","integrate(cos(d*x+c)^3*cot(d*x+c)/(a+b*sin(d*x+c))^(5/2),x, algorithm=""maxima"")","\int \frac{\cos\left(d x + c\right)^{3} \cot\left(d x + c\right)}{{\left(b \sin\left(d x + c\right) + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(cos(d*x + c)^3*cot(d*x + c)/(b*sin(d*x + c) + a)^(5/2), 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=""maxima"")","\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=""maxima"")","\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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1190,0,0,0,0.000000," ","integrate(cos(f*x+e)^4/(a+b*sin(f*x+e))^(9/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{4}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{9}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(cos(f*x + e)^4/((b*sin(f*x + e) + a)^(9/2)*sqrt(d*sin(f*x + e))), x)","F",0
1191,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(1/3)/(a+b*sin(d*x+c))^(1/2),x, algorithm=""maxima"")","\int \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}}\,{d x}"," ",0,"integrate(cos(d*x + c)^4*sin(d*x + c)^(1/3)/sqrt(b*sin(d*x + c) + a), x)","F",0
1192,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^p*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
1193,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(-3-p)*(a+b*sin(d*x+c))^p,x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^p*sin(d*x + c)^(-p - 3)*cos(d*x + c)^4, x)","F",0
1194,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^(-4-p)*(a+b*sin(d*x+c))^p,x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^p*sin(d*x + c)^(-p - 4)*cos(d*x + c)^4, x)","F",0
1195,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{3} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
1196,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
1197,0,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{4}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)*sin(d*x + c)^n*cos(d*x + c)^4, x)","F",0
1198,1,72,0,0.315824," ","integrate(cos(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{1260 \, b \sin\left(d x + c\right)^{11} + 1386 \, a \sin\left(d x + c\right)^{10} - 3080 \, b \sin\left(d x + c\right)^{9} - 3465 \, a \sin\left(d x + c\right)^{8} + 1980 \, b \sin\left(d x + c\right)^{7} + 2310 \, a \sin\left(d x + c\right)^{6}}{13860 \, d}"," ",0,"1/13860*(1260*b*sin(d*x + c)^11 + 1386*a*sin(d*x + c)^10 - 3080*b*sin(d*x + c)^9 - 3465*a*sin(d*x + c)^8 + 1980*b*sin(d*x + c)^7 + 2310*a*sin(d*x + c)^6)/d","A",0
1199,1,72,0,0.319939," ","integrate(cos(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{126 \, b \sin\left(d x + c\right)^{10} + 140 \, a \sin\left(d x + c\right)^{9} - 315 \, b \sin\left(d x + c\right)^{8} - 360 \, a \sin\left(d x + c\right)^{7} + 210 \, b \sin\left(d x + c\right)^{6} + 252 \, a \sin\left(d x + c\right)^{5}}{1260 \, d}"," ",0,"1/1260*(126*b*sin(d*x + c)^10 + 140*a*sin(d*x + c)^9 - 315*b*sin(d*x + c)^8 - 360*a*sin(d*x + c)^7 + 210*b*sin(d*x + c)^6 + 252*a*sin(d*x + c)^5)/d","A",0
1200,1,72,0,0.314024," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{280 \, b \sin\left(d x + c\right)^{9} + 315 \, a \sin\left(d x + c\right)^{8} - 720 \, b \sin\left(d x + c\right)^{7} - 840 \, a \sin\left(d x + c\right)^{6} + 504 \, b \sin\left(d x + c\right)^{5} + 630 \, a \sin\left(d x + c\right)^{4}}{2520 \, d}"," ",0,"1/2520*(280*b*sin(d*x + c)^9 + 315*a*sin(d*x + c)^8 - 720*b*sin(d*x + c)^7 - 840*a*sin(d*x + c)^6 + 504*b*sin(d*x + c)^5 + 630*a*sin(d*x + c)^4)/d","A",0
1201,1,72,0,0.315046," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{105 \, b \sin\left(d x + c\right)^{8} + 120 \, a \sin\left(d x + c\right)^{7} - 280 \, b \sin\left(d x + c\right)^{6} - 336 \, a \sin\left(d x + c\right)^{5} + 210 \, b \sin\left(d x + c\right)^{4} + 280 \, a \sin\left(d x + c\right)^{3}}{840 \, d}"," ",0,"1/840*(105*b*sin(d*x + c)^8 + 120*a*sin(d*x + c)^7 - 280*b*sin(d*x + c)^6 - 336*a*sin(d*x + c)^5 + 210*b*sin(d*x + c)^4 + 280*a*sin(d*x + c)^3)/d","A",0
1202,1,72,0,0.311781," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{30 \, b \sin\left(d x + c\right)^{7} + 35 \, a \sin\left(d x + c\right)^{6} - 84 \, b \sin\left(d x + c\right)^{5} - 105 \, a \sin\left(d x + c\right)^{4} + 70 \, b \sin\left(d x + c\right)^{3} + 105 \, a \sin\left(d x + c\right)^{2}}{210 \, d}"," ",0,"1/210*(30*b*sin(d*x + c)^7 + 35*a*sin(d*x + c)^6 - 84*b*sin(d*x + c)^5 - 105*a*sin(d*x + c)^4 + 70*b*sin(d*x + c)^3 + 105*a*sin(d*x + c)^2)/d","A",0
1203,1,69,0,0.315175," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, b \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 40 \, b \sin\left(d x + c\right)^{3} - 60 \, a \sin\left(d x + c\right)^{2} + 60 \, a \log\left(\sin\left(d x + c\right)\right) + 60 \, b \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*b*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 40*b*sin(d*x + c)^3 - 60*a*sin(d*x + c)^2 + 60*a*log(sin(d*x + c)) + 60*b*sin(d*x + c))/d","A",0
1204,1,69,0,0.313467," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, b \sin\left(d x + c\right)^{4} + 4 \, a \sin\left(d x + c\right)^{3} - 12 \, b \sin\left(d x + c\right)^{2} + 12 \, b \log\left(\sin\left(d x + c\right)\right) - 24 \, a \sin\left(d x + c\right) - \frac{12 \, a}{\sin\left(d x + c\right)}}{12 \, d}"," ",0,"1/12*(3*b*sin(d*x + c)^4 + 4*a*sin(d*x + c)^3 - 12*b*sin(d*x + c)^2 + 12*b*log(sin(d*x + c)) - 24*a*sin(d*x + c) - 12*a/sin(d*x + c))/d","A",0
1205,1,68,0,0.316039," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, b \sin\left(d x + c\right)^{3} + 3 \, a \sin\left(d x + c\right)^{2} - 12 \, a \log\left(\sin\left(d x + c\right)\right) - 12 \, b \sin\left(d x + c\right) - \frac{3 \, {\left(2 \, b \sin\left(d x + c\right) + a\right)}}{\sin\left(d x + c\right)^{2}}}{6 \, d}"," ",0,"1/6*(2*b*sin(d*x + c)^3 + 3*a*sin(d*x + c)^2 - 12*a*log(sin(d*x + c)) - 12*b*sin(d*x + c) - 3*(2*b*sin(d*x + c) + a)/sin(d*x + c)^2)/d","A",0
1206,1,69,0,0.329353," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, b \sin\left(d x + c\right)^{2} - 12 \, b \log\left(\sin\left(d x + c\right)\right) + 6 \, a \sin\left(d x + c\right) + \frac{12 \, a \sin\left(d x + c\right)^{2} - 3 \, b \sin\left(d x + c\right) - 2 \, a}{\sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(3*b*sin(d*x + c)^2 - 12*b*log(sin(d*x + c)) + 6*a*sin(d*x + c) + (12*a*sin(d*x + c)^2 - 3*b*sin(d*x + c) - 2*a)/sin(d*x + c)^3)/d","A",0
1207,1,69,0,0.315284," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{12 \, a \log\left(\sin\left(d x + c\right)\right) + 12 \, b \sin\left(d x + c\right) + \frac{24 \, b \sin\left(d x + c\right)^{3} + 12 \, a \sin\left(d x + c\right)^{2} - 4 \, b \sin\left(d x + c\right) - 3 \, a}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(12*a*log(sin(d*x + c)) + 12*b*sin(d*x + c) + (24*b*sin(d*x + c)^3 + 12*a*sin(d*x + c)^2 - 4*b*sin(d*x + c) - 3*a)/sin(d*x + c)^4)/d","A",0
1208,1,72,0,0.315606," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{60 \, b \log\left(\sin\left(d x + c\right)\right) - \frac{60 \, a \sin\left(d x + c\right)^{4} - 60 \, b \sin\left(d x + c\right)^{3} - 40 \, a \sin\left(d x + c\right)^{2} + 15 \, b \sin\left(d x + c\right) + 12 \, a}{\sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*b*log(sin(d*x + c)) - (60*a*sin(d*x + c)^4 - 60*b*sin(d*x + c)^3 - 40*a*sin(d*x + c)^2 + 15*b*sin(d*x + c) + 12*a)/sin(d*x + c)^5)/d","A",0
1209,1,70,0,0.315746," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{30 \, b \sin\left(d x + c\right)^{5} + 15 \, a \sin\left(d x + c\right)^{4} - 20 \, b \sin\left(d x + c\right)^{3} - 15 \, a \sin\left(d x + c\right)^{2} + 6 \, b \sin\left(d x + c\right) + 5 \, a}{30 \, d \sin\left(d x + c\right)^{6}}"," ",0,"-1/30*(30*b*sin(d*x + c)^5 + 15*a*sin(d*x + c)^4 - 20*b*sin(d*x + c)^3 - 15*a*sin(d*x + c)^2 + 6*b*sin(d*x + c) + 5*a)/(d*sin(d*x + c)^6)","A",0
1210,1,70,0,0.338715," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{105 \, b \sin\left(d x + c\right)^{5} + 70 \, a \sin\left(d x + c\right)^{4} - 105 \, b \sin\left(d x + c\right)^{3} - 84 \, a \sin\left(d x + c\right)^{2} + 35 \, b \sin\left(d x + c\right) + 30 \, a}{210 \, d \sin\left(d x + c\right)^{7}}"," ",0,"-1/210*(105*b*sin(d*x + c)^5 + 70*a*sin(d*x + c)^4 - 105*b*sin(d*x + c)^3 - 84*a*sin(d*x + c)^2 + 35*b*sin(d*x + c) + 30*a)/(d*sin(d*x + c)^7)","A",0
1211,1,70,0,0.346876," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{280 \, b \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} - 336 \, b \sin\left(d x + c\right)^{3} - 280 \, a \sin\left(d x + c\right)^{2} + 120 \, b \sin\left(d x + c\right) + 105 \, a}{840 \, d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(280*b*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 - 336*b*sin(d*x + c)^3 - 280*a*sin(d*x + c)^2 + 120*b*sin(d*x + c) + 105*a)/(d*sin(d*x + c)^8)","A",0
1212,1,70,0,0.318827," ","integrate(cos(d*x+c)^5*csc(d*x+c)^10*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{630 \, b \sin\left(d x + c\right)^{5} + 504 \, a \sin\left(d x + c\right)^{4} - 840 \, b \sin\left(d x + c\right)^{3} - 720 \, a \sin\left(d x + c\right)^{2} + 315 \, b \sin\left(d x + c\right) + 280 \, a}{2520 \, d \sin\left(d x + c\right)^{9}}"," ",0,"-1/2520*(630*b*sin(d*x + c)^5 + 504*a*sin(d*x + c)^4 - 840*b*sin(d*x + c)^3 - 720*a*sin(d*x + c)^2 + 315*b*sin(d*x + c) + 280*a)/(d*sin(d*x + c)^9)","A",0
1213,1,70,0,0.328895," ","integrate(cos(d*x+c)^5*csc(d*x+c)^11*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{252 \, b \sin\left(d x + c\right)^{5} + 210 \, a \sin\left(d x + c\right)^{4} - 360 \, b \sin\left(d x + c\right)^{3} - 315 \, a \sin\left(d x + c\right)^{2} + 140 \, b \sin\left(d x + c\right) + 126 \, a}{1260 \, d \sin\left(d x + c\right)^{10}}"," ",0,"-1/1260*(252*b*sin(d*x + c)^5 + 210*a*sin(d*x + c)^4 - 360*b*sin(d*x + c)^3 - 315*a*sin(d*x + c)^2 + 140*b*sin(d*x + c) + 126*a)/(d*sin(d*x + c)^10)","A",0
1214,1,70,0,0.338597," ","integrate(cos(d*x+c)^5*csc(d*x+c)^12*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{2310 \, b \sin\left(d x + c\right)^{5} + 1980 \, a \sin\left(d x + c\right)^{4} - 3465 \, b \sin\left(d x + c\right)^{3} - 3080 \, a \sin\left(d x + c\right)^{2} + 1386 \, b \sin\left(d x + c\right) + 1260 \, a}{13860 \, d \sin\left(d x + c\right)^{11}}"," ",0,"-1/13860*(2310*b*sin(d*x + c)^5 + 1980*a*sin(d*x + c)^4 - 3465*b*sin(d*x + c)^3 - 3080*a*sin(d*x + c)^2 + 1386*b*sin(d*x + c) + 1260*a)/(d*sin(d*x + c)^11)","A",0
1215,1,108,0,0.327105," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{140 \, b^{2} \sin\left(d x + c\right)^{9} + 315 \, a b \sin\left(d x + c\right)^{8} - 840 \, a b \sin\left(d x + c\right)^{6} + 180 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{7} + 630 \, a b \sin\left(d x + c\right)^{4} - 252 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{5} + 420 \, a^{2} \sin\left(d x + c\right)^{3}}{1260 \, d}"," ",0,"1/1260*(140*b^2*sin(d*x + c)^9 + 315*a*b*sin(d*x + c)^8 - 840*a*b*sin(d*x + c)^6 + 180*(a^2 - 2*b^2)*sin(d*x + c)^7 + 630*a*b*sin(d*x + c)^4 - 252*(2*a^2 - b^2)*sin(d*x + c)^5 + 420*a^2*sin(d*x + c)^3)/d","A",0
1216,1,108,0,0.314396," ","integrate(cos(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{105 \, b^{2} \sin\left(d x + c\right)^{8} + 240 \, a b \sin\left(d x + c\right)^{7} - 672 \, a b \sin\left(d x + c\right)^{5} + 140 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{6} + 560 \, a b \sin\left(d x + c\right)^{3} - 210 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{4} + 420 \, a^{2} \sin\left(d x + c\right)^{2}}{840 \, d}"," ",0,"1/840*(105*b^2*sin(d*x + c)^8 + 240*a*b*sin(d*x + c)^7 - 672*a*b*sin(d*x + c)^5 + 140*(a^2 - 2*b^2)*sin(d*x + c)^6 + 560*a*b*sin(d*x + c)^3 - 210*(2*a^2 - b^2)*sin(d*x + c)^4 + 420*a^2*sin(d*x + c)^2)/d","A",0
1217,1,105,0,0.317317," ","integrate(cos(d*x+c)^5*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{10 \, b^{2} \sin\left(d x + c\right)^{6} + 24 \, a b \sin\left(d x + c\right)^{5} - 80 \, a b \sin\left(d x + c\right)^{3} + 15 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{4} + 60 \, a^{2} \log\left(\sin\left(d x + c\right)\right) + 120 \, a b \sin\left(d x + c\right) - 30 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2}}{60 \, d}"," ",0,"1/60*(10*b^2*sin(d*x + c)^6 + 24*a*b*sin(d*x + c)^5 - 80*a*b*sin(d*x + c)^3 + 15*(a^2 - 2*b^2)*sin(d*x + c)^4 + 60*a^2*log(sin(d*x + c)) + 120*a*b*sin(d*x + c) - 30*(2*a^2 - b^2)*sin(d*x + c)^2)/d","A",0
1218,1,105,0,0.329824," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, b^{2} \sin\left(d x + c\right)^{5} + 15 \, a b \sin\left(d x + c\right)^{4} - 60 \, a b \sin\left(d x + c\right)^{2} + 10 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{3} + 60 \, a b \log\left(\sin\left(d x + c\right)\right) - 30 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right) - \frac{30 \, a^{2}}{\sin\left(d x + c\right)}}{30 \, d}"," ",0,"1/30*(6*b^2*sin(d*x + c)^5 + 15*a*b*sin(d*x + c)^4 - 60*a*b*sin(d*x + c)^2 + 10*(a^2 - 2*b^2)*sin(d*x + c)^3 + 60*a*b*log(sin(d*x + c)) - 30*(2*a^2 - b^2)*sin(d*x + c) - 30*a^2/sin(d*x + c))/d","A",0
1219,1,104,0,0.330440," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, b^{2} \sin\left(d x + c\right)^{4} + 8 \, a b \sin\left(d x + c\right)^{3} - 48 \, a b \sin\left(d x + c\right) + 6 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{2} - 12 \, {\left(2 \, a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right)\right) - \frac{6 \, {\left(4 \, a b \sin\left(d x + c\right) + a^{2}\right)}}{\sin\left(d x + c\right)^{2}}}{12 \, d}"," ",0,"1/12*(3*b^2*sin(d*x + c)^4 + 8*a*b*sin(d*x + c)^3 - 48*a*b*sin(d*x + c) + 6*(a^2 - 2*b^2)*sin(d*x + c)^2 - 12*(2*a^2 - b^2)*log(sin(d*x + c)) - 6*(4*a*b*sin(d*x + c) + a^2)/sin(d*x + c)^2)/d","A",0
1220,1,103,0,0.330839," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{b^{2} \sin\left(d x + c\right)^{3} + 3 \, a b \sin\left(d x + c\right)^{2} - 12 \, a b \log\left(\sin\left(d x + c\right)\right) + 3 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right) - \frac{3 \, a b \sin\left(d x + c\right) - 3 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} + a^{2}}{\sin\left(d x + c\right)^{3}}}{3 \, d}"," ",0,"1/3*(b^2*sin(d*x + c)^3 + 3*a*b*sin(d*x + c)^2 - 12*a*b*log(sin(d*x + c)) + 3*(a^2 - 2*b^2)*sin(d*x + c) - (3*a*b*sin(d*x + c) - 3*(2*a^2 - b^2)*sin(d*x + c)^2 + a^2)/sin(d*x + c)^3)/d","A",0
1221,1,105,0,0.317912," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{6 \, b^{2} \sin\left(d x + c\right)^{2} + 24 \, a b \sin\left(d x + c\right) + 12 \, {\left(a^{2} - 2 \, b^{2}\right)} \log\left(\sin\left(d x + c\right)\right) + \frac{48 \, a b \sin\left(d x + c\right)^{3} - 8 \, a b \sin\left(d x + c\right) + 6 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - 3 \, a^{2}}{\sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"1/12*(6*b^2*sin(d*x + c)^2 + 24*a*b*sin(d*x + c) + 12*(a^2 - 2*b^2)*log(sin(d*x + c)) + (48*a*b*sin(d*x + c)^3 - 8*a*b*sin(d*x + c) + 6*(2*a^2 - b^2)*sin(d*x + c)^2 - 3*a^2)/sin(d*x + c)^4)/d","A",0
1222,1,105,0,0.320111," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{60 \, a b \log\left(\sin\left(d x + c\right)\right) + 30 \, b^{2} \sin\left(d x + c\right) + \frac{60 \, a b \sin\left(d x + c\right)^{3} - 30 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{4} - 15 \, a b \sin\left(d x + c\right) + 10 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - 6 \, a^{2}}{\sin\left(d x + c\right)^{5}}}{30 \, d}"," ",0,"1/30*(60*a*b*log(sin(d*x + c)) + 30*b^2*sin(d*x + c) + (60*a*b*sin(d*x + c)^3 - 30*(a^2 - 2*b^2)*sin(d*x + c)^4 - 15*a*b*sin(d*x + c) + 10*(2*a^2 - b^2)*sin(d*x + c)^2 - 6*a^2)/sin(d*x + c)^5)/d","A",0
1223,1,108,0,0.342484," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{60 \, b^{2} \log\left(\sin\left(d x + c\right)\right) - \frac{120 \, a b \sin\left(d x + c\right)^{5} - 80 \, a b \sin\left(d x + c\right)^{3} + 30 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{4} + 24 \, a b \sin\left(d x + c\right) - 15 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} + 10 \, a^{2}}{\sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"1/60*(60*b^2*log(sin(d*x + c)) - (120*a*b*sin(d*x + c)^5 - 80*a*b*sin(d*x + c)^3 + 30*(a^2 - 2*b^2)*sin(d*x + c)^4 + 24*a*b*sin(d*x + c) - 15*(2*a^2 - b^2)*sin(d*x + c)^2 + 10*a^2)/sin(d*x + c)^6)/d","A",0
1224,1,106,0,0.329493," ","integrate(cos(d*x+c)^5*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{105 \, b^{2} \sin\left(d x + c\right)^{6} + 105 \, a b \sin\left(d x + c\right)^{5} - 105 \, a b \sin\left(d x + c\right)^{3} + 35 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{4} + 35 \, a b \sin\left(d x + c\right) - 21 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} + 15 \, a^{2}}{105 \, d \sin\left(d x + c\right)^{7}}"," ",0,"-1/105*(105*b^2*sin(d*x + c)^6 + 105*a*b*sin(d*x + c)^5 - 105*a*b*sin(d*x + c)^3 + 35*(a^2 - 2*b^2)*sin(d*x + c)^4 + 35*a*b*sin(d*x + c) - 21*(2*a^2 - b^2)*sin(d*x + c)^2 + 15*a^2)/(d*sin(d*x + c)^7)","A",0
1225,1,106,0,0.333195," ","integrate(cos(d*x+c)^5*csc(d*x+c)^9*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{420 \, b^{2} \sin\left(d x + c\right)^{6} + 560 \, a b \sin\left(d x + c\right)^{5} - 672 \, a b \sin\left(d x + c\right)^{3} + 210 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{4} + 240 \, a b \sin\left(d x + c\right) - 140 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} + 105 \, a^{2}}{840 \, d \sin\left(d x + c\right)^{8}}"," ",0,"-1/840*(420*b^2*sin(d*x + c)^6 + 560*a*b*sin(d*x + c)^5 - 672*a*b*sin(d*x + c)^3 + 210*(a^2 - 2*b^2)*sin(d*x + c)^4 + 240*a*b*sin(d*x + c) - 140*(2*a^2 - b^2)*sin(d*x + c)^2 + 105*a^2)/(d*sin(d*x + c)^8)","A",0
1226,1,218,0,0.320491," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{60 \, {\left(a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}\right)}}{b^{9} \sin\left(d x + c\right) + a b^{8}} + \frac{10 \, b^{5} \sin\left(d x + c\right)^{6} - 24 \, a b^{4} \sin\left(d x + c\right)^{5} + 15 \, {\left(3 \, a^{2} b^{3} - 2 \, b^{5}\right)} \sin\left(d x + c\right)^{4} - 80 \, {\left(a^{3} b^{2} - a b^{4}\right)} \sin\left(d x + c\right)^{3} + 30 \, {\left(5 \, a^{4} b - 6 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)^{2} - 120 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{b^{7}} + \frac{60 \, {\left(7 \, a^{6} - 10 \, a^{4} b^{2} + 3 \, a^{2} b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{8}}}{60 \, d}"," ",0,"1/60*(60*(a^7 - 2*a^5*b^2 + a^3*b^4)/(b^9*sin(d*x + c) + a*b^8) + (10*b^5*sin(d*x + c)^6 - 24*a*b^4*sin(d*x + c)^5 + 15*(3*a^2*b^3 - 2*b^5)*sin(d*x + c)^4 - 80*(a^3*b^2 - a*b^4)*sin(d*x + c)^3 + 30*(5*a^4*b - 6*a^2*b^3 + b^5)*sin(d*x + c)^2 - 120*(3*a^5 - 4*a^3*b^2 + a*b^4)*sin(d*x + c))/b^7 + 60*(7*a^6 - 10*a^4*b^2 + 3*a^2*b^4)*log(b*sin(d*x + c) + a)/b^8)/d","A",0
1227,1,184,0,0.334897," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{30 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)}}{b^{8} \sin\left(d x + c\right) + a b^{7}} - \frac{6 \, b^{4} \sin\left(d x + c\right)^{5} - 15 \, a b^{3} \sin\left(d x + c\right)^{4} + 10 \, {\left(3 \, a^{2} b^{2} - 2 \, b^{4}\right)} \sin\left(d x + c\right)^{3} - 60 \, {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)^{2} + 30 \, {\left(5 \, a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{b^{6}} + \frac{60 \, {\left(3 \, a^{5} - 4 \, a^{3} b^{2} + a b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{7}}}{30 \, d}"," ",0,"-1/30*(30*(a^6 - 2*a^4*b^2 + a^2*b^4)/(b^8*sin(d*x + c) + a*b^7) - (6*b^4*sin(d*x + c)^5 - 15*a*b^3*sin(d*x + c)^4 + 10*(3*a^2*b^2 - 2*b^4)*sin(d*x + c)^3 - 60*(a^3*b - a*b^3)*sin(d*x + c)^2 + 30*(5*a^4 - 6*a^2*b^2 + b^4)*sin(d*x + c))/b^6 + 60*(3*a^5 - 4*a^3*b^2 + a*b^4)*log(b*sin(d*x + c) + a)/b^7)/d","A",0
1228,1,148,0,0.332220," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{12 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)}}{b^{7} \sin\left(d x + c\right) + a b^{6}} + \frac{3 \, b^{3} \sin\left(d x + c\right)^{4} - 8 \, a b^{2} \sin\left(d x + c\right)^{3} + 6 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2} - 48 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{b^{5}} + \frac{12 \, {\left(5 \, a^{4} - 6 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{6}}}{12 \, d}"," ",0,"1/12*(12*(a^5 - 2*a^3*b^2 + a*b^4)/(b^7*sin(d*x + c) + a*b^6) + (3*b^3*sin(d*x + c)^4 - 8*a*b^2*sin(d*x + c)^3 + 6*(3*a^2*b - 2*b^3)*sin(d*x + c)^2 - 48*(a^3 - a*b^2)*sin(d*x + c))/b^5 + 12*(5*a^4 - 6*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/b^6)/d","A",0
1229,1,118,0,0.325170," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)}}{a b^{5} \sin\left(d x + c\right) + a^{2} b^{4}} + \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a^{2}} + \frac{b \sin\left(d x + c\right)^{2} - 4 \, a \sin\left(d x + c\right)}{b^{3}} + \frac{2 \, {\left(3 \, a^{4} - 2 \, a^{2} b^{2} - b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} b^{4}}}{2 \, d}"," ",0,"1/2*(2*(a^4 - 2*a^2*b^2 + b^4)/(a*b^5*sin(d*x + c) + a^2*b^4) + 2*log(sin(d*x + c))/a^2 + (b*sin(d*x + c)^2 - 4*a*sin(d*x + c))/b^3 + 2*(3*a^4 - 2*a^2*b^2 - b^4)*log(b*sin(d*x + c) + a)/(a^2*b^4))/d","A",0
1230,1,120,0,0.333230," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{a b^{3} + {\left(a^{4} - 2 \, a^{2} b^{2} + 2 \, b^{4}\right)} \sin\left(d x + c\right)}{a^{2} b^{4} \sin\left(d x + c\right)^{2} + a^{3} b^{3} \sin\left(d x + c\right)} + \frac{2 \, b \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{\sin\left(d x + c\right)}{b^{2}} + \frac{2 \, {\left(a^{4} - b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{3} b^{3}}}{d}"," ",0,"-((a*b^3 + (a^4 - 2*a^2*b^2 + 2*b^4)*sin(d*x + c))/(a^2*b^4*sin(d*x + c)^2 + a^3*b^3*sin(d*x + c)) + 2*b*log(sin(d*x + c))/a^3 - sin(d*x + c)/b^2 + 2*(a^4 - b^4)*log(b*sin(d*x + c) + a)/(a^3*b^3))/d","A",0
1231,1,147,0,0.336957," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{3 \, a b^{3} \sin\left(d x + c\right) - a^{2} b^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + 3 \, b^{4}\right)} \sin\left(d x + c\right)^{2}}{a^{3} b^{3} \sin\left(d x + c\right)^{3} + a^{4} b^{2} \sin\left(d x + c\right)^{2}} - \frac{2 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{4}} + \frac{2 \, {\left(a^{4} + 2 \, a^{2} b^{2} - 3 \, b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} b^{2}}}{2 \, d}"," ",0,"1/2*((3*a*b^3*sin(d*x + c) - a^2*b^2 + 2*(a^4 - 2*a^2*b^2 + 3*b^4)*sin(d*x + c)^2)/(a^3*b^3*sin(d*x + c)^3 + a^4*b^2*sin(d*x + c)^2) - 2*(2*a^2 - 3*b^2)*log(sin(d*x + c))/a^4 + 2*(a^4 + 2*a^2*b^2 - 3*b^4)*log(b*sin(d*x + c) + a)/(a^4*b^2))/d","A",0
1232,1,158,0,0.320532," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} b^{2} \sin\left(d x + c\right) - a^{3} b - 3 \, {\left(a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}\right)} \sin\left(d x + c\right)^{3} + 6 \, {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)^{2}}{a^{4} b^{2} \sin\left(d x + c\right)^{4} + a^{5} b \sin\left(d x + c\right)^{3}} - \frac{12 \, {\left(a^{2} b - b^{3}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{5}} + \frac{12 \, {\left(a^{2} b - b^{3}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{5}}}{3 \, d}"," ",0,"1/3*((2*a^2*b^2*sin(d*x + c) - a^3*b - 3*(a^4 - 4*a^2*b^2 + 4*b^4)*sin(d*x + c)^3 + 6*(a^3*b - a*b^3)*sin(d*x + c)^2)/(a^4*b^2*sin(d*x + c)^4 + a^5*b*sin(d*x + c)^3) - 12*(a^2*b - b^3)*log(b*sin(d*x + c) + a)/a^5 + 12*(a^2*b - b^3)*log(sin(d*x + c))/a^5)/d","A",0
1233,1,189,0,0.367332," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{5 \, a^{3} b \sin\left(d x + c\right) + 12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \sin\left(d x + c\right)^{4} - 3 \, a^{4} - 6 \, {\left(6 \, a^{3} b - 5 \, a b^{3}\right)} \sin\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{4} - 5 \, a^{2} b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{5} b \sin\left(d x + c\right)^{5} + a^{6} \sin\left(d x + c\right)^{4}} - \frac{12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6}} + \frac{12 \, {\left(a^{4} - 6 \, a^{2} b^{2} + 5 \, b^{4}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{6}}}{12 \, d}"," ",0,"1/12*((5*a^3*b*sin(d*x + c) + 12*(a^4 - 6*a^2*b^2 + 5*b^4)*sin(d*x + c)^4 - 3*a^4 - 6*(6*a^3*b - 5*a*b^3)*sin(d*x + c)^3 + 2*(6*a^4 - 5*a^2*b^2)*sin(d*x + c)^2)/(a^5*b*sin(d*x + c)^5 + a^6*sin(d*x + c)^4) - 12*(a^4 - 6*a^2*b^2 + 5*b^4)*log(b*sin(d*x + c) + a)/a^6 + 12*(a^4 - 6*a^2*b^2 + 5*b^4)*log(sin(d*x + c))/a^6)/d","A",0
1234,1,225,0,0.352240," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{9 \, a^{4} b \sin\left(d x + c\right) - 60 \, {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \sin\left(d x + c\right)^{5} - 6 \, a^{5} - 30 \, {\left(a^{5} - 4 \, a^{3} b^{2} + 3 \, a b^{4}\right)} \sin\left(d x + c\right)^{4} - 10 \, {\left(4 \, a^{4} b - 3 \, a^{2} b^{3}\right)} \sin\left(d x + c\right)^{3} + 5 \, {\left(4 \, a^{5} - 3 \, a^{3} b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{6} b \sin\left(d x + c\right)^{6} + a^{7} \sin\left(d x + c\right)^{5}} + \frac{60 \, {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{7}} - \frac{60 \, {\left(a^{4} b - 4 \, a^{2} b^{3} + 3 \, b^{5}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{7}}}{30 \, d}"," ",0,"1/30*((9*a^4*b*sin(d*x + c) - 60*(a^4*b - 4*a^2*b^3 + 3*b^5)*sin(d*x + c)^5 - 6*a^5 - 30*(a^5 - 4*a^3*b^2 + 3*a*b^4)*sin(d*x + c)^4 - 10*(4*a^4*b - 3*a^2*b^3)*sin(d*x + c)^3 + 5*(4*a^5 - 3*a^3*b^2)*sin(d*x + c)^2)/(a^6*b*sin(d*x + c)^6 + a^7*sin(d*x + c)^5) + 60*(a^4*b - 4*a^2*b^3 + 3*b^5)*log(b*sin(d*x + c) + a)/a^7 - 60*(a^4*b - 4*a^2*b^3 + 3*b^5)*log(sin(d*x + c))/a^7)/d","A",0
1235,1,178,0,0.371037," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{b^{2} \sin\left(d x + c\right)^{n + 7}}{n + 7} + \frac{2 \, a b \sin\left(d x + c\right)^{n + 6}}{n + 6} + \frac{a^{2} \sin\left(d x + c\right)^{n + 5}}{n + 5} - \frac{2 \, b^{2} \sin\left(d x + c\right)^{n + 5}}{n + 5} - \frac{4 \, a b \sin\left(d x + c\right)^{n + 4}}{n + 4} - \frac{2 \, a^{2} \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{b^{2} \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{2 \, a b \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a^{2} \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(b^2*sin(d*x + c)^(n + 7)/(n + 7) + 2*a*b*sin(d*x + c)^(n + 6)/(n + 6) + a^2*sin(d*x + c)^(n + 5)/(n + 5) - 2*b^2*sin(d*x + c)^(n + 5)/(n + 5) - 4*a*b*sin(d*x + c)^(n + 4)/(n + 4) - 2*a^2*sin(d*x + c)^(n + 3)/(n + 3) + b^2*sin(d*x + c)^(n + 3)/(n + 3) + 2*a*b*sin(d*x + c)^(n + 2)/(n + 2) + a^2*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
1236,1,109,0,0.329304," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{b \sin\left(d x + c\right)^{n + 6}}{n + 6} + \frac{a \sin\left(d x + c\right)^{n + 5}}{n + 5} - \frac{2 \, b \sin\left(d x + c\right)^{n + 4}}{n + 4} - \frac{2 \, a \sin\left(d x + c\right)^{n + 3}}{n + 3} + \frac{b \sin\left(d x + c\right)^{n + 2}}{n + 2} + \frac{a \sin\left(d x + c\right)^{n + 1}}{n + 1}}{d}"," ",0,"(b*sin(d*x + c)^(n + 6)/(n + 6) + a*sin(d*x + c)^(n + 5)/(n + 5) - 2*b*sin(d*x + c)^(n + 4)/(n + 4) - 2*a*sin(d*x + c)^(n + 3)/(n + 3) + b*sin(d*x + c)^(n + 2)/(n + 2) + a*sin(d*x + c)^(n + 1)/(n + 1))/d","A",0
1237,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(b*sin(d*x + c) + a), x)","F",0
1238,0,0,0,0.000000," ","integrate(cos(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \cos\left(d x + c\right)^{5}}{{\left(b \sin\left(d x + c\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*cos(d*x + c)^5/(b*sin(d*x + c) + a)^2, x)","F",0
1239,1,135,0,0.339200," ","integrate(cos(d*x+c)^6*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{53248 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a^{2} - 3003 \, {\left(4 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 120 \, d x + 120 \, c + 9 \, \sin\left(8 \, d x + 8 \, c\right) - 48 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b - 12288 \, {\left(231 \, \cos\left(d x + c\right)^{13} - 819 \, \cos\left(d x + c\right)^{11} + 1001 \, \cos\left(d x + c\right)^{9} - 429 \, \cos\left(d x + c\right)^{7}\right)} b^{2}}{36900864 \, d}"," ",0,"-1/36900864*(53248*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a^2 - 3003*(4*sin(4*d*x + 4*c)^3 + 120*d*x + 120*c + 9*sin(8*d*x + 8*c) - 48*sin(4*d*x + 4*c))*a*b - 12288*(231*cos(d*x + c)^13 - 819*cos(d*x + c)^11 + 1001*cos(d*x + c)^9 - 429*cos(d*x + c)^7)*b^2)/d","A",0
1240,1,137,0,0.427089," ","integrate(cos(d*x+c)^6*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{2772 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} - 81920 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} a b + 1155 \, {\left(4 \, \sin\left(4 \, d x + 4 \, c\right)^{3} + 120 \, d x + 120 \, c + 9 \, \sin\left(8 \, d x + 8 \, c\right) - 48 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{28385280 \, d}"," ",0,"1/28385280*(2772*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a^2 - 81920*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*a*b + 1155*(4*sin(4*d*x + 4*c)^3 + 120*d*x + 120*c + 9*sin(8*d*x + 8*c) - 48*sin(4*d*x + 4*c))*b^2)/d","A",0
1241,1,115,0,0.337897," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{56320 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a^{2} + 693 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b - 5120 \, {\left(63 \, \cos\left(d x + c\right)^{11} - 154 \, \cos\left(d x + c\right)^{9} + 99 \, \cos\left(d x + c\right)^{7}\right)} b^{2}}{3548160 \, d}"," ",0,"1/3548160*(56320*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a^2 + 693*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*a*b - 5120*(63*cos(d*x + c)^11 - 154*cos(d*x + c)^9 + 99*cos(d*x + c)^7)*b^2)/d","A",0
1242,1,127,0,0.668308," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{210 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a^{2} + 20480 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} a b + 63 \, {\left(32 \, \sin\left(2 \, d x + 2 \, c\right)^{5} + 120 \, d x + 120 \, c + 5 \, \sin\left(8 \, d x + 8 \, c\right) - 40 \, \sin\left(4 \, d x + 4 \, c\right)\right)} b^{2}}{645120 \, d}"," ",0,"1/645120*(210*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a^2 + 20480*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*a*b + 63*(32*sin(2*d*x + 2*c)^5 + 120*d*x + 120*c + 5*sin(8*d*x + 8*c) - 40*sin(4*d*x + 4*c))*b^2)/d","A",0
1243,1,92,0,0.993588," ","integrate(cos(d*x+c)^6*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4608 \, a^{2} \cos\left(d x + c\right)^{7} - 21 \, {\left(64 \, \sin\left(2 \, d x + 2 \, c\right)^{3} + 120 \, d x + 120 \, c - 3 \, \sin\left(8 \, d x + 8 \, c\right) - 24 \, \sin\left(4 \, d x + 4 \, c\right)\right)} a b - 512 \, {\left(7 \, \cos\left(d x + c\right)^{9} - 9 \, \cos\left(d x + c\right)^{7}\right)} b^{2}}{32256 \, d}"," ",0,"-1/32256*(4608*a^2*cos(d*x + c)^7 - 21*(64*sin(2*d*x + 2*c)^3 + 120*d*x + 120*c - 3*sin(8*d*x + 8*c) - 24*sin(4*d*x + 4*c))*a*b - 512*(7*cos(d*x + c)^9 - 9*cos(d*x + c)^7)*b^2)/d","A",0
1244,1,122,0,0.552951," ","integrate(cos(d*x+c)^6*csc(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{480 \, b^{2} \cos\left(d x + c\right)^{7} - 112 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} + 35 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} a b}{3360 \, d}"," ",0,"-1/3360*(480*b^2*cos(d*x + c)^7 - 112*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^2 + 35*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*a*b)/d","A",0
1245,1,172,0,0.765493," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{120 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a^{2} - 64 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a b + 5 \, {\left(4 \, \sin\left(2 \, d x + 2 \, c\right)^{3} - 60 \, d x - 60 \, c - 9 \, \sin\left(4 \, d x + 4 \, c\right) - 48 \, \sin\left(2 \, d x + 2 \, c\right)\right)} b^{2}}{960 \, d}"," ",0,"-1/960*(120*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a^2 - 64*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a*b + 5*(4*sin(2*d*x + 2*c)^3 - 60*d*x - 60*c - 9*sin(4*d*x + 4*c) - 48*sin(2*d*x + 2*c))*b^2)/d","A",0
1246,1,190,0,0.585719," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{5 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a^{2} + 15 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} a b - 2 \, {\left(6 \, \cos\left(d x + c\right)^{5} + 10 \, \cos\left(d x + c\right)^{3} + 30 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} b^{2}}{60 \, d}"," ",0,"-1/60*(5*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a^2 + 15*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*a*b - 2*(6*cos(d*x + c)^5 + 10*cos(d*x + c)^3 + 30*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*b^2)/d","A",0
1247,1,189,0,0.583292," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{4 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a^{2} - 4 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} a b - 3 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 25 \, \tan\left(d x + c\right)^{2} + 8}{\tan\left(d x + c\right)^{5} + 2 \, \tan\left(d x + c\right)^{3} + \tan\left(d x + c\right)}\right)} b^{2}}{24 \, d}"," ",0,"1/24*(4*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a^2 - 4*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*a*b - 3*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 25*tan(d*x + c)^2 + 8)/(tan(d*x + c)^5 + 2*tan(d*x + c)^3 + tan(d*x + c)))*b^2)/d","A",0
1248,1,205,0,0.503024," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{16 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} a b - 4 \, {\left(4 \, \cos\left(d x + c\right)^{3} - \frac{6 \, \cos\left(d x + c\right)}{\cos\left(d x + c\right)^{2} - 1} + 24 \, \cos\left(d x + c\right) - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} b^{2} - 3 \, a^{2} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{48 \, d}"," ",0,"1/48*(16*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*a*b - 4*(4*cos(d*x + c)^3 - 6*cos(d*x + c)/(cos(d*x + c)^2 - 1) + 24*cos(d*x + c) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1))*b^2 - 3*a^2*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
1249,1,183,0,0.555971," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{8 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a^{2} - 20 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} + 10 \, \tan\left(d x + c\right)^{2} - 2}{\tan\left(d x + c\right)^{5} + \tan\left(d x + c\right)^{3}}\right)} b^{2} + 15 \, a b {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{120 \, d}"," ",0,"-1/120*(8*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a^2 - 20*(15*d*x + 15*c + (15*tan(d*x + c)^4 + 10*tan(d*x + c)^2 - 2)/(tan(d*x + c)^5 + tan(d*x + c)^3))*b^2 + 15*a*b*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
1250,1,219,0,0.423361," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{64 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} a b - 5 \, a^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 30 \, b^{2} {\left(\frac{2 \, {\left(9 \, \cos\left(d x + c\right)^{3} - 7 \, \cos\left(d x + c\right)\right)}}{\cos\left(d x + c\right)^{4} - 2 \, \cos\left(d x + c\right)^{2} + 1} - 16 \, \cos\left(d x + c\right) + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)}}{480 \, d}"," ",0,"-1/480*(64*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*a*b - 5*a^2*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 30*b^2*(2*(9*cos(d*x + c)^3 - 7*cos(d*x + c))/(cos(d*x + c)^4 - 2*cos(d*x + c)^2 + 1) - 16*cos(d*x + c) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)))/d","A",0
1251,1,153,0,0.418189," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{112 \, {\left(15 \, d x + 15 \, c + \frac{15 \, \tan\left(d x + c\right)^{4} - 5 \, \tan\left(d x + c\right)^{2} + 3}{\tan\left(d x + c\right)^{5}}\right)} b^{2} - 35 \, a b {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{240 \, a^{2}}{\tan\left(d x + c\right)^{7}}}{1680 \, d}"," ",0,"-1/1680*(112*(15*d*x + 15*c + (15*tan(d*x + c)^4 - 5*tan(d*x + c)^2 + 3)/tan(d*x + c)^5)*b^2 - 35*a*b*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 240*a^2/tan(d*x + c)^7)/d","A",0
1252,1,220,0,0.336587," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{7 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 56 \, b^{2} {\left(\frac{2 \, {\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)}}{\cos\left(d x + c\right)^{6} - 3 \, \cos\left(d x + c\right)^{4} + 3 \, \cos\left(d x + c\right)^{2} - 1} + 15 \, \log\left(\cos\left(d x + c\right) + 1\right) - 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{1536 \, a b}{\tan\left(d x + c\right)^{7}}}{5376 \, d}"," ",0,"-1/5376*(7*a^2*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) - 56*b^2*(2*(33*cos(d*x + c)^5 - 40*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^6 - 3*cos(d*x + c)^4 + 3*cos(d*x + c)^2 - 1) + 15*log(cos(d*x + c) + 1) - 15*log(cos(d*x + c) - 1)) + 1536*a*b/tan(d*x + c)^7)/d","A",0
1253,1,154,0,0.331651," ","integrate(cos(d*x+c)^6*csc(d*x+c)^10*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{21 \, a b {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{1152 \, b^{2}}{\tan\left(d x + c\right)^{7}} + \frac{128 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a^{2}}{\tan\left(d x + c\right)^{9}}}{8064 \, d}"," ",0,"-1/8064*(21*a*b*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 1152*b^2/tan(d*x + c)^7 + 128*(9*tan(d*x + c)^2 + 7)*a^2/tan(d*x + c)^9)/d","A",0
1254,1,272,0,0.333741," ","integrate(cos(d*x+c)^6*csc(d*x+c)^11*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{63 \, a^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 210 \, b^{2} {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{5120 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} a b}{\tan\left(d x + c\right)^{9}}}{161280 \, d}"," ",0,"-1/161280*(63*a^2*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 210*b^2*(2*(15*cos(d*x + c)^7 + 73*cos(d*x + c)^5 - 55*cos(d*x + c)^3 + 15*cos(d*x + c))/(cos(d*x + c)^8 - 4*cos(d*x + c)^6 + 6*cos(d*x + c)^4 - 4*cos(d*x + c)^2 + 1) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 5120*(9*tan(d*x + c)^2 + 7)*a*b/tan(d*x + c)^9)/d","A",0
1255,1,196,0,0.340722," ","integrate(cos(d*x+c)^6*csc(d*x+c)^12*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{693 \, a b {\left(\frac{2 \, {\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)}}{\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} - 15 \, \log\left(\cos\left(d x + c\right) + 1\right) + 15 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + \frac{14080 \, {\left(9 \, \tan\left(d x + c\right)^{2} + 7\right)} b^{2}}{\tan\left(d x + c\right)^{9}} + \frac{1280 \, {\left(99 \, \tan\left(d x + c\right)^{4} + 154 \, \tan\left(d x + c\right)^{2} + 63\right)} a^{2}}{\tan\left(d x + c\right)^{11}}}{887040 \, d}"," ",0,"-1/887040*(693*a*b*(2*(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))/(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) - 15*log(cos(d*x + c) + 1) + 15*log(cos(d*x + c) - 1)) + 14080*(9*tan(d*x + c)^2 + 7)*b^2/tan(d*x + c)^9 + 1280*(99*tan(d*x + c)^4 + 154*tan(d*x + c)^2 + 63)*a^2/tan(d*x + c)^11)/d","A",0
1256,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1257,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1258,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1259,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1260,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1261,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1262,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1263,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1264,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1265,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1266,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1267,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1268,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1269,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1270,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1271,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1272,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1273,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1274,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1275,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1276,0,0,0,0.000000," ","integrate(cos(f*x+e)^6/(a+b*sin(f*x+e))^(13/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\cos\left(f x + e\right)^{6}}{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{13}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(cos(f*x + e)^6/((b*sin(f*x + e) + a)^(13/2)*sqrt(d*sin(f*x + e))), x)","F",0
1277,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/((g*cos(f*x + e))^(5/2)*sqrt(d*sin(f*x + e))), x)","F",0
1278,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^2/(g*cos(f*x+e))^(7/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{7}{2}} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2/((g*cos(f*x + e))^(7/2)*sqrt(d*sin(f*x + e))), x)","F",0
1279,1,67,0,0.321404," ","integrate(cos(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{6 \, a^{3} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{4}} - \frac{2 \, b^{2} \sin\left(d x + c\right)^{3} - 3 \, a b \sin\left(d x + c\right)^{2} + 6 \, a^{2} \sin\left(d x + c\right)}{b^{3}}}{6 \, d}"," ",0,"-1/6*(6*a^3*log(b*sin(d*x + c) + a)/b^4 - (2*b^2*sin(d*x + c)^3 - 3*a*b*sin(d*x + c)^2 + 6*a^2*sin(d*x + c))/b^3)/d","A",0
1280,1,49,0,0.314475," ","integrate(cos(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a^{2} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{3}} + \frac{b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{b^{2}}}{2 \, d}"," ",0,"1/2*(2*a^2*log(b*sin(d*x + c) + a)/b^3 + (b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2)/d","A",0
1281,1,33,0,0.337831," ","integrate(cos(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{a \log\left(b \sin\left(d x + c\right) + a\right)}{b^{2}} - \frac{\sin\left(d x + c\right)}{b}}{d}"," ",0,"-(a*log(b*sin(d*x + c) + a)/b^2 - sin(d*x + c)/b)/d","A",0
1282,1,33,0,0.312908," ","integrate(cos(d*x+c)*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{\log\left(b \sin\left(d x + c\right) + a\right)}{a} - \frac{\log\left(\sin\left(d x + c\right)\right)}{a}}{d}"," ",0,"-(log(b*sin(d*x + c) + a)/a - log(sin(d*x + c))/a)/d","A",0
1283,1,47,0,0.335365," ","integrate(cos(d*x+c)*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{b \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2}} - \frac{b \log\left(\sin\left(d x + c\right)\right)}{a^{2}} - \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"(b*log(b*sin(d*x + c) + a)/a^2 - b*log(sin(d*x + c))/a^2 - 1/(a*sin(d*x + c)))/d","A",0
1284,1,66,0,0.332351," ","integrate(cos(d*x+c)*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b^{2} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{3}} - \frac{2 \, b^{2} \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{2 \, b \sin\left(d x + c\right) - a}{a^{2} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"-1/2*(2*b^2*log(b*sin(d*x + c) + a)/a^3 - 2*b^2*log(sin(d*x + c))/a^3 - (2*b*sin(d*x + c) - a)/(a^2*sin(d*x + c)^2))/d","A",0
1285,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1286,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1287,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1288,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1289,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1290,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1291,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1292,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1293,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1294,-2,0,0,0.000000," ","integrate(cos(d*x+c)^2*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1295,1,131,0,0.333017," ","integrate(cos(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{12 \, b^{4} \sin\left(d x + c\right)^{5} - 15 \, a b^{3} \sin\left(d x + c\right)^{4} + 20 \, {\left(a^{2} b^{2} - b^{4}\right)} \sin\left(d x + c\right)^{3} - 30 \, {\left(a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)^{2} + 60 \, {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(d x + c\right)}{b^{5}} - \frac{60 \, {\left(a^{5} - a^{3} b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{6}}}{60 \, d}"," ",0,"-1/60*((12*b^4*sin(d*x + c)^5 - 15*a*b^3*sin(d*x + c)^4 + 20*(a^2*b^2 - b^4)*sin(d*x + c)^3 - 30*(a^3*b - a*b^3)*sin(d*x + c)^2 + 60*(a^4 - a^2*b^2)*sin(d*x + c))/b^5 - 60*(a^5 - a^3*b^2)*log(b*sin(d*x + c) + a)/b^6)/d","A",0
1296,1,105,0,0.314209," ","integrate(cos(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{3 \, b^{3} \sin\left(d x + c\right)^{4} - 4 \, a b^{2} \sin\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{2} - 12 \, {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)}{b^{4}} + \frac{12 \, {\left(a^{4} - a^{2} b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{5}}}{12 \, d}"," ",0,"-1/12*((3*b^3*sin(d*x + c)^4 - 4*a*b^2*sin(d*x + c)^3 + 6*(a^2*b - b^3)*sin(d*x + c)^2 - 12*(a^3 - a*b^2)*sin(d*x + c))/b^4 + 12*(a^4 - a^2*b^2)*log(b*sin(d*x + c) + a)/b^5)/d","A",0
1297,1,79,0,0.321704," ","integrate(cos(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b^{2} \sin\left(d x + c\right)^{3} - 3 \, a b \sin\left(d x + c\right)^{2} + 6 \, {\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)}{b^{3}} - \frac{6 \, {\left(a^{3} - a b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{4}}}{6 \, d}"," ",0,"-1/6*((2*b^2*sin(d*x + c)^3 - 3*a*b*sin(d*x + c)^2 + 6*(a^2 - b^2)*sin(d*x + c))/b^3 - 6*(a^3 - a*b^2)*log(b*sin(d*x + c) + a)/b^4)/d","A",0
1298,1,54,0,0.322721," ","integrate(cos(d*x+c)^3*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{\log\left(\sin\left(d x + c\right)\right)}{a} - \frac{\sin\left(d x + c\right)}{b} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a b^{2}}}{d}"," ",0,"(log(sin(d*x + c))/a - sin(d*x + c)/b + (a^2 - b^2)*log(b*sin(d*x + c) + a)/(a*b^2))/d","A",0
1299,1,57,0,0.307988," ","integrate(cos(d*x+c)^3*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{b \log\left(\sin\left(d x + c\right)\right)}{a^{2}} + \frac{{\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} b} + \frac{1}{a \sin\left(d x + c\right)}}{d}"," ",0,"-(b*log(sin(d*x + c))/a^2 + (a^2 - b^2)*log(b*sin(d*x + c) + a)/(a^2*b) + 1/(a*sin(d*x + c)))/d","A",0
1300,1,77,0,0.310040," ","integrate(cos(d*x+c)^3*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{3}} - \frac{2 \, {\left(a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{3}} + \frac{2 \, b \sin\left(d x + c\right) - a}{a^{2} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*(a^2 - b^2)*log(b*sin(d*x + c) + a)/a^3 - 2*(a^2 - b^2)*log(sin(d*x + c))/a^3 + (2*b*sin(d*x + c) - a)/(a^2*sin(d*x + c)^2))/d","A",0
1301,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1302,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1303,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1304,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1305,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1306,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1307,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1308,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1309,-2,0,0,0.000000," ","integrate(cos(d*x+c)^4*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1310,1,205,0,0.308474," ","integrate(cos(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{60 \, b^{6} \sin\left(d x + c\right)^{7} - 70 \, a b^{5} \sin\left(d x + c\right)^{6} + 84 \, {\left(a^{2} b^{4} - 2 \, b^{6}\right)} \sin\left(d x + c\right)^{5} - 105 \, {\left(a^{3} b^{3} - 2 \, a b^{5}\right)} \sin\left(d x + c\right)^{4} + 140 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \sin\left(d x + c\right)^{3} - 210 \, {\left(a^{5} b - 2 \, a^{3} b^{3} + a b^{5}\right)} \sin\left(d x + c\right)^{2} + 420 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(d x + c\right)}{b^{7}} - \frac{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)}{b^{8}}}{420 \, d}"," ",0,"1/420*((60*b^6*sin(d*x + c)^7 - 70*a*b^5*sin(d*x + c)^6 + 84*(a^2*b^4 - 2*b^6)*sin(d*x + c)^5 - 105*(a^3*b^3 - 2*a*b^5)*sin(d*x + c)^4 + 140*(a^4*b^2 - 2*a^2*b^4 + b^6)*sin(d*x + c)^3 - 210*(a^5*b - 2*a^3*b^3 + a*b^5)*sin(d*x + c)^2 + 420*(a^6 - 2*a^4*b^2 + a^2*b^4)*sin(d*x + c))/b^7 - 420*(a^7 - 2*a^5*b^2 + a^3*b^4)*log(b*sin(d*x + c) + a)/b^8)/d","A",0
1311,1,172,0,0.314615," ","integrate(cos(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{10 \, b^{5} \sin\left(d x + c\right)^{6} - 12 \, a b^{4} \sin\left(d x + c\right)^{5} + 15 \, {\left(a^{2} b^{3} - 2 \, b^{5}\right)} \sin\left(d x + c\right)^{4} - 20 \, {\left(a^{3} b^{2} - 2 \, a b^{4}\right)} \sin\left(d x + c\right)^{3} + 30 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)^{2} - 60 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)}{b^{6}} + \frac{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)}{b^{7}}}{60 \, d}"," ",0,"1/60*((10*b^5*sin(d*x + c)^6 - 12*a*b^4*sin(d*x + c)^5 + 15*(a^2*b^3 - 2*b^5)*sin(d*x + c)^4 - 20*(a^3*b^2 - 2*a*b^4)*sin(d*x + c)^3 + 30*(a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c)^2 - 60*(a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c))/b^6 + 60*(a^6 - 2*a^4*b^2 + a^2*b^4)*log(b*sin(d*x + c) + a)/b^7)/d","A",0
1312,1,139,0,0.309586," ","integrate(cos(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{12 \, b^{4} \sin\left(d x + c\right)^{5} - 15 \, a b^{3} \sin\left(d x + c\right)^{4} + 20 \, {\left(a^{2} b^{2} - 2 \, b^{4}\right)} \sin\left(d x + c\right)^{3} - 30 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)^{2} + 60 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)}{b^{5}} - \frac{60 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{6}}}{60 \, d}"," ",0,"1/60*((12*b^4*sin(d*x + c)^5 - 15*a*b^3*sin(d*x + c)^4 + 20*(a^2*b^2 - 2*b^4)*sin(d*x + c)^3 - 30*(a^3*b - 2*a*b^3)*sin(d*x + c)^2 + 60*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c))/b^5 - 60*(a^5 - 2*a^3*b^2 + a*b^4)*log(b*sin(d*x + c) + a)/b^6)/d","A",0
1313,1,99,0,0.301109," ","integrate(cos(d*x+c)^5*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{6 \, \log\left(\sin\left(d x + c\right)\right)}{a} + \frac{2 \, b^{2} \sin\left(d x + c\right)^{3} - 3 \, a b \sin\left(d x + c\right)^{2} + 6 \, {\left(a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)}{b^{3}} - \frac{6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a b^{4}}}{6 \, d}"," ",0,"1/6*(6*log(sin(d*x + c))/a + (2*b^2*sin(d*x + c)^3 - 3*a*b*sin(d*x + c)^2 + 6*(a^2 - 2*b^2)*sin(d*x + c))/b^3 - 6*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/(a*b^4))/d","A",0
1314,1,91,0,0.301470," ","integrate(cos(d*x+c)^5*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b \log\left(\sin\left(d x + c\right)\right)}{a^{2}} - \frac{b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)}{b^{2}} + \frac{2}{a \sin\left(d x + c\right)} - \frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} b^{3}}}{2 \, d}"," ",0,"-1/2*(2*b*log(sin(d*x + c))/a^2 - (b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2 + 2/(a*sin(d*x + c)) - 2*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/(a^2*b^3))/d","A",0
1315,1,99,0,0.313867," ","integrate(cos(d*x+c)^5*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, \sin\left(d x + c\right)}{b} - \frac{2 \, {\left(2 \, a^{2} - b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{3}} - \frac{2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{3} b^{2}} + \frac{2 \, b \sin\left(d x + c\right) - a}{a^{2} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*sin(d*x + c)/b - 2*(2*a^2 - b^2)*log(sin(d*x + c))/a^3 - 2*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/(a^3*b^2) + (2*b*sin(d*x + c) - a)/(a^2*sin(d*x + c)^2))/d","A",0
1316,1,113,0,0.304655," ","integrate(cos(d*x+c)^5*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{6 \, {\left(2 \, a^{2} b - b^{3}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{4}} + \frac{6 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} b} + \frac{3 \, a b \sin\left(d x + c\right) + 6 \, {\left(2 \, a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, a^{2}}{a^{3} \sin\left(d x + c\right)^{3}}}{6 \, d}"," ",0,"1/6*(6*(2*a^2*b - b^3)*log(sin(d*x + c))/a^4 + 6*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/(a^4*b) + (3*a*b*sin(d*x + c) + 6*(2*a^2 - b^2)*sin(d*x + c)^2 - 2*a^2)/(a^3*sin(d*x + c)^3))/d","A",0
1317,1,139,0,0.306172," ","integrate(cos(d*x+c)^5*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{5}} - \frac{12 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{5}} - \frac{4 \, a^{2} b \sin\left(d x + c\right) - 12 \, {\left(2 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{3} - 3 \, a^{3} + 6 \, {\left(2 \, a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{4} \sin\left(d x + c\right)^{4}}}{12 \, d}"," ",0,"-1/12*(12*(a^4 - 2*a^2*b^2 + b^4)*log(b*sin(d*x + c) + a)/a^5 - 12*(a^4 - 2*a^2*b^2 + b^4)*log(sin(d*x + c))/a^5 - (4*a^2*b*sin(d*x + c) - 12*(2*a^2*b - b^3)*sin(d*x + c)^3 - 3*a^3 + 6*(2*a^3 - a*b^2)*sin(d*x + c)^2)/(a^4*sin(d*x + c)^4))/d","A",0
1318,1,170,0,0.307234," ","integrate(cos(d*x+c)^5*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6}} - \frac{60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{6}} + \frac{15 \, a^{3} b \sin\left(d x + c\right) - 60 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\left(d x + c\right)^{4} - 12 \, a^{4} - 30 \, {\left(2 \, a^{3} b - a b^{3}\right)} \sin\left(d x + c\right)^{3} + 20 \, {\left(2 \, a^{4} - a^{2} b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{5} \sin\left(d x + c\right)^{5}}}{60 \, d}"," ",0,"1/60*(60*(a^4*b - 2*a^2*b^3 + b^5)*log(b*sin(d*x + c) + a)/a^6 - 60*(a^4*b - 2*a^2*b^3 + b^5)*log(sin(d*x + c))/a^6 + (15*a^3*b*sin(d*x + c) - 60*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 - 12*a^4 - 30*(2*a^3*b - a*b^3)*sin(d*x + c)^3 + 20*(2*a^4 - a^2*b^2)*sin(d*x + c)^2)/(a^5*sin(d*x + c)^5))/d","A",0
1319,1,206,0,0.318367," ","integrate(cos(d*x+c)^5*csc(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{60 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{7}} - \frac{60 \, {\left(a^{4} b^{2} - 2 \, a^{2} b^{4} + b^{6}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{7}} - \frac{12 \, a^{4} b \sin\left(d x + c\right) + 60 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)^{5} - 10 \, a^{5} - 30 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{4} - 20 \, {\left(2 \, a^{4} b - a^{2} b^{3}\right)} \sin\left(d x + c\right)^{3} + 15 \, {\left(2 \, a^{5} - a^{3} b^{2}\right)} \sin\left(d x + c\right)^{2}}{a^{6} \sin\left(d x + c\right)^{6}}}{60 \, d}"," ",0,"-1/60*(60*(a^4*b^2 - 2*a^2*b^4 + b^6)*log(b*sin(d*x + c) + a)/a^7 - 60*(a^4*b^2 - 2*a^2*b^4 + b^6)*log(sin(d*x + c))/a^7 - (12*a^4*b*sin(d*x + c) + 60*(a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c)^5 - 10*a^5 - 30*(a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c)^4 - 20*(2*a^4*b - a^2*b^3)*sin(d*x + c)^3 + 15*(2*a^5 - a^3*b^2)*sin(d*x + c)^2)/(a^6*sin(d*x + c)^6))/d","A",0
1320,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1321,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1322,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1323,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1324,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1325,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1326,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1327,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1328,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1329,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1330,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^8/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1331,-2,0,0,0.000000," ","integrate(cos(d*x+c)^6*csc(d*x+c)^9/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1332,1,82,0,0.310969," ","integrate(sec(d*x+c)*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a^{3} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} b^{2} - b^{4}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b} - \frac{2 \, \sin\left(d x + c\right)}{b}}{2 \, d}"," ",0,"1/2*(2*a^3*log(b*sin(d*x + c) + a)/(a^2*b^2 - b^4) - log(sin(d*x + c) + 1)/(a - b) - log(sin(d*x + c) - 1)/(a + b) - 2*sin(d*x + c)/b)/d","A",0
1333,1,68,0,0.383224," ","integrate(sec(d*x+c)*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, a^{2} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} b - b^{3}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b}}{2 \, d}"," ",0,"-1/2*(2*a^2*log(b*sin(d*x + c) + a)/(a^2*b - b^3) - log(sin(d*x + c) + 1)/(a - b) + log(sin(d*x + c) - 1)/(a + b))/d","A",0
1334,1,65,0,0.314243," ","integrate(sec(d*x+c)*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, a \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} - b^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*a*log(b*sin(d*x + c) + a)/(a^2 - b^2) - log(sin(d*x + c) + 1)/(a - b) - log(sin(d*x + c) - 1)/(a + b))/d","A",0
1335,1,80,0,0.312229," ","integrate(csc(d*x+c)*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{2} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{3} - a b^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b} + \frac{2 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{2 \, d}"," ",0,"1/2*(2*b^2*log(b*sin(d*x + c) + a)/(a^3 - a*b^2) - log(sin(d*x + c) + 1)/(a - b) - log(sin(d*x + c) - 1)/(a + b) + 2*log(sin(d*x + c))/a)/d","A",0
1336,1,95,0,0.320809," ","integrate(csc(d*x+c)^2*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, b^{3} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - a^{2} b^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} + \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b} + \frac{2 \, b \log\left(\sin\left(d x + c\right)\right)}{a^{2}} + \frac{2}{a \sin\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*b^3*log(b*sin(d*x + c) + a)/(a^4 - a^2*b^2) - log(sin(d*x + c) + 1)/(a - b) + log(sin(d*x + c) - 1)/(a + b) + 2*b*log(sin(d*x + c))/a^2 + 2/(a*sin(d*x + c)))/d","A",0
1337,1,114,0,0.307033," ","integrate(csc(d*x+c)^3*sec(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, b^{4} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{5} - a^{3} b^{2}} - \frac{\log\left(\sin\left(d x + c\right) + 1\right)}{a - b} - \frac{\log\left(\sin\left(d x + c\right) - 1\right)}{a + b} + \frac{2 \, {\left(a^{2} + b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{3}} + \frac{2 \, b \sin\left(d x + c\right) - a}{a^{2} \sin\left(d x + c\right)^{2}}}{2 \, d}"," ",0,"1/2*(2*b^4*log(b*sin(d*x + c) + a)/(a^5 - a^3*b^2) - log(sin(d*x + c) + 1)/(a - b) - log(sin(d*x + c) - 1)/(a + b) + 2*(a^2 + b^2)*log(sin(d*x + c))/a^3 + (2*b*sin(d*x + c) - a)/(a^2*sin(d*x + c)^2))/d","A",0
1338,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1339,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1340,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1341,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1342,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1343,-2,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1344,-2,0,0,0.000000," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1345,-2,0,0,0.000000," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1346,1,142,0,0.319944," ","integrate(sec(d*x+c)^3*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, a^{3} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(2 \, a - b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(2 \, a + b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(b \sin\left(d x + c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(4*a^3*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) - (2*a - b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) - (2*a + b)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) - 2*(b*sin(d*x + c) - a)/((a^2 - b^2)*sin(d*x + c)^2 - a^2 + b^2))/d","A",0
1347,1,132,0,0.313705," ","integrate(sec(d*x+c)^3*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{4 \, a^{2} b \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{a \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{a \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(a \sin\left(d x + c\right) - b\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} + b^{2}}}{4 \, d}"," ",0,"1/4*(4*a^2*b*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) - a*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + a*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) - 2*(a*sin(d*x + c) - b)/((a^2 - b^2)*sin(d*x + c)^2 - a^2 + b^2))/d","A",0
1348,1,132,0,0.316775," ","integrate(sec(d*x+c)^3*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, a b^{2} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{b \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{b \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(b \sin\left(d x + c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(4*a*b^2*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) - b*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + b*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) - 2*(b*sin(d*x + c) - a)/((a^2 - b^2)*sin(d*x + c)^2 - a^2 + b^2))/d","A",0
1349,1,156,0,0.316997," ","integrate(csc(d*x+c)*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, b^{4} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{5} - 2 \, a^{3} b^{2} + a b^{4}} + \frac{{\left(2 \, a - 3 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{{\left(2 \, a + 3 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(b \sin\left(d x + c\right) - a\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} + b^{2}} - \frac{4 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{4 \, d}"," ",0,"-1/4*(4*b^4*log(b*sin(d*x + c) + a)/(a^5 - 2*a^3*b^2 + a*b^4) + (2*a - 3*b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + (2*a + 3*b)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) - 2*(b*sin(d*x + c) - a)/((a^2 - b^2)*sin(d*x + c)^2 - a^2 + b^2) - 4*log(sin(d*x + c))/a)/d","A",0
1350,1,200,0,0.321831," ","integrate(csc(d*x+c)^2*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{4 \, b^{5} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}} + \frac{{\left(3 \, a - 4 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(3 \, a + 4 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(a b \sin\left(d x + c\right) - {\left(3 \, a^{2} - 2 \, b^{2}\right)} \sin\left(d x + c\right)^{2} + 2 \, a^{2} - 2 \, b^{2}\right)}}{{\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{3} - {\left(a^{3} - a b^{2}\right)} \sin\left(d x + c\right)} - \frac{4 \, b \log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{4 \, d}"," ",0,"1/4*(4*b^5*log(b*sin(d*x + c) + a)/(a^6 - 2*a^4*b^2 + a^2*b^4) + (3*a - 4*b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) - (3*a + 4*b)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) + 2*(a*b*sin(d*x + c) - (3*a^2 - 2*b^2)*sin(d*x + c)^2 + 2*a^2 - 2*b^2)/((a^3 - a*b^2)*sin(d*x + c)^3 - (a^3 - a*b^2)*sin(d*x + c)) - 4*b*log(sin(d*x + c))/a^2)/d","A",0
1351,1,244,0,0.322234," ","integrate(csc(d*x+c)^3*sec(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, b^{6} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{7} - 2 \, a^{5} b^{2} + a^{3} b^{4}} + \frac{{\left(4 \, a - 5 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{{\left(4 \, a + 5 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left({\left(3 \, a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)^{3} + a^{3} - a b^{2} - {\left(2 \, a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - a^{2} b^{2}\right)} \sin\left(d x + c\right)^{4} - {\left(a^{4} - a^{2} b^{2}\right)} \sin\left(d x + c\right)^{2}} - \frac{4 \, {\left(2 \, a^{2} + b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{4 \, d}"," ",0,"-1/4*(4*b^6*log(b*sin(d*x + c) + a)/(a^7 - 2*a^5*b^2 + a^3*b^4) + (4*a - 5*b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + (4*a + 5*b)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) - 2*((3*a^2*b - 2*b^3)*sin(d*x + c)^3 + a^3 - a*b^2 - (2*a^3 - a*b^2)*sin(d*x + c)^2 - 2*(a^2*b - b^3)*sin(d*x + c))/((a^4 - a^2*b^2)*sin(d*x + c)^4 - (a^4 - a^2*b^2)*sin(d*x + c)^2) - 4*(2*a^2 + b^2)*log(sin(d*x + c))/a^3)/d","A",0
1352,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1353,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1354,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1355,-2,0,0,0.000000," ","integrate(sec(d*x+c)^4*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1356,-2,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1357,-2,0,0,0.000000," ","integrate(csc(d*x+c)^2*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1358,-2,0,0,0.000000," ","integrate(csc(d*x+c)^3*sec(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1359,1,316,0,0.379592," ","integrate(sec(d*x+c)^5*sin(d*x+c)^8/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{16 \, a^{8} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} b^{3} - 3 \, a^{4} b^{5} + 3 \, a^{2} b^{7} - b^{9}} - \frac{{\left(35 \, a^{2} - 57 \, a b + 24 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(35 \, a^{2} + 57 \, a b + 24 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left({\left(13 \, a^{3} - 9 \, a b^{2}\right)} \sin\left(d x + c\right)^{3} + 14 \, a^{2} b - 10 \, b^{3} - 4 \, {\left(4 \, a^{2} b - 3 \, b^{3}\right)} \sin\left(d x + c\right)^{2} - {\left(11 \, a^{3} - 7 \, a b^{2}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}} + \frac{8 \, {\left(b \sin\left(d x + c\right)^{2} - 2 \, a \sin\left(d x + c\right)\right)}}{b^{2}}}{16 \, d}"," ",0,"-1/16*(16*a^8*log(b*sin(d*x + c) + a)/(a^6*b^3 - 3*a^4*b^5 + 3*a^2*b^7 - b^9) - (35*a^2 - 57*a*b + 24*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (35*a^2 + 57*a*b + 24*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*((13*a^3 - 9*a*b^2)*sin(d*x + c)^3 + 14*a^2*b - 10*b^3 - 4*(4*a^2*b - 3*b^3)*sin(d*x + c)^2 - (11*a^3 - 7*a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2) + 8*(b*sin(d*x + c)^2 - 2*a*sin(d*x + c))/b^2)/d","A",0
1360,1,303,0,0.325733," ","integrate(sec(d*x+c)^5*sin(d*x+c)^7/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, a^{7} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} b^{2} - 3 \, a^{4} b^{4} + 3 \, a^{2} b^{6} - b^{8}} - \frac{{\left(24 \, a^{2} - 37 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(24 \, a^{2} + 37 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left({\left(13 \, a^{2} b - 9 \, b^{3}\right)} \sin\left(d x + c\right)^{3} + 10 \, a^{3} - 6 \, a b^{2} - 4 \, {\left(3 \, a^{3} - 2 \, a b^{2}\right)} \sin\left(d x + c\right)^{2} - {\left(11 \, a^{2} b - 7 \, b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}} - \frac{16 \, \sin\left(d x + c\right)}{b}}{16 \, d}"," ",0,"1/16*(16*a^7*log(b*sin(d*x + c) + a)/(a^6*b^2 - 3*a^4*b^4 + 3*a^2*b^6 - b^8) - (24*a^2 - 37*a*b + 15*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (24*a^2 + 37*a*b + 15*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*((13*a^2*b - 9*b^3)*sin(d*x + c)^3 + 10*a^3 - 6*a*b^2 - 4*(3*a^3 - 2*a*b^2)*sin(d*x + c)^2 - (11*a^2*b - 7*b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2) - 16*sin(d*x + c)/b)/d","A",0
1361,1,289,0,0.335403," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{16 \, a^{6} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}} - \frac{{\left(15 \, a^{2} - 21 \, a b + 8 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(15 \, a^{2} + 21 \, a b + 8 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left({\left(9 \, a^{3} - 5 \, a b^{2}\right)} \sin\left(d x + c\right)^{3} + 10 \, a^{2} b - 6 \, b^{3} - 4 \, {\left(3 \, a^{2} b - 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2} - {\left(7 \, a^{3} - 3 \, a b^{2}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"-1/16*(16*a^6*log(b*sin(d*x + c) + a)/(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7) - (15*a^2 - 21*a*b + 8*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (15*a^2 + 21*a*b + 8*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*((9*a^3 - 5*a*b^2)*sin(d*x + c)^3 + 10*a^2*b - 6*b^3 - 4*(3*a^2*b - 2*b^3)*sin(d*x + c)^2 - (7*a^3 - 3*a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
1362,1,288,0,0.325964," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, a^{5} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{{\left(8 \, a^{2} - 9 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(8 \, a^{2} + 9 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left({\left(9 \, a^{2} b - 5 \, b^{3}\right)} \sin\left(d x + c\right)^{3} + 6 \, a^{3} - 2 \, a b^{2} - 4 \, {\left(2 \, a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{2} - {\left(7 \, a^{2} b - 3 \, b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"1/16*(16*a^5*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (8*a^2 - 9*a*b + 3*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (8*a^2 + 9*a*b + 3*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*((9*a^2*b - 5*b^3)*sin(d*x + c)^3 + 6*a^3 - 2*a*b^2 - 4*(2*a^3 - a*b^2)*sin(d*x + c)^2 - (7*a^2*b - 3*b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
1363,1,276,0,0.510476," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{16 \, a^{4} b \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{{\left(3 \, a^{2} - a b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(3 \, a^{2} + a b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left({\left(5 \, a^{3} - a b^{2}\right)} \sin\left(d x + c\right)^{3} + 6 \, a^{2} b - 2 \, b^{3} - 4 \, {\left(2 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{2} - {\left(3 \, a^{3} + a b^{2}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"-1/16*(16*a^4*b*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (3*a^2 - a*b)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*a^2 + a*b)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*((5*a^3 - a*b^2)*sin(d*x + c)^3 + 6*a^2*b - 2*b^3 - 4*(2*a^2*b - b^3)*sin(d*x + c)^2 - (3*a^3 + a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
1364,1,267,0,0.320915," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, a^{3} b^{2} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{{\left(3 \, a b - b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(3 \, a b + b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(4 \, a^{3} \sin\left(d x + c\right)^{2} - {\left(5 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{3} - 2 \, a^{3} - 2 \, a b^{2} + {\left(3 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"1/16*(16*a^3*b^2*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (3*a*b - b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (3*a*b + b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(4*a^3*sin(d*x + c)^2 - (5*a^2*b - b^3)*sin(d*x + c)^3 - 2*a^3 - 2*a*b^2 + (3*a^2*b + b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
1365,1,265,0,0.329675," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{16 \, a^{2} b^{3} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{{\left(a^{2} - 3 \, a b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(a^{2} + 3 \, a b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(4 \, a^{2} b \sin\left(d x + c\right)^{2} - {\left(a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)^{3} - 2 \, a^{2} b - 2 \, b^{3} - {\left(a^{3} - 5 \, a b^{2}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"-1/16*(16*a^2*b^3*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + (a^2 - 3*a*b)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (a^2 + 3*a*b)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(4*a^2*b*sin(d*x + c)^2 - (a^3 + 3*a*b^2)*sin(d*x + c)^3 - 2*a^2*b - 2*b^3 - (a^3 - 5*a*b^2)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
1366,1,267,0,0.323079," ","integrate(sec(d*x+c)^5*sin(d*x+c)/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, a b^{4} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{{\left(a b - 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(4 \, a b^{2} \sin\left(d x + c\right)^{2} - {\left(a^{2} b + 3 \, b^{3}\right)} \sin\left(d x + c\right)^{3} + 2 \, a^{3} - 6 \, a b^{2} - {\left(a^{2} b - 5 \, b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"1/16*(16*a*b^4*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + (a*b - 3*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (a*b + 3*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(4*a*b^2*sin(d*x + c)^2 - (a^2*b + 3*b^3)*sin(d*x + c)^3 + 2*a^3 - 6*a*b^2 - (a^2*b - 5*b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
1367,1,299,0,0.340996," ","integrate(csc(d*x+c)*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, b^{6} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}} - \frac{{\left(8 \, a^{2} - 21 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(8 \, a^{2} + 21 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left({\left(3 \, a^{2} b - 7 \, b^{3}\right)} \sin\left(d x + c\right)^{3} + 6 \, a^{3} - 10 \, a b^{2} - 4 \, {\left(a^{3} - 2 \, a b^{2}\right)} \sin\left(d x + c\right)^{2} - {\left(5 \, a^{2} b - 9 \, b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}} + \frac{16 \, \log\left(\sin\left(d x + c\right)\right)}{a}}{16 \, d}"," ",0,"1/16*(16*b^6*log(b*sin(d*x + c) + a)/(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6) - (8*a^2 - 21*a*b + 15*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (8*a^2 + 21*a*b + 15*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*((3*a^2*b - 7*b^3)*sin(d*x + c)^3 + 6*a^3 - 10*a*b^2 - 4*(a^3 - 2*a*b^2)*sin(d*x + c)^2 - (5*a^2*b - 9*b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2) + 16*log(sin(d*x + c))/a)/d","A",0
1368,1,361,0,0.346905," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{16 \, b^{7} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{8} - 3 \, a^{6} b^{2} + 3 \, a^{4} b^{4} - a^{2} b^{6}} - \frac{{\left(15 \, a^{2} - 37 \, a b + 24 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(15 \, a^{2} + 37 \, a b + 24 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left({\left(15 \, a^{4} - 27 \, a^{2} b^{2} + 8 \, b^{4}\right)} \sin\left(d x + c\right)^{4} + 8 \, a^{4} - 16 \, a^{2} b^{2} + 8 \, b^{4} - 4 \, {\left(a^{3} b - 2 \, a b^{3}\right)} \sin\left(d x + c\right)^{3} - {\left(25 \, a^{4} - 45 \, a^{2} b^{2} + 16 \, b^{4}\right)} \sin\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{3} b - 5 \, a b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{5} - 2 \, {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{3} + {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)} + \frac{16 \, b \log\left(\sin\left(d x + c\right)\right)}{a^{2}}}{16 \, d}"," ",0,"-1/16*(16*b^7*log(b*sin(d*x + c) + a)/(a^8 - 3*a^6*b^2 + 3*a^4*b^4 - a^2*b^6) - (15*a^2 - 37*a*b + 24*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (15*a^2 + 37*a*b + 24*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*((15*a^4 - 27*a^2*b^2 + 8*b^4)*sin(d*x + c)^4 + 8*a^4 - 16*a^2*b^2 + 8*b^4 - 4*(a^3*b - 2*a*b^3)*sin(d*x + c)^3 - (25*a^4 - 45*a^2*b^2 + 16*b^4)*sin(d*x + c)^2 + 2*(3*a^3*b - 5*a*b^3)*sin(d*x + c))/((a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c)^5 - 2*(a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c)^3 + (a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c)) + 16*b*log(sin(d*x + c))/a^2)/d","A",0
1369,1,422,0,0.348354," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, b^{8} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{9} - 3 \, a^{7} b^{2} + 3 \, a^{5} b^{4} - a^{3} b^{6}} - \frac{{\left(24 \, a^{2} - 57 \, a b + 35 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(24 \, a^{2} + 57 \, a b + 35 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left({\left(15 \, a^{4} b - 27 \, a^{2} b^{3} + 8 \, b^{5}\right)} \sin\left(d x + c\right)^{5} - 4 \, a^{5} + 8 \, a^{3} b^{2} - 4 \, a b^{4} - 4 \, {\left(3 \, a^{5} - 5 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{4} - {\left(25 \, a^{4} b - 45 \, a^{2} b^{3} + 16 \, b^{5}\right)} \sin\left(d x + c\right)^{3} + 2 \, {\left(9 \, a^{5} - 15 \, a^{3} b^{2} + 4 \, a b^{4}\right)} \sin\left(d x + c\right)^{2} + 8 \, {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(d x + c\right)^{6} - 2 \, {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(d x + c\right)^{4} + {\left(a^{6} - 2 \, a^{4} b^{2} + a^{2} b^{4}\right)} \sin\left(d x + c\right)^{2}} + \frac{16 \, {\left(3 \, a^{2} + b^{2}\right)} \log\left(\sin\left(d x + c\right)\right)}{a^{3}}}{16 \, d}"," ",0,"1/16*(16*b^8*log(b*sin(d*x + c) + a)/(a^9 - 3*a^7*b^2 + 3*a^5*b^4 - a^3*b^6) - (24*a^2 - 57*a*b + 35*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (24*a^2 + 57*a*b + 35*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*((15*a^4*b - 27*a^2*b^3 + 8*b^5)*sin(d*x + c)^5 - 4*a^5 + 8*a^3*b^2 - 4*a*b^4 - 4*(3*a^5 - 5*a^3*b^2 + a*b^4)*sin(d*x + c)^4 - (25*a^4*b - 45*a^2*b^3 + 16*b^5)*sin(d*x + c)^3 + 2*(9*a^5 - 15*a^3*b^2 + 4*a*b^4)*sin(d*x + c)^2 + 8*(a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c))/((a^6 - 2*a^4*b^2 + a^2*b^4)*sin(d*x + c)^6 - 2*(a^6 - 2*a^4*b^2 + a^2*b^4)*sin(d*x + c)^4 + (a^6 - 2*a^4*b^2 + a^2*b^4)*sin(d*x + c)^2) + 16*(3*a^2 + b^2)*log(sin(d*x + c))/a^3)/d","A",0
1370,0,0,0,0.000000," ","integrate(sin(f*x+e)^4*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sin\left(f x + e\right)^{4}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sin(f*x + e)^4/(b*sin(f*x + e) + a), x)","F",0
1371,0,0,0,0.000000," ","integrate(sin(f*x+e)^3*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sin\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sin(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1372,0,0,0,0.000000," ","integrate(sin(f*x+e)^2*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sin\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sin(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1373,0,0,0,0.000000," ","integrate(sin(f*x+e)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sin\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sin(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1374,0,0,0,0.000000," ","integrate(csc(f*x+e)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \csc\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*csc(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1375,0,0,0,0.000000," ","integrate(csc(f*x+e)^2*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \csc\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*csc(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1376,0,0,0,0.000000," ","integrate(csc(f*x+e)^3*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \csc\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*csc(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1377,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*sin(f*x+e)^3/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sin\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sin(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1378,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*sin(f*x+e)^2/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sin\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sin(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1379,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sin\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sin(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1380,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \csc\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*csc(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1381,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*csc(f*x+e)^2/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \csc\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*csc(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1382,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*csc(f*x+e)^3/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \csc\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*csc(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1383,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*sin(f*x+e)^3/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sin\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*sin(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1384,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*sin(f*x+e)^2/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sin\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*sin(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1385,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*sin(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sin\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*sin(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1386,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*csc(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \csc\left(f x + e\right)}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*csc(f*x + e)/(b*sin(f*x + e) + a), x)","F",0
1387,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*csc(f*x+e)^2/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \csc\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*csc(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1388,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*csc(f*x+e)^3/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \csc\left(f x + e\right)^{3}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*csc(f*x + e)^3/(b*sin(f*x + e) + a), x)","F",0
1389,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1390,0,0,0,0.000000," ","integrate(sin(f*x+e)^3/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{3}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^3/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1391,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1392,0,0,0,0.000000," ","integrate(sin(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1393,0,0,0,0.000000," ","integrate(csc(f*x+e)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1394,0,0,0,0.000000," ","integrate(csc(f*x+e)^2/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{2}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)^2/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1395,0,0,0,0.000000," ","integrate(csc(f*x+e)^3/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)^{3}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)^3/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1396,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1397,0,0,0,0.000000," ","integrate(sin(f*x+e)^3/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{3}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^3/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1398,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1399,0,0,0,0.000000," ","integrate(sin(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1400,0,0,0,0.000000," ","integrate(csc(f*x+e)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1402,0,0,0,0.000000," ","integrate(sin(f*x+e)^4/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{4}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^4/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1403,0,0,0,0.000000," ","integrate(sin(f*x+e)^3/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{3}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^3/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1404,0,0,0,0.000000," ","integrate(sin(f*x+e)^2/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)^{2}}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)^2/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1405,0,0,0,0.000000," ","integrate(sin(f*x+e)/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sin\left(f x + e\right)}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sin(f*x + e)/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",0
1406,0,0,0,0.000000," ","integrate(csc(f*x+e)/(g*cos(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\csc\left(f x + e\right)}{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(csc(f*x + e)/((g*cos(f*x + e))^(5/2)*(b*sin(f*x + e) + a)), x)","F",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=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1408,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(5/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*(d*sin(f*x + e))^(5/2)/(b*sin(f*x + e) + a), x)","F",0
1409,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(3/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*(d*sin(f*x + e))^(3/2)/(b*sin(f*x + e) + a), x)","F",0
1410,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)*(g*cos(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)} \sqrt{d \sin\left(f x + e\right)}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))*sqrt(d*sin(f*x + e))/(b*sin(f*x + e) + a), x)","F",0
1411,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1412,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1413,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1414,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(7/2)), x)","F",0
1415,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(1/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{g \cos\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate(sqrt(g*cos(f*x + e))/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(9/2)), x)","F",0
1416,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*(d*sin(f*x + e))^(3/2)/(b*sin(f*x + e) + a), x)","F",0
1417,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)*(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} \sqrt{d \sin\left(f x + e\right)}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)*sqrt(d*sin(f*x + e))/(b*sin(f*x + e) + a), x)","F",0
1418,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1419,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1420,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1421,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(7/2)), x)","F",0
1422,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(9/2)), x)","F",0
1423,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)*(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}} \sqrt{d \sin\left(f x + e\right)}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)*sqrt(d*sin(f*x + e))/(b*sin(f*x + e) + a), x)","F",0
1424,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1425,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1426,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1427,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(7/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(7/2)), x)","F",0
1428,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(9/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{9}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(9/2)), x)","F",0
1429,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(5/2)/(d*sin(f*x+e))^(11/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{5}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{11}{2}}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(5/2)/((b*sin(f*x + e) + a)*(d*sin(f*x + e))^(11/2)), x)","F",0
1430,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^(5/2)/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1431,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^(3/2)/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1432,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right)}}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e))/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)), x)","F",0
1433,0,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1434,0,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1435,0,0,0,0.000000," ","integrate(1/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e))/(g*cos(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{g \cos\left(f x + e\right)} {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(g*cos(f*x + e))*(b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1436,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(5/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^(5/2)/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1437,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(3/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate((d*sin(f*x + e))^(3/2)/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1438,0,0,0,0.000000," ","integrate((d*sin(f*x+e))^(1/2)/(g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right)}}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)}}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e))/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)), x)","F",0
1439,0,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(1/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e))), x)","F",0
1440,0,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)*(d*sin(f*x + e))^(3/2)), x)","F",0
1441,0,0,0,0.000000," ","integrate(1/(g*cos(f*x+e))^(3/2)/(d*sin(f*x+e))^(5/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{1}{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}} {\left(b \sin\left(f x + e\right) + a\right)} \left(d \sin\left(f x + e\right)\right)^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(1/((g*cos(f*x + e))^(3/2)*(b*sin(f*x + e) + a)*(d*sin(f*x + e))^(5/2)), x)","F",0
1442,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(3/2)/(a+b*sin(f*x+e))^2/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{\frac{3}{2}}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2} \sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^(3/2)/((b*sin(f*x + e) + a)^2*sqrt(d*sin(f*x + e))), x)","F",0
1443,1,75,0,0.439386," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a + 2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} b}{6 \, d}"," ",0,"-1/6*(3*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a + 2*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*b)/d","A",0
1444,1,62,0,0.424090," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} b - 2 \, a {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{2 \, d}"," ",0,"-1/2*((3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*b - 2*a*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
1445,1,39,0,0.434435," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} a - b {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*a - b*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
1446,1,32,0,0.504089," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(d x + c - \tan\left(d x + c\right)\right)} b - \frac{a}{\cos\left(d x + c\right)}}{d}"," ",0,"-((d*x + c - tan(d*x + c))*b - a/cos(d*x + c))/d","A",0
1447,1,48,0,0.348622," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2 \, b \tan\left(d x + c\right)}{2 \, d}"," ",0,"1/2*(a*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 2*b*tan(d*x + c))/d","A",0
1448,1,59,0,0.332313," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{b {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 2 \, a {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)}}{2 \, d}"," ",0,"1/2*(b*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 2*a*(1/tan(d*x + c) - tan(d*x + c)))/d","A",0
1449,1,84,0,0.328587," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{a {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 4 \, b {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*(a*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 4*b*(1/tan(d*x + c) - tan(d*x + c)))/d","A",0
1450,1,97,0,0.616437," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{3 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a b + {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} b^{2} - 3 \, a^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{3 \, d}"," ",0,"-1/3*(3*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a*b + (cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*b^2 - 3*a^2*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
1451,1,83,0,0.428466," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} + {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} b^{2} - 4 \, a b {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c - tan(d*x + c))*a^2 + (3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*b^2 - 4*a*b*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
1452,1,56,0,0.455938," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a b - b^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - \frac{a^{2}}{\cos\left(d x + c\right)}}{d}"," ",0,"-(2*(d*x + c - tan(d*x + c))*a*b - b^2*(1/cos(d*x + c) + cos(d*x + c)) - a^2/cos(d*x + c))/d","A",0
1453,1,64,0,0.361951," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 4 \, a b \tan\left(d x + c\right) + \frac{2 \, b^{2}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(a^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) + 4*a*b*tan(d*x + c) + 2*b^2/cos(d*x + c))/d","A",0
1454,1,71,0,0.448971," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a b {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - a^{2} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + b^{2} \tan\left(d x + c\right)}{d}"," ",0,"(a*b*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - a^2*(1/tan(d*x + c) - tan(d*x + c)) + b^2*tan(d*x + c))/d","A",0
1455,1,123,0,0.452525," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{a^{2} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 2 \, b^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 8 \, a b {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)}}{4 \, d}"," ",0,"1/4*(a^2*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 2*b^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 8*a*b*(1/tan(d*x + c) - tan(d*x + c)))/d","A",0
1456,1,123,0,0.380572," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{3 \, a b {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 6 \, b^{2} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} - 2 \, a^{2} {\left(\frac{6 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} - 3 \, \tan\left(d x + c\right)\right)}}{6 \, d}"," ",0,"1/6*(3*a*b*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) - 6*b^2*(1/tan(d*x + c) - tan(d*x + c)) - 2*a^2*((6*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 - 3*tan(d*x + c)))/d","A",0
1457,1,164,0,0.476183," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{12 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a^{2} b + 8 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} a b^{2} + {\left(15 \, d x + 15 \, c - \frac{9 \, \tan\left(d x + c\right)^{3} + 7 \, \tan\left(d x + c\right)}{\tan\left(d x + c\right)^{4} + 2 \, \tan\left(d x + c\right)^{2} + 1} - 8 \, \tan\left(d x + c\right)\right)} b^{3} - 8 \, a^{3} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{8 \, d}"," ",0,"-1/8*(12*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a^2*b + 8*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*a*b^2 + (15*d*x + 15*c - (9*tan(d*x + c)^3 + 7*tan(d*x + c))/(tan(d*x + c)^4 + 2*tan(d*x + c)^2 + 1) - 8*tan(d*x + c))*b^3 - 8*a^3*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
1458,1,119,0,0.467906," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{3} + 9 \, {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} a b^{2} + 2 \, {\left(\cos\left(d x + c\right)^{3} - \frac{3}{\cos\left(d x + c\right)} - 6 \, \cos\left(d x + c\right)\right)} b^{3} - 18 \, a^{2} b {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)}}{6 \, d}"," ",0,"-1/6*(6*(d*x + c - tan(d*x + c))*a^3 + 9*(3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*a*b^2 + 2*(cos(d*x + c)^3 - 3/cos(d*x + c) - 6*cos(d*x + c))*b^3 - 18*a^2*b*(1/cos(d*x + c) + cos(d*x + c)))/d","A",0
1459,1,99,0,0.478147," ","integrate(sec(d*x+c)^2*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{6 \, {\left(d x + c - \tan\left(d x + c\right)\right)} a^{2} b + {\left(3 \, d x + 3 \, c - \frac{\tan\left(d x + c\right)}{\tan\left(d x + c\right)^{2} + 1} - 2 \, \tan\left(d x + c\right)\right)} b^{3} - 6 \, a b^{2} {\left(\frac{1}{\cos\left(d x + c\right)} + \cos\left(d x + c\right)\right)} - \frac{2 \, a^{3}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(6*(d*x + c - tan(d*x + c))*a^2*b + (3*d*x + 3*c - tan(d*x + c)/(tan(d*x + c)^2 + 1) - 2*tan(d*x + c))*b^3 - 6*a*b^2*(1/cos(d*x + c) + cos(d*x + c)) - 2*a^3/cos(d*x + c))/d","A",0
1460,1,86,0,0.412523," ","integrate(csc(d*x+c)*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{2 \, {\left(d x + c - \tan\left(d x + c\right)\right)} b^{3} - a^{3} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 6 \, a^{2} b \tan\left(d x + c\right) - \frac{6 \, a b^{2}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"-1/2*(2*(d*x + c - tan(d*x + c))*b^3 - a^3*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 6*a^2*b*tan(d*x + c) - 6*a*b^2/cos(d*x + c))/d","A",0
1461,1,90,0,0.375817," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{3 \, a^{2} b {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 2 \, a^{3} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + 6 \, a b^{2} \tan\left(d x + c\right) + \frac{2 \, b^{3}}{\cos\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(3*a^2*b*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 2*a^3*(1/tan(d*x + c) - tan(d*x + c)) + 6*a*b^2*tan(d*x + c) + 2*b^3/cos(d*x + c))/d","A",0
1462,1,137,0,0.325329," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{a^{3} {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 6 \, a b^{2} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 12 \, a^{2} b {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} + 4 \, b^{3} \tan\left(d x + c\right)}{4 \, d}"," ",0,"1/4*(a^3*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 6*a*b^2*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 12*a^2*b*(1/tan(d*x + c) - tan(d*x + c)) + 4*b^3*tan(d*x + c))/d","A",0
1463,1,162,0,0.369791," ","integrate(csc(d*x+c)^4*sec(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{9 \, a^{2} b {\left(\frac{2 \, {\left(3 \, \cos\left(d x + c\right)^{2} - 2\right)}}{\cos\left(d x + c\right)^{3} - \cos\left(d x + c\right)} - 3 \, \log\left(\cos\left(d x + c\right) + 1\right) + 3 \, \log\left(\cos\left(d x + c\right) - 1\right)\right)} + 6 \, b^{3} {\left(\frac{2}{\cos\left(d x + c\right)} - \log\left(\cos\left(d x + c\right) + 1\right) + \log\left(\cos\left(d x + c\right) - 1\right)\right)} - 36 \, a b^{2} {\left(\frac{1}{\tan\left(d x + c\right)} - \tan\left(d x + c\right)\right)} - 4 \, a^{3} {\left(\frac{6 \, \tan\left(d x + c\right)^{2} + 1}{\tan\left(d x + c\right)^{3}} - 3 \, \tan\left(d x + c\right)\right)}}{12 \, d}"," ",0,"1/12*(9*a^2*b*(2*(3*cos(d*x + c)^2 - 2)/(cos(d*x + c)^3 - cos(d*x + c)) - 3*log(cos(d*x + c) + 1) + 3*log(cos(d*x + c) - 1)) + 6*b^3*(2/cos(d*x + c) - log(cos(d*x + c) + 1) + log(cos(d*x + c) - 1)) - 36*a*b^2*(1/tan(d*x + c) - tan(d*x + c)) - 4*a^3*((6*tan(d*x + c)^2 + 1)/tan(d*x + c)^3 - 3*tan(d*x + c)))/d","A",0
1464,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1465,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1466,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1467,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1468,-2,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1469,-2,0,0,0.000000," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1470,-2,0,0,0.000000," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1471,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^4/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1472,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^3/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1473,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1474,-2,0,0,0.000000," ","integrate(sec(d*x+c)^2*sin(d*x+c)/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1475,-2,0,0,0.000000," ","integrate(csc(d*x+c)*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1476,-2,0,0,0.000000," ","integrate(csc(d*x+c)^2*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1477,-2,0,0,0.000000," ","integrate(csc(d*x+c)^3*sec(d*x+c)^2/(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\text{Exception raised: ValueError}"," ",0,"Exception raised: ValueError >> Computation failed since Maxima requested additional constraints; using the 'assume' command before evaluation *may* help (example of legal syntax is 'assume(4*b^2-4*a^2>0)', see `assume?` for more details)Is 4*b^2-4*a^2 positive or negative?","F(-2)",0
1478,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e))^(1/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a} \sec\left(f x + e\right)^{2}}{\sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sec(f*x + e)^2/sqrt(d*sin(f*x + e)), x)","F",0
1479,0,0,0,0.000000," ","integrate(sec(f*x+e)^2*(a+b*sin(f*x+e))^(3/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{3}{2}} \sec\left(f x + e\right)^{2}}{\sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(3/2)*sec(f*x + e)^2/sqrt(d*sin(f*x + e)), x)","F",0
1480,0,0,0,0.000000," ","integrate(sec(f*x+e)^4*(a+b*sin(f*x+e))^(5/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{5}{2}} \sec\left(f x + e\right)^{4}}{\sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(5/2)*sec(f*x + e)^4/sqrt(d*sin(f*x + e)), x)","F",0
1481,1,132,0,0.300162," ","integrate(sec(d*x+c)^5*sin(d*x+c)^7*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{16 \, b \sin\left(d x + c\right)^{3} + 24 \, a \sin\left(d x + c\right)^{2} + 3 \, {\left(24 \, a - 35 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(24 \, a + 35 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 144 \, b \sin\left(d x + c\right) - \frac{6 \, {\left(13 \, b \sin\left(d x + c\right)^{3} + 12 \, a \sin\left(d x + c\right)^{2} - 11 \, b \sin\left(d x + c\right) - 10 \, a\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"-1/48*(16*b*sin(d*x + c)^3 + 24*a*sin(d*x + c)^2 + 3*(24*a - 35*b)*log(sin(d*x + c) + 1) + 3*(24*a + 35*b)*log(sin(d*x + c) - 1) + 144*b*sin(d*x + c) - 6*(13*b*sin(d*x + c)^3 + 12*a*sin(d*x + c)^2 - 11*b*sin(d*x + c) - 10*a)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1482,1,121,0,0.307179," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{8 \, b \sin\left(d x + c\right)^{2} - 3 \, {\left(5 \, a - 8 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(5 \, a + 8 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 16 \, a \sin\left(d x + c\right) - \frac{2 \, {\left(9 \, a \sin\left(d x + c\right)^{3} + 12 \, b \sin\left(d x + c\right)^{2} - 7 \, a \sin\left(d x + c\right) - 10 \, b\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*(8*b*sin(d*x + c)^2 - 3*(5*a - 8*b)*log(sin(d*x + c) + 1) + 3*(5*a + 8*b)*log(sin(d*x + c) - 1) + 16*a*sin(d*x + c) - 2*(9*a*sin(d*x + c)^3 + 12*b*sin(d*x + c)^2 - 7*a*sin(d*x + c) - 10*b)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1483,1,108,0,0.306085," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(8 \, a - 15 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(8 \, a + 15 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 16 \, b \sin\left(d x + c\right) - \frac{2 \, {\left(9 \, b \sin\left(d x + c\right)^{3} + 8 \, a \sin\left(d x + c\right)^{2} - 7 \, b \sin\left(d x + c\right) - 6 \, a\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*((8*a - 15*b)*log(sin(d*x + c) + 1) + (8*a + 15*b)*log(sin(d*x + c) - 1) + 16*b*sin(d*x + c) - 2*(9*b*sin(d*x + c)^3 + 8*a*sin(d*x + c)^2 - 7*b*sin(d*x + c) - 6*a)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1484,1,100,0,0.406549," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, a - 8 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, a + 8 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) + \frac{2 \, {\left(5 \, a \sin\left(d x + c\right)^{3} + 8 \, b \sin\left(d x + c\right)^{2} - 3 \, a \sin\left(d x + c\right) - 6 \, b\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*((3*a - 8*b)*log(sin(d*x + c) + 1) - (3*a + 8*b)*log(sin(d*x + c) - 1) + 2*(5*a*sin(d*x + c)^3 + 8*b*sin(d*x + c)^2 - 3*a*sin(d*x + c) - 6*b)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1485,1,89,0,0.404036," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, b \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, b \log\left(\sin\left(d x + c\right) - 1\right) + \frac{2 \, {\left(5 \, b \sin\left(d x + c\right)^{3} + 4 \, a \sin\left(d x + c\right)^{2} - 3 \, b \sin\left(d x + c\right) - 2 \, a\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*(3*b*log(sin(d*x + c) + 1) - 3*b*log(sin(d*x + c) - 1) + 2*(5*b*sin(d*x + c)^3 + 4*a*sin(d*x + c)^2 - 3*b*sin(d*x + c) - 2*a)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1486,1,86,0,0.350323," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{a \log\left(\sin\left(d x + c\right) + 1\right) - a \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(a \sin\left(d x + c\right)^{3} + 4 \, b \sin\left(d x + c\right)^{2} + a \sin\left(d x + c\right) - 2 \, b\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*(a*log(sin(d*x + c) + 1) - a*log(sin(d*x + c) - 1) - 2*(a*sin(d*x + c)^3 + 4*b*sin(d*x + c)^2 + a*sin(d*x + c) - 2*b)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1487,1,75,0,0.339300," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{b \log\left(\sin\left(d x + c\right) + 1\right) - b \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(b \sin\left(d x + c\right)^{3} + b \sin\left(d x + c\right) + 2 \, a\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*(b*log(sin(d*x + c) + 1) - b*log(sin(d*x + c) - 1) - 2*(b*sin(d*x + c)^3 + b*sin(d*x + c) + 2*a)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1488,1,109,0,0.374596," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{{\left(8 \, a - 3 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(8 \, a + 3 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) - 16 \, a \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, {\left(3 \, b \sin\left(d x + c\right)^{3} + 4 \, a \sin\left(d x + c\right)^{2} - 5 \, b \sin\left(d x + c\right) - 6 \, a\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*((8*a - 3*b)*log(sin(d*x + c) + 1) + (8*a + 3*b)*log(sin(d*x + c) - 1) - 16*a*log(sin(d*x + c)) + 2*(3*b*sin(d*x + c)^3 + 4*a*sin(d*x + c)^2 - 5*b*sin(d*x + c) - 6*a)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1489,1,126,0,0.312418," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(15 \, a - 8 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(15 \, a + 8 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 16 \, b \log\left(\sin\left(d x + c\right)\right) - \frac{2 \, {\left(15 \, a \sin\left(d x + c\right)^{4} + 4 \, b \sin\left(d x + c\right)^{3} - 25 \, a \sin\left(d x + c\right)^{2} - 6 \, b \sin\left(d x + c\right) + 8 \, a\right)}}{\sin\left(d x + c\right)^{5} - 2 \, \sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)}}{16 \, d}"," ",0,"1/16*((15*a - 8*b)*log(sin(d*x + c) + 1) - (15*a + 8*b)*log(sin(d*x + c) - 1) + 16*b*log(sin(d*x + c)) - 2*(15*a*sin(d*x + c)^4 + 4*b*sin(d*x + c)^3 - 25*a*sin(d*x + c)^2 - 6*b*sin(d*x + c) + 8*a)/(sin(d*x + c)^5 - 2*sin(d*x + c)^3 + sin(d*x + c)))/d","A",0
1490,1,140,0,0.325104," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{3 \, {\left(8 \, a - 5 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(8 \, a + 5 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) - 48 \, a \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, {\left(15 \, b \sin\left(d x + c\right)^{5} + 12 \, a \sin\left(d x + c\right)^{4} - 25 \, b \sin\left(d x + c\right)^{3} - 18 \, a \sin\left(d x + c\right)^{2} + 8 \, b \sin\left(d x + c\right) + 4 \, a\right)}}{\sin\left(d x + c\right)^{6} - 2 \, \sin\left(d x + c\right)^{4} + \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"-1/16*(3*(8*a - 5*b)*log(sin(d*x + c) + 1) + 3*(8*a + 5*b)*log(sin(d*x + c) - 1) - 48*a*log(sin(d*x + c)) + 2*(15*b*sin(d*x + c)^5 + 12*a*sin(d*x + c)^4 - 25*b*sin(d*x + c)^3 - 18*a*sin(d*x + c)^2 + 8*b*sin(d*x + c) + 4*a)/(sin(d*x + c)^6 - 2*sin(d*x + c)^4 + sin(d*x + c)^2))/d","A",0
1491,1,151,0,0.363737," ","integrate(csc(d*x+c)^4*sec(d*x+c)^5*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(35 \, a - 24 \, b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(35 \, a + 24 \, b\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 144 \, b \log\left(\sin\left(d x + c\right)\right) - \frac{2 \, {\left(105 \, a \sin\left(d x + c\right)^{6} + 36 \, b \sin\left(d x + c\right)^{5} - 175 \, a \sin\left(d x + c\right)^{4} - 54 \, b \sin\left(d x + c\right)^{3} + 56 \, a \sin\left(d x + c\right)^{2} + 12 \, b \sin\left(d x + c\right) + 8 \, a\right)}}{\sin\left(d x + c\right)^{7} - 2 \, \sin\left(d x + c\right)^{5} + \sin\left(d x + c\right)^{3}}}{48 \, d}"," ",0,"1/48*(3*(35*a - 24*b)*log(sin(d*x + c) + 1) - 3*(35*a + 24*b)*log(sin(d*x + c) - 1) + 144*b*log(sin(d*x + c)) - 2*(105*a*sin(d*x + c)^6 + 36*b*sin(d*x + c)^5 - 175*a*sin(d*x + c)^4 - 54*b*sin(d*x + c)^3 + 56*a*sin(d*x + c)^2 + 12*b*sin(d*x + c) + 8*a)/(sin(d*x + c)^7 - 2*sin(d*x + c)^5 + sin(d*x + c)^3))/d","A",0
1492,1,180,0,0.304873," ","integrate(sec(d*x+c)^5*sin(d*x+c)^6*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{16 \, b^{2} \sin\left(d x + c\right)^{3} + 48 \, a b \sin\left(d x + c\right)^{2} - 3 \, {\left(15 \, a^{2} - 48 \, a b + 35 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(15 \, a^{2} + 48 \, a b + 35 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + 48 \, {\left(a^{2} + 3 \, b^{2}\right)} \sin\left(d x + c\right) - \frac{6 \, {\left(24 \, a b \sin\left(d x + c\right)^{2} + {\left(9 \, a^{2} + 13 \, b^{2}\right)} \sin\left(d x + c\right)^{3} - 20 \, a b - {\left(7 \, a^{2} + 11 \, b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"-1/48*(16*b^2*sin(d*x + c)^3 + 48*a*b*sin(d*x + c)^2 - 3*(15*a^2 - 48*a*b + 35*b^2)*log(sin(d*x + c) + 1) + 3*(15*a^2 + 48*a*b + 35*b^2)*log(sin(d*x + c) - 1) + 48*(a^2 + 3*b^2)*sin(d*x + c) - 6*(24*a*b*sin(d*x + c)^2 + (9*a^2 + 13*b^2)*sin(d*x + c)^3 - 20*a*b - (7*a^2 + 11*b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1493,1,157,0,0.444854," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{4 \, b^{2} \sin\left(d x + c\right)^{2} + 16 \, a b \sin\left(d x + c\right) + {\left(4 \, a^{2} - 15 \, a b + 12 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(4 \, a^{2} + 15 \, a b + 12 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(9 \, a b \sin\left(d x + c\right)^{3} - 7 \, a b \sin\left(d x + c\right) + 2 \, {\left(2 \, a^{2} + 3 \, b^{2}\right)} \sin\left(d x + c\right)^{2} - 3 \, a^{2} - 5 \, b^{2}\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"-1/8*(4*b^2*sin(d*x + c)^2 + 16*a*b*sin(d*x + c) + (4*a^2 - 15*a*b + 12*b^2)*log(sin(d*x + c) + 1) + (4*a^2 + 15*a*b + 12*b^2)*log(sin(d*x + c) - 1) - 2*(9*a*b*sin(d*x + c)^3 - 7*a*b*sin(d*x + c) + 2*(2*a^2 + 3*b^2)*sin(d*x + c)^2 - 3*a^2 - 5*b^2)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1494,1,148,0,0.329012," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{16 \, b^{2} \sin\left(d x + c\right) - {\left(3 \, a^{2} - 16 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(3 \, a^{2} + 16 \, a b + 15 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(16 \, a b \sin\left(d x + c\right)^{2} + {\left(5 \, a^{2} + 9 \, b^{2}\right)} \sin\left(d x + c\right)^{3} - 12 \, a b - {\left(3 \, a^{2} + 7 \, b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*(16*b^2*sin(d*x + c) - (3*a^2 - 16*a*b + 15*b^2)*log(sin(d*x + c) + 1) + (3*a^2 + 16*a*b + 15*b^2)*log(sin(d*x + c) - 1) - 2*(16*a*b*sin(d*x + c)^2 + (5*a^2 + 9*b^2)*sin(d*x + c)^3 - 12*a*b - (3*a^2 + 7*b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1495,1,123,0,0.335483," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{{\left(3 \, a b - 4 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, a b + 4 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + \frac{2 \, {\left(5 \, a b \sin\left(d x + c\right)^{3} - 3 \, a b \sin\left(d x + c\right) + 2 \, {\left(a^{2} + 2 \, b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} - 3 \, b^{2}\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*((3*a*b - 4*b^2)*log(sin(d*x + c) + 1) - (3*a*b + 4*b^2)*log(sin(d*x + c) - 1) + 2*(5*a*b*sin(d*x + c)^3 - 3*a*b*sin(d*x + c) + 2*(a^2 + 2*b^2)*sin(d*x + c)^2 - a^2 - 3*b^2)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1496,1,120,0,0.308370," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(a^{2} - 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{2} - 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(8 \, a b \sin\left(d x + c\right)^{2} + {\left(a^{2} + 5 \, b^{2}\right)} \sin\left(d x + c\right)^{3} - 4 \, a b + {\left(a^{2} - 3 \, b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*((a^2 - 3*b^2)*log(sin(d*x + c) + 1) - (a^2 - 3*b^2)*log(sin(d*x + c) - 1) - 2*(8*a*b*sin(d*x + c)^2 + (a^2 + 5*b^2)*sin(d*x + c)^3 - 4*a*b + (a^2 - 3*b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1497,1,97,0,0.389241," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{a b \log\left(\sin\left(d x + c\right) + 1\right) - a b \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(a b \sin\left(d x + c\right)^{3} + 2 \, b^{2} \sin\left(d x + c\right)^{2} + a b \sin\left(d x + c\right) + a^{2} - b^{2}\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"-1/8*(a*b*log(sin(d*x + c) + 1) - a*b*log(sin(d*x + c) - 1) - 2*(a*b*sin(d*x + c)^3 + 2*b^2*sin(d*x + c)^2 + a*b*sin(d*x + c) + a^2 - b^2)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1498,1,130,0,0.332507," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{8 \, a^{2} \log\left(\sin\left(d x + c\right)\right) - {\left(4 \, a^{2} - 3 \, a b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(4 \, a^{2} + 3 \, a b\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, a b \sin\left(d x + c\right)^{3} + 2 \, a^{2} \sin\left(d x + c\right)^{2} - 5 \, a b \sin\left(d x + c\right) - 3 \, a^{2} - b^{2}\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{8 \, d}"," ",0,"1/8*(8*a^2*log(sin(d*x + c)) - (4*a^2 - 3*a*b)*log(sin(d*x + c) + 1) - (4*a^2 + 3*a*b)*log(sin(d*x + c) - 1) - 2*(3*a*b*sin(d*x + c)^3 + 2*a^2*sin(d*x + c)^2 - 5*a*b*sin(d*x + c) - 3*a^2 - b^2)/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1499,1,163,0,0.347065," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{32 \, a b \log\left(\sin\left(d x + c\right)\right) + {\left(15 \, a^{2} - 16 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(15 \, a^{2} + 16 \, a b + 3 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(8 \, a b \sin\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{4} - 12 \, a b \sin\left(d x + c\right) - 5 \, {\left(5 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{2} + 8 \, a^{2}\right)}}{\sin\left(d x + c\right)^{5} - 2 \, \sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)}}{16 \, d}"," ",0,"1/16*(32*a*b*log(sin(d*x + c)) + (15*a^2 - 16*a*b + 3*b^2)*log(sin(d*x + c) + 1) - (15*a^2 + 16*a*b + 3*b^2)*log(sin(d*x + c) - 1) - 2*(8*a*b*sin(d*x + c)^3 + 3*(5*a^2 + b^2)*sin(d*x + c)^4 - 12*a*b*sin(d*x + c) - 5*(5*a^2 + b^2)*sin(d*x + c)^2 + 8*a^2)/(sin(d*x + c)^5 - 2*sin(d*x + c)^3 + sin(d*x + c)))/d","A",0
1500,1,183,0,0.407390," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{{\left(12 \, a^{2} - 15 \, a b + 4 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + {\left(12 \, a^{2} + 15 \, a b + 4 \, b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - 8 \, {\left(3 \, a^{2} + b^{2}\right)} \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, {\left(15 \, a b \sin\left(d x + c\right)^{5} - 25 \, a b \sin\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{4} + 8 \, a b \sin\left(d x + c\right) - 3 \, {\left(3 \, a^{2} + b^{2}\right)} \sin\left(d x + c\right)^{2} + 2 \, a^{2}\right)}}{\sin\left(d x + c\right)^{6} - 2 \, \sin\left(d x + c\right)^{4} + \sin\left(d x + c\right)^{2}}}{8 \, d}"," ",0,"-1/8*((12*a^2 - 15*a*b + 4*b^2)*log(sin(d*x + c) + 1) + (12*a^2 + 15*a*b + 4*b^2)*log(sin(d*x + c) - 1) - 8*(3*a^2 + b^2)*log(sin(d*x + c)) + 2*(15*a*b*sin(d*x + c)^5 - 25*a*b*sin(d*x + c)^3 + 2*(3*a^2 + b^2)*sin(d*x + c)^4 + 8*a*b*sin(d*x + c) - 3*(3*a^2 + b^2)*sin(d*x + c)^2 + 2*a^2)/(sin(d*x + c)^6 - 2*sin(d*x + c)^4 + sin(d*x + c)^2))/d","A",0
1501,1,217,0,0.354791," ","integrate(sec(d*x+c)^5*sin(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{16 \, b^{3} \sin\left(d x + c\right)^{3} + 72 \, a b^{2} \sin\left(d x + c\right)^{2} + 3 \, {\left(8 \, a^{3} - 45 \, a^{2} b + 72 \, a b^{2} - 35 \, b^{3}\right)} \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)} \log\left(\sin\left(d x + c\right) - 1\right) + 144 \, {\left(a^{2} b + b^{3}\right)} \sin\left(d x + c\right) - \frac{6 \, {\left({\left(27 \, a^{2} b + 13 \, b^{3}\right)} \sin\left(d x + c\right)^{3} - 6 \, a^{3} - 30 \, a b^{2} + 4 \, {\left(2 \, a^{3} + 9 \, a b^{2}\right)} \sin\left(d x + c\right)^{2} - {\left(21 \, a^{2} b + 11 \, b^{3}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{48 \, d}"," ",0,"-1/48*(16*b^3*sin(d*x + c)^3 + 72*a*b^2*sin(d*x + c)^2 + 3*(8*a^3 - 45*a^2*b + 72*a*b^2 - 35*b^3)*log(sin(d*x + c) + 1) + 3*(8*a^3 + 45*a^2*b + 72*a*b^2 + 35*b^3)*log(sin(d*x + c) - 1) + 144*(a^2*b + b^3)*sin(d*x + c) - 6*((27*a^2*b + 13*b^3)*sin(d*x + c)^3 - 6*a^3 - 30*a*b^2 + 4*(2*a^3 + 9*a*b^2)*sin(d*x + c)^2 - (21*a^2*b + 11*b^3)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1502,1,190,0,0.324565," ","integrate(sec(d*x+c)^5*sin(d*x+c)^4*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{8 \, b^{3} \sin\left(d x + c\right)^{2} + 48 \, a b^{2} \sin\left(d x + c\right) - 3 \, {\left(a^{3} - 8 \, a^{2} b + 15 \, a b^{2} - 8 \, b^{3}\right)} \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)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left({\left(5 \, a^{3} + 27 \, a b^{2}\right)} \sin\left(d x + c\right)^{3} - 18 \, a^{2} b - 10 \, b^{3} + 12 \, {\left(2 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)^{2} - 3 \, {\left(a^{3} + 7 \, a b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*(8*b^3*sin(d*x + c)^2 + 48*a*b^2*sin(d*x + c) - 3*(a^3 - 8*a^2*b + 15*a*b^2 - 8*b^3)*log(sin(d*x + c) + 1) + 3*(a^3 + 8*a^2*b + 15*a*b^2 + 8*b^3)*log(sin(d*x + c) - 1) - 2*((5*a^3 + 27*a*b^2)*sin(d*x + c)^3 - 18*a^2*b - 10*b^3 + 12*(2*a^2*b + b^3)*sin(d*x + c)^2 - 3*(a^3 + 7*a*b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1503,1,173,0,0.337903," ","integrate(sec(d*x+c)^5*sin(d*x+c)^3*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{16 \, b^{3} \sin\left(d x + c\right) - 3 \, {\left(3 \, a^{2} b - 8 \, a b^{2} + 5 \, b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(3 \, a^{2} b + 8 \, a b^{2} + 5 \, b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(5 \, a^{2} b + 3 \, b^{3}\right)} \sin\left(d x + c\right)^{3} - 2 \, a^{3} - 18 \, a b^{2} + 4 \, {\left(a^{3} + 6 \, a b^{2}\right)} \sin\left(d x + c\right)^{2} - {\left(9 \, a^{2} b + 7 \, b^{3}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*(16*b^3*sin(d*x + c) - 3*(3*a^2*b - 8*a*b^2 + 5*b^3)*log(sin(d*x + c) + 1) + 3*(3*a^2*b + 8*a*b^2 + 5*b^3)*log(sin(d*x + c) - 1) - 2*(3*(5*a^2*b + 3*b^3)*sin(d*x + c)^3 - 2*a^3 - 18*a*b^2 + 4*(a^3 + 6*a*b^2)*sin(d*x + c)^2 - (9*a^2*b + 7*b^3)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1504,1,151,0,0.332759," ","integrate(sec(d*x+c)^5*sin(d*x+c)^2*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{{\left(a^{3} - 9 \, a b^{2} + 8 \, b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(a^{3} - 9 \, a b^{2} - 8 \, b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left({\left(a^{3} + 15 \, a b^{2}\right)} \sin\left(d x + c\right)^{3} - 6 \, a^{2} b - 6 \, b^{3} + 4 \, {\left(3 \, a^{2} b + 2 \, b^{3}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{3} - 9 \, a b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*((a^3 - 9*a*b^2 + 8*b^3)*log(sin(d*x + c) + 1) - (a^3 - 9*a*b^2 - 8*b^3)*log(sin(d*x + c) - 1) - 2*((a^3 + 15*a*b^2)*sin(d*x + c)^3 - 6*a^2*b - 6*b^3 + 4*(3*a^2*b + 2*b^3)*sin(d*x + c)^2 + (a^3 - 9*a*b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1505,1,140,0,0.380162," ","integrate(sec(d*x+c)^5*sin(d*x+c)*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(a^{2} b - b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(a^{2} b - b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(12 \, a b^{2} \sin\left(d x + c\right)^{2} + {\left(3 \, a^{2} b + 5 \, b^{3}\right)} \sin\left(d x + c\right)^{3} + 2 \, a^{3} - 6 \, a b^{2} + 3 \, {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"-1/16*(3*(a^2*b - b^3)*log(sin(d*x + c) + 1) - 3*(a^2*b - b^3)*log(sin(d*x + c) - 1) - 2*(12*a*b^2*sin(d*x + c)^2 + (3*a^2*b + 5*b^3)*sin(d*x + c)^3 + 2*a^3 - 6*a*b^2 + 3*(a^2*b - b^3)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1506,1,160,0,0.331190," ","integrate(csc(d*x+c)*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{16 \, a^{3} \log\left(\sin\left(d x + c\right)\right) - {\left(8 \, a^{3} - 9 \, a^{2} b + b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(8 \, a^{3} + 9 \, a^{2} b - b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(4 \, a^{3} \sin\left(d x + c\right)^{2} + {\left(9 \, a^{2} b - b^{3}\right)} \sin\left(d x + c\right)^{3} - 6 \, a^{3} - 6 \, a b^{2} - {\left(15 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*(16*a^3*log(sin(d*x + c)) - (8*a^3 - 9*a^2*b + b^3)*log(sin(d*x + c) + 1) - (8*a^3 + 9*a^2*b - b^3)*log(sin(d*x + c) - 1) - 2*(4*a^3*sin(d*x + c)^2 + (9*a^2*b - b^3)*sin(d*x + c)^3 - 6*a^3 - 6*a*b^2 - (15*a^2*b + b^3)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1507,1,188,0,0.342282," ","integrate(csc(d*x+c)^2*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\frac{48 \, a^{2} b \log\left(\sin\left(d x + c\right)\right) + 3 \, {\left(5 \, a^{3} - 8 \, a^{2} b + 3 \, a b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, a^{3} + 8 \, a^{2} b + 3 \, a b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(12 \, a^{2} b \sin\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)^{4} + 8 \, a^{3} - 5 \, {\left(5 \, a^{3} + 3 \, a b^{2}\right)} \sin\left(d x + c\right)^{2} - 2 \, {\left(9 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{5} - 2 \, \sin\left(d x + c\right)^{3} + \sin\left(d x + c\right)}}{16 \, d}"," ",0,"1/16*(48*a^2*b*log(sin(d*x + c)) + 3*(5*a^3 - 8*a^2*b + 3*a*b^2)*log(sin(d*x + c) + 1) - 3*(5*a^3 + 8*a^2*b + 3*a*b^2)*log(sin(d*x + c) - 1) - 2*(12*a^2*b*sin(d*x + c)^3 + 3*(5*a^3 + 3*a*b^2)*sin(d*x + c)^4 + 8*a^3 - 5*(5*a^3 + 3*a*b^2)*sin(d*x + c)^2 - 2*(9*a^2*b + b^3)*sin(d*x + c))/(sin(d*x + c)^5 - 2*sin(d*x + c)^3 + sin(d*x + c)))/d","A",0
1508,1,217,0,0.342947," ","integrate(csc(d*x+c)^3*sec(d*x+c)^5*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","-\frac{3 \, {\left(8 \, a^{3} - 15 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right) + 3 \, {\left(8 \, a^{3} + 15 \, a^{2} b + 8 \, a b^{2} + b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - 48 \, {\left(a^{3} + a b^{2}\right)} \log\left(\sin\left(d x + c\right)\right) + \frac{2 \, {\left(3 \, {\left(15 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)^{5} + 12 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)^{4} + 24 \, a^{2} b \sin\left(d x + c\right) - 5 \, {\left(15 \, a^{2} b + b^{3}\right)} \sin\left(d x + c\right)^{3} + 4 \, a^{3} - 18 \, {\left(a^{3} + a b^{2}\right)} \sin\left(d x + c\right)^{2}\right)}}{\sin\left(d x + c\right)^{6} - 2 \, \sin\left(d x + c\right)^{4} + \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"-1/16*(3*(8*a^3 - 15*a^2*b + 8*a*b^2 - b^3)*log(sin(d*x + c) + 1) + 3*(8*a^3 + 15*a^2*b + 8*a*b^2 + b^3)*log(sin(d*x + c) - 1) - 48*(a^3 + a*b^2)*log(sin(d*x + c)) + 2*(3*(15*a^2*b + b^3)*sin(d*x + c)^5 + 12*(a^3 + a*b^2)*sin(d*x + c)^4 + 24*a^2*b*sin(d*x + c) - 5*(15*a^2*b + b^3)*sin(d*x + c)^3 + 4*a^3 - 18*(a^3 + a*b^2)*sin(d*x + c)^2)/(sin(d*x + c)^6 - 2*sin(d*x + c)^4 + sin(d*x + c)^2))/d","A",0
1509,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^4,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{4} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^4*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1510,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^3,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{3} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^3*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1511,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)}^{2} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)^2*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1512,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int {\left(b \sin\left(d x + c\right) + a\right)} \sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}\,{d x}"," ",0,"integrate((b*sin(d*x + c) + a)*sin(d*x + c)^n*sec(d*x + c)^5, x)","F",0
1513,0,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\int \frac{\sin\left(d x + c\right)^{n} \sec\left(d x + c\right)^{5}}{b \sin\left(d x + c\right) + a}\,{d x}"," ",0,"integrate(sin(d*x + c)^n*sec(d*x + c)^5/(b*sin(d*x + c) + a), x)","F",0
1514,-1,0,0,0.000000," ","integrate(sec(d*x+c)^5*sin(d*x+c)^n*(a+b*sin(d*x+c))^p,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1515,0,0,0,0.000000," ","integrate(sec(f*x+e)^6*(a+b*sin(f*x+e))^(9/2)/(d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{{\left(b \sin\left(f x + e\right) + a\right)}^{\frac{9}{2}} \sec\left(f x + e\right)^{6}}{\sqrt{d \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^(9/2)*sec(f*x + e)^6/sqrt(d*sin(f*x + e)), x)","F",0
1516,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^(4/3),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2, x)","F",0
1517,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^(4/3),x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2, x)","F",0
1518,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3),x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2, x)","F",0
1519,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1520,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^(4/3)/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} \cos\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(4/3)*cos(f*x + e)^2/(b*sin(f*x + e) + a)^2, x)","F",0
1521,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1522,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^m*(c+d*sin(f*x+e))^(4/3),x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{\frac{4}{3}} {\left(b \sin\left(f x + e\right) + a\right)}^{m} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^(4/3)*(b*sin(f*x + e) + a)^m*cos(f*x + e)^2, x)","F",0
1523,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))^2*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)}^{2} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)^2*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1524,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(a+b*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1525,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2, x)","F",0
1526,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \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}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(b*sin(f*x + e) + a), x)","F",0
1527,0,0,0,0.000000," ","integrate(cos(f*x+e)^2*(c+d*sin(f*x+e))^n/(a+b*sin(f*x+e))^2,x, algorithm=""maxima"")","\int \frac{{\left(d \sin\left(f x + e\right) + c\right)}^{n} \cos\left(f x + e\right)^{2}}{{\left(b \sin\left(f x + e\right) + a\right)}^{2}}\,{d x}"," ",0,"integrate((d*sin(f*x + e) + c)^n*cos(f*x + e)^2/(b*sin(f*x + e) + a)^2, x)","F",0
1528,1,151,0,0.348354," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{280 \, B b \sin\left(d x + c\right)^{9} + 315 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{8} + 360 \, {\left(A a - 3 \, B b\right)} \sin\left(d x + c\right)^{7} - 1260 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{6} - 1512 \, {\left(A a - B b\right)} \sin\left(d x + c\right)^{5} + 1890 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{4} + 840 \, {\left(3 \, A a - B b\right)} \sin\left(d x + c\right)^{3} - 2520 \, A a \sin\left(d x + c\right) - 1260 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{2}}{2520 \, d}"," ",0,"-1/2520*(280*B*b*sin(d*x + c)^9 + 315*(B*a + A*b)*sin(d*x + c)^8 + 360*(A*a - 3*B*b)*sin(d*x + c)^7 - 1260*(B*a + A*b)*sin(d*x + c)^6 - 1512*(A*a - B*b)*sin(d*x + c)^5 + 1890*(B*a + A*b)*sin(d*x + c)^4 + 840*(3*A*a - B*b)*sin(d*x + c)^3 - 2520*A*a*sin(d*x + c) - 1260*(B*a + A*b)*sin(d*x + c)^2)/d","A",0
1529,1,116,0,0.527647," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{30 \, B b \sin\left(d x + c\right)^{7} + 35 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{6} + 42 \, {\left(A a - 2 \, B b\right)} \sin\left(d x + c\right)^{5} - 105 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{4} - 70 \, {\left(2 \, A a - B b\right)} \sin\left(d x + c\right)^{3} + 210 \, A a \sin\left(d x + c\right) + 105 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{2}}{210 \, d}"," ",0,"1/210*(30*B*b*sin(d*x + c)^7 + 35*(B*a + A*b)*sin(d*x + c)^6 + 42*(A*a - 2*B*b)*sin(d*x + c)^5 - 105*(B*a + A*b)*sin(d*x + c)^4 - 70*(2*A*a - B*b)*sin(d*x + c)^3 + 210*A*a*sin(d*x + c) + 105*(B*a + A*b)*sin(d*x + c)^2)/d","A",0
1530,1,80,0,1.129113," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{12 \, B b \sin\left(d x + c\right)^{5} + 15 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{4} + 20 \, {\left(A a - B b\right)} \sin\left(d x + c\right)^{3} - 60 \, A a \sin\left(d x + c\right) - 30 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{2}}{60 \, d}"," ",0,"-1/60*(12*B*b*sin(d*x + c)^5 + 15*(B*a + A*b)*sin(d*x + c)^4 + 20*(A*a - B*b)*sin(d*x + c)^3 - 60*A*a*sin(d*x + c) - 30*(B*a + A*b)*sin(d*x + c)^2)/d","A",0
1531,1,45,0,0.318055," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{2 \, B b \sin\left(d x + c\right)^{3} + 6 \, A a \sin\left(d x + c\right) + 3 \, {\left(B a + A b\right)} \sin\left(d x + c\right)^{2}}{6 \, d}"," ",0,"1/6*(2*B*b*sin(d*x + c)^3 + 6*A*a*sin(d*x + c) + 3*(B*a + A*b)*sin(d*x + c)^2)/d","A",0
1532,1,64,0,0.314055," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\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
1533,1,78,0,0.309908," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(A a - B b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(A a - B b\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(B a + A b + {\left(A a + B b\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((A*a - B*b)*log(sin(d*x + c) + 1) - (A*a - B*b)*log(sin(d*x + c) - 1) - 2*(B*a + A*b + (A*a + B*b)*sin(d*x + c))/(sin(d*x + c)^2 - 1))/d","A",0
1534,1,112,0,0.315956," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, A a - B b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A a - B b\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left({\left(3 \, A a - B b\right)} \sin\left(d x + c\right)^{3} - 2 \, B a - 2 \, A b - {\left(5 \, A a + B b\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*((3*A*a - B*b)*log(sin(d*x + c) + 1) - (3*A*a - B*b)*log(sin(d*x + c) - 1) - 2*((3*A*a - B*b)*sin(d*x + c)^3 - 2*B*a - 2*A*b - (5*A*a + B*b)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1535,1,143,0,0.313172," ","integrate(sec(d*x+c)^7*(a+b*sin(d*x+c))*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, A a - B b\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A a - B b\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(5 \, A a - B b\right)} \sin\left(d x + c\right)^{5} - 8 \, {\left(5 \, A a - B b\right)} \sin\left(d x + c\right)^{3} + 8 \, B a + 8 \, A b + 3 \, {\left(11 \, A a + B b\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1}}{96 \, d}"," ",0,"1/96*(3*(5*A*a - B*b)*log(sin(d*x + c) + 1) - 3*(5*A*a - B*b)*log(sin(d*x + c) - 1) - 2*(3*(5*A*a - B*b)*sin(d*x + c)^5 - 8*(5*A*a - B*b)*sin(d*x + c)^3 + 8*B*a + 8*A*b + 3*(11*A*a + B*b)*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1))/d","A",0
1536,1,238,0,0.310577," ","integrate(cos(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{252 \, B b^{2} \sin\left(d x + c\right)^{10} + 280 \, {\left(2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)^{9} + 315 \, {\left(B a^{2} + 2 \, A a b - 3 \, B b^{2}\right)} \sin\left(d x + c\right)^{8} + 360 \, {\left(A a^{2} - 6 \, B a b - 3 \, A b^{2}\right)} \sin\left(d x + c\right)^{7} - 1260 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \sin\left(d x + c\right)^{6} - 1512 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \sin\left(d x + c\right)^{5} + 630 \, {\left(3 \, B a^{2} + 6 \, A a b - B b^{2}\right)} \sin\left(d x + c\right)^{4} - 2520 \, A a^{2} \sin\left(d x + c\right) + 840 \, {\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \sin\left(d x + c\right)^{3} - 1260 \, {\left(B a^{2} + 2 \, A a b\right)} \sin\left(d x + c\right)^{2}}{2520 \, d}"," ",0,"-1/2520*(252*B*b^2*sin(d*x + c)^10 + 280*(2*B*a*b + A*b^2)*sin(d*x + c)^9 + 315*(B*a^2 + 2*A*a*b - 3*B*b^2)*sin(d*x + c)^8 + 360*(A*a^2 - 6*B*a*b - 3*A*b^2)*sin(d*x + c)^7 - 1260*(B*a^2 + 2*A*a*b - B*b^2)*sin(d*x + c)^6 - 1512*(A*a^2 - 2*B*a*b - A*b^2)*sin(d*x + c)^5 + 630*(3*B*a^2 + 6*A*a*b - B*b^2)*sin(d*x + c)^4 - 2520*A*a^2*sin(d*x + c) + 840*(3*A*a^2 - 2*B*a*b - A*b^2)*sin(d*x + c)^3 - 1260*(B*a^2 + 2*A*a*b)*sin(d*x + c)^2)/d","A",0
1537,1,184,0,0.321299," ","integrate(cos(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{105 \, B b^{2} \sin\left(d x + c\right)^{8} + 120 \, {\left(2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)^{7} + 140 \, {\left(B a^{2} + 2 \, A a b - 2 \, B b^{2}\right)} \sin\left(d x + c\right)^{6} + 168 \, {\left(A a^{2} - 4 \, B a b - 2 \, A b^{2}\right)} \sin\left(d x + c\right)^{5} - 210 \, {\left(2 \, B a^{2} + 4 \, A a b - B b^{2}\right)} \sin\left(d x + c\right)^{4} + 840 \, A a^{2} \sin\left(d x + c\right) - 280 \, {\left(2 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \sin\left(d x + c\right)^{3} + 420 \, {\left(B a^{2} + 2 \, A a b\right)} \sin\left(d x + c\right)^{2}}{840 \, d}"," ",0,"1/840*(105*B*b^2*sin(d*x + c)^8 + 120*(2*B*a*b + A*b^2)*sin(d*x + c)^7 + 140*(B*a^2 + 2*A*a*b - 2*B*b^2)*sin(d*x + c)^6 + 168*(A*a^2 - 4*B*a*b - 2*A*b^2)*sin(d*x + c)^5 - 210*(2*B*a^2 + 4*A*a*b - B*b^2)*sin(d*x + c)^4 + 840*A*a^2*sin(d*x + c) - 280*(2*A*a^2 - 2*B*a*b - A*b^2)*sin(d*x + c)^3 + 420*(B*a^2 + 2*A*a*b)*sin(d*x + c)^2)/d","A",0
1538,1,128,0,0.333080," ","integrate(cos(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{10 \, B b^{2} \sin\left(d x + c\right)^{6} + 12 \, {\left(2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)^{5} + 15 \, {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} \sin\left(d x + c\right)^{4} - 60 \, A a^{2} \sin\left(d x + c\right) + 20 \, {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} \sin\left(d x + c\right)^{3} - 30 \, {\left(B a^{2} + 2 \, A a b\right)} \sin\left(d x + c\right)^{2}}{60 \, d}"," ",0,"-1/60*(10*B*b^2*sin(d*x + c)^6 + 12*(2*B*a*b + A*b^2)*sin(d*x + c)^5 + 15*(B*a^2 + 2*A*a*b - B*b^2)*sin(d*x + c)^4 - 60*A*a^2*sin(d*x + c) + 20*(A*a^2 - 2*B*a*b - A*b^2)*sin(d*x + c)^3 - 30*(B*a^2 + 2*A*a*b)*sin(d*x + c)^2)/d","A",0
1539,1,74,0,0.306602," ","integrate(cos(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, B b^{2} \sin\left(d x + c\right)^{4} + 12 \, A a^{2} \sin\left(d x + c\right) + 4 \, {\left(2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)^{3} + 6 \, {\left(B a^{2} + 2 \, A a b\right)} \sin\left(d x + c\right)^{2}}{12 \, d}"," ",0,"1/12*(3*B*b^2*sin(d*x + c)^4 + 12*A*a^2*sin(d*x + c) + 4*(2*B*a*b + A*b^2)*sin(d*x + c)^3 + 6*(B*a^2 + 2*A*a*b)*sin(d*x + c)^2)/d","A",0
1540,1,109,0,0.335130," ","integrate(sec(d*x+c)*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{B b^{2} \sin\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*sin(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
1541,1,122,0,0.341133," ","integrate(sec(d*x+c)^3*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(A a^{2} - 2 \, B a b - {\left(A - 2 \, B\right)} b^{2}\right)} \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)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(B a^{2} + 2 \, A a b + B b^{2} + {\left(A a^{2} + 2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{2} - 1}}{4 \, d}"," ",0,"1/4*((A*a^2 - 2*B*a*b - (A - 2*B)*b^2)*log(sin(d*x + c) + 1) - (A*a^2 - 2*B*a*b - (A + 2*B)*b^2)*log(sin(d*x + c) - 1) - 2*(B*a^2 + 2*A*a*b + B*b^2 + (A*a^2 + 2*B*a*b + A*b^2)*sin(d*x + c))/(sin(d*x + c)^2 - 1))/d","A",0
1542,1,171,0,0.438494," ","integrate(sec(d*x+c)^5*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{{\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - {\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) + \frac{2 \, {\left(4 \, B b^{2} \sin\left(d x + c\right)^{2} - {\left(3 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \sin\left(d x + c\right)^{3} + 2 \, B a^{2} + 4 \, A a b - 2 \, B b^{2} + {\left(5 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{4} - 2 \, \sin\left(d x + c\right)^{2} + 1}}{16 \, d}"," ",0,"1/16*((3*A*a^2 - 2*B*a*b - A*b^2)*log(sin(d*x + c) + 1) - (3*A*a^2 - 2*B*a*b - A*b^2)*log(sin(d*x + c) - 1) + 2*(4*B*b^2*sin(d*x + c)^2 - (3*A*a^2 - 2*B*a*b - A*b^2)*sin(d*x + c)^3 + 2*B*a^2 + 4*A*a*b - 2*B*b^2 + (5*A*a^2 + 2*B*a*b + A*b^2)*sin(d*x + c))/(sin(d*x + c)^4 - 2*sin(d*x + c)^2 + 1))/d","A",0
1543,1,211,0,0.445602," ","integrate(sec(d*x+c)^7*(a+b*sin(d*x+c))^2*(A+B*sin(d*x+c)),x, algorithm=""maxima"")","\frac{3 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right) - 3 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right) - \frac{2 \, {\left(3 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \sin\left(d x + c\right)^{5} + 12 \, B b^{2} \sin\left(d x + c\right)^{2} - 8 \, {\left(5 \, A a^{2} - 2 \, B a b - A b^{2}\right)} \sin\left(d x + c\right)^{3} + 8 \, B a^{2} + 16 \, A a b - 4 \, B b^{2} + 3 \, {\left(11 \, A a^{2} + 2 \, B a b + A b^{2}\right)} \sin\left(d x + c\right)\right)}}{\sin\left(d x + c\right)^{6} - 3 \, \sin\left(d x + c\right)^{4} + 3 \, \sin\left(d x + c\right)^{2} - 1}}{96 \, d}"," ",0,"1/96*(3*(5*A*a^2 - 2*B*a*b - A*b^2)*log(sin(d*x + c) + 1) - 3*(5*A*a^2 - 2*B*a*b - A*b^2)*log(sin(d*x + c) - 1) - 2*(3*(5*A*a^2 - 2*B*a*b - A*b^2)*sin(d*x + c)^5 + 12*B*b^2*sin(d*x + c)^2 - 8*(5*A*a^2 - 2*B*a*b - A*b^2)*sin(d*x + c)^3 + 8*B*a^2 + 16*A*a*b - 4*B*b^2 + 3*(11*A*a^2 + 2*B*a*b + A*b^2)*sin(d*x + c))/(sin(d*x + c)^6 - 3*sin(d*x + c)^4 + 3*sin(d*x + c)^2 - 1))/d","A",0
1544,1,366,0,0.440434," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{60 \, B b^{6} \sin\left(d x + c\right)^{7} - 70 \, {\left(B a b^{5} - A b^{6}\right)} \sin\left(d x + c\right)^{6} + 84 \, {\left(B a^{2} b^{4} - A a b^{5} - 3 \, B b^{6}\right)} \sin\left(d x + c\right)^{5} - 105 \, {\left(B a^{3} b^{3} - A a^{2} b^{4} - 3 \, B a b^{5} + 3 \, A b^{6}\right)} \sin\left(d x + c\right)^{4} + 140 \, {\left(B a^{4} b^{2} - A a^{3} b^{3} - 3 \, B a^{2} b^{4} + 3 \, A a b^{5} + 3 \, B b^{6}\right)} \sin\left(d x + c\right)^{3} - 210 \, {\left(B a^{5} b - A a^{4} b^{2} - 3 \, B a^{3} b^{3} + 3 \, A a^{2} b^{4} + 3 \, B a b^{5} - 3 \, A b^{6}\right)} \sin\left(d x + c\right)^{2} + 420 \, {\left(B a^{6} - A a^{5} b - 3 \, B a^{4} b^{2} + 3 \, A a^{3} b^{3} + 3 \, B a^{2} b^{4} - 3 \, A a b^{5} - B b^{6}\right)} \sin\left(d x + c\right)}{b^{7}} - \frac{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)}{b^{8}}}{420 \, d}"," ",0,"-1/420*((60*B*b^6*sin(d*x + c)^7 - 70*(B*a*b^5 - A*b^6)*sin(d*x + c)^6 + 84*(B*a^2*b^4 - A*a*b^5 - 3*B*b^6)*sin(d*x + c)^5 - 105*(B*a^3*b^3 - A*a^2*b^4 - 3*B*a*b^5 + 3*A*b^6)*sin(d*x + c)^4 + 140*(B*a^4*b^2 - A*a^3*b^3 - 3*B*a^2*b^4 + 3*A*a*b^5 + 3*B*b^6)*sin(d*x + c)^3 - 210*(B*a^5*b - A*a^4*b^2 - 3*B*a^3*b^3 + 3*A*a^2*b^4 + 3*B*a*b^5 - 3*A*b^6)*sin(d*x + c)^2 + 420*(B*a^6 - A*a^5*b - 3*B*a^4*b^2 + 3*A*a^3*b^3 + 3*B*a^2*b^4 - 3*A*a*b^5 - B*b^6)*sin(d*x + c))/b^7 - 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)/b^8)/d","A",0
1545,1,220,0,0.572162," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{12 \, B b^{4} \sin\left(d x + c\right)^{5} - 15 \, {\left(B a b^{3} - A b^{4}\right)} \sin\left(d x + c\right)^{4} + 20 \, {\left(B a^{2} b^{2} - A a b^{3} - 2 \, B b^{4}\right)} \sin\left(d x + c\right)^{3} - 30 \, {\left(B a^{3} b - A a^{2} b^{2} - 2 \, B a b^{3} + 2 \, A b^{4}\right)} \sin\left(d x + c\right)^{2} + 60 \, {\left(B a^{4} - A a^{3} b - 2 \, B a^{2} b^{2} + 2 \, A a b^{3} + B b^{4}\right)} \sin\left(d x + c\right)}{b^{5}} - \frac{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)}{b^{6}}}{60 \, d}"," ",0,"1/60*((12*B*b^4*sin(d*x + c)^5 - 15*(B*a*b^3 - A*b^4)*sin(d*x + c)^4 + 20*(B*a^2*b^2 - A*a*b^3 - 2*B*b^4)*sin(d*x + c)^3 - 30*(B*a^3*b - A*a^2*b^2 - 2*B*a*b^3 + 2*A*b^4)*sin(d*x + c)^2 + 60*(B*a^4 - A*a^3*b - 2*B*a^2*b^2 + 2*A*a*b^3 + B*b^4)*sin(d*x + c))/b^5 - 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)/b^6)/d","A",0
1546,1,112,0,0.505113," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{2 \, B b^{2} \sin\left(d x + c\right)^{3} - 3 \, {\left(B a b - A b^{2}\right)} \sin\left(d x + c\right)^{2} + 6 \, {\left(B a^{2} - A a b - B b^{2}\right)} \sin\left(d x + c\right)}{b^{3}} - \frac{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)}{b^{4}}}{6 \, d}"," ",0,"-1/6*((2*B*b^2*sin(d*x + c)^3 - 3*(B*a*b - A*b^2)*sin(d*x + c)^2 + 6*(B*a^2 - A*a*b - B*b^2)*sin(d*x + c))/b^3 - 6*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)*log(b*sin(d*x + c) + a)/b^4)/d","A",0
1547,1,40,0,0.519096," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{B \sin\left(d x + c\right)}{b} - \frac{{\left(B a - A b\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{2}}}{d}"," ",0,"(B*sin(d*x + c)/b - (B*a - A*b)*log(b*sin(d*x + c) + a)/b^2)/d","A",0
1548,1,79,0,0.559639," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a - A b\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{2} - b^{2}} + \frac{{\left(A - B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a - b} - \frac{{\left(A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a + b}}{2 \, d}"," ",0,"1/2*(2*(B*a - A*b)*log(b*sin(d*x + c) + a)/(a^2 - b^2) + (A - B)*log(sin(d*x + c) + 1)/(a - b) - (A + B)*log(sin(d*x + c) - 1)/(a + b))/d","A",0
1549,1,175,0,0.726116," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(B a b^{2} - A b^{3}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} - \frac{{\left(A a - {\left(2 \, A - B\right)} b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} + \frac{{\left(A a + {\left(2 \, A + B\right)} b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} + \frac{2 \, {\left(B a - A b + {\left(A a - B b\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{2} - b^{2}\right)} \sin\left(d x + c\right)^{2} - a^{2} + b^{2}}}{4 \, d}"," ",0,"-1/4*(4*(B*a*b^2 - A*b^3)*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) - (A*a - (2*A - B)*b)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) + (A*a + (2*A + B)*b)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) + 2*(B*a - A*b + (A*a - B*b)*sin(d*x + c))/((a^2 - b^2)*sin(d*x + c)^2 - a^2 + b^2))/d","A",0
1550,1,367,0,0.384422," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","\frac{\frac{16 \, {\left(B a b^{4} - A b^{5}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} + \frac{{\left(3 \, A a^{2} - {\left(9 \, A - B\right)} a b + {\left(8 \, A - 3 \, B\right)} b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} - \frac{{\left(3 \, A a^{2} + {\left(9 \, A + B\right)} a b + {\left(8 \, A + 3 \, B\right)} b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} + \frac{2 \, {\left(2 \, B a^{3} - 2 \, A a^{2} b - 6 \, B a b^{2} + 6 \, A b^{3} - {\left(3 \, A a^{3} + B a^{2} b - 7 \, A a b^{2} + 3 \, B b^{3}\right)} \sin\left(d x + c\right)^{3} + 4 \, {\left(B a b^{2} - A b^{3}\right)} \sin\left(d x + c\right)^{2} + {\left(5 \, A a^{3} - B a^{2} b - 9 \, A a b^{2} + 5 \, B b^{3}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} \sin\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)} \sin\left(d x + c\right)^{2}}}{16 \, d}"," ",0,"1/16*(16*(B*a*b^4 - A*b^5)*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) + (3*A*a^2 - (9*A - B)*a*b + (8*A - 3*B)*b^2)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) - (3*A*a^2 + (9*A + B)*a*b + (8*A + 3*B)*b^2)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) + 2*(2*B*a^3 - 2*A*a^2*b - 6*B*a*b^2 + 6*A*b^3 - (3*A*a^3 + B*a^2*b - 7*A*a*b^2 + 3*B*b^3)*sin(d*x + c)^3 + 4*(B*a*b^2 - A*b^3)*sin(d*x + c)^2 + (5*A*a^3 - B*a^2*b - 9*A*a*b^2 + 5*B*b^3)*sin(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^4 + a^4 - 2*a^2*b^2 + b^4 - 2*(a^4 - 2*a^2*b^2 + b^4)*sin(d*x + c)^2))/d","A",0
1551,1,632,0,0.454942," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c)),x, algorithm=""maxima"")","-\frac{\frac{96 \, {\left(B a b^{6} - A b^{7}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} - \frac{3 \, {\left(5 \, A a^{3} - {\left(20 \, A - B\right)} a^{2} b + {\left(29 \, A - 4 \, B\right)} a b^{2} - {\left(16 \, A - 5 \, B\right)} b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} + \frac{3 \, {\left(5 \, A a^{3} + {\left(20 \, A + B\right)} a^{2} b + {\left(29 \, A + 4 \, B\right)} a b^{2} + {\left(16 \, A + 5 \, B\right)} b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{2 \, {\left(8 \, B a^{5} - 8 \, A a^{4} b - 28 \, B a^{3} b^{2} + 28 \, A a^{2} b^{3} + 44 \, B a b^{4} - 44 \, A b^{5} + 3 \, {\left(5 \, A a^{5} + B a^{4} b - 16 \, A a^{3} b^{2} - 4 \, B a^{2} b^{3} + 19 \, A a b^{4} - 5 \, B b^{5}\right)} \sin\left(d x + c\right)^{5} + 24 \, {\left(B a b^{4} - A b^{5}\right)} \sin\left(d x + c\right)^{4} - 8 \, {\left(5 \, A a^{5} + B a^{4} b - 16 \, A a^{3} b^{2} - 2 \, B a^{2} b^{3} + 17 \, A a b^{4} - 5 \, B b^{5}\right)} \sin\left(d x + c\right)^{3} + 12 \, {\left(B a^{3} b^{2} - A a^{2} b^{3} - 5 \, B a b^{4} + 5 \, A b^{5}\right)} \sin\left(d x + c\right)^{2} + 3 \, {\left(11 \, A a^{5} - B a^{4} b - 32 \, A a^{3} b^{2} + 4 \, B a^{2} b^{3} + 29 \, A a b^{4} - 11 \, B b^{5}\right)} \sin\left(d x + c\right)\right)}}{{\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sin\left(d x + c\right)^{6} - a^{6} + 3 \, a^{4} b^{2} - 3 \, a^{2} b^{4} + b^{6} - 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sin\left(d x + c\right)^{4} + 3 \, {\left(a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}\right)} \sin\left(d x + c\right)^{2}}}{96 \, d}"," ",0,"-1/96*(96*(B*a*b^6 - A*b^7)*log(b*sin(d*x + c) + a)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) - 3*(5*A*a^3 - (20*A - B)*a^2*b + (29*A - 4*B)*a*b^2 - (16*A - 5*B)*b^3)*log(sin(d*x + c) + 1)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) + 3*(5*A*a^3 + (20*A + B)*a^2*b + (29*A + 4*B)*a*b^2 + (16*A + 5*B)*b^3)*log(sin(d*x + c) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 2*(8*B*a^5 - 8*A*a^4*b - 28*B*a^3*b^2 + 28*A*a^2*b^3 + 44*B*a*b^4 - 44*A*b^5 + 3*(5*A*a^5 + B*a^4*b - 16*A*a^3*b^2 - 4*B*a^2*b^3 + 19*A*a*b^4 - 5*B*b^5)*sin(d*x + c)^5 + 24*(B*a*b^4 - A*b^5)*sin(d*x + c)^4 - 8*(5*A*a^5 + B*a^4*b - 16*A*a^3*b^2 - 2*B*a^2*b^3 + 17*A*a*b^4 - 5*B*b^5)*sin(d*x + c)^3 + 12*(B*a^3*b^2 - A*a^2*b^3 - 5*B*a*b^4 + 5*A*b^5)*sin(d*x + c)^2 + 3*(11*A*a^5 - B*a^4*b - 32*A*a^3*b^2 + 4*B*a^2*b^3 + 29*A*a*b^4 - 11*B*b^5)*sin(d*x + c))/((a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sin(d*x + c)^6 - a^6 + 3*a^4*b^2 - 3*a^2*b^4 + b^6 - 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sin(d*x + c)^4 + 3*(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6)*sin(d*x + c)^2))/d","A",0
1552,1,377,0,0.466583," ","integrate(cos(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{60 \, {\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)}}{b^{9} \sin\left(d x + c\right) + a b^{8}} + \frac{10 \, B b^{5} \sin\left(d x + c\right)^{6} - 12 \, {\left(2 \, B a b^{4} - A b^{5}\right)} \sin\left(d x + c\right)^{5} + 15 \, {\left(3 \, B a^{2} b^{3} - 2 \, A a b^{4} - 3 \, B b^{5}\right)} \sin\left(d x + c\right)^{4} - 20 \, {\left(4 \, B a^{3} b^{2} - 3 \, A a^{2} b^{3} - 6 \, B a b^{4} + 3 \, A b^{5}\right)} \sin\left(d x + c\right)^{3} + 30 \, {\left(5 \, B a^{4} b - 4 \, A a^{3} b^{2} - 9 \, B a^{2} b^{3} + 6 \, A a b^{4} + 3 \, B b^{5}\right)} \sin\left(d x + c\right)^{2} - 60 \, {\left(6 \, B a^{5} - 5 \, A a^{4} b - 12 \, B a^{3} b^{2} + 9 \, A a^{2} b^{3} + 6 \, B a b^{4} - 3 \, A b^{5}\right)} \sin\left(d x + c\right)}{b^{7}} + \frac{60 \, {\left(7 \, B a^{6} - 6 \, A a^{5} b - 15 \, B a^{4} b^{2} + 12 \, A a^{3} b^{3} + 9 \, B a^{2} b^{4} - 6 \, A a b^{5} - B b^{6}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{8}}}{60 \, d}"," ",0,"-1/60*(60*(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)/(b^9*sin(d*x + c) + a*b^8) + (10*B*b^5*sin(d*x + c)^6 - 12*(2*B*a*b^4 - A*b^5)*sin(d*x + c)^5 + 15*(3*B*a^2*b^3 - 2*A*a*b^4 - 3*B*b^5)*sin(d*x + c)^4 - 20*(4*B*a^3*b^2 - 3*A*a^2*b^3 - 6*B*a*b^4 + 3*A*b^5)*sin(d*x + c)^3 + 30*(5*B*a^4*b - 4*A*a^3*b^2 - 9*B*a^2*b^3 + 6*A*a*b^4 + 3*B*b^5)*sin(d*x + c)^2 - 60*(6*B*a^5 - 5*A*a^4*b - 12*B*a^3*b^2 + 9*A*a^2*b^3 + 6*B*a*b^4 - 3*A*b^5)*sin(d*x + c))/b^7 + 60*(7*B*a^6 - 6*A*a^5*b - 15*B*a^4*b^2 + 12*A*a^3*b^3 + 9*B*a^2*b^4 - 6*A*a*b^5 - B*b^6)*log(b*sin(d*x + c) + a)/b^8)/d","A",0
1553,1,229,0,0.386495," ","integrate(cos(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{12 \, {\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)}}{b^{7} \sin\left(d x + c\right) + a b^{6}} + \frac{3 \, B b^{3} \sin\left(d x + c\right)^{4} - 4 \, {\left(2 \, B a b^{2} - A b^{3}\right)} \sin\left(d x + c\right)^{3} + 6 \, {\left(3 \, B a^{2} b - 2 \, A a b^{2} - 2 \, B b^{3}\right)} \sin\left(d x + c\right)^{2} - 12 \, {\left(4 \, B a^{3} - 3 \, A a^{2} b - 4 \, B a b^{2} + 2 \, A b^{3}\right)} \sin\left(d x + c\right)}{b^{5}} + \frac{12 \, {\left(5 \, B a^{4} - 4 \, A a^{3} b - 6 \, B a^{2} b^{2} + 4 \, A a b^{3} + B b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{6}}}{12 \, d}"," ",0,"1/12*(12*(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)/(b^7*sin(d*x + c) + a*b^6) + (3*B*b^3*sin(d*x + c)^4 - 4*(2*B*a*b^2 - A*b^3)*sin(d*x + c)^3 + 6*(3*B*a^2*b - 2*A*a*b^2 - 2*B*b^3)*sin(d*x + c)^2 - 12*(4*B*a^3 - 3*A*a^2*b - 4*B*a*b^2 + 2*A*b^3)*sin(d*x + c))/b^5 + 12*(5*B*a^4 - 4*A*a^3*b - 6*B*a^2*b^2 + 4*A*a*b^3 + B*b^4)*log(b*sin(d*x + c) + a)/b^6)/d","A",0
1554,1,118,0,0.310449," ","integrate(cos(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{2 \, {\left(B a^{3} - A a^{2} b - B a b^{2} + A b^{3}\right)}}{b^{5} \sin\left(d x + c\right) + a b^{4}} + \frac{B b \sin\left(d x + c\right)^{2} - 2 \, {\left(2 \, B a - A b\right)} \sin\left(d x + c\right)}{b^{3}} + \frac{2 \, {\left(3 \, B a^{2} - 2 \, A a b - B b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{b^{4}}}{2 \, d}"," ",0,"-1/2*(2*(B*a^3 - A*a^2*b - B*a*b^2 + A*b^3)/(b^5*sin(d*x + c) + a*b^4) + (B*b*sin(d*x + c)^2 - 2*(2*B*a - A*b)*sin(d*x + c))/b^3 + 2*(3*B*a^2 - 2*A*a*b - B*b^2)*log(b*sin(d*x + c) + a)/b^4)/d","A",0
1555,1,48,0,0.458540," ","integrate(cos(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{B a - A b}{b^{3} \sin\left(d x + c\right) + a b^{2}} + \frac{B \log\left(b \sin\left(d x + c\right) + a\right)}{b^{2}}}{d}"," ",0,"((B*a - A*b)/(b^3*sin(d*x + c) + a*b^2) + B*log(b*sin(d*x + c) + a)/b^2)/d","A",0
1556,1,147,0,0.489706," ","integrate(sec(d*x+c)*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{2 \, {\left(B a^{2} - 2 \, A a b + B b^{2}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{4} - 2 \, a^{2} b^{2} + b^{4}} + \frac{{\left(A - B\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{2} - 2 \, a b + b^{2}} - \frac{{\left(A + B\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{2} + 2 \, a b + b^{2}} - \frac{2 \, {\left(B a - A b\right)}}{a^{3} - a b^{2} + {\left(a^{2} b - b^{3}\right)} \sin\left(d x + c\right)}}{2 \, d}"," ",0,"1/2*(2*(B*a^2 - 2*A*a*b + B*b^2)*log(b*sin(d*x + c) + a)/(a^4 - 2*a^2*b^2 + b^4) + (A - B)*log(sin(d*x + c) + 1)/(a^2 - 2*a*b + b^2) - (A + B)*log(sin(d*x + c) - 1)/(a^2 + 2*a*b + b^2) - 2*(B*a - A*b)/(a^3 - a*b^2 + (a^2*b - b^3)*sin(d*x + c)))/d","A",0
1557,1,346,0,0.522153," ","integrate(sec(d*x+c)^3*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left(3 \, B a^{2} b^{2} - 4 \, A a b^{3} + B b^{4}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{6} - 3 \, a^{4} b^{2} + 3 \, a^{2} b^{4} - b^{6}} - \frac{{\left(A a - {\left(3 \, A - 2 \, B\right)} b\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}} + \frac{{\left(A a + {\left(3 \, A + 2 \, B\right)} b\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}} - \frac{2 \, {\left(B a^{3} - 2 \, A a^{2} b + 3 \, B a b^{2} - 2 \, A b^{3} + {\left(A a^{2} b - 4 \, B a b^{2} + 3 \, A b^{3}\right)} \sin\left(d x + c\right)^{2} + {\left(A a^{3} - B a^{2} b - A a b^{2} + B b^{3}\right)} \sin\left(d x + c\right)\right)}}{a^{5} - 2 \, a^{3} b^{2} + a b^{4} - {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)^{3} - {\left(a^{5} - 2 \, a^{3} b^{2} + a b^{4}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{4} b - 2 \, a^{2} b^{3} + b^{5}\right)} \sin\left(d x + c\right)}}{4 \, d}"," ",0,"-1/4*(4*(3*B*a^2*b^2 - 4*A*a*b^3 + B*b^4)*log(b*sin(d*x + c) + a)/(a^6 - 3*a^4*b^2 + 3*a^2*b^4 - b^6) - (A*a - (3*A - 2*B)*b)*log(sin(d*x + c) + 1)/(a^3 - 3*a^2*b + 3*a*b^2 - b^3) + (A*a + (3*A + 2*B)*b)*log(sin(d*x + c) - 1)/(a^3 + 3*a^2*b + 3*a*b^2 + b^3) - 2*(B*a^3 - 2*A*a^2*b + 3*B*a*b^2 - 2*A*b^3 + (A*a^2*b - 4*B*a*b^2 + 3*A*b^3)*sin(d*x + c)^2 + (A*a^3 - B*a^2*b - A*a*b^2 + B*b^3)*sin(d*x + c))/(a^5 - 2*a^3*b^2 + a*b^4 - (a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c)^3 - (a^5 - 2*a^3*b^2 + a*b^4)*sin(d*x + c)^2 + (a^4*b - 2*a^2*b^3 + b^5)*sin(d*x + c)))/d","A",0
1558,1,659,0,0.399008," ","integrate(sec(d*x+c)^5*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","\frac{\frac{16 \, {\left(5 \, B a^{2} b^{4} - 6 \, A a b^{5} + B b^{6}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}} + \frac{{\left(3 \, A a^{2} - 2 \, {\left(6 \, A - B\right)} a b + {\left(15 \, A - 8 \, B\right)} b^{2}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} - 4 \, a b^{3} + b^{4}} - \frac{{\left(3 \, A a^{2} + 2 \, {\left(6 \, A + B\right)} a b + {\left(15 \, A + 8 \, B\right)} b^{2}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}} + \frac{2 \, {\left(2 \, B a^{5} - 4 \, A a^{4} b - 12 \, B a^{3} b^{2} + 20 \, A a^{2} b^{3} - 14 \, B a b^{4} + 8 \, A b^{5} - {\left(3 \, A a^{4} b + 2 \, B a^{3} b^{2} - 12 \, A a^{2} b^{3} + 22 \, B a b^{4} - 15 \, A b^{5}\right)} \sin\left(d x + c\right)^{4} - {\left(3 \, A a^{5} + 2 \, B a^{4} b - 12 \, A a^{3} b^{2} + 2 \, B a^{2} b^{3} + 9 \, A a b^{4} - 4 \, B b^{5}\right)} \sin\left(d x + c\right)^{3} + {\left(5 \, A a^{4} b + 10 \, B a^{3} b^{2} - 28 \, A a^{2} b^{3} + 38 \, B a b^{4} - 25 \, A b^{5}\right)} \sin\left(d x + c\right)^{2} + {\left(5 \, A a^{5} - 16 \, A a^{3} b^{2} + 6 \, B a^{2} b^{3} + 11 \, A a b^{4} - 6 \, B b^{5}\right)} \sin\left(d x + c\right)\right)}}{a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6} + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)^{5} + {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{4} - 2 \, {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)^{3} - 2 \, {\left(a^{7} - 3 \, a^{5} b^{2} + 3 \, a^{3} b^{4} - a b^{6}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{6} b - 3 \, a^{4} b^{3} + 3 \, a^{2} b^{5} - b^{7}\right)} \sin\left(d x + c\right)}}{16 \, d}"," ",0,"1/16*(16*(5*B*a^2*b^4 - 6*A*a*b^5 + B*b^6)*log(b*sin(d*x + c) + a)/(a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8) + (3*A*a^2 - 2*(6*A - B)*a*b + (15*A - 8*B)*b^2)*log(sin(d*x + c) + 1)/(a^4 - 4*a^3*b + 6*a^2*b^2 - 4*a*b^3 + b^4) - (3*A*a^2 + 2*(6*A + B)*a*b + (15*A + 8*B)*b^2)*log(sin(d*x + c) - 1)/(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4) + 2*(2*B*a^5 - 4*A*a^4*b - 12*B*a^3*b^2 + 20*A*a^2*b^3 - 14*B*a*b^4 + 8*A*b^5 - (3*A*a^4*b + 2*B*a^3*b^2 - 12*A*a^2*b^3 + 22*B*a*b^4 - 15*A*b^5)*sin(d*x + c)^4 - (3*A*a^5 + 2*B*a^4*b - 12*A*a^3*b^2 + 2*B*a^2*b^3 + 9*A*a*b^4 - 4*B*b^5)*sin(d*x + c)^3 + (5*A*a^4*b + 10*B*a^3*b^2 - 28*A*a^2*b^3 + 38*B*a*b^4 - 25*A*b^5)*sin(d*x + c)^2 + (5*A*a^5 - 16*A*a^3*b^2 + 6*B*a^2*b^3 + 11*A*a*b^4 - 6*B*b^5)*sin(d*x + c))/(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6 + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*sin(d*x + c)^5 + (a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sin(d*x + c)^4 - 2*(a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*sin(d*x + c)^3 - 2*(a^7 - 3*a^5*b^2 + 3*a^3*b^4 - a*b^6)*sin(d*x + c)^2 + (a^6*b - 3*a^4*b^3 + 3*a^2*b^5 - b^7)*sin(d*x + c)))/d","A",0
1559,1,1083,0,0.398066," ","integrate(sec(d*x+c)^7*(A+B*sin(d*x+c))/(a+b*sin(d*x+c))^2,x, algorithm=""maxima"")","-\frac{\frac{96 \, {\left(7 \, B a^{2} b^{6} - 8 \, A a b^{7} + B b^{8}\right)} \log\left(b \sin\left(d x + c\right) + a\right)}{a^{10} - 5 \, a^{8} b^{2} + 10 \, a^{6} b^{4} - 10 \, a^{4} b^{6} + 5 \, a^{2} b^{8} - b^{10}} - \frac{3 \, {\left(5 \, A a^{3} - {\left(25 \, A - 2 \, B\right)} a^{2} b + {\left(47 \, A - 10 \, B\right)} a b^{2} - {\left(35 \, A - 16 \, B\right)} b^{3}\right)} \log\left(\sin\left(d x + c\right) + 1\right)}{a^{5} - 5 \, a^{4} b + 10 \, a^{3} b^{2} - 10 \, a^{2} b^{3} + 5 \, a b^{4} - b^{5}} + \frac{3 \, {\left(5 \, A a^{3} + {\left(25 \, A + 2 \, B\right)} a^{2} b + {\left(47 \, A + 10 \, B\right)} a b^{2} + {\left(35 \, A + 16 \, B\right)} b^{3}\right)} \log\left(\sin\left(d x + c\right) - 1\right)}{a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}} - \frac{2 \, {\left(8 \, B a^{7} - 16 \, A a^{6} b - 44 \, B a^{5} b^{2} + 80 \, A a^{4} b^{3} + 136 \, B a^{3} b^{4} - 208 \, A a^{2} b^{5} + 92 \, B a b^{6} - 48 \, A b^{7} + 3 \, {\left(5 \, A a^{6} b + 2 \, B a^{5} b^{2} - 23 \, A a^{4} b^{3} - 12 \, B a^{3} b^{4} + 47 \, A a^{2} b^{5} - 54 \, B a b^{6} + 35 \, A b^{7}\right)} \sin\left(d x + c\right)^{6} + 3 \, {\left(5 \, A a^{7} + 2 \, B a^{6} b - 23 \, A a^{5} b^{2} - 12 \, B a^{4} b^{3} + 47 \, A a^{3} b^{4} + 2 \, B a^{2} b^{5} - 29 \, A a b^{6} + 8 \, B b^{7}\right)} \sin\left(d x + c\right)^{5} - 8 \, {\left(5 \, A a^{6} b + 2 \, B a^{5} b^{2} - 23 \, A a^{4} b^{3} - 19 \, B a^{3} b^{4} + 55 \, A a^{2} b^{5} - 55 \, B a b^{6} + 35 \, A b^{7}\right)} \sin\left(d x + c\right)^{4} - 4 \, {\left(10 \, A a^{7} + 4 \, B a^{6} b - 46 \, A a^{5} b^{2} - 17 \, B a^{4} b^{3} + 86 \, A a^{3} b^{4} - 2 \, B a^{2} b^{5} - 50 \, A a b^{6} + 15 \, B b^{7}\right)} \sin\left(d x + c\right)^{3} + 3 \, {\left(11 \, A a^{6} b + 10 \, B a^{5} b^{2} - 57 \, A a^{4} b^{3} - 76 \, B a^{3} b^{4} + 161 \, A a^{2} b^{5} - 126 \, B a b^{6} + 77 \, A b^{7}\right)} \sin\left(d x + c\right)^{2} + {\left(33 \, A a^{7} + 2 \, B a^{6} b - 139 \, A a^{5} b^{2} - 8 \, B a^{4} b^{3} + 227 \, A a^{3} b^{4} - 38 \, B a^{2} b^{5} - 121 \, A a b^{6} + 44 \, B b^{7}\right)} \sin\left(d x + c\right)\right)}}{a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8} - {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)^{7} - {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} \sin\left(d x + c\right)^{6} + 3 \, {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)^{5} + 3 \, {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} \sin\left(d x + c\right)^{4} - 3 \, {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)^{3} - 3 \, {\left(a^{9} - 4 \, a^{7} b^{2} + 6 \, a^{5} b^{4} - 4 \, a^{3} b^{6} + a b^{8}\right)} \sin\left(d x + c\right)^{2} + {\left(a^{8} b - 4 \, a^{6} b^{3} + 6 \, a^{4} b^{5} - 4 \, a^{2} b^{7} + b^{9}\right)} \sin\left(d x + c\right)}}{96 \, d}"," ",0,"-1/96*(96*(7*B*a^2*b^6 - 8*A*a*b^7 + B*b^8)*log(b*sin(d*x + c) + a)/(a^10 - 5*a^8*b^2 + 10*a^6*b^4 - 10*a^4*b^6 + 5*a^2*b^8 - b^10) - 3*(5*A*a^3 - (25*A - 2*B)*a^2*b + (47*A - 10*B)*a*b^2 - (35*A - 16*B)*b^3)*log(sin(d*x + c) + 1)/(a^5 - 5*a^4*b + 10*a^3*b^2 - 10*a^2*b^3 + 5*a*b^4 - b^5) + 3*(5*A*a^3 + (25*A + 2*B)*a^2*b + (47*A + 10*B)*a*b^2 + (35*A + 16*B)*b^3)*log(sin(d*x + c) - 1)/(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5) - 2*(8*B*a^7 - 16*A*a^6*b - 44*B*a^5*b^2 + 80*A*a^4*b^3 + 136*B*a^3*b^4 - 208*A*a^2*b^5 + 92*B*a*b^6 - 48*A*b^7 + 3*(5*A*a^6*b + 2*B*a^5*b^2 - 23*A*a^4*b^3 - 12*B*a^3*b^4 + 47*A*a^2*b^5 - 54*B*a*b^6 + 35*A*b^7)*sin(d*x + c)^6 + 3*(5*A*a^7 + 2*B*a^6*b - 23*A*a^5*b^2 - 12*B*a^4*b^3 + 47*A*a^3*b^4 + 2*B*a^2*b^5 - 29*A*a*b^6 + 8*B*b^7)*sin(d*x + c)^5 - 8*(5*A*a^6*b + 2*B*a^5*b^2 - 23*A*a^4*b^3 - 19*B*a^3*b^4 + 55*A*a^2*b^5 - 55*B*a*b^6 + 35*A*b^7)*sin(d*x + c)^4 - 4*(10*A*a^7 + 4*B*a^6*b - 46*A*a^5*b^2 - 17*B*a^4*b^3 + 86*A*a^3*b^4 - 2*B*a^2*b^5 - 50*A*a*b^6 + 15*B*b^7)*sin(d*x + c)^3 + 3*(11*A*a^6*b + 10*B*a^5*b^2 - 57*A*a^4*b^3 - 76*B*a^3*b^4 + 161*A*a^2*b^5 - 126*B*a*b^6 + 77*A*b^7)*sin(d*x + c)^2 + (33*A*a^7 + 2*B*a^6*b - 139*A*a^5*b^2 - 8*B*a^4*b^3 + 227*A*a^3*b^4 - 38*B*a^2*b^5 - 121*A*a*b^6 + 44*B*b^7)*sin(d*x + c))/(a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8 - (a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*sin(d*x + c)^7 - (a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*sin(d*x + c)^6 + 3*(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*sin(d*x + c)^5 + 3*(a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*sin(d*x + c)^4 - 3*(a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*sin(d*x + c)^3 - 3*(a^9 - 4*a^7*b^2 + 6*a^5*b^4 - 4*a^3*b^6 + a*b^8)*sin(d*x + c)^2 + (a^8*b - 4*a^6*b^3 + 6*a^4*b^5 - 4*a^2*b^7 + b^9)*sin(d*x + c)))/d","B",0
1560,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^(-1-m)*(a+b*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""maxima"")","\int {\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}\,{d x}"," ",0,"integrate((B*sin(f*x + e) + A)*(g*cos(f*x + e))^(-m - 1)*(b*sin(f*x + e) + a)^m, x)","F",0
1561,0,0,0,0.000000," ","integrate((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \cos\left(f x + e\right)\right)^{p}}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((g*cos(f*x + e))^p/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)), x)","F",0
1562,-1,0,0,0.000000," ","integrate((g*cos(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""maxima"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
1563,0,0,0,0.000000," ","integrate((g*sec(f*x+e))^p/(a+b*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\left(g \sec\left(f x + e\right)\right)^{p}}{{\left(b \sin\left(f x + e\right) + a\right)} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate((g*sec(f*x + e))^p/((b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)), x)","F",0
