1,1,147,0,0.349795," ","integrate(sin(f*x+e)^3*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{64 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} c + 320 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c - 5 \, {\left(4 \, \sin\left(2 \, f x + 2 \, e\right)^{3} + 60 \, f x + 60 \, e + 9 \, \sin\left(4 \, f x + 4 \, e\right) - 48 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c + 30 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c}{960 \, f}"," ",0,"1/960*(64*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2*c + 320*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c - 5*(4*sin(2*f*x + 2*e)^3 + 60*f*x + 60*e + 9*sin(4*f*x + 4*e) - 48*sin(2*f*x + 2*e))*a^2*c + 30*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c)/f","A",0
2,1,123,0,0.335964," ","integrate(sin(f*x+e)^2*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{32 \, {\left(3 \, \cos\left(f x + e\right)^{5} - 10 \, \cos\left(f x + e\right)^{3} + 15 \, \cos\left(f x + e\right)\right)} a^{2} c + 160 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c - 15 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c + 120 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c}{480 \, f}"," ",0,"1/480*(32*(3*cos(f*x + e)^5 - 10*cos(f*x + e)^3 + 15*cos(f*x + e))*a^2*c + 160*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c - 15*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c + 120*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c)/f","A",0
3,1,100,0,0.329232," ","integrate(sin(f*x+e)*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{32 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c + 3 \, {\left(12 \, f x + 12 \, e + \sin\left(4 \, f x + 4 \, e\right) - 8 \, \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c - 24 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c + 96 \, a^{2} c \cos\left(f x + e\right)}{96 \, f}"," ",0,"-1/96*(32*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c + 3*(12*f*x + 12*e + sin(4*f*x + 4*e) - 8*sin(2*f*x + 2*e))*a^2*c - 24*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c + 96*a^2*c*cos(f*x + e))/f","A",0
4,1,77,0,0.339242," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{4 \, {\left(\cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)\right)} a^{2} c + 3 \, {\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c - 12 \, {\left(f x + e\right)} a^{2} c + 12 \, a^{2} c \cos\left(f x + e\right)}{12 \, f}"," ",0,"-1/12*(4*(cos(f*x + e)^3 - 3*cos(f*x + e))*a^2*c + 3*(2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c - 12*(f*x + e)*a^2*c + 12*a^2*c*cos(f*x + e))/f","A",0
5,1,73,0,0.352746," ","integrate(csc(f*x+e)*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{{\left(2 \, f x + 2 \, e - \sin\left(2 \, f x + 2 \, e\right)\right)} a^{2} c - 4 \, {\left(f x + e\right)} a^{2} c - 4 \, a^{2} c \cos\left(f x + e\right) + 4 \, a^{2} c \log\left(\cot\left(f x + e\right) + \csc\left(f x + e\right)\right)}{4 \, f}"," ",0,"-1/4*((2*f*x + 2*e - sin(2*f*x + 2*e))*a^2*c - 4*(f*x + e)*a^2*c - 4*a^2*c*cos(f*x + e) + 4*a^2*c*log(cot(f*x + e) + csc(f*x + e)))/f","A",0
6,1,69,0,0.338134," ","integrate(csc(f*x+e)^2*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{2 \, {\left(f x + e\right)} a^{2} c + a^{2} c {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 2 \, a^{2} c \cos\left(f x + e\right) + \frac{2 \, a^{2} c}{\tan\left(f x + e\right)}}{2 \, f}"," ",0,"-1/2*(2*(f*x + e)*a^2*c + a^2*c*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) - 2*a^2*c*cos(f*x + e) + 2*a^2*c/tan(f*x + e))/f","A",0
7,1,105,0,0.368154," ","integrate(csc(f*x+e)^3*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\frac{4 \, {\left(f x + e\right)} a^{2} c - a^{2} c {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 2 \, a^{2} c {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} + \frac{4 \, a^{2} c}{\tan\left(f x + e\right)}}{4 \, f}"," ",0,"-1/4*(4*(f*x + e)*a^2*c - a^2*c*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) - 2*a^2*c*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) + 4*a^2*c/tan(f*x + e))/f","A",0
8,1,120,0,0.359708," ","integrate(csc(f*x+e)^4*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, a^{2} c {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} + 6 \, a^{2} c {\left(\log\left(\cos\left(f x + e\right) + 1\right) - \log\left(\cos\left(f x + e\right) - 1\right)\right)} + \frac{12 \, a^{2} c}{\tan\left(f x + e\right)} - \frac{4 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a^{2} c}{\tan\left(f x + e\right)^{3}}}{12 \, f}"," ",0,"1/12*(3*a^2*c*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) + 6*a^2*c*(log(cos(f*x + e) + 1) - log(cos(f*x + e) - 1)) + 12*a^2*c/tan(f*x + e) - 4*(3*tan(f*x + e)^2 + 1)*a^2*c/tan(f*x + e)^3)/f","B",0
9,1,165,0,0.362204," ","integrate(csc(f*x+e)^5*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{3 \, a^{2} c {\left(\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)}}{\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\cos\left(f x + e\right) + 1\right) + 3 \, \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 12 \, a^{2} c {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} + \frac{48 \, a^{2} c}{\tan\left(f x + e\right)} - \frac{16 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a^{2} c}{\tan\left(f x + e\right)^{3}}}{48 \, f}"," ",0,"1/48*(3*a^2*c*(2*(3*cos(f*x + e)^3 - 5*cos(f*x + e))/(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1) - 3*log(cos(f*x + e) + 1) + 3*log(cos(f*x + e) - 1)) - 12*a^2*c*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) + 48*a^2*c/tan(f*x + e) - 16*(3*tan(f*x + e)^2 + 1)*a^2*c/tan(f*x + e)^3)/f","B",0
10,1,187,0,0.360092," ","integrate(csc(f*x+e)^6*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{15 \, a^{2} c {\left(\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)}}{\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\cos\left(f x + e\right) + 1\right) + 3 \, \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 60 \, a^{2} c {\left(\frac{2 \, \cos\left(f x + e\right)}{\cos\left(f x + e\right)^{2} - 1} - \log\left(\cos\left(f x + e\right) + 1\right) + \log\left(\cos\left(f x + e\right) - 1\right)\right)} + \frac{80 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a^{2} c}{\tan\left(f x + e\right)^{3}} - \frac{16 \, {\left(15 \, \tan\left(f x + e\right)^{4} + 10 \, \tan\left(f x + e\right)^{2} + 3\right)} a^{2} c}{\tan\left(f x + e\right)^{5}}}{240 \, f}"," ",0,"1/240*(15*a^2*c*(2*(3*cos(f*x + e)^3 - 5*cos(f*x + e))/(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1) - 3*log(cos(f*x + e) + 1) + 3*log(cos(f*x + e) - 1)) - 60*a^2*c*(2*cos(f*x + e)/(cos(f*x + e)^2 - 1) - log(cos(f*x + e) + 1) + log(cos(f*x + e) - 1)) + 80*(3*tan(f*x + e)^2 + 1)*a^2*c/tan(f*x + e)^3 - 16*(15*tan(f*x + e)^4 + 10*tan(f*x + e)^2 + 3)*a^2*c/tan(f*x + e)^5)/f","A",0
11,1,232,0,0.357248," ","integrate(csc(f*x+e)^7*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""maxima"")","\frac{5 \, a^{2} c {\left(\frac{2 \, {\left(15 \, \cos\left(f x + e\right)^{5} - 40 \, \cos\left(f x + e\right)^{3} + 33 \, \cos\left(f x + e\right)\right)}}{\cos\left(f x + e\right)^{6} - 3 \, \cos\left(f x + e\right)^{4} + 3 \, \cos\left(f x + e\right)^{2} - 1} - 15 \, \log\left(\cos\left(f x + e\right) + 1\right) + 15 \, \log\left(\cos\left(f x + e\right) - 1\right)\right)} - 30 \, a^{2} c {\left(\frac{2 \, {\left(3 \, \cos\left(f x + e\right)^{3} - 5 \, \cos\left(f x + e\right)\right)}}{\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1} - 3 \, \log\left(\cos\left(f x + e\right) + 1\right) + 3 \, \log\left(\cos\left(f x + e\right) - 1\right)\right)} + \frac{160 \, {\left(3 \, \tan\left(f x + e\right)^{2} + 1\right)} a^{2} c}{\tan\left(f x + e\right)^{3}} - \frac{32 \, {\left(15 \, \tan\left(f x + e\right)^{4} + 10 \, \tan\left(f x + e\right)^{2} + 3\right)} a^{2} c}{\tan\left(f x + e\right)^{5}}}{480 \, f}"," ",0,"1/480*(5*a^2*c*(2*(15*cos(f*x + e)^5 - 40*cos(f*x + e)^3 + 33*cos(f*x + e))/(cos(f*x + e)^6 - 3*cos(f*x + e)^4 + 3*cos(f*x + e)^2 - 1) - 15*log(cos(f*x + e) + 1) + 15*log(cos(f*x + e) - 1)) - 30*a^2*c*(2*(3*cos(f*x + e)^3 - 5*cos(f*x + e))/(cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1) - 3*log(cos(f*x + e) + 1) + 3*log(cos(f*x + e) - 1)) + 160*(3*tan(f*x + e)^2 + 1)*a^2*c/tan(f*x + e)^3 - 32*(15*tan(f*x + e)^4 + 10*tan(f*x + e)^2 + 3)*a^2*c/tan(f*x + e)^5)/f","A",0
12,0,0,0,0.000000," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2)*(c-c*sin(d*x+c)),x, algorithm=""maxima"")","-\int {\left(a \sin\left(d x + c\right) + a\right)}^{\frac{3}{2}} {\left(c \sin\left(d x + c\right) - c\right)} \sin\left(d x + c\right)^{2}\,{d x}"," ",0,"-integrate((a*sin(d*x + c) + a)^(3/2)*(c*sin(d*x + c) - c)*sin(d*x + c)^2, x)","F",0
13,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{{\left(c \sin\left(f x + e\right) - c\right)} \sin\left(f x + e\right)}\,{d x}"," ",0,"-integrate(sqrt(a*sin(f*x + e) + a)/((c*sin(f*x + e) - c)*sin(f*x + e)), x)","F",0
14,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) - c\right)} \sin\left(f x + e\right)}\,{d x}"," ",0,"-integrate(1/(sqrt(a*sin(f*x + e) + a)*(c*sin(f*x + e) - c)*sin(f*x + e)), x)","F",0
15,0,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e)),x, algorithm=""maxima"")","-\int \frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{c \sin\left(f x + e\right) - c}\,{d x}"," ",0,"-integrate(sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(c*sin(f*x + e) - c), x)","F",0
16,1,309,0,0.486045," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\frac{4 \, {\left({\left(\frac{3 \, \sqrt{2} \sqrt{a} \sqrt{g} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{\sqrt{2} \sqrt{a} \sqrt{g} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{2 \, {\left(\frac{3 \, \sqrt{2} \sqrt{a} \sqrt{g} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + \frac{\sqrt{2} \sqrt{a} \sqrt{g} \sin\left(f x + e\right)^{2}}{{\left(\cos\left(f x + e\right) + 1\right)}^{2}}\right)}}{\sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}\right)}}{c g - \frac{c g \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{2 \, \sqrt{2} \sqrt{a} \left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)^{\frac{3}{2}} + \frac{3 \, \sqrt{2} \sqrt{a} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}{c \sqrt{g}} - \frac{2 \, \sqrt{2} \sqrt{a} \left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)^{\frac{3}{2}} - \frac{3 \, \sqrt{2} \sqrt{a} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}{c \sqrt{g}}}{12 \, f}"," ",0,"-1/12*(4*((3*sqrt(2)*sqrt(a)*sqrt(g)*sin(f*x + e)/(cos(f*x + e) + 1) - sqrt(2)*sqrt(a)*sqrt(g)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1)) - 2*(3*sqrt(2)*sqrt(a)*sqrt(g)*sin(f*x + e)/(cos(f*x + e) + 1) + sqrt(2)*sqrt(a)*sqrt(g)*sin(f*x + e)^2/(cos(f*x + e) + 1)^2)/sqrt(sin(f*x + e)/(cos(f*x + e) + 1)))/(c*g - c*g*sin(f*x + e)/(cos(f*x + e) + 1)) - (2*sqrt(2)*sqrt(a)*(sin(f*x + e)/(cos(f*x + e) + 1))^(3/2) + 3*sqrt(2)*sqrt(a)*sin(f*x + e)/(cos(f*x + e) + 1))/(c*sqrt(g)) - (2*sqrt(2)*sqrt(a)*(sin(f*x + e)/(cos(f*x + e) + 1))^(3/2) - 3*sqrt(2)*sqrt(a)*sin(f*x + e)/(cos(f*x + e) + 1))/(c*sqrt(g)))/f","B",0
17,1,270,0,0.533073," ","integrate((g*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\frac{4 \, \sqrt{2} \sqrt{g} \left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)^{\frac{3}{2}}}{\sqrt{a} c + \frac{\sqrt{a} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - \frac{{\left(\sqrt{a} c + \frac{\sqrt{a} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \frac{2 \, \sqrt{2} \sqrt{g} \arctan\left(\sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}\right)}{\sqrt{a} c} + \frac{\sqrt{2} \sqrt{g} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} + \sqrt{2} \sqrt{g}}{\sqrt{a} c + \frac{\sqrt{a} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} + \frac{\sqrt{2} \sqrt{g} \sqrt{\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}} - \sqrt{2} \sqrt{g}}{\sqrt{a} c + \frac{\sqrt{a} c \sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}}}{2 \, f}"," ",0,"1/2*(4*sqrt(2)*sqrt(g)*(sin(f*x + e)/(cos(f*x + e) + 1))^(3/2)/(sqrt(a)*c + sqrt(a)*c*sin(f*x + e)/(cos(f*x + e) + 1) - (sqrt(a)*c + sqrt(a)*c*sin(f*x + e)/(cos(f*x + e) + 1))*sin(f*x + e)/(cos(f*x + e) + 1)) - 2*sqrt(2)*sqrt(g)*arctan(sqrt(sin(f*x + e)/(cos(f*x + e) + 1)))/(sqrt(a)*c) + (sqrt(2)*sqrt(g)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1)) + sqrt(2)*sqrt(g))/(sqrt(a)*c + sqrt(a)*c*sin(f*x + e)/(cos(f*x + e) + 1)) + (sqrt(2)*sqrt(g)*sqrt(sin(f*x + e)/(cos(f*x + e) + 1)) - sqrt(2)*sqrt(g))/(sqrt(a)*c + sqrt(a)*c*sin(f*x + e)/(cos(f*x + e) + 1)))/f","B",0
18,0,0,0,0.000000," ","integrate(1/(c-c*sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) - c\right)} \sqrt{g \sin\left(f x + e\right)}}\,{d x}"," ",0,"-integrate(1/(sqrt(a*sin(f*x + e) + a)*(c*sin(f*x + e) - c)*sqrt(g*sin(f*x + e))), x)","F",0
19,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2)/sin(f*x+e),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{\sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/sin(f*x + e), x)","F",0
20,1,59,0,0.428515," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} - 1\right)}{\sqrt{c}} - \frac{\sqrt{a} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{\sqrt{c}}}{f}"," ",0,"(2*sqrt(a)*log(sin(f*x + e)/(cos(f*x + e) + 1) - 1)/sqrt(c) - sqrt(a)*log(sin(f*x + e)/(cos(f*x + e) + 1))/sqrt(c))/f","A",0
21,1,59,0,0.422382," ","integrate((c-c*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\frac{\frac{2 \, \sqrt{c} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1} + 1\right)}{\sqrt{a}} - \frac{\sqrt{c} \log\left(\frac{\sin\left(f x + e\right)}{\cos\left(f x + e\right) + 1}\right)}{\sqrt{a}}}{f}"," ",0,"(2*sqrt(c)*log(sin(f*x + e)/(cos(f*x + e) + 1) + 1)/sqrt(a) - sqrt(c)*log(sin(f*x + e)/(cos(f*x + e) + 1))/sqrt(a))/f","A",0
22,1,190,0,0.611720," ","integrate(1/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","-\frac{\left(-1\right)^{4 \, \cos\left(2 \, f x + 2 \, e\right)} \cosh\left(4 \, \pi \sin\left(2 \, f x + 2 \, e\right)\right) \log\left(\frac{16 \, {\left(\cos\left(2 \, f x + 2 \, e\right)^{2} + \sin\left(2 \, f x + 2 \, e\right)^{2} + 2 \, \cos\left(2 \, f x + 2 \, e\right) + 1\right)}}{a c {\left| e^{\left(2 i \, f x + 2 i \, e\right)} - 1 \right|}^{2}}\right) - 2 i \, \left(-1\right)^{4 \, \cos\left(2 \, f x + 2 \, e\right)} \arctan\left(\frac{4 \, \sin\left(2 \, f x + 2 \, e\right)}{\sqrt{a} \sqrt{c} {\left| e^{\left(2 i \, f x + 2 i \, e\right)} - 1 \right|}}, \frac{4 \, {\left(\cos\left(2 \, f x + 2 \, e\right) + 1\right)}}{\sqrt{a} \sqrt{c} {\left| e^{\left(2 i \, f x + 2 i \, e\right)} - 1 \right|}}\right) \sinh\left(4 \, \pi \sin\left(2 \, f x + 2 \, e\right)\right)}{2 \, \sqrt{a} \sqrt{c} f}"," ",0,"-1/2*((-1)^(4*cos(2*f*x + 2*e))*cosh(4*pi*sin(2*f*x + 2*e))*log(16*(cos(2*f*x + 2*e)^2 + sin(2*f*x + 2*e)^2 + 2*cos(2*f*x + 2*e) + 1)/(a*c*abs(e^(2*I*f*x + 2*I*e) - 1)^2)) - 2*I*(-1)^(4*cos(2*f*x + 2*e))*arctan2(4*sin(2*f*x + 2*e)/(sqrt(a)*sqrt(c)*abs(e^(2*I*f*x + 2*I*e) - 1)), 4*(cos(2*f*x + 2*e) + 1)/(sqrt(a)*sqrt(c)*abs(e^(2*I*f*x + 2*I*e) - 1)))*sinh(4*pi*sin(2*f*x + 2*e)))/(sqrt(a)*sqrt(c)*f)","C",0
23,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/((d*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
24,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
25,0,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(d*sin(f*x + e) + c), x)","F",0
26,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)} \sqrt{g \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/((d*sin(f*x + e) + c)*sqrt(g*sin(f*x + e))), x)","F",0
27,0,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{g \sin\left(f x + e\right)}}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sqrt(g*sin(f*x + e))/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)), x)","F",0
28,0,0,0,0.000000," ","integrate(1/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)} \sqrt{g \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)*sqrt(g*sin(f*x + e))), x)","F",0
29,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+c*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{{\left(c \sin\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/((c*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
30,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(c+c*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*(c*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
31,0,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)*(a+b*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{c \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(c*sin(f*x + e) + c), x)","F",0
32,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{{\left(c \sin\left(f x + e\right) + c\right)} \sqrt{g \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/((c*sin(f*x + e) + c)*sqrt(g*sin(f*x + e))), x)","F",0
33,0,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{g \sin\left(f x + e\right)}}{\sqrt{b \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sqrt(g*sin(f*x + e))/(sqrt(b*sin(f*x + e) + a)*(c*sin(f*x + e) + c)), x)","F",0
34,0,0,0,0.000000," ","integrate(1/(c+c*sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)} \sqrt{g \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*(c*sin(f*x + e) + c)*sqrt(g*sin(f*x + e))), x)","F",0
35,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{\sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/sin(f*x + e), x)","F",0
36,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{a \sin\left(f x + e\right) + a}}{\sqrt{d \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(a*sin(f*x + e) + a)/(sqrt(d*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
37,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/(sqrt(a*sin(f*x + e) + a)*sin(f*x + e)), x)","F",0
38,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(1/(sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
39,-2,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e)),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*d^2-4*c^2>0)', see `assume?` for more details)Is 4*d^2-4*c^2 positive or negative?","F(-2)",0
40,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c}}{{\left(b \sin\left(f x + e\right) + a\right)} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)/((b*sin(f*x + e) + a)*sin(f*x + e)), x)","F",0
41,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(1/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
42,0,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)*(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{d \sin\left(f x + e\right) + c}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(d*sin(f*x + e) + c), x)","F",0
43,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{{\left(d \sin\left(f x + e\right) + c\right)} \sqrt{g \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/((d*sin(f*x + e) + c)*sqrt(g*sin(f*x + e))), x)","F",0
44,0,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{g \sin\left(f x + e\right)}}{\sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}}\,{d x}"," ",0,"integrate(sqrt(g*sin(f*x + e))/(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)), x)","F",0
45,0,0,0,0.000000," ","integrate(1/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)} \sqrt{g \sin\left(f x + e\right)}}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*(d*sin(f*x + e) + c)*sqrt(g*sin(f*x + e))), x)","F",0
46,0,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)*(g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""maxima"")","\int \frac{\sqrt{d \sin\left(f x + e\right) + c} \sqrt{g \sin\left(f x + e\right)}}{b \sin\left(f x + e\right) + a}\,{d x}"," ",0,"integrate(sqrt(d*sin(f*x + e) + c)*sqrt(g*sin(f*x + e))/(b*sin(f*x + e) + a), x)","F",0
47,0,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{g \sin\left(f x + e\right)}}{{\left(b \sin\left(f x + e\right) + a\right)} \sqrt{d \sin\left(f x + e\right) + c}}\,{d x}"," ",0,"integrate(sqrt(g*sin(f*x + e))/((b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)), x)","F",0
48,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{\sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/sin(f*x + e), x)","F",0
49,0,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{\sqrt{b \sin\left(f x + e\right) + a}}{\sqrt{d \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(sqrt(b*sin(f*x + e) + a)/(sqrt(d*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
50,0,0,0,0.000000," ","integrate(1/sin(f*x+e)/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""maxima"")","\int \frac{1}{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}\,{d x}"," ",0,"integrate(1/(sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sin(f*x + e)), x)","F",0
51,0,0,0,0.000000," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))^p*(c-c*sin(f*x+e))^n,x, algorithm=""maxima"")","\int {\left(B \sin\left(f x + e\right) + A\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((B*sin(f*x + e) + A)^p*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
