1,1,91,0,0.909438," ","integrate(sin(f*x+e)^3*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{48 \, a^{2} c \cos\left(f x + e\right)^{5} - 80 \, a^{2} c \cos\left(f x + e\right)^{3} + 15 \, a^{2} c f x + 5 \, {\left(8 \, a^{2} c \cos\left(f x + e\right)^{5} - 14 \, a^{2} c \cos\left(f x + e\right)^{3} + 3 \, a^{2} c \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f}"," ",0,"1/240*(48*a^2*c*cos(f*x + e)^5 - 80*a^2*c*cos(f*x + e)^3 + 15*a^2*c*f*x + 5*(8*a^2*c*cos(f*x + e)^5 - 14*a^2*c*cos(f*x + e)^3 + 3*a^2*c*cos(f*x + e))*sin(f*x + e))/f","A",0
2,1,77,0,0.934609," ","integrate(sin(f*x+e)^2*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{24 \, a^{2} c \cos\left(f x + e\right)^{5} - 40 \, a^{2} c \cos\left(f x + e\right)^{3} + 15 \, a^{2} c f x - 15 \, {\left(2 \, a^{2} c \cos\left(f x + e\right)^{3} - a^{2} c \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{120 \, f}"," ",0,"1/120*(24*a^2*c*cos(f*x + e)^5 - 40*a^2*c*cos(f*x + e)^3 + 15*a^2*c*f*x - 15*(2*a^2*c*cos(f*x + e)^3 - a^2*c*cos(f*x + e))*sin(f*x + e))/f","A",0
3,1,63,0,0.663557," ","integrate(sin(f*x+e)*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{8 \, a^{2} c \cos\left(f x + e\right)^{3} - 3 \, a^{2} c f x + 3 \, {\left(2 \, a^{2} c \cos\left(f x + e\right)^{3} - a^{2} c \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, f}"," ",0,"-1/24*(8*a^2*c*cos(f*x + e)^3 - 3*a^2*c*f*x + 3*(2*a^2*c*cos(f*x + e)^3 - a^2*c*cos(f*x + e))*sin(f*x + e))/f","A",0
4,1,46,0,0.831911," ","integrate((a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, a^{2} c \cos\left(f x + e\right)^{3} - 3 \, a^{2} c f x - 3 \, a^{2} c \cos\left(f x + e\right) \sin\left(f x + e\right)}{6 \, f}"," ",0,"-1/6*(2*a^2*c*cos(f*x + e)^3 - 3*a^2*c*f*x - 3*a^2*c*cos(f*x + e)*sin(f*x + e))/f","A",0
5,1,75,0,1.394192," ","integrate(csc(f*x+e)*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{a^{2} c f x + a^{2} c \cos\left(f x + e\right) \sin\left(f x + e\right) + 2 \, a^{2} c \cos\left(f x + e\right) - a^{2} c \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) + a^{2} c \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right)}{2 \, f}"," ",0,"1/2*(a^2*c*f*x + a^2*c*cos(f*x + e)*sin(f*x + e) + 2*a^2*c*cos(f*x + e) - a^2*c*log(1/2*cos(f*x + e) + 1/2) + a^2*c*log(-1/2*cos(f*x + e) + 1/2))/f","A",0
6,1,99,0,1.011571," ","integrate(csc(f*x+e)^2*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{a^{2} c \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) - a^{2} c \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) + 2 \, a^{2} c \cos\left(f x + e\right) + 2 \, {\left(a^{2} c f x - a^{2} c \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, f \sin\left(f x + e\right)}"," ",0,"-1/2*(a^2*c*log(1/2*cos(f*x + e) + 1/2)*sin(f*x + e) - a^2*c*log(-1/2*cos(f*x + e) + 1/2)*sin(f*x + e) + 2*a^2*c*cos(f*x + e) + 2*(a^2*c*f*x - a^2*c*cos(f*x + e))*sin(f*x + e))/(f*sin(f*x + e))","A",0
7,1,138,0,0.846705," ","integrate(csc(f*x+e)^3*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{4 \, a^{2} c f x \cos\left(f x + e\right)^{2} - 4 \, a^{2} c f x - 4 \, a^{2} c \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{2} c \cos\left(f x + e\right) - {\left(a^{2} c \cos\left(f x + e\right)^{2} - a^{2} c\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) + {\left(a^{2} c \cos\left(f x + e\right)^{2} - a^{2} c\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right)}{4 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)}}"," ",0,"-1/4*(4*a^2*c*f*x*cos(f*x + e)^2 - 4*a^2*c*f*x - 4*a^2*c*cos(f*x + e)*sin(f*x + e) - 2*a^2*c*cos(f*x + e) - (a^2*c*cos(f*x + e)^2 - a^2*c)*log(1/2*cos(f*x + e) + 1/2) + (a^2*c*cos(f*x + e)^2 - a^2*c)*log(-1/2*cos(f*x + e) + 1/2))/(f*cos(f*x + e)^2 - f)","B",0
8,1,137,0,1.209828," ","integrate(csc(f*x+e)^4*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, a^{2} c \cos\left(f x + e\right)^{3} + 6 \, a^{2} c \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, {\left(a^{2} c \cos\left(f x + e\right)^{2} - a^{2} c\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) - 3 \, {\left(a^{2} c \cos\left(f x + e\right)^{2} - a^{2} c\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right)}{12 \, {\left(f \cos\left(f x + e\right)^{2} - f\right)} \sin\left(f x + e\right)}"," ",0,"1/12*(4*a^2*c*cos(f*x + e)^3 + 6*a^2*c*cos(f*x + e)*sin(f*x + e) + 3*(a^2*c*cos(f*x + e)^2 - a^2*c)*log(1/2*cos(f*x + e) + 1/2)*sin(f*x + e) - 3*(a^2*c*cos(f*x + e)^2 - a^2*c)*log(-1/2*cos(f*x + e) + 1/2)*sin(f*x + e))/((f*cos(f*x + e)^2 - f)*sin(f*x + e))","B",0
9,1,166,0,1.135311," ","integrate(csc(f*x+e)^5*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{16 \, a^{2} c \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + 6 \, a^{2} c \cos\left(f x + e\right)^{3} + 6 \, a^{2} c \cos\left(f x + e\right) - 3 \, {\left(a^{2} c \cos\left(f x + e\right)^{4} - 2 \, a^{2} c \cos\left(f x + e\right)^{2} + a^{2} c\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) + 3 \, {\left(a^{2} c \cos\left(f x + e\right)^{4} - 2 \, a^{2} c \cos\left(f x + e\right)^{2} + a^{2} c\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right)}{48 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)}}"," ",0,"-1/48*(16*a^2*c*cos(f*x + e)^3*sin(f*x + e) + 6*a^2*c*cos(f*x + e)^3 + 6*a^2*c*cos(f*x + e) - 3*(a^2*c*cos(f*x + e)^4 - 2*a^2*c*cos(f*x + e)^2 + a^2*c)*log(1/2*cos(f*x + e) + 1/2) + 3*(a^2*c*cos(f*x + e)^4 - 2*a^2*c*cos(f*x + e)^2 + a^2*c)*log(-1/2*cos(f*x + e) + 1/2))/(f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)","B",0
10,1,201,0,1.163560," ","integrate(csc(f*x+e)^6*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{32 \, a^{2} c \cos\left(f x + e\right)^{5} - 80 \, a^{2} c \cos\left(f x + e\right)^{3} + 15 \, {\left(a^{2} c \cos\left(f x + e\right)^{4} - 2 \, a^{2} c \cos\left(f x + e\right)^{2} + a^{2} c\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) - 15 \, {\left(a^{2} c \cos\left(f x + e\right)^{4} - 2 \, a^{2} c \cos\left(f x + e\right)^{2} + a^{2} c\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) \sin\left(f x + e\right) - 30 \, {\left(a^{2} c \cos\left(f x + e\right)^{3} + a^{2} c \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, {\left(f \cos\left(f x + e\right)^{4} - 2 \, f \cos\left(f x + e\right)^{2} + f\right)} \sin\left(f x + e\right)}"," ",0,"1/240*(32*a^2*c*cos(f*x + e)^5 - 80*a^2*c*cos(f*x + e)^3 + 15*(a^2*c*cos(f*x + e)^4 - 2*a^2*c*cos(f*x + e)^2 + a^2*c)*log(1/2*cos(f*x + e) + 1/2)*sin(f*x + e) - 15*(a^2*c*cos(f*x + e)^4 - 2*a^2*c*cos(f*x + e)^2 + a^2*c)*log(-1/2*cos(f*x + e) + 1/2)*sin(f*x + e) - 30*(a^2*c*cos(f*x + e)^3 + a^2*c*cos(f*x + e))*sin(f*x + e))/((f*cos(f*x + e)^4 - 2*f*cos(f*x + e)^2 + f)*sin(f*x + e))","B",0
11,1,240,0,0.879225," ","integrate(csc(f*x+e)^7*(a+a*sin(f*x+e))^2*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{30 \, a^{2} c \cos\left(f x + e\right)^{5} - 80 \, a^{2} c \cos\left(f x + e\right)^{3} - 30 \, a^{2} c \cos\left(f x + e\right) - 15 \, {\left(a^{2} c \cos\left(f x + e\right)^{6} - 3 \, a^{2} c \cos\left(f x + e\right)^{4} + 3 \, a^{2} c \cos\left(f x + e\right)^{2} - a^{2} c\right)} \log\left(\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) + 15 \, {\left(a^{2} c \cos\left(f x + e\right)^{6} - 3 \, a^{2} c \cos\left(f x + e\right)^{4} + 3 \, a^{2} c \cos\left(f x + e\right)^{2} - a^{2} c\right)} \log\left(-\frac{1}{2} \, \cos\left(f x + e\right) + \frac{1}{2}\right) + 32 \, {\left(2 \, a^{2} c \cos\left(f x + e\right)^{5} - 5 \, a^{2} c \cos\left(f x + e\right)^{3}\right)} \sin\left(f x + e\right)}{480 \, {\left(f \cos\left(f x + e\right)^{6} - 3 \, f \cos\left(f x + e\right)^{4} + 3 \, f \cos\left(f x + e\right)^{2} - f\right)}}"," ",0,"-1/480*(30*a^2*c*cos(f*x + e)^5 - 80*a^2*c*cos(f*x + e)^3 - 30*a^2*c*cos(f*x + e) - 15*(a^2*c*cos(f*x + e)^6 - 3*a^2*c*cos(f*x + e)^4 + 3*a^2*c*cos(f*x + e)^2 - a^2*c)*log(1/2*cos(f*x + e) + 1/2) + 15*(a^2*c*cos(f*x + e)^6 - 3*a^2*c*cos(f*x + e)^4 + 3*a^2*c*cos(f*x + e)^2 - a^2*c)*log(-1/2*cos(f*x + e) + 1/2) + 32*(2*a^2*c*cos(f*x + e)^5 - 5*a^2*c*cos(f*x + e)^3)*sin(f*x + e))/(f*cos(f*x + e)^6 - 3*f*cos(f*x + e)^4 + 3*f*cos(f*x + e)^2 - f)","B",0
12,1,155,0,0.863423," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^(3/2)*(c-c*sin(d*x+c)),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, a c \cos\left(d x + c\right)^{5} - a c \cos\left(d x + c\right)^{4} - 11 \, a c \cos\left(d x + c\right)^{3} + a c \cos\left(d x + c\right)^{2} - 4 \, a c \cos\left(d x + c\right) - 8 \, a c - {\left(7 \, a c \cos\left(d x + c\right)^{4} + 8 \, a c \cos\left(d x + c\right)^{3} - 3 \, a c \cos\left(d x + c\right)^{2} - 4 \, a c \cos\left(d x + c\right) - 8 \, a c\right)} \sin\left(d x + c\right)\right)} \sqrt{a \sin\left(d x + c\right) + a}}{63 \, {\left(d \cos\left(d x + c\right) + d \sin\left(d x + c\right) + d\right)}}"," ",0,"2/63*(7*a*c*cos(d*x + c)^5 - a*c*cos(d*x + c)^4 - 11*a*c*cos(d*x + c)^3 + a*c*cos(d*x + c)^2 - 4*a*c*cos(d*x + c) - 8*a*c - (7*a*c*cos(d*x + c)^4 + 8*a*c*cos(d*x + c)^3 - 3*a*c*cos(d*x + c)^2 - 4*a*c*cos(d*x + c) - 8*a*c)*sin(d*x + c))*sqrt(a*sin(d*x + c) + a)/(d*cos(d*x + c) + d*sin(d*x + c) + d)","A",0
13,1,202,0,0.891880," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{\sqrt{a} \cos\left(f x + e\right) \log\left(\frac{a \cos\left(f x + e\right)^{3} - 7 \, a \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right) + 3\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 3\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} - 9 \, a \cos\left(f x + e\right) + {\left(a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) - a\right)} \sin\left(f x + e\right) - a}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 1}\right) + 4 \, \sqrt{a \sin\left(f x + e\right) + a}}{2 \, c f \cos\left(f x + e\right)}"," ",0,"1/2*(sqrt(a)*cos(f*x + e)*log((a*cos(f*x + e)^3 - 7*a*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + (cos(f*x + e) + 3)*sin(f*x + e) - 2*cos(f*x + e) - 3)*sqrt(a*sin(f*x + e) + a)*sqrt(a) - 9*a*cos(f*x + e) + (a*cos(f*x + e)^2 + 8*a*cos(f*x + e) - a)*sin(f*x + e) - a)/(cos(f*x + e)^3 + cos(f*x + e)^2 + (cos(f*x + e)^2 - 1)*sin(f*x + e) - cos(f*x + e) - 1)) + 4*sqrt(a*sin(f*x + e) + a))/(c*f*cos(f*x + e))","B",0
14,1,328,0,0.981683," ","integrate(1/sin(f*x+e)/(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} \sqrt{a} \cos\left(f x + e\right) \log\left(-\frac{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) - 2\right)} \sin\left(f x + e\right) + \frac{2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(f x + e\right) + 2}{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2}\right) + 2 \, \sqrt{a} \cos\left(f x + e\right) \log\left(\frac{a \cos\left(f x + e\right)^{3} - 7 \, a \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right) + 3\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 3\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} - 9 \, a \cos\left(f x + e\right) + {\left(a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) - a\right)} \sin\left(f x + e\right) - a}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 1}\right) + 4 \, \sqrt{a \sin\left(f x + e\right) + a}}{4 \, a c f \cos\left(f x + e\right)}"," ",0,"1/4*(sqrt(2)*sqrt(a)*cos(f*x + e)*log(-(cos(f*x + e)^2 - (cos(f*x + e) - 2)*sin(f*x + e) + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*(cos(f*x + e) - sin(f*x + e) + 1)/sqrt(a) + 3*cos(f*x + e) + 2)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 2*sqrt(a)*cos(f*x + e)*log((a*cos(f*x + e)^3 - 7*a*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + (cos(f*x + e) + 3)*sin(f*x + e) - 2*cos(f*x + e) - 3)*sqrt(a*sin(f*x + e) + a)*sqrt(a) - 9*a*cos(f*x + e) + (a*cos(f*x + e)^2 + 8*a*cos(f*x + e) - a)*sin(f*x + e) - a)/(cos(f*x + e)^3 + cos(f*x + e)^2 + (cos(f*x + e)^2 - 1)*sin(f*x + e) - cos(f*x + e) - 1)) + 4*sqrt(a*sin(f*x + e) + a))/(a*c*f*cos(f*x + e))","B",0
15,1,442,0,1.419453," ","integrate((g*sin(f*x+e))^(1/2)*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-a g} \cos\left(f x + e\right) \log\left(\frac{128 \, a g \cos\left(f x + e\right)^{5} - 128 \, a g \cos\left(f x + e\right)^{4} - 416 \, a g \cos\left(f x + e\right)^{3} + 128 \, a g \cos\left(f x + e\right)^{2} + 289 \, a g \cos\left(f x + e\right) + 8 \, {\left(16 \, \cos\left(f x + e\right)^{4} - 24 \, \cos\left(f x + e\right)^{3} - 66 \, \cos\left(f x + e\right)^{2} + {\left(16 \, \cos\left(f x + e\right)^{3} + 40 \, \cos\left(f x + e\right)^{2} - 26 \, \cos\left(f x + e\right) - 51\right)} \sin\left(f x + e\right) + 25 \, \cos\left(f x + e\right) + 51\right)} \sqrt{-a g} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} + a g + {\left(128 \, a g \cos\left(f x + e\right)^{4} + 256 \, a g \cos\left(f x + e\right)^{3} - 160 \, a g \cos\left(f x + e\right)^{2} - 288 \, a g \cos\left(f x + e\right) + a g\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1}\right) + 8 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, c f \cos\left(f x + e\right)}, -\frac{\sqrt{a g} \arctan\left(\frac{\sqrt{a g} {\left(8 \, \cos\left(f x + e\right)^{2} + 8 \, \sin\left(f x + e\right) - 9\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, {\left(2 \, a g \cos\left(f x + e\right)^{3} + a g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a g \cos\left(f x + e\right)\right)}}\right) \cos\left(f x + e\right) - 4 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{2 \, c f \cos\left(f x + e\right)}\right]"," ",0,"[1/4*(sqrt(-a*g)*cos(f*x + e)*log((128*a*g*cos(f*x + e)^5 - 128*a*g*cos(f*x + e)^4 - 416*a*g*cos(f*x + e)^3 + 128*a*g*cos(f*x + e)^2 + 289*a*g*cos(f*x + e) + 8*(16*cos(f*x + e)^4 - 24*cos(f*x + e)^3 - 66*cos(f*x + e)^2 + (16*cos(f*x + e)^3 + 40*cos(f*x + e)^2 - 26*cos(f*x + e) - 51)*sin(f*x + e) + 25*cos(f*x + e) + 51)*sqrt(-a*g)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)) + a*g + (128*a*g*cos(f*x + e)^4 + 256*a*g*cos(f*x + e)^3 - 160*a*g*cos(f*x + e)^2 - 288*a*g*cos(f*x + e) + a*g)*sin(f*x + e))/(cos(f*x + e) + sin(f*x + e) + 1)) + 8*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)))/(c*f*cos(f*x + e)), -1/2*(sqrt(a*g)*arctan(1/4*sqrt(a*g)*(8*cos(f*x + e)^2 + 8*sin(f*x + e) - 9)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(2*a*g*cos(f*x + e)^3 + a*g*cos(f*x + e)*sin(f*x + e) - 2*a*g*cos(f*x + e)))*cos(f*x + e) - 4*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)))/(c*f*cos(f*x + e))]","A",0
16,1,41,0,0.861110," ","integrate((a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{c f g \cos\left(f x + e\right)}"," ",0,"2*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(c*f*g*cos(f*x + e))","A",0
17,1,385,0,0.938684," ","integrate((g*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} a \sqrt{-\frac{g}{a}} \cos\left(f x + e\right) \log\left(\frac{17 \, g \cos\left(f x + e\right)^{3} + 4 \, \sqrt{2} {\left(3 \, \cos\left(f x + e\right)^{2} + {\left(3 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 4\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{g}{a}} + 3 \, g \cos\left(f x + e\right)^{2} - 18 \, g \cos\left(f x + e\right) + {\left(17 \, g \cos\left(f x + e\right)^{2} + 14 \, g \cos\left(f x + e\right) - 4 \, g\right)} \sin\left(f x + e\right) - 4 \, g}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right) + 8 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{8 \, a c f \cos\left(f x + e\right)}, -\frac{\sqrt{2} a \sqrt{\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{g}{a}} {\left(3 \, \sin\left(f x + e\right) - 1\right)}}{4 \, g \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) \cos\left(f x + e\right) - 4 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, a c f \cos\left(f x + e\right)}\right]"," ",0,"[1/8*(sqrt(2)*a*sqrt(-g/a)*cos(f*x + e)*log((17*g*cos(f*x + e)^3 + 4*sqrt(2)*(3*cos(f*x + e)^2 + (3*cos(f*x + e) + 4)*sin(f*x + e) - cos(f*x + e) - 4)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-g/a) + 3*g*cos(f*x + e)^2 - 18*g*cos(f*x + e) + (17*g*cos(f*x + e)^2 + 14*g*cos(f*x + e) - 4*g)*sin(f*x + e) - 4*g)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4)) + 8*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)))/(a*c*f*cos(f*x + e)), -1/4*(sqrt(2)*a*sqrt(g/a)*arctan(1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(g/a)*(3*sin(f*x + e) - 1)/(g*cos(f*x + e)*sin(f*x + e)))*cos(f*x + e) - 4*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)))/(a*c*f*cos(f*x + e))]","A",0
18,1,391,0,1.282503," ","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=""fricas"")","\left[\frac{\sqrt{2} a g \sqrt{-\frac{1}{a g}} \cos\left(f x + e\right) \log\left(-\frac{4 \, \sqrt{2} {\left(3 \, \cos\left(f x + e\right)^{2} + {\left(3 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 4\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{1}{a g}} - 17 \, \cos\left(f x + e\right)^{3} - 3 \, \cos\left(f x + e\right)^{2} - {\left(17 \, \cos\left(f x + e\right)^{2} + 14 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) + 18 \, \cos\left(f x + e\right) + 4}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right) + 8 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{8 \, a c f g \cos\left(f x + e\right)}, \frac{\sqrt{2} a g \sqrt{\frac{1}{a g}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{1}{a g}} {\left(3 \, \sin\left(f x + e\right) - 1\right)}}{4 \, \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) \cos\left(f x + e\right) + 4 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, a c f g \cos\left(f x + e\right)}\right]"," ",0,"[1/8*(sqrt(2)*a*g*sqrt(-1/(a*g))*cos(f*x + e)*log(-(4*sqrt(2)*(3*cos(f*x + e)^2 + (3*cos(f*x + e) + 4)*sin(f*x + e) - cos(f*x + e) - 4)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-1/(a*g)) - 17*cos(f*x + e)^3 - 3*cos(f*x + e)^2 - (17*cos(f*x + e)^2 + 14*cos(f*x + e) - 4)*sin(f*x + e) + 18*cos(f*x + e) + 4)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4)) + 8*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)))/(a*c*f*g*cos(f*x + e)), 1/4*(sqrt(2)*a*g*sqrt(1/(a*g))*arctan(1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(1/(a*g))*(3*sin(f*x + e) - 1)/(cos(f*x + e)*sin(f*x + e)))*cos(f*x + e) + 4*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)))/(a*c*f*g*cos(f*x + e))]","A",0
19,1,202,0,1.233197," ","integrate((a+a*sin(f*x+e))^(1/2)*(c-c*sin(f*x+e))^(1/2)/sin(f*x+e),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} \log\left(\frac{4 \, {\left(256 \, a c \cos\left(f x + e\right)^{5} - 512 \, a c \cos\left(f x + e\right)^{3} + 337 \, a c \cos\left(f x + e\right) + {\left(256 \, \cos\left(f x + e\right)^{4} - 512 \, \cos\left(f x + e\right)^{2} + 175\right)} \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}\right)}}{\cos\left(f x + e\right)^{3} - \cos\left(f x + e\right)}\right)}{2 \, f}, -\frac{\sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} {\left(16 \, \cos\left(f x + e\right)^{2} - 7\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{16 \, a c \cos\left(f x + e\right)^{3} - 25 \, a c \cos\left(f x + e\right)}\right)}{f}\right]"," ",0,"[1/2*sqrt(a*c)*log(4*(256*a*c*cos(f*x + e)^5 - 512*a*c*cos(f*x + e)^3 + 337*a*c*cos(f*x + e) + (256*cos(f*x + e)^4 - 512*cos(f*x + e)^2 + 175)*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(cos(f*x + e)^3 - cos(f*x + e)))/f, -sqrt(-a*c)*arctan(sqrt(-a*c)*(16*cos(f*x + e)^2 - 7)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(16*a*c*cos(f*x + e)^3 - 25*a*c*cos(f*x + e)))/f]","A",0
20,0,0,0,1.256985," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c \cos\left(f x + e\right)^{2} + c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*cos(f*x + e)^2 + c*sin(f*x + e) - c), x)","F",0
21,0,0,0,1.311781," ","integrate((c-c*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a \cos\left(f x + e\right)^{2} - a \sin\left(f x + e\right) - a}, x\right)"," ",0,"integral(-sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*cos(f*x + e)^2 - a*sin(f*x + e) - a), x)","F",0
22,1,193,0,1.190481," ","integrate(1/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} \log\left(-\frac{4 \, {\left(2 \, a c \cos\left(f x + e\right)^{5} - 2 \, a c \cos\left(f x + e\right)^{3} + a c \cos\left(f x + e\right) - \sqrt{a c} {\left(2 \, \cos\left(f x + e\right)^{2} - 1\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}\right)}}{\cos\left(f x + e\right)^{5} - \cos\left(f x + e\right)^{3}}\right)}{2 \, a c f}, \frac{\sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, a c \cos\left(f x + e\right)^{3} - a c \cos\left(f x + e\right)}\right)}{a c f}\right]"," ",0,"[1/2*sqrt(a*c)*log(-4*(2*a*c*cos(f*x + e)^5 - 2*a*c*cos(f*x + e)^3 + a*c*cos(f*x + e) - sqrt(a*c)*(2*cos(f*x + e)^2 - 1)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(cos(f*x + e)^5 - cos(f*x + e)^3))/(a*c*f), sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(2*a*c*cos(f*x + e)^3 - a*c*cos(f*x + e)))/(a*c*f)]","A",0
23,1,781,0,2.020215," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{a d}{c + d}} \log\left(\frac{a d^{2} \cos\left(f x + e\right)^{3} - a c^{2} - 2 \, a c d - a d^{2} - {\left(6 \, a c d + 7 \, a d^{2}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left({\left(c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} - 4 \, c d - 3 \, d^{2} - {\left(c^{2} + 3 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right) + {\left(c^{2} + 4 \, c d + 3 \, d^{2} + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{\frac{a d}{c + d}} - {\left(a c^{2} + 8 \, a c d + 9 \, a d^{2}\right)} \cos\left(f x + e\right) + {\left(a d^{2} \cos\left(f x + e\right)^{2} - a c^{2} - 2 \, a c d - a d^{2} + 2 \, {\left(3 \, a c d + 4 \, a d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{d^{2} \cos\left(f x + e\right)^{3} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} - 2 \, c d - d^{2} - {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right) + {\left(d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \cos\left(f x + e\right) - c^{2} - 2 \, c d - d^{2}\right)} \sin\left(f x + e\right)}\right) + \sqrt{a} \log\left(\frac{a \cos\left(f x + e\right)^{3} - 7 \, a \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right) + 3\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 3\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} - 9 \, a \cos\left(f x + e\right) + {\left(a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) - a\right)} \sin\left(f x + e\right) - a}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 1}\right)}{2 \, c f}, \frac{2 \, \sqrt{-\frac{a d}{c + d}} \arctan\left(\frac{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) - c - 2 \, d\right)} \sqrt{-\frac{a d}{c + d}}}{2 \, a d \cos\left(f x + e\right)}\right) + \sqrt{a} \log\left(\frac{a \cos\left(f x + e\right)^{3} - 7 \, a \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right) + 3\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 3\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} - 9 \, a \cos\left(f x + e\right) + {\left(a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) - a\right)} \sin\left(f x + e\right) - a}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 1}\right)}{2 \, c f}\right]"," ",0,"[1/2*(sqrt(a*d/(c + d))*log((a*d^2*cos(f*x + e)^3 - a*c^2 - 2*a*c*d - a*d^2 - (6*a*c*d + 7*a*d^2)*cos(f*x + e)^2 + 4*((c*d + d^2)*cos(f*x + e)^2 - c^2 - 4*c*d - 3*d^2 - (c^2 + 3*c*d + 2*d^2)*cos(f*x + e) + (c^2 + 4*c*d + 3*d^2 + (c*d + d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a*d/(c + d)) - (a*c^2 + 8*a*c*d + 9*a*d^2)*cos(f*x + e) + (a*d^2*cos(f*x + e)^2 - a*c^2 - 2*a*c*d - a*d^2 + 2*(3*a*c*d + 4*a*d^2)*cos(f*x + e))*sin(f*x + e))/(d^2*cos(f*x + e)^3 + (2*c*d + d^2)*cos(f*x + e)^2 - c^2 - 2*c*d - d^2 - (c^2 + d^2)*cos(f*x + e) + (d^2*cos(f*x + e)^2 - 2*c*d*cos(f*x + e) - c^2 - 2*c*d - d^2)*sin(f*x + e))) + sqrt(a)*log((a*cos(f*x + e)^3 - 7*a*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + (cos(f*x + e) + 3)*sin(f*x + e) - 2*cos(f*x + e) - 3)*sqrt(a*sin(f*x + e) + a)*sqrt(a) - 9*a*cos(f*x + e) + (a*cos(f*x + e)^2 + 8*a*cos(f*x + e) - a)*sin(f*x + e) - a)/(cos(f*x + e)^3 + cos(f*x + e)^2 + (cos(f*x + e)^2 - 1)*sin(f*x + e) - cos(f*x + e) - 1)))/(c*f), 1/2*(2*sqrt(-a*d/(c + d))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a*d/(c + d))/(a*d*cos(f*x + e))) + sqrt(a)*log((a*cos(f*x + e)^3 - 7*a*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + (cos(f*x + e) + 3)*sin(f*x + e) - 2*cos(f*x + e) - 3)*sqrt(a*sin(f*x + e) + a)*sqrt(a) - 9*a*cos(f*x + e) + (a*cos(f*x + e)^2 + 8*a*cos(f*x + e) - a)*sin(f*x + e) - a)/(cos(f*x + e)^3 + cos(f*x + e)^2 + (cos(f*x + e)^2 - 1)*sin(f*x + e) - cos(f*x + e) - 1)))/(c*f)]","B",0
24,1,1044,0,5.183014," ","integrate(1/sin(f*x+e)/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{a d \sqrt{\frac{d}{a c + a d}} \log\left(\frac{d^{2} \cos\left(f x + e\right)^{3} - {\left(6 \, c d + 7 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} - 2 \, c d - d^{2} + 4 \, {\left({\left(c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} - 4 \, c d - 3 \, d^{2} - {\left(c^{2} + 3 \, c d + 2 \, d^{2}\right)} \cos\left(f x + e\right) + {\left(c^{2} + 4 \, c d + 3 \, d^{2} + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{\frac{d}{a c + a d}} - {\left(c^{2} + 8 \, c d + 9 \, d^{2}\right)} \cos\left(f x + e\right) + {\left(d^{2} \cos\left(f x + e\right)^{2} - c^{2} - 2 \, c d - d^{2} + 2 \, {\left(3 \, c d + 4 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{d^{2} \cos\left(f x + e\right)^{3} + {\left(2 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - c^{2} - 2 \, c d - d^{2} - {\left(c^{2} + d^{2}\right)} \cos\left(f x + e\right) + {\left(d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \cos\left(f x + e\right) - c^{2} - 2 \, c d - d^{2}\right)} \sin\left(f x + e\right)}\right) + \sqrt{2} \sqrt{a} c \log\left(-\frac{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) - 2\right)} \sin\left(f x + e\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(f x + e\right) + 2}{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2}\right) - \sqrt{a} {\left(c - d\right)} \log\left(\frac{a \cos\left(f x + e\right)^{3} - 7 \, a \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right) + 3\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 3\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} - 9 \, a \cos\left(f x + e\right) + {\left(a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) - a\right)} \sin\left(f x + e\right) - a}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 1}\right)}{2 \, {\left(a c^{2} - a c d\right)} f}, -\frac{2 \, a d \sqrt{-\frac{d}{a c + a d}} \arctan\left(\frac{\sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) - c - 2 \, d\right)} \sqrt{-\frac{d}{a c + a d}}}{2 \, d \cos\left(f x + e\right)}\right) + \sqrt{2} \sqrt{a} c \log\left(-\frac{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) - 2\right)} \sin\left(f x + e\right) - \frac{2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)}}{\sqrt{a}} + 3 \, \cos\left(f x + e\right) + 2}{\cos\left(f x + e\right)^{2} - {\left(\cos\left(f x + e\right) + 2\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 2}\right) - \sqrt{a} {\left(c - d\right)} \log\left(\frac{a \cos\left(f x + e\right)^{3} - 7 \, a \cos\left(f x + e\right)^{2} - 4 \, {\left(\cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right) + 3\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 3\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} - 9 \, a \cos\left(f x + e\right) + {\left(a \cos\left(f x + e\right)^{2} + 8 \, a \cos\left(f x + e\right) - a\right)} \sin\left(f x + e\right) - a}{\cos\left(f x + e\right)^{3} + \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 1\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 1}\right)}{2 \, {\left(a c^{2} - a c d\right)} f}\right]"," ",0,"[-1/2*(a*d*sqrt(d/(a*c + a*d))*log((d^2*cos(f*x + e)^3 - (6*c*d + 7*d^2)*cos(f*x + e)^2 - c^2 - 2*c*d - d^2 + 4*((c*d + d^2)*cos(f*x + e)^2 - c^2 - 4*c*d - 3*d^2 - (c^2 + 3*c*d + 2*d^2)*cos(f*x + e) + (c^2 + 4*c*d + 3*d^2 + (c*d + d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d/(a*c + a*d)) - (c^2 + 8*c*d + 9*d^2)*cos(f*x + e) + (d^2*cos(f*x + e)^2 - c^2 - 2*c*d - d^2 + 2*(3*c*d + 4*d^2)*cos(f*x + e))*sin(f*x + e))/(d^2*cos(f*x + e)^3 + (2*c*d + d^2)*cos(f*x + e)^2 - c^2 - 2*c*d - d^2 - (c^2 + d^2)*cos(f*x + e) + (d^2*cos(f*x + e)^2 - 2*c*d*cos(f*x + e) - c^2 - 2*c*d - d^2)*sin(f*x + e))) + sqrt(2)*sqrt(a)*c*log(-(cos(f*x + e)^2 - (cos(f*x + e) - 2)*sin(f*x + e) - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*(cos(f*x + e) - sin(f*x + e) + 1)/sqrt(a) + 3*cos(f*x + e) + 2)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - sqrt(a)*(c - d)*log((a*cos(f*x + e)^3 - 7*a*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + (cos(f*x + e) + 3)*sin(f*x + e) - 2*cos(f*x + e) - 3)*sqrt(a*sin(f*x + e) + a)*sqrt(a) - 9*a*cos(f*x + e) + (a*cos(f*x + e)^2 + 8*a*cos(f*x + e) - a)*sin(f*x + e) - a)/(cos(f*x + e)^3 + cos(f*x + e)^2 + (cos(f*x + e)^2 - 1)*sin(f*x + e) - cos(f*x + e) - 1)))/((a*c^2 - a*c*d)*f), -1/2*(2*a*d*sqrt(-d/(a*c + a*d))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-d/(a*c + a*d))/(d*cos(f*x + e))) + sqrt(2)*sqrt(a)*c*log(-(cos(f*x + e)^2 - (cos(f*x + e) - 2)*sin(f*x + e) - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*(cos(f*x + e) - sin(f*x + e) + 1)/sqrt(a) + 3*cos(f*x + e) + 2)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - sqrt(a)*(c - d)*log((a*cos(f*x + e)^3 - 7*a*cos(f*x + e)^2 - 4*(cos(f*x + e)^2 + (cos(f*x + e) + 3)*sin(f*x + e) - 2*cos(f*x + e) - 3)*sqrt(a*sin(f*x + e) + a)*sqrt(a) - 9*a*cos(f*x + e) + (a*cos(f*x + e)^2 + 8*a*cos(f*x + e) - a)*sin(f*x + e) - a)/(cos(f*x + e)^3 + cos(f*x + e)^2 + (cos(f*x + e)^2 - 1)*sin(f*x + e) - cos(f*x + e) - 1)))/((a*c^2 - a*c*d)*f)]","B",0
25,1,3273,0,4.448672," ","integrate((g*sin(f*x+e))^(1/2)*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a c g}{c + d}} \log\left(\frac{{\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{5} - {\left(128 \, a c^{4} + 192 \, a c^{3} d + 64 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} g \cos\left(f x + e\right)^{4} - 2 \, {\left(208 \, a c^{4} + 368 \, a c^{3} d + 195 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{3} + 2 \, {\left(64 \, a c^{4} + 94 \, a c^{3} d + 29 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} g \cos\left(f x + e\right)^{2} + {\left(289 \, a c^{4} + 480 \, a c^{3} d + 230 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right) + 8 \, {\left({\left(16 \, c^{4} + 40 \, c^{3} d + 34 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + 51 \, c^{4} + 110 \, c^{3} d + 76 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4} - {\left(24 \, c^{4} + 52 \, c^{3} d + 35 \, c^{2} d^{2} + 7 \, c d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(66 \, c^{4} + 149 \, c^{3} d + 110 \, c^{2} d^{2} + 29 \, c d^{3} + 2 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(25 \, c^{4} + 53 \, c^{3} d + 35 \, c^{2} d^{2} + 7 \, c d^{3}\right)} \cos\left(f x + e\right) - {\left(51 \, c^{4} + 110 \, c^{3} d + 76 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4} - {\left(16 \, c^{4} + 40 \, c^{3} d + 34 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(40 \, c^{4} + 92 \, c^{3} d + 69 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(26 \, c^{4} + 57 \, c^{3} d + 41 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a c g}{c + d}} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} g + {\left({\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{4} + 4 \, {\left(64 \, a c^{4} + 112 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} g \cos\left(f x + e\right)^{3} - 2 \, {\left(80 \, a c^{4} + 144 \, a c^{3} d + 83 \, a c^{2} d^{2} + 18 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{2} - 4 \, {\left(72 \, a c^{4} + 119 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} g \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} g\right)} \sin\left(f x + e\right)}{d^{4} \cos\left(f x + e\right)^{5} + {\left(4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(2 \, c^{3} d + 3 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{4} + 6 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right) + {\left(d^{4} \cos\left(f x + e\right)^{4} - 4 \, c d^{3} \cos\left(f x + e\right)^{3} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}\right) + \sqrt{-a g} \log\left(\frac{128 \, a g \cos\left(f x + e\right)^{5} - 128 \, a g \cos\left(f x + e\right)^{4} - 416 \, a g \cos\left(f x + e\right)^{3} + 128 \, a g \cos\left(f x + e\right)^{2} + 289 \, a g \cos\left(f x + e\right) - 8 \, {\left(16 \, \cos\left(f x + e\right)^{4} - 24 \, \cos\left(f x + e\right)^{3} - 66 \, \cos\left(f x + e\right)^{2} + {\left(16 \, \cos\left(f x + e\right)^{3} + 40 \, \cos\left(f x + e\right)^{2} - 26 \, \cos\left(f x + e\right) - 51\right)} \sin\left(f x + e\right) + 25 \, \cos\left(f x + e\right) + 51\right)} \sqrt{-a g} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} + a g + {\left(128 \, a g \cos\left(f x + e\right)^{4} + 256 \, a g \cos\left(f x + e\right)^{3} - 160 \, a g \cos\left(f x + e\right)^{2} - 288 \, a g \cos\left(f x + e\right) + a g\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1}\right)}{4 \, d f}, -\frac{2 \, \sqrt{\frac{a c g}{c + d}} \arctan\left(\frac{{\left({\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} - 8 \, c d - d^{2} + 2 \, {\left(4 \, c^{2} + 3 \, c d\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a c g}{c + d}} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, {\left(a c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, a c^{2} + a c d\right)} g \cos\left(f x + e\right)^{3} - {\left(2 \, a c^{2} + a c d\right)} g \cos\left(f x + e\right)\right)}}\right) - \sqrt{-a g} \log\left(\frac{128 \, a g \cos\left(f x + e\right)^{5} - 128 \, a g \cos\left(f x + e\right)^{4} - 416 \, a g \cos\left(f x + e\right)^{3} + 128 \, a g \cos\left(f x + e\right)^{2} + 289 \, a g \cos\left(f x + e\right) - 8 \, {\left(16 \, \cos\left(f x + e\right)^{4} - 24 \, \cos\left(f x + e\right)^{3} - 66 \, \cos\left(f x + e\right)^{2} + {\left(16 \, \cos\left(f x + e\right)^{3} + 40 \, \cos\left(f x + e\right)^{2} - 26 \, \cos\left(f x + e\right) - 51\right)} \sin\left(f x + e\right) + 25 \, \cos\left(f x + e\right) + 51\right)} \sqrt{-a g} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} + a g + {\left(128 \, a g \cos\left(f x + e\right)^{4} + 256 \, a g \cos\left(f x + e\right)^{3} - 160 \, a g \cos\left(f x + e\right)^{2} - 288 \, a g \cos\left(f x + e\right) + a g\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1}\right)}{4 \, d f}, \frac{2 \, \sqrt{a g} \arctan\left(\frac{\sqrt{a g} {\left(8 \, \cos\left(f x + e\right)^{2} + 8 \, \sin\left(f x + e\right) - 9\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, {\left(2 \, a g \cos\left(f x + e\right)^{3} + a g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a g \cos\left(f x + e\right)\right)}}\right) + \sqrt{-\frac{a c g}{c + d}} \log\left(\frac{{\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{5} - {\left(128 \, a c^{4} + 192 \, a c^{3} d + 64 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} g \cos\left(f x + e\right)^{4} - 2 \, {\left(208 \, a c^{4} + 368 \, a c^{3} d + 195 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{3} + 2 \, {\left(64 \, a c^{4} + 94 \, a c^{3} d + 29 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} g \cos\left(f x + e\right)^{2} + {\left(289 \, a c^{4} + 480 \, a c^{3} d + 230 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right) + 8 \, {\left({\left(16 \, c^{4} + 40 \, c^{3} d + 34 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + 51 \, c^{4} + 110 \, c^{3} d + 76 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4} - {\left(24 \, c^{4} + 52 \, c^{3} d + 35 \, c^{2} d^{2} + 7 \, c d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(66 \, c^{4} + 149 \, c^{3} d + 110 \, c^{2} d^{2} + 29 \, c d^{3} + 2 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(25 \, c^{4} + 53 \, c^{3} d + 35 \, c^{2} d^{2} + 7 \, c d^{3}\right)} \cos\left(f x + e\right) - {\left(51 \, c^{4} + 110 \, c^{3} d + 76 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4} - {\left(16 \, c^{4} + 40 \, c^{3} d + 34 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(40 \, c^{4} + 92 \, c^{3} d + 69 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(26 \, c^{4} + 57 \, c^{3} d + 41 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a c g}{c + d}} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} g + {\left({\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{4} + 4 \, {\left(64 \, a c^{4} + 112 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} g \cos\left(f x + e\right)^{3} - 2 \, {\left(80 \, a c^{4} + 144 \, a c^{3} d + 83 \, a c^{2} d^{2} + 18 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{2} - 4 \, {\left(72 \, a c^{4} + 119 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} g \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} g\right)} \sin\left(f x + e\right)}{d^{4} \cos\left(f x + e\right)^{5} + {\left(4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(2 \, c^{3} d + 3 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{4} + 6 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right) + {\left(d^{4} \cos\left(f x + e\right)^{4} - 4 \, c d^{3} \cos\left(f x + e\right)^{3} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}\right)}{4 \, d f}, -\frac{\sqrt{\frac{a c g}{c + d}} \arctan\left(\frac{{\left({\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} - 8 \, c d - d^{2} + 2 \, {\left(4 \, c^{2} + 3 \, c d\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a c g}{c + d}} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, {\left(a c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, a c^{2} + a c d\right)} g \cos\left(f x + e\right)^{3} - {\left(2 \, a c^{2} + a c d\right)} g \cos\left(f x + e\right)\right)}}\right) - \sqrt{a g} \arctan\left(\frac{\sqrt{a g} {\left(8 \, \cos\left(f x + e\right)^{2} + 8 \, \sin\left(f x + e\right) - 9\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, {\left(2 \, a g \cos\left(f x + e\right)^{3} + a g \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a g \cos\left(f x + e\right)\right)}}\right)}{2 \, d f}\right]"," ",0,"[1/4*(sqrt(-a*c*g/(c + d))*log(((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^5 - (128*a*c^4 + 192*a*c^3*d + 64*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*g*cos(f*x + e)^4 - 2*(208*a*c^4 + 368*a*c^3*d + 195*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^3 + 2*(64*a*c^4 + 94*a*c^3*d + 29*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*g*cos(f*x + e)^2 + (289*a*c^4 + 480*a*c^3*d + 230*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e) + 8*((16*c^4 + 40*c^3*d + 34*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e)^4 + 51*c^4 + 110*c^3*d + 76*c^2*d^2 + 18*c*d^3 + d^4 - (24*c^4 + 52*c^3*d + 35*c^2*d^2 + 7*c*d^3)*cos(f*x + e)^3 - (66*c^4 + 149*c^3*d + 110*c^2*d^2 + 29*c*d^3 + 2*d^4)*cos(f*x + e)^2 + (25*c^4 + 53*c^3*d + 35*c^2*d^2 + 7*c*d^3)*cos(f*x + e) - (51*c^4 + 110*c^3*d + 76*c^2*d^2 + 18*c*d^3 + d^4 - (16*c^4 + 40*c^3*d + 34*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e)^3 - (40*c^4 + 92*c^3*d + 69*c^2*d^2 + 18*c*d^3 + d^4)*cos(f*x + e)^2 + (26*c^4 + 57*c^3*d + 41*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(-a*c*g/(c + d))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*g + ((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^4 + 4*(64*a*c^4 + 112*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*g*cos(f*x + e)^3 - 2*(80*a*c^4 + 144*a*c^3*d + 83*a*c^2*d^2 + 18*a*c*d^3 + a*d^4)*g*cos(f*x + e)^2 - 4*(72*a*c^4 + 119*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*g*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*g)*sin(f*x + e))/(d^4*cos(f*x + e)^5 + (4*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + d^4)*cos(f*x + e)^3 - 2*(2*c^3*d + 3*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e)^2 + (c^4 + 6*c^2*d^2 + d^4)*cos(f*x + e) + (d^4*cos(f*x + e)^4 - 4*c*d^3*cos(f*x + e)^3 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + 2*c*d^3 + d^4)*cos(f*x + e)^2 + 4*(c^3*d + c*d^3)*cos(f*x + e))*sin(f*x + e))) + sqrt(-a*g)*log((128*a*g*cos(f*x + e)^5 - 128*a*g*cos(f*x + e)^4 - 416*a*g*cos(f*x + e)^3 + 128*a*g*cos(f*x + e)^2 + 289*a*g*cos(f*x + e) - 8*(16*cos(f*x + e)^4 - 24*cos(f*x + e)^3 - 66*cos(f*x + e)^2 + (16*cos(f*x + e)^3 + 40*cos(f*x + e)^2 - 26*cos(f*x + e) - 51)*sin(f*x + e) + 25*cos(f*x + e) + 51)*sqrt(-a*g)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)) + a*g + (128*a*g*cos(f*x + e)^4 + 256*a*g*cos(f*x + e)^3 - 160*a*g*cos(f*x + e)^2 - 288*a*g*cos(f*x + e) + a*g)*sin(f*x + e))/(cos(f*x + e) + sin(f*x + e) + 1)))/(d*f), -1/4*(2*sqrt(a*c*g/(c + d))*arctan(1/4*((8*c^2 + 8*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 - 8*c*d - d^2 + 2*(4*c^2 + 3*c*d)*sin(f*x + e))*sqrt(a*c*g/(c + d))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(a*c^2*g*cos(f*x + e)*sin(f*x + e) + (2*a*c^2 + a*c*d)*g*cos(f*x + e)^3 - (2*a*c^2 + a*c*d)*g*cos(f*x + e))) - sqrt(-a*g)*log((128*a*g*cos(f*x + e)^5 - 128*a*g*cos(f*x + e)^4 - 416*a*g*cos(f*x + e)^3 + 128*a*g*cos(f*x + e)^2 + 289*a*g*cos(f*x + e) - 8*(16*cos(f*x + e)^4 - 24*cos(f*x + e)^3 - 66*cos(f*x + e)^2 + (16*cos(f*x + e)^3 + 40*cos(f*x + e)^2 - 26*cos(f*x + e) - 51)*sin(f*x + e) + 25*cos(f*x + e) + 51)*sqrt(-a*g)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)) + a*g + (128*a*g*cos(f*x + e)^4 + 256*a*g*cos(f*x + e)^3 - 160*a*g*cos(f*x + e)^2 - 288*a*g*cos(f*x + e) + a*g)*sin(f*x + e))/(cos(f*x + e) + sin(f*x + e) + 1)))/(d*f), 1/4*(2*sqrt(a*g)*arctan(1/4*sqrt(a*g)*(8*cos(f*x + e)^2 + 8*sin(f*x + e) - 9)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(2*a*g*cos(f*x + e)^3 + a*g*cos(f*x + e)*sin(f*x + e) - 2*a*g*cos(f*x + e))) + sqrt(-a*c*g/(c + d))*log(((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^5 - (128*a*c^4 + 192*a*c^3*d + 64*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*g*cos(f*x + e)^4 - 2*(208*a*c^4 + 368*a*c^3*d + 195*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^3 + 2*(64*a*c^4 + 94*a*c^3*d + 29*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*g*cos(f*x + e)^2 + (289*a*c^4 + 480*a*c^3*d + 230*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e) + 8*((16*c^4 + 40*c^3*d + 34*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e)^4 + 51*c^4 + 110*c^3*d + 76*c^2*d^2 + 18*c*d^3 + d^4 - (24*c^4 + 52*c^3*d + 35*c^2*d^2 + 7*c*d^3)*cos(f*x + e)^3 - (66*c^4 + 149*c^3*d + 110*c^2*d^2 + 29*c*d^3 + 2*d^4)*cos(f*x + e)^2 + (25*c^4 + 53*c^3*d + 35*c^2*d^2 + 7*c*d^3)*cos(f*x + e) - (51*c^4 + 110*c^3*d + 76*c^2*d^2 + 18*c*d^3 + d^4 - (16*c^4 + 40*c^3*d + 34*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e)^3 - (40*c^4 + 92*c^3*d + 69*c^2*d^2 + 18*c*d^3 + d^4)*cos(f*x + e)^2 + (26*c^4 + 57*c^3*d + 41*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(-a*c*g/(c + d))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*g + ((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^4 + 4*(64*a*c^4 + 112*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*g*cos(f*x + e)^3 - 2*(80*a*c^4 + 144*a*c^3*d + 83*a*c^2*d^2 + 18*a*c*d^3 + a*d^4)*g*cos(f*x + e)^2 - 4*(72*a*c^4 + 119*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*g*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*g)*sin(f*x + e))/(d^4*cos(f*x + e)^5 + (4*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + d^4)*cos(f*x + e)^3 - 2*(2*c^3*d + 3*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e)^2 + (c^4 + 6*c^2*d^2 + d^4)*cos(f*x + e) + (d^4*cos(f*x + e)^4 - 4*c*d^3*cos(f*x + e)^3 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + 2*c*d^3 + d^4)*cos(f*x + e)^2 + 4*(c^3*d + c*d^3)*cos(f*x + e))*sin(f*x + e))))/(d*f), -1/2*(sqrt(a*c*g/(c + d))*arctan(1/4*((8*c^2 + 8*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 - 8*c*d - d^2 + 2*(4*c^2 + 3*c*d)*sin(f*x + e))*sqrt(a*c*g/(c + d))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(a*c^2*g*cos(f*x + e)*sin(f*x + e) + (2*a*c^2 + a*c*d)*g*cos(f*x + e)^3 - (2*a*c^2 + a*c*d)*g*cos(f*x + e))) - sqrt(a*g)*arctan(1/4*sqrt(a*g)*(8*cos(f*x + e)^2 + 8*sin(f*x + e) - 9)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(2*a*g*cos(f*x + e)^3 + a*g*cos(f*x + e)*sin(f*x + e) - 2*a*g*cos(f*x + e))))/(d*f)]","B",0
26,1,1303,0,2.696336," ","integrate((a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a}{{\left(c^{2} + c d\right)} g}} \log\left(\frac{{\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - {\left(128 \, a c^{4} + 192 \, a c^{3} d + 64 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(208 \, a c^{4} + 368 \, a c^{3} d + 195 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(64 \, a c^{4} + 94 \, a c^{3} d + 29 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left(51 \, c^{5} + 110 \, c^{4} d + 76 \, c^{3} d^{2} + 18 \, c^{2} d^{3} + c d^{4} + {\left(16 \, c^{5} + 40 \, c^{4} d + 34 \, c^{3} d^{2} + 11 \, c^{2} d^{3} + c d^{4}\right)} \cos\left(f x + e\right)^{4} - {\left(24 \, c^{5} + 52 \, c^{4} d + 35 \, c^{3} d^{2} + 7 \, c^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(66 \, c^{5} + 149 \, c^{4} d + 110 \, c^{3} d^{2} + 29 \, c^{2} d^{3} + 2 \, c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(25 \, c^{5} + 53 \, c^{4} d + 35 \, c^{3} d^{2} + 7 \, c^{2} d^{3}\right)} \cos\left(f x + e\right) - {\left(51 \, c^{5} + 110 \, c^{4} d + 76 \, c^{3} d^{2} + 18 \, c^{2} d^{3} + c d^{4} - {\left(16 \, c^{5} + 40 \, c^{4} d + 34 \, c^{3} d^{2} + 11 \, c^{2} d^{3} + c d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(40 \, c^{5} + 92 \, c^{4} d + 69 \, c^{3} d^{2} + 18 \, c^{2} d^{3} + c d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(26 \, c^{5} + 57 \, c^{4} d + 41 \, c^{3} d^{2} + 11 \, c^{2} d^{3} + c d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{a}{{\left(c^{2} + c d\right)} g}} + {\left(289 \, a c^{4} + 480 \, a c^{3} d + 230 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + {\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(64 \, a c^{4} + 112 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(80 \, a c^{4} + 144 \, a c^{3} d + 83 \, a c^{2} d^{2} + 18 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left(72 \, a c^{4} + 119 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{d^{4} \cos\left(f x + e\right)^{5} + {\left(4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(2 \, c^{3} d + 3 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{4} + 6 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right) + {\left(d^{4} \cos\left(f x + e\right)^{4} - 4 \, c d^{3} \cos\left(f x + e\right)^{3} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}\right)}{4 \, f}, \frac{\sqrt{\frac{a}{{\left(c^{2} + c d\right)} g}} \arctan\left(\frac{{\left({\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} - 8 \, c d - d^{2} + 2 \, {\left(4 \, c^{2} + 3 \, c d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{a}{{\left(c^{2} + c d\right)} g}}}{4 \, {\left({\left(2 \, a c + a d\right)} \cos\left(f x + e\right)^{3} + a c \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(2 \, a c + a d\right)} \cos\left(f x + e\right)\right)}}\right)}{2 \, f}\right]"," ",0,"[1/4*sqrt(-a/((c^2 + c*d)*g))*log(((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - (128*a*c^4 + 192*a*c^3*d + 64*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 2*(208*a*c^4 + 368*a*c^3*d + 195*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*cos(f*x + e)^3 + 2*(64*a*c^4 + 94*a*c^3*d + 29*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^2 - 8*(51*c^5 + 110*c^4*d + 76*c^3*d^2 + 18*c^2*d^3 + c*d^4 + (16*c^5 + 40*c^4*d + 34*c^3*d^2 + 11*c^2*d^3 + c*d^4)*cos(f*x + e)^4 - (24*c^5 + 52*c^4*d + 35*c^3*d^2 + 7*c^2*d^3)*cos(f*x + e)^3 - (66*c^5 + 149*c^4*d + 110*c^3*d^2 + 29*c^2*d^3 + 2*c*d^4)*cos(f*x + e)^2 + (25*c^5 + 53*c^4*d + 35*c^3*d^2 + 7*c^2*d^3)*cos(f*x + e) - (51*c^5 + 110*c^4*d + 76*c^3*d^2 + 18*c^2*d^3 + c*d^4 - (16*c^5 + 40*c^4*d + 34*c^3*d^2 + 11*c^2*d^3 + c*d^4)*cos(f*x + e)^3 - (40*c^5 + 92*c^4*d + 69*c^3*d^2 + 18*c^2*d^3 + c*d^4)*cos(f*x + e)^2 + (26*c^5 + 57*c^4*d + 41*c^3*d^2 + 11*c^2*d^3 + c*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-a/((c^2 + c*d)*g)) + (289*a*c^4 + 480*a*c^3*d + 230*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + (128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*cos(f*x + e)^4 + 4*(64*a*c^4 + 112*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*cos(f*x + e)^3 - 2*(80*a*c^4 + 144*a*c^3*d + 83*a*c^2*d^2 + 18*a*c*d^3 + a*d^4)*cos(f*x + e)^2 - 4*(72*a*c^4 + 119*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*cos(f*x + e))*sin(f*x + e))/(d^4*cos(f*x + e)^5 + (4*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + d^4)*cos(f*x + e)^3 - 2*(2*c^3*d + 3*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e)^2 + (c^4 + 6*c^2*d^2 + d^4)*cos(f*x + e) + (d^4*cos(f*x + e)^4 - 4*c*d^3*cos(f*x + e)^3 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + 2*c*d^3 + d^4)*cos(f*x + e)^2 + 4*(c^3*d + c*d^3)*cos(f*x + e))*sin(f*x + e)))/f, 1/2*sqrt(a/((c^2 + c*d)*g))*arctan(1/4*((8*c^2 + 8*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 - 8*c*d - d^2 + 2*(4*c^2 + 3*c*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(a/((c^2 + c*d)*g))/((2*a*c + a*d)*cos(f*x + e)^3 + a*c*cos(f*x + e)*sin(f*x + e) - (2*a*c + a*d)*cos(f*x + e)))/f]","B",0
27,1,3048,0,4.126990," ","integrate((g*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} \sqrt{-\frac{g}{a}} \log\left(\frac{17 \, g \cos\left(f x + e\right)^{3} - 4 \, \sqrt{2} {\left(3 \, \cos\left(f x + e\right)^{2} + {\left(3 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 4\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{g}{a}} + 3 \, g \cos\left(f x + e\right)^{2} - 18 \, g \cos\left(f x + e\right) + {\left(17 \, g \cos\left(f x + e\right)^{2} + 14 \, g \cos\left(f x + e\right) - 4 \, g\right)} \sin\left(f x + e\right) - 4 \, g}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right) + \sqrt{-\frac{c g}{a c + a d}} \log\left(\frac{{\left(128 \, c^{4} + 256 \, c^{3} d + 160 \, c^{2} d^{2} + 32 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right)^{5} - {\left(128 \, c^{4} + 192 \, c^{3} d + 64 \, c^{2} d^{2} - 4 \, c d^{3} - d^{4}\right)} g \cos\left(f x + e\right)^{4} - 2 \, {\left(208 \, c^{4} + 368 \, c^{3} d + 195 \, c^{2} d^{2} + 32 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right)^{3} + 2 \, {\left(64 \, c^{4} + 94 \, c^{3} d + 29 \, c^{2} d^{2} - 4 \, c d^{3} - d^{4}\right)} g \cos\left(f x + e\right)^{2} + {\left(289 \, c^{4} + 480 \, c^{3} d + 230 \, c^{2} d^{2} + 32 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right) + 8 \, {\left({\left(16 \, c^{4} + 40 \, c^{3} d + 34 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + 51 \, c^{4} + 110 \, c^{3} d + 76 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4} - {\left(24 \, c^{4} + 52 \, c^{3} d + 35 \, c^{2} d^{2} + 7 \, c d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(66 \, c^{4} + 149 \, c^{3} d + 110 \, c^{2} d^{2} + 29 \, c d^{3} + 2 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(25 \, c^{4} + 53 \, c^{3} d + 35 \, c^{2} d^{2} + 7 \, c d^{3}\right)} \cos\left(f x + e\right) - {\left(51 \, c^{4} + 110 \, c^{3} d + 76 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4} - {\left(16 \, c^{4} + 40 \, c^{3} d + 34 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(40 \, c^{4} + 92 \, c^{3} d + 69 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(26 \, c^{4} + 57 \, c^{3} d + 41 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{c g}{a c + a d}} + {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} g + {\left({\left(128 \, c^{4} + 256 \, c^{3} d + 160 \, c^{2} d^{2} + 32 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right)^{4} + 4 \, {\left(64 \, c^{4} + 112 \, c^{3} d + 56 \, c^{2} d^{2} + 7 \, c d^{3}\right)} g \cos\left(f x + e\right)^{3} - 2 \, {\left(80 \, c^{4} + 144 \, c^{3} d + 83 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right)^{2} - 4 \, {\left(72 \, c^{4} + 119 \, c^{3} d + 56 \, c^{2} d^{2} + 7 \, c d^{3}\right)} g \cos\left(f x + e\right) + {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} g\right)} \sin\left(f x + e\right)}{d^{4} \cos\left(f x + e\right)^{5} + {\left(4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(2 \, c^{3} d + 3 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{4} + 6 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right) + {\left(d^{4} \cos\left(f x + e\right)^{4} - 4 \, c d^{3} \cos\left(f x + e\right)^{3} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}\right)}{4 \, {\left(c - d\right)} f}, -\frac{\sqrt{2} \sqrt{-\frac{g}{a}} \log\left(\frac{17 \, g \cos\left(f x + e\right)^{3} - 4 \, \sqrt{2} {\left(3 \, \cos\left(f x + e\right)^{2} + {\left(3 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 4\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{g}{a}} + 3 \, g \cos\left(f x + e\right)^{2} - 18 \, g \cos\left(f x + e\right) + {\left(17 \, g \cos\left(f x + e\right)^{2} + 14 \, g \cos\left(f x + e\right) - 4 \, g\right)} \sin\left(f x + e\right) - 4 \, g}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right) - 2 \, \sqrt{\frac{c g}{a c + a d}} \arctan\left(\frac{{\left({\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} - 8 \, c d - d^{2} + 2 \, {\left(4 \, c^{2} + 3 \, c d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{c g}{a c + a d}}}{4 \, {\left({\left(2 \, c^{2} + c d\right)} g \cos\left(f x + e\right)^{3} + c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(2 \, c^{2} + c d\right)} g \cos\left(f x + e\right)\right)}}\right)}{4 \, {\left(c - d\right)} f}, -\frac{2 \, \sqrt{2} \sqrt{\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{g}{a}} {\left(3 \, \sin\left(f x + e\right) - 1\right)}}{4 \, g \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) + \sqrt{-\frac{c g}{a c + a d}} \log\left(\frac{{\left(128 \, c^{4} + 256 \, c^{3} d + 160 \, c^{2} d^{2} + 32 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right)^{5} - {\left(128 \, c^{4} + 192 \, c^{3} d + 64 \, c^{2} d^{2} - 4 \, c d^{3} - d^{4}\right)} g \cos\left(f x + e\right)^{4} - 2 \, {\left(208 \, c^{4} + 368 \, c^{3} d + 195 \, c^{2} d^{2} + 32 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right)^{3} + 2 \, {\left(64 \, c^{4} + 94 \, c^{3} d + 29 \, c^{2} d^{2} - 4 \, c d^{3} - d^{4}\right)} g \cos\left(f x + e\right)^{2} + {\left(289 \, c^{4} + 480 \, c^{3} d + 230 \, c^{2} d^{2} + 32 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right) + 8 \, {\left({\left(16 \, c^{4} + 40 \, c^{3} d + 34 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + 51 \, c^{4} + 110 \, c^{3} d + 76 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4} - {\left(24 \, c^{4} + 52 \, c^{3} d + 35 \, c^{2} d^{2} + 7 \, c d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(66 \, c^{4} + 149 \, c^{3} d + 110 \, c^{2} d^{2} + 29 \, c d^{3} + 2 \, d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(25 \, c^{4} + 53 \, c^{3} d + 35 \, c^{2} d^{2} + 7 \, c d^{3}\right)} \cos\left(f x + e\right) - {\left(51 \, c^{4} + 110 \, c^{3} d + 76 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4} - {\left(16 \, c^{4} + 40 \, c^{3} d + 34 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(40 \, c^{4} + 92 \, c^{3} d + 69 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(26 \, c^{4} + 57 \, c^{3} d + 41 \, c^{2} d^{2} + 11 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{c g}{a c + a d}} + {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} g + {\left({\left(128 \, c^{4} + 256 \, c^{3} d + 160 \, c^{2} d^{2} + 32 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right)^{4} + 4 \, {\left(64 \, c^{4} + 112 \, c^{3} d + 56 \, c^{2} d^{2} + 7 \, c d^{3}\right)} g \cos\left(f x + e\right)^{3} - 2 \, {\left(80 \, c^{4} + 144 \, c^{3} d + 83 \, c^{2} d^{2} + 18 \, c d^{3} + d^{4}\right)} g \cos\left(f x + e\right)^{2} - 4 \, {\left(72 \, c^{4} + 119 \, c^{3} d + 56 \, c^{2} d^{2} + 7 \, c d^{3}\right)} g \cos\left(f x + e\right) + {\left(c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} g\right)} \sin\left(f x + e\right)}{d^{4} \cos\left(f x + e\right)^{5} + {\left(4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(2 \, c^{3} d + 3 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{4} + 6 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right) + {\left(d^{4} \cos\left(f x + e\right)^{4} - 4 \, c d^{3} \cos\left(f x + e\right)^{3} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}\right)}{4 \, {\left(c - d\right)} f}, -\frac{\sqrt{2} \sqrt{\frac{g}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{g}{a}} {\left(3 \, \sin\left(f x + e\right) - 1\right)}}{4 \, g \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) - \sqrt{\frac{c g}{a c + a d}} \arctan\left(\frac{{\left({\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} - 8 \, c d - d^{2} + 2 \, {\left(4 \, c^{2} + 3 \, c d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{c g}{a c + a d}}}{4 \, {\left({\left(2 \, c^{2} + c d\right)} g \cos\left(f x + e\right)^{3} + c^{2} g \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(2 \, c^{2} + c d\right)} g \cos\left(f x + e\right)\right)}}\right)}{2 \, {\left(c - d\right)} f}\right]"," ",0,"[-1/4*(sqrt(2)*sqrt(-g/a)*log((17*g*cos(f*x + e)^3 - 4*sqrt(2)*(3*cos(f*x + e)^2 + (3*cos(f*x + e) + 4)*sin(f*x + e) - cos(f*x + e) - 4)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-g/a) + 3*g*cos(f*x + e)^2 - 18*g*cos(f*x + e) + (17*g*cos(f*x + e)^2 + 14*g*cos(f*x + e) - 4*g)*sin(f*x + e) - 4*g)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4)) + sqrt(-c*g/(a*c + a*d))*log(((128*c^4 + 256*c^3*d + 160*c^2*d^2 + 32*c*d^3 + d^4)*g*cos(f*x + e)^5 - (128*c^4 + 192*c^3*d + 64*c^2*d^2 - 4*c*d^3 - d^4)*g*cos(f*x + e)^4 - 2*(208*c^4 + 368*c^3*d + 195*c^2*d^2 + 32*c*d^3 + d^4)*g*cos(f*x + e)^3 + 2*(64*c^4 + 94*c^3*d + 29*c^2*d^2 - 4*c*d^3 - d^4)*g*cos(f*x + e)^2 + (289*c^4 + 480*c^3*d + 230*c^2*d^2 + 32*c*d^3 + d^4)*g*cos(f*x + e) + 8*((16*c^4 + 40*c^3*d + 34*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e)^4 + 51*c^4 + 110*c^3*d + 76*c^2*d^2 + 18*c*d^3 + d^4 - (24*c^4 + 52*c^3*d + 35*c^2*d^2 + 7*c*d^3)*cos(f*x + e)^3 - (66*c^4 + 149*c^3*d + 110*c^2*d^2 + 29*c*d^3 + 2*d^4)*cos(f*x + e)^2 + (25*c^4 + 53*c^3*d + 35*c^2*d^2 + 7*c*d^3)*cos(f*x + e) - (51*c^4 + 110*c^3*d + 76*c^2*d^2 + 18*c*d^3 + d^4 - (16*c^4 + 40*c^3*d + 34*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e)^3 - (40*c^4 + 92*c^3*d + 69*c^2*d^2 + 18*c*d^3 + d^4)*cos(f*x + e)^2 + (26*c^4 + 57*c^3*d + 41*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-c*g/(a*c + a*d)) + (c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*g + ((128*c^4 + 256*c^3*d + 160*c^2*d^2 + 32*c*d^3 + d^4)*g*cos(f*x + e)^4 + 4*(64*c^4 + 112*c^3*d + 56*c^2*d^2 + 7*c*d^3)*g*cos(f*x + e)^3 - 2*(80*c^4 + 144*c^3*d + 83*c^2*d^2 + 18*c*d^3 + d^4)*g*cos(f*x + e)^2 - 4*(72*c^4 + 119*c^3*d + 56*c^2*d^2 + 7*c*d^3)*g*cos(f*x + e) + (c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*g)*sin(f*x + e))/(d^4*cos(f*x + e)^5 + (4*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + d^4)*cos(f*x + e)^3 - 2*(2*c^3*d + 3*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e)^2 + (c^4 + 6*c^2*d^2 + d^4)*cos(f*x + e) + (d^4*cos(f*x + e)^4 - 4*c*d^3*cos(f*x + e)^3 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + 2*c*d^3 + d^4)*cos(f*x + e)^2 + 4*(c^3*d + c*d^3)*cos(f*x + e))*sin(f*x + e))))/((c - d)*f), -1/4*(sqrt(2)*sqrt(-g/a)*log((17*g*cos(f*x + e)^3 - 4*sqrt(2)*(3*cos(f*x + e)^2 + (3*cos(f*x + e) + 4)*sin(f*x + e) - cos(f*x + e) - 4)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-g/a) + 3*g*cos(f*x + e)^2 - 18*g*cos(f*x + e) + (17*g*cos(f*x + e)^2 + 14*g*cos(f*x + e) - 4*g)*sin(f*x + e) - 4*g)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4)) - 2*sqrt(c*g/(a*c + a*d))*arctan(1/4*((8*c^2 + 8*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 - 8*c*d - d^2 + 2*(4*c^2 + 3*c*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(c*g/(a*c + a*d))/((2*c^2 + c*d)*g*cos(f*x + e)^3 + c^2*g*cos(f*x + e)*sin(f*x + e) - (2*c^2 + c*d)*g*cos(f*x + e))))/((c - d)*f), -1/4*(2*sqrt(2)*sqrt(g/a)*arctan(1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(g/a)*(3*sin(f*x + e) - 1)/(g*cos(f*x + e)*sin(f*x + e))) + sqrt(-c*g/(a*c + a*d))*log(((128*c^4 + 256*c^3*d + 160*c^2*d^2 + 32*c*d^3 + d^4)*g*cos(f*x + e)^5 - (128*c^4 + 192*c^3*d + 64*c^2*d^2 - 4*c*d^3 - d^4)*g*cos(f*x + e)^4 - 2*(208*c^4 + 368*c^3*d + 195*c^2*d^2 + 32*c*d^3 + d^4)*g*cos(f*x + e)^3 + 2*(64*c^4 + 94*c^3*d + 29*c^2*d^2 - 4*c*d^3 - d^4)*g*cos(f*x + e)^2 + (289*c^4 + 480*c^3*d + 230*c^2*d^2 + 32*c*d^3 + d^4)*g*cos(f*x + e) + 8*((16*c^4 + 40*c^3*d + 34*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e)^4 + 51*c^4 + 110*c^3*d + 76*c^2*d^2 + 18*c*d^3 + d^4 - (24*c^4 + 52*c^3*d + 35*c^2*d^2 + 7*c*d^3)*cos(f*x + e)^3 - (66*c^4 + 149*c^3*d + 110*c^2*d^2 + 29*c*d^3 + 2*d^4)*cos(f*x + e)^2 + (25*c^4 + 53*c^3*d + 35*c^2*d^2 + 7*c*d^3)*cos(f*x + e) - (51*c^4 + 110*c^3*d + 76*c^2*d^2 + 18*c*d^3 + d^4 - (16*c^4 + 40*c^3*d + 34*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e)^3 - (40*c^4 + 92*c^3*d + 69*c^2*d^2 + 18*c*d^3 + d^4)*cos(f*x + e)^2 + (26*c^4 + 57*c^3*d + 41*c^2*d^2 + 11*c*d^3 + d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-c*g/(a*c + a*d)) + (c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*g + ((128*c^4 + 256*c^3*d + 160*c^2*d^2 + 32*c*d^3 + d^4)*g*cos(f*x + e)^4 + 4*(64*c^4 + 112*c^3*d + 56*c^2*d^2 + 7*c*d^3)*g*cos(f*x + e)^3 - 2*(80*c^4 + 144*c^3*d + 83*c^2*d^2 + 18*c*d^3 + d^4)*g*cos(f*x + e)^2 - 4*(72*c^4 + 119*c^3*d + 56*c^2*d^2 + 7*c*d^3)*g*cos(f*x + e) + (c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4)*g)*sin(f*x + e))/(d^4*cos(f*x + e)^5 + (4*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + d^4)*cos(f*x + e)^3 - 2*(2*c^3*d + 3*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e)^2 + (c^4 + 6*c^2*d^2 + d^4)*cos(f*x + e) + (d^4*cos(f*x + e)^4 - 4*c*d^3*cos(f*x + e)^3 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + 2*c*d^3 + d^4)*cos(f*x + e)^2 + 4*(c^3*d + c*d^3)*cos(f*x + e))*sin(f*x + e))))/((c - d)*f), -1/2*(sqrt(2)*sqrt(g/a)*arctan(1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(g/a)*(3*sin(f*x + e) - 1)/(g*cos(f*x + e)*sin(f*x + e))) - sqrt(c*g/(a*c + a*d))*arctan(1/4*((8*c^2 + 8*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 - 8*c*d - d^2 + 2*(4*c^2 + 3*c*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(c*g/(a*c + a*d))/((2*c^2 + c*d)*g*cos(f*x + e)^3 + c^2*g*cos(f*x + e)*sin(f*x + e) - (2*c^2 + c*d)*g*cos(f*x + e))))/((c - d)*f)]","A",0
28,1,3175,0,4.894402," ","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=""fricas"")","\left[-\frac{\sqrt{2} {\left(a c^{2} + a c d\right)} g \sqrt{-\frac{1}{a g}} \log\left(\frac{4 \, \sqrt{2} {\left(3 \, \cos\left(f x + e\right)^{2} + {\left(3 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 4\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{1}{a g}} + 17 \, \cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(17 \, \cos\left(f x + e\right)^{2} + 14 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 18 \, \cos\left(f x + e\right) - 4}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right) - \sqrt{-{\left(a c^{2} + a c d\right)} g} d \log\left(\frac{{\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{5} - {\left(128 \, a c^{4} + 192 \, a c^{3} d + 64 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} g \cos\left(f x + e\right)^{4} - 2 \, {\left(208 \, a c^{4} + 368 \, a c^{3} d + 195 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{3} + 2 \, {\left(64 \, a c^{4} + 94 \, a c^{3} d + 29 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} g \cos\left(f x + e\right)^{2} + {\left(289 \, a c^{4} + 480 \, a c^{3} d + 230 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right) + 8 \, {\left({\left(16 \, c^{3} + 24 \, c^{2} d + 10 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{4} - {\left(24 \, c^{3} + 28 \, c^{2} d + 7 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + 51 \, c^{3} + 59 \, c^{2} d + 17 \, c d^{2} + d^{3} - {\left(66 \, c^{3} + 83 \, c^{2} d + 27 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(25 \, c^{3} + 28 \, c^{2} d + 7 \, c d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(16 \, c^{3} + 24 \, c^{2} d + 10 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{3} - 51 \, c^{3} - 59 \, c^{2} d - 17 \, c d^{2} - d^{3} + {\left(40 \, c^{3} + 52 \, c^{2} d + 17 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(26 \, c^{3} + 31 \, c^{2} d + 10 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-{\left(a c^{2} + a c d\right)} g} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} g + {\left({\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{4} + 4 \, {\left(64 \, a c^{4} + 112 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} g \cos\left(f x + e\right)^{3} - 2 \, {\left(80 \, a c^{4} + 144 \, a c^{3} d + 83 \, a c^{2} d^{2} + 18 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{2} - 4 \, {\left(72 \, a c^{4} + 119 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} g \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} g\right)} \sin\left(f x + e\right)}{d^{4} \cos\left(f x + e\right)^{5} + {\left(4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(2 \, c^{3} d + 3 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{4} + 6 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right) + {\left(d^{4} \cos\left(f x + e\right)^{4} - 4 \, c d^{3} \cos\left(f x + e\right)^{3} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}\right)}{4 \, {\left(a c^{3} - a c d^{2}\right)} f g}, \frac{2 \, \sqrt{2} {\left(a c^{2} + a c d\right)} g \sqrt{\frac{1}{a g}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{1}{a g}} {\left(3 \, \sin\left(f x + e\right) - 1\right)}}{4 \, \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) + \sqrt{-{\left(a c^{2} + a c d\right)} g} d \log\left(\frac{{\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{5} - {\left(128 \, a c^{4} + 192 \, a c^{3} d + 64 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} g \cos\left(f x + e\right)^{4} - 2 \, {\left(208 \, a c^{4} + 368 \, a c^{3} d + 195 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{3} + 2 \, {\left(64 \, a c^{4} + 94 \, a c^{3} d + 29 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} g \cos\left(f x + e\right)^{2} + {\left(289 \, a c^{4} + 480 \, a c^{3} d + 230 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right) + 8 \, {\left({\left(16 \, c^{3} + 24 \, c^{2} d + 10 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{4} - {\left(24 \, c^{3} + 28 \, c^{2} d + 7 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + 51 \, c^{3} + 59 \, c^{2} d + 17 \, c d^{2} + d^{3} - {\left(66 \, c^{3} + 83 \, c^{2} d + 27 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(25 \, c^{3} + 28 \, c^{2} d + 7 \, c d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(16 \, c^{3} + 24 \, c^{2} d + 10 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{3} - 51 \, c^{3} - 59 \, c^{2} d - 17 \, c d^{2} - d^{3} + {\left(40 \, c^{3} + 52 \, c^{2} d + 17 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(26 \, c^{3} + 31 \, c^{2} d + 10 \, c d^{2} + d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-{\left(a c^{2} + a c d\right)} g} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} g + {\left({\left(128 \, a c^{4} + 256 \, a c^{3} d + 160 \, a c^{2} d^{2} + 32 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{4} + 4 \, {\left(64 \, a c^{4} + 112 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} g \cos\left(f x + e\right)^{3} - 2 \, {\left(80 \, a c^{4} + 144 \, a c^{3} d + 83 \, a c^{2} d^{2} + 18 \, a c d^{3} + a d^{4}\right)} g \cos\left(f x + e\right)^{2} - 4 \, {\left(72 \, a c^{4} + 119 \, a c^{3} d + 56 \, a c^{2} d^{2} + 7 \, a c d^{3}\right)} g \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4}\right)} g\right)} \sin\left(f x + e\right)}{d^{4} \cos\left(f x + e\right)^{5} + {\left(4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(2 \, c^{3} d + 3 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{4} + 6 \, c^{2} d^{2} + d^{4}\right)} \cos\left(f x + e\right) + {\left(d^{4} \cos\left(f x + e\right)^{4} - 4 \, c d^{3} \cos\left(f x + e\right)^{3} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(3 \, c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(c^{3} d + c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}\right)}{4 \, {\left(a c^{3} - a c d^{2}\right)} f g}, -\frac{\sqrt{2} {\left(a c^{2} + a c d\right)} g \sqrt{-\frac{1}{a g}} \log\left(\frac{4 \, \sqrt{2} {\left(3 \, \cos\left(f x + e\right)^{2} + {\left(3 \, \cos\left(f x + e\right) + 4\right)} \sin\left(f x + e\right) - \cos\left(f x + e\right) - 4\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{-\frac{1}{a g}} + 17 \, \cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(17 \, \cos\left(f x + e\right)^{2} + 14 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 18 \, \cos\left(f x + e\right) - 4}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right) + 2 \, \sqrt{{\left(a c^{2} + a c d\right)} g} d \arctan\left(\frac{{\left({\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} - 8 \, c d - d^{2} + 2 \, {\left(4 \, c^{2} + 3 \, c d\right)} \sin\left(f x + e\right)\right)} \sqrt{{\left(a c^{2} + a c d\right)} g} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, {\left({\left(2 \, a c^{3} + 3 \, a c^{2} d + a c d^{2}\right)} g \cos\left(f x + e\right)^{3} + {\left(a c^{3} + a c^{2} d\right)} g \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(2 \, a c^{3} + 3 \, a c^{2} d + a c d^{2}\right)} g \cos\left(f x + e\right)\right)}}\right)}{4 \, {\left(a c^{3} - a c d^{2}\right)} f g}, \frac{\sqrt{2} {\left(a c^{2} + a c d\right)} g \sqrt{\frac{1}{a g}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)} \sqrt{\frac{1}{a g}} {\left(3 \, \sin\left(f x + e\right) - 1\right)}}{4 \, \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) - \sqrt{{\left(a c^{2} + a c d\right)} g} d \arctan\left(\frac{{\left({\left(8 \, c^{2} + 8 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} - 8 \, c d - d^{2} + 2 \, {\left(4 \, c^{2} + 3 \, c d\right)} \sin\left(f x + e\right)\right)} \sqrt{{\left(a c^{2} + a c d\right)} g} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{4 \, {\left({\left(2 \, a c^{3} + 3 \, a c^{2} d + a c d^{2}\right)} g \cos\left(f x + e\right)^{3} + {\left(a c^{3} + a c^{2} d\right)} g \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(2 \, a c^{3} + 3 \, a c^{2} d + a c d^{2}\right)} g \cos\left(f x + e\right)\right)}}\right)}{2 \, {\left(a c^{3} - a c d^{2}\right)} f g}\right]"," ",0,"[-1/4*(sqrt(2)*(a*c^2 + a*c*d)*g*sqrt(-1/(a*g))*log((4*sqrt(2)*(3*cos(f*x + e)^2 + (3*cos(f*x + e) + 4)*sin(f*x + e) - cos(f*x + e) - 4)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-1/(a*g)) + 17*cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (17*cos(f*x + e)^2 + 14*cos(f*x + e) - 4)*sin(f*x + e) - 18*cos(f*x + e) - 4)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4)) - sqrt(-(a*c^2 + a*c*d)*g)*d*log(((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^5 - (128*a*c^4 + 192*a*c^3*d + 64*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*g*cos(f*x + e)^4 - 2*(208*a*c^4 + 368*a*c^3*d + 195*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^3 + 2*(64*a*c^4 + 94*a*c^3*d + 29*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*g*cos(f*x + e)^2 + (289*a*c^4 + 480*a*c^3*d + 230*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e) + 8*((16*c^3 + 24*c^2*d + 10*c*d^2 + d^3)*cos(f*x + e)^4 - (24*c^3 + 28*c^2*d + 7*c*d^2)*cos(f*x + e)^3 + 51*c^3 + 59*c^2*d + 17*c*d^2 + d^3 - (66*c^3 + 83*c^2*d + 27*c*d^2 + 2*d^3)*cos(f*x + e)^2 + (25*c^3 + 28*c^2*d + 7*c*d^2)*cos(f*x + e) + ((16*c^3 + 24*c^2*d + 10*c*d^2 + d^3)*cos(f*x + e)^3 - 51*c^3 - 59*c^2*d - 17*c*d^2 - d^3 + (40*c^3 + 52*c^2*d + 17*c*d^2 + d^3)*cos(f*x + e)^2 - (26*c^3 + 31*c^2*d + 10*c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-(a*c^2 + a*c*d)*g)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*g + ((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^4 + 4*(64*a*c^4 + 112*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*g*cos(f*x + e)^3 - 2*(80*a*c^4 + 144*a*c^3*d + 83*a*c^2*d^2 + 18*a*c*d^3 + a*d^4)*g*cos(f*x + e)^2 - 4*(72*a*c^4 + 119*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*g*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*g)*sin(f*x + e))/(d^4*cos(f*x + e)^5 + (4*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + d^4)*cos(f*x + e)^3 - 2*(2*c^3*d + 3*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e)^2 + (c^4 + 6*c^2*d^2 + d^4)*cos(f*x + e) + (d^4*cos(f*x + e)^4 - 4*c*d^3*cos(f*x + e)^3 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + 2*c*d^3 + d^4)*cos(f*x + e)^2 + 4*(c^3*d + c*d^3)*cos(f*x + e))*sin(f*x + e))))/((a*c^3 - a*c*d^2)*f*g), 1/4*(2*sqrt(2)*(a*c^2 + a*c*d)*g*sqrt(1/(a*g))*arctan(1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(1/(a*g))*(3*sin(f*x + e) - 1)/(cos(f*x + e)*sin(f*x + e))) + sqrt(-(a*c^2 + a*c*d)*g)*d*log(((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^5 - (128*a*c^4 + 192*a*c^3*d + 64*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*g*cos(f*x + e)^4 - 2*(208*a*c^4 + 368*a*c^3*d + 195*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^3 + 2*(64*a*c^4 + 94*a*c^3*d + 29*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*g*cos(f*x + e)^2 + (289*a*c^4 + 480*a*c^3*d + 230*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e) + 8*((16*c^3 + 24*c^2*d + 10*c*d^2 + d^3)*cos(f*x + e)^4 - (24*c^3 + 28*c^2*d + 7*c*d^2)*cos(f*x + e)^3 + 51*c^3 + 59*c^2*d + 17*c*d^2 + d^3 - (66*c^3 + 83*c^2*d + 27*c*d^2 + 2*d^3)*cos(f*x + e)^2 + (25*c^3 + 28*c^2*d + 7*c*d^2)*cos(f*x + e) + ((16*c^3 + 24*c^2*d + 10*c*d^2 + d^3)*cos(f*x + e)^3 - 51*c^3 - 59*c^2*d - 17*c*d^2 - d^3 + (40*c^3 + 52*c^2*d + 17*c*d^2 + d^3)*cos(f*x + e)^2 - (26*c^3 + 31*c^2*d + 10*c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-(a*c^2 + a*c*d)*g)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e)) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*g + ((128*a*c^4 + 256*a*c^3*d + 160*a*c^2*d^2 + 32*a*c*d^3 + a*d^4)*g*cos(f*x + e)^4 + 4*(64*a*c^4 + 112*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*g*cos(f*x + e)^3 - 2*(80*a*c^4 + 144*a*c^3*d + 83*a*c^2*d^2 + 18*a*c*d^3 + a*d^4)*g*cos(f*x + e)^2 - 4*(72*a*c^4 + 119*a*c^3*d + 56*a*c^2*d^2 + 7*a*c*d^3)*g*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4)*g)*sin(f*x + e))/(d^4*cos(f*x + e)^5 + (4*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + d^4)*cos(f*x + e)^3 - 2*(2*c^3*d + 3*c^2*d^2 + 4*c*d^3 + d^4)*cos(f*x + e)^2 + (c^4 + 6*c^2*d^2 + d^4)*cos(f*x + e) + (d^4*cos(f*x + e)^4 - 4*c*d^3*cos(f*x + e)^3 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(3*c^2*d^2 + 2*c*d^3 + d^4)*cos(f*x + e)^2 + 4*(c^3*d + c*d^3)*cos(f*x + e))*sin(f*x + e))))/((a*c^3 - a*c*d^2)*f*g), -1/4*(sqrt(2)*(a*c^2 + a*c*d)*g*sqrt(-1/(a*g))*log((4*sqrt(2)*(3*cos(f*x + e)^2 + (3*cos(f*x + e) + 4)*sin(f*x + e) - cos(f*x + e) - 4)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(-1/(a*g)) + 17*cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (17*cos(f*x + e)^2 + 14*cos(f*x + e) - 4)*sin(f*x + e) - 18*cos(f*x + e) - 4)/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4)) + 2*sqrt((a*c^2 + a*c*d)*g)*d*arctan(1/4*((8*c^2 + 8*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 - 8*c*d - d^2 + 2*(4*c^2 + 3*c*d)*sin(f*x + e))*sqrt((a*c^2 + a*c*d)*g)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/((2*a*c^3 + 3*a*c^2*d + a*c*d^2)*g*cos(f*x + e)^3 + (a*c^3 + a*c^2*d)*g*cos(f*x + e)*sin(f*x + e) - (2*a*c^3 + 3*a*c^2*d + a*c*d^2)*g*cos(f*x + e))))/((a*c^3 - a*c*d^2)*f*g), 1/2*(sqrt(2)*(a*c^2 + a*c*d)*g*sqrt(1/(a*g))*arctan(1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))*sqrt(1/(a*g))*(3*sin(f*x + e) - 1)/(cos(f*x + e)*sin(f*x + e))) - sqrt((a*c^2 + a*c*d)*g)*d*arctan(1/4*((8*c^2 + 8*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 - 8*c*d - d^2 + 2*(4*c^2 + 3*c*d)*sin(f*x + e))*sqrt((a*c^2 + a*c*d)*g)*sqrt(a*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/((2*a*c^3 + 3*a*c^2*d + a*c*d^2)*g*cos(f*x + e)^3 + (a*c^3 + a*c^2*d)*g*cos(f*x + e)*sin(f*x + e) - (2*a*c^3 + 3*a*c^2*d + a*c*d^2)*g*cos(f*x + e))))/((a*c^3 - a*c*d^2)*f*g)]","B",0
29,-2,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+c*sin(f*x+e)),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   failed of mode Union(SparseUnivariatePolynomial(SimpleAlgebraicExtension(InnerPrimeField(17),SparseUnivariatePolynomial(InnerPrimeField(17)),?^2+2*?+13)),failed) cannot be coerced to mode SparseUnivariatePolynomial(SimpleAlgebraicExtension(InnerPrimeField(17),SparseUnivariatePolynomial(InnerPrimeField(17)),?^2+2*?+13))","F(-2)",0
30,0,0,0,1.124318," ","integrate(1/sin(f*x+e)/(c+c*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a}}{{\left(a + b\right)} c \cos\left(f x + e\right)^{2} - {\left(a + b\right)} c + {\left(b c \cos\left(f x + e\right)^{2} - {\left(a + b\right)} c\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)/((a + b)*c*cos(f*x + e)^2 - (a + b)*c + (b*c*cos(f*x + e)^2 - (a + b)*c)*sin(f*x + e)), x)","F",0
31,-1,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)*(a+b*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,0,0,0,1.192034," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{c g \cos\left(f x + e\right)^{2} - c g \sin\left(f x + e\right) - c g}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(c*g*cos(f*x + e)^2 - c*g*sin(f*x + e) - c*g), x)","F",0
33,0,0,0,0.816045," ","integrate((g*sin(f*x+e))^(1/2)/(c+c*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{b c \cos\left(f x + e\right)^{2} - {\left(a + b\right)} c \sin\left(f x + e\right) - {\left(a + b\right)} c}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(b*c*cos(f*x + e)^2 - (a + b)*c*sin(f*x + e) - (a + b)*c), x)","F",0
34,0,0,0,1.237323," ","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=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{{\left(a + b\right)} c g \cos\left(f x + e\right)^{2} - {\left(a + b\right)} c g + {\left(b c g \cos\left(f x + e\right)^{2} - {\left(a + b\right)} c g\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/((a + b)*c*g*cos(f*x + e)^2 - (a + b)*c*g + (b*c*g*cos(f*x + e)^2 - (a + b)*c*g)*sin(f*x + e)), x)","F",0
35,1,3539,0,3.450645," ","integrate((a+a*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} \log\left(\frac{{\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - {\left(31 \, a c^{4} - 196 \, a c^{3} d + 154 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(81 \, a c^{4} - 252 \, a c^{3} d + 150 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(79 \, a c^{4} - 100 \, a c^{3} d + 74 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(5 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + 51 \, c^{3} - 59 \, c^{2} d + 17 \, c d^{2} - d^{3} - 2 \, {\left(18 \, c^{3} - 33 \, c^{2} d + 12 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - 51 \, c^{3} + 59 \, c^{2} d - 17 \, c d^{2} + d^{3} + {\left(11 \, c^{3} - 35 \, c^{2} d + 17 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(25 \, c^{3} - 31 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} + {\left(289 \, a c^{4} - 476 \, a c^{3} d + 230 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + {\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{4} + 32 \, {\left(a c^{4} - 7 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(65 \, a c^{4} - 140 \, a c^{3} d + 38 \, a c^{2} d^{2} - 12 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{2} - 32 \, {\left(9 \, a c^{4} - 15 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right) + 1}\right) + \sqrt{-a d} \log\left(\frac{128 \, a d^{4} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + 128 \, {\left(2 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 32 \, {\left(5 \, a c^{2} d^{2} - 14 \, a c d^{3} + 13 \, a d^{4}\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(a c^{3} d - 2 \, a c^{2} d^{2} + 9 \, a c d^{3} - 4 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left(16 \, d^{3} \cos\left(f x + e\right)^{4} + 24 \, {\left(c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - c^{3} + 17 \, c^{2} d - 59 \, c d^{2} + 51 \, d^{3} - 2 \, {\left(5 \, c^{2} d - 26 \, c d^{2} + 33 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{3} - 7 \, c^{2} d + 31 \, c d^{2} - 25 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(16 \, d^{3} \cos\left(f x + e\right)^{3} + c^{3} - 17 \, c^{2} d + 59 \, c d^{2} - 51 \, d^{3} - 8 \, {\left(3 \, c d^{2} - 5 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, c^{2} d - 14 \, c d^{2} + 13 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-a d} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} + {\left(a c^{4} - 28 \, a c^{3} d + 230 \, a c^{2} d^{2} - 476 \, a c d^{3} + 289 \, a d^{4}\right)} \cos\left(f x + e\right) + {\left(128 \, a d^{4} \cos\left(f x + e\right)^{4} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - 256 \, {\left(a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(5 \, a c^{2} d^{2} - 6 \, a c d^{3} + 5 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} + 32 \, {\left(a c^{3} d - 7 \, a c^{2} d^{2} + 15 \, a c d^{3} - 9 \, a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1}\right)}{4 \, f}, \frac{2 \, \sqrt{-a c} \arctan\left(-\frac{{\left({\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} + 6 \, c d - d^{2} + 8 \, {\left(c^{2} - c d\right)} \sin\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{4 \, {\left({\left(a c^{2} d - a c d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(a c^{3} - 3 \, a c^{2} d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, a c^{3} - a c^{2} d + a c d^{2}\right)} \cos\left(f x + e\right)\right)}}\right) + \sqrt{-a d} \log\left(\frac{128 \, a d^{4} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + 128 \, {\left(2 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 32 \, {\left(5 \, a c^{2} d^{2} - 14 \, a c d^{3} + 13 \, a d^{4}\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(a c^{3} d - 2 \, a c^{2} d^{2} + 9 \, a c d^{3} - 4 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left(16 \, d^{3} \cos\left(f x + e\right)^{4} + 24 \, {\left(c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - c^{3} + 17 \, c^{2} d - 59 \, c d^{2} + 51 \, d^{3} - 2 \, {\left(5 \, c^{2} d - 26 \, c d^{2} + 33 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(c^{3} - 7 \, c^{2} d + 31 \, c d^{2} - 25 \, d^{3}\right)} \cos\left(f x + e\right) + {\left(16 \, d^{3} \cos\left(f x + e\right)^{3} + c^{3} - 17 \, c^{2} d + 59 \, c d^{2} - 51 \, d^{3} - 8 \, {\left(3 \, c d^{2} - 5 \, d^{3}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, c^{2} d - 14 \, c d^{2} + 13 \, d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-a d} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} + {\left(a c^{4} - 28 \, a c^{3} d + 230 \, a c^{2} d^{2} - 476 \, a c d^{3} + 289 \, a d^{4}\right)} \cos\left(f x + e\right) + {\left(128 \, a d^{4} \cos\left(f x + e\right)^{4} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - 256 \, {\left(a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{3} - 32 \, {\left(5 \, a c^{2} d^{2} - 6 \, a c d^{3} + 5 \, a d^{4}\right)} \cos\left(f x + e\right)^{2} + 32 \, {\left(a c^{3} d - 7 \, a c^{2} d^{2} + 15 \, a c d^{3} - 9 \, a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1}\right)}{4 \, f}, \frac{2 \, \sqrt{a d} \arctan\left(\frac{{\left(8 \, d^{2} \cos\left(f x + e\right)^{2} - c^{2} + 6 \, c d - 9 \, d^{2} - 8 \, {\left(c d - d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a d} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{4 \, {\left(2 \, a d^{3} \cos\left(f x + e\right)^{3} - {\left(3 \, a c d^{2} - a d^{3}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} d - a c d^{2} + 2 \, a d^{3}\right)} \cos\left(f x + e\right)\right)}}\right) + \sqrt{a c} \log\left(\frac{{\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - {\left(31 \, a c^{4} - 196 \, a c^{3} d + 154 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(81 \, a c^{4} - 252 \, a c^{3} d + 150 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(79 \, a c^{4} - 100 \, a c^{3} d + 74 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(5 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + 51 \, c^{3} - 59 \, c^{2} d + 17 \, c d^{2} - d^{3} - 2 \, {\left(18 \, c^{3} - 33 \, c^{2} d + 12 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - 51 \, c^{3} + 59 \, c^{2} d - 17 \, c d^{2} + d^{3} + {\left(11 \, c^{3} - 35 \, c^{2} d + 17 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(25 \, c^{3} - 31 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} + {\left(289 \, a c^{4} - 476 \, a c^{3} d + 230 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + {\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{4} + 32 \, {\left(a c^{4} - 7 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(65 \, a c^{4} - 140 \, a c^{3} d + 38 \, a c^{2} d^{2} - 12 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{2} - 32 \, {\left(9 \, a c^{4} - 15 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right) + 1}\right)}{4 \, f}, \frac{\sqrt{-a c} \arctan\left(-\frac{{\left({\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} + 6 \, c d - d^{2} + 8 \, {\left(c^{2} - c d\right)} \sin\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{4 \, {\left({\left(a c^{2} d - a c d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(a c^{3} - 3 \, a c^{2} d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, a c^{3} - a c^{2} d + a c d^{2}\right)} \cos\left(f x + e\right)\right)}}\right) + \sqrt{a d} \arctan\left(\frac{{\left(8 \, d^{2} \cos\left(f x + e\right)^{2} - c^{2} + 6 \, c d - 9 \, d^{2} - 8 \, {\left(c d - d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a d} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{4 \, {\left(2 \, a d^{3} \cos\left(f x + e\right)^{3} - {\left(3 \, a c d^{2} - a d^{3}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(a c^{2} d - a c d^{2} + 2 \, a d^{3}\right)} \cos\left(f x + e\right)\right)}}\right)}{2 \, f}\right]"," ",0,"[1/4*(sqrt(a*c)*log(((a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - (31*a*c^4 - 196*a*c^3*d + 154*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 2*(81*a*c^4 - 252*a*c^3*d + 150*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^3 + 2*(79*a*c^4 - 100*a*c^3*d + 74*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^2 - 8*((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^4 - 2*(5*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e)^3 + 51*c^3 - 59*c^2*d + 17*c*d^2 - d^3 - 2*(18*c^3 - 33*c^2*d + 12*c*d^2 - d^3)*cos(f*x + e)^2 + 2*(13*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e) + ((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^3 - 51*c^3 + 59*c^2*d - 17*c*d^2 + d^3 + (11*c^3 - 35*c^2*d + 17*c*d^2 - d^3)*cos(f*x + e)^2 - (25*c^3 - 31*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c) + (289*a*c^4 - 476*a*c^3*d + 230*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + (a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^4 + 32*(a*c^4 - 7*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e)^3 - 2*(65*a*c^4 - 140*a*c^3*d + 38*a*c^2*d^2 - 12*a*c*d^3 + a*d^4)*cos(f*x + e)^2 - 32*(9*a*c^4 - 15*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^5 + cos(f*x + e)^4 - 2*cos(f*x + e)^3 - 2*cos(f*x + e)^2 + (cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sin(f*x + e) + cos(f*x + e) + 1)) + sqrt(-a*d)*log((128*a*d^4*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + 128*(2*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 32*(5*a*c^2*d^2 - 14*a*c*d^3 + 13*a*d^4)*cos(f*x + e)^3 - 32*(a*c^3*d - 2*a*c^2*d^2 + 9*a*c*d^3 - 4*a*d^4)*cos(f*x + e)^2 - 8*(16*d^3*cos(f*x + e)^4 + 24*(c*d^2 - d^3)*cos(f*x + e)^3 - c^3 + 17*c^2*d - 59*c*d^2 + 51*d^3 - 2*(5*c^2*d - 26*c*d^2 + 33*d^3)*cos(f*x + e)^2 - (c^3 - 7*c^2*d + 31*c*d^2 - 25*d^3)*cos(f*x + e) + (16*d^3*cos(f*x + e)^3 + c^3 - 17*c^2*d + 59*c*d^2 - 51*d^3 - 8*(3*c*d^2 - 5*d^3)*cos(f*x + e)^2 - 2*(5*c^2*d - 14*c*d^2 + 13*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-a*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c) + (a*c^4 - 28*a*c^3*d + 230*a*c^2*d^2 - 476*a*c*d^3 + 289*a*d^4)*cos(f*x + e) + (128*a*d^4*cos(f*x + e)^4 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - 256*(a*c*d^3 - a*d^4)*cos(f*x + e)^3 - 32*(5*a*c^2*d^2 - 6*a*c*d^3 + 5*a*d^4)*cos(f*x + e)^2 + 32*(a*c^3*d - 7*a*c^2*d^2 + 15*a*c*d^3 - 9*a*d^4)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e) + sin(f*x + e) + 1)))/f, 1/4*(2*sqrt(-a*c)*arctan(-1/4*((c^2 - 6*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 + 6*c*d - d^2 + 8*(c^2 - c*d)*sin(f*x + e))*sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/((a*c^2*d - a*c*d^2)*cos(f*x + e)^3 - (a*c^3 - 3*a*c^2*d)*cos(f*x + e)*sin(f*x + e) + (2*a*c^3 - a*c^2*d + a*c*d^2)*cos(f*x + e))) + sqrt(-a*d)*log((128*a*d^4*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + 128*(2*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 32*(5*a*c^2*d^2 - 14*a*c*d^3 + 13*a*d^4)*cos(f*x + e)^3 - 32*(a*c^3*d - 2*a*c^2*d^2 + 9*a*c*d^3 - 4*a*d^4)*cos(f*x + e)^2 - 8*(16*d^3*cos(f*x + e)^4 + 24*(c*d^2 - d^3)*cos(f*x + e)^3 - c^3 + 17*c^2*d - 59*c*d^2 + 51*d^3 - 2*(5*c^2*d - 26*c*d^2 + 33*d^3)*cos(f*x + e)^2 - (c^3 - 7*c^2*d + 31*c*d^2 - 25*d^3)*cos(f*x + e) + (16*d^3*cos(f*x + e)^3 + c^3 - 17*c^2*d + 59*c*d^2 - 51*d^3 - 8*(3*c*d^2 - 5*d^3)*cos(f*x + e)^2 - 2*(5*c^2*d - 14*c*d^2 + 13*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-a*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c) + (a*c^4 - 28*a*c^3*d + 230*a*c^2*d^2 - 476*a*c*d^3 + 289*a*d^4)*cos(f*x + e) + (128*a*d^4*cos(f*x + e)^4 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - 256*(a*c*d^3 - a*d^4)*cos(f*x + e)^3 - 32*(5*a*c^2*d^2 - 6*a*c*d^3 + 5*a*d^4)*cos(f*x + e)^2 + 32*(a*c^3*d - 7*a*c^2*d^2 + 15*a*c*d^3 - 9*a*d^4)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e) + sin(f*x + e) + 1)))/f, 1/4*(2*sqrt(a*d)*arctan(1/4*(8*d^2*cos(f*x + e)^2 - c^2 + 6*c*d - 9*d^2 - 8*(c*d - d^2)*sin(f*x + e))*sqrt(a*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(2*a*d^3*cos(f*x + e)^3 - (3*a*c*d^2 - a*d^3)*cos(f*x + e)*sin(f*x + e) - (a*c^2*d - a*c*d^2 + 2*a*d^3)*cos(f*x + e))) + sqrt(a*c)*log(((a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - (31*a*c^4 - 196*a*c^3*d + 154*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 2*(81*a*c^4 - 252*a*c^3*d + 150*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^3 + 2*(79*a*c^4 - 100*a*c^3*d + 74*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^2 - 8*((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^4 - 2*(5*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e)^3 + 51*c^3 - 59*c^2*d + 17*c*d^2 - d^3 - 2*(18*c^3 - 33*c^2*d + 12*c*d^2 - d^3)*cos(f*x + e)^2 + 2*(13*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e) + ((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^3 - 51*c^3 + 59*c^2*d - 17*c*d^2 + d^3 + (11*c^3 - 35*c^2*d + 17*c*d^2 - d^3)*cos(f*x + e)^2 - (25*c^3 - 31*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c) + (289*a*c^4 - 476*a*c^3*d + 230*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + (a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^4 + 32*(a*c^4 - 7*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e)^3 - 2*(65*a*c^4 - 140*a*c^3*d + 38*a*c^2*d^2 - 12*a*c*d^3 + a*d^4)*cos(f*x + e)^2 - 32*(9*a*c^4 - 15*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^5 + cos(f*x + e)^4 - 2*cos(f*x + e)^3 - 2*cos(f*x + e)^2 + (cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sin(f*x + e) + cos(f*x + e) + 1)))/f, 1/2*(sqrt(-a*c)*arctan(-1/4*((c^2 - 6*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 + 6*c*d - d^2 + 8*(c^2 - c*d)*sin(f*x + e))*sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/((a*c^2*d - a*c*d^2)*cos(f*x + e)^3 - (a*c^3 - 3*a*c^2*d)*cos(f*x + e)*sin(f*x + e) + (2*a*c^3 - a*c^2*d + a*c*d^2)*cos(f*x + e))) + sqrt(a*d)*arctan(1/4*(8*d^2*cos(f*x + e)^2 - c^2 + 6*c*d - 9*d^2 - 8*(c*d - d^2)*sin(f*x + e))*sqrt(a*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(2*a*d^3*cos(f*x + e)^3 - (3*a*c*d^2 - a*d^3)*cos(f*x + e)*sin(f*x + e) - (a*c^2*d - a*c*d^2 + 2*a*d^3)*cos(f*x + e))))/f]","B",0
36,1,1044,0,1.669159," ","integrate((a+a*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{a}{c}} \log\left(\frac{{\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - {\left(31 \, a c^{4} - 196 \, a c^{3} d + 154 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(81 \, a c^{4} - 252 \, a c^{3} d + 150 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(79 \, a c^{4} - 100 \, a c^{3} d + 74 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left({\left(c^{4} - 7 \, c^{3} d + 7 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)^{4} + 51 \, c^{4} - 59 \, c^{3} d + 17 \, c^{2} d^{2} - c d^{3} - 2 \, {\left(5 \, c^{4} - 14 \, c^{3} d + 5 \, c^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(18 \, c^{4} - 33 \, c^{3} d + 12 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{4} - 14 \, c^{3} d + 5 \, c^{2} d^{2}\right)} \cos\left(f x + e\right) - {\left(51 \, c^{4} - 59 \, c^{3} d + 17 \, c^{2} d^{2} - c d^{3} - {\left(c^{4} - 7 \, c^{3} d + 7 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(11 \, c^{4} - 35 \, c^{3} d + 17 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(25 \, c^{4} - 31 \, c^{3} d + 7 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{\frac{a}{c}} + {\left(289 \, a c^{4} - 476 \, a c^{3} d + 230 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + {\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{4} + 32 \, {\left(a c^{4} - 7 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(65 \, a c^{4} - 140 \, a c^{3} d + 38 \, a c^{2} d^{2} - 12 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{2} - 32 \, {\left(9 \, a c^{4} - 15 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right) + 1}\right)}{4 \, f}, \frac{\sqrt{-\frac{a}{c}} \arctan\left(-\frac{{\left({\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} + 6 \, c d - d^{2} + 8 \, {\left(c^{2} - c d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{a}{c}}}{4 \, {\left({\left(a c d - a d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(a c^{2} - 3 \, a c d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, a c^{2} - a c d + a d^{2}\right)} \cos\left(f x + e\right)\right)}}\right)}{2 \, f}\right]"," ",0,"[1/4*sqrt(a/c)*log(((a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - (31*a*c^4 - 196*a*c^3*d + 154*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 2*(81*a*c^4 - 252*a*c^3*d + 150*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^3 + 2*(79*a*c^4 - 100*a*c^3*d + 74*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^2 - 8*((c^4 - 7*c^3*d + 7*c^2*d^2 - c*d^3)*cos(f*x + e)^4 + 51*c^4 - 59*c^3*d + 17*c^2*d^2 - c*d^3 - 2*(5*c^4 - 14*c^3*d + 5*c^2*d^2)*cos(f*x + e)^3 - 2*(18*c^4 - 33*c^3*d + 12*c^2*d^2 - c*d^3)*cos(f*x + e)^2 + 2*(13*c^4 - 14*c^3*d + 5*c^2*d^2)*cos(f*x + e) - (51*c^4 - 59*c^3*d + 17*c^2*d^2 - c*d^3 - (c^4 - 7*c^3*d + 7*c^2*d^2 - c*d^3)*cos(f*x + e)^3 - (11*c^4 - 35*c^3*d + 17*c^2*d^2 - c*d^3)*cos(f*x + e)^2 + (25*c^4 - 31*c^3*d + 7*c^2*d^2 - c*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt(a/c) + (289*a*c^4 - 476*a*c^3*d + 230*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + (a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^4 + 32*(a*c^4 - 7*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e)^3 - 2*(65*a*c^4 - 140*a*c^3*d + 38*a*c^2*d^2 - 12*a*c*d^3 + a*d^4)*cos(f*x + e)^2 - 32*(9*a*c^4 - 15*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^5 + cos(f*x + e)^4 - 2*cos(f*x + e)^3 - 2*cos(f*x + e)^2 + (cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sin(f*x + e) + cos(f*x + e) + 1))/f, 1/2*sqrt(-a/c)*arctan(-1/4*((c^2 - 6*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 + 6*c*d - d^2 + 8*(c^2 - c*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt(-a/c)/((a*c*d - a*d^2)*cos(f*x + e)^3 - (a*c^2 - 3*a*c*d)*cos(f*x + e)*sin(f*x + e) + (2*a*c^2 - a*c*d + a*d^2)*cos(f*x + e)))/f]","B",0
37,1,2791,0,2.177339," ","integrate((c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \log\left(\frac{{\left(c^{2} - 14 \, c d + 17 \, d^{2}\right)} \cos\left(f x + e\right)^{3} + 4 \, \sqrt{2} {\left({\left(c - 3 \, d\right)} \cos\left(f x + e\right)^{2} - {\left(3 \, c - d\right)} \cos\left(f x + e\right) + {\left({\left(c - 3 \, d\right)} \cos\left(f x + e\right) + 4 \, c - 4 \, d\right)} \sin\left(f x + e\right) - 4 \, c + 4 \, d\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{\frac{c - d}{a}} - {\left(13 \, c^{2} - 22 \, c d - 3 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 4 \, c^{2} - 8 \, c d - 4 \, d^{2} - 2 \, {\left(9 \, c^{2} - 14 \, c d + 9 \, d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{2} - 14 \, c d + 17 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 4 \, c^{2} - 8 \, c d - 4 \, d^{2} + 2 \, {\left(7 \, c^{2} - 18 \, c d + 7 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right) + \sqrt{\frac{c}{a}} \log\left(\frac{{\left(c^{4} - 28 \, c^{3} d + 70 \, c^{2} d^{2} - 28 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{5} - {\left(31 \, c^{4} - 196 \, c^{3} d + 154 \, c^{2} d^{2} - 4 \, c d^{3} - d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(81 \, c^{4} - 252 \, c^{3} d + 150 \, c^{2} d^{2} - 28 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(79 \, c^{4} - 100 \, c^{3} d + 74 \, c^{2} d^{2} - 4 \, c d^{3} - d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(5 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + 51 \, c^{3} - 59 \, c^{2} d + 17 \, c d^{2} - d^{3} - 2 \, {\left(18 \, c^{3} - 33 \, c^{2} d + 12 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - 51 \, c^{3} + 59 \, c^{2} d - 17 \, c d^{2} + d^{3} + {\left(11 \, c^{3} - 35 \, c^{2} d + 17 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(25 \, c^{3} - 31 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{\frac{c}{a}} + {\left(289 \, c^{4} - 476 \, c^{3} d + 230 \, c^{2} d^{2} - 28 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right) + {\left({\left(c^{4} - 28 \, c^{3} d + 70 \, c^{2} d^{2} - 28 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} + 32 \, {\left(c^{4} - 7 \, c^{3} d + 7 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(65 \, c^{4} - 140 \, c^{3} d + 38 \, c^{2} d^{2} - 12 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} - 32 \, {\left(9 \, c^{4} - 15 \, c^{3} d + 7 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right) + 1}\right)}{4 \, f}, \frac{\sqrt{2} \sqrt{\frac{c - d}{a}} \log\left(\frac{{\left(c^{2} - 14 \, c d + 17 \, d^{2}\right)} \cos\left(f x + e\right)^{3} + 4 \, \sqrt{2} {\left({\left(c - 3 \, d\right)} \cos\left(f x + e\right)^{2} - {\left(3 \, c - d\right)} \cos\left(f x + e\right) + {\left({\left(c - 3 \, d\right)} \cos\left(f x + e\right) + 4 \, c - 4 \, d\right)} \sin\left(f x + e\right) - 4 \, c + 4 \, d\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{\frac{c - d}{a}} - {\left(13 \, c^{2} - 22 \, c d - 3 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 4 \, c^{2} - 8 \, c d - 4 \, d^{2} - 2 \, {\left(9 \, c^{2} - 14 \, c d + 9 \, d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{2} - 14 \, c d + 17 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 4 \, c^{2} - 8 \, c d - 4 \, d^{2} + 2 \, {\left(7 \, c^{2} - 18 \, c d + 7 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right) + 2 \, \sqrt{-\frac{c}{a}} \arctan\left(-\frac{{\left({\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} + 6 \, c d - d^{2} + 8 \, {\left(c^{2} - c d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{c}{a}}}{4 \, {\left({\left(c^{2} d - c d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(c^{3} - 3 \, c^{2} d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, c^{3} - c^{2} d + c d^{2}\right)} \cos\left(f x + e\right)\right)}}\right)}{4 \, f}, \frac{2 \, \sqrt{2} \sqrt{-\frac{c - d}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left({\left(c - 3 \, d\right)} \sin\left(f x + e\right) - 3 \, c + d\right)} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{c - d}{a}}}{4 \, {\left({\left(c d - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - c d\right)} \cos\left(f x + e\right)\right)}}\right) + \sqrt{\frac{c}{a}} \log\left(\frac{{\left(c^{4} - 28 \, c^{3} d + 70 \, c^{2} d^{2} - 28 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{5} - {\left(31 \, c^{4} - 196 \, c^{3} d + 154 \, c^{2} d^{2} - 4 \, c d^{3} - d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} - 2 \, {\left(81 \, c^{4} - 252 \, c^{3} d + 150 \, c^{2} d^{2} - 28 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(79 \, c^{4} - 100 \, c^{3} d + 74 \, c^{2} d^{2} - 4 \, c d^{3} - d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(5 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + 51 \, c^{3} - 59 \, c^{2} d + 17 \, c d^{2} - d^{3} - 2 \, {\left(18 \, c^{3} - 33 \, c^{2} d + 12 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - 51 \, c^{3} + 59 \, c^{2} d - 17 \, c d^{2} + d^{3} + {\left(11 \, c^{3} - 35 \, c^{2} d + 17 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(25 \, c^{3} - 31 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{\frac{c}{a}} + {\left(289 \, c^{4} - 476 \, c^{3} d + 230 \, c^{2} d^{2} - 28 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right) + {\left({\left(c^{4} - 28 \, c^{3} d + 70 \, c^{2} d^{2} - 28 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{4} + c^{4} + 4 \, c^{3} d + 6 \, c^{2} d^{2} + 4 \, c d^{3} + d^{4} + 32 \, {\left(c^{4} - 7 \, c^{3} d + 7 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(65 \, c^{4} - 140 \, c^{3} d + 38 \, c^{2} d^{2} - 12 \, c d^{3} + d^{4}\right)} \cos\left(f x + e\right)^{2} - 32 \, {\left(9 \, c^{4} - 15 \, c^{3} d + 7 \, c^{2} d^{2} - c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right) + 1}\right)}{4 \, f}, \frac{\sqrt{2} \sqrt{-\frac{c - d}{a}} \arctan\left(\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left({\left(c - 3 \, d\right)} \sin\left(f x + e\right) - 3 \, c + d\right)} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{c - d}{a}}}{4 \, {\left({\left(c d - d^{2}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c^{2} - c d\right)} \cos\left(f x + e\right)\right)}}\right) + \sqrt{-\frac{c}{a}} \arctan\left(-\frac{{\left({\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} + 6 \, c d - d^{2} + 8 \, {\left(c^{2} - c d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{c}{a}}}{4 \, {\left({\left(c^{2} d - c d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(c^{3} - 3 \, c^{2} d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, c^{3} - c^{2} d + c d^{2}\right)} \cos\left(f x + e\right)\right)}}\right)}{2 \, f}\right]"," ",0,"[1/4*(sqrt(2)*sqrt((c - d)/a)*log(((c^2 - 14*c*d + 17*d^2)*cos(f*x + e)^3 + 4*sqrt(2)*((c - 3*d)*cos(f*x + e)^2 - (3*c - d)*cos(f*x + e) + ((c - 3*d)*cos(f*x + e) + 4*c - 4*d)*sin(f*x + e) - 4*c + 4*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt((c - d)/a) - (13*c^2 - 22*c*d - 3*d^2)*cos(f*x + e)^2 - 4*c^2 - 8*c*d - 4*d^2 - 2*(9*c^2 - 14*c*d + 9*d^2)*cos(f*x + e) + ((c^2 - 14*c*d + 17*d^2)*cos(f*x + e)^2 - 4*c^2 - 8*c*d - 4*d^2 + 2*(7*c^2 - 18*c*d + 7*d^2)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4)) + sqrt(c/a)*log(((c^4 - 28*c^3*d + 70*c^2*d^2 - 28*c*d^3 + d^4)*cos(f*x + e)^5 - (31*c^4 - 196*c^3*d + 154*c^2*d^2 - 4*c*d^3 - d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(81*c^4 - 252*c^3*d + 150*c^2*d^2 - 28*c*d^3 + d^4)*cos(f*x + e)^3 + 2*(79*c^4 - 100*c^3*d + 74*c^2*d^2 - 4*c*d^3 - d^4)*cos(f*x + e)^2 - 8*((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^4 - 2*(5*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e)^3 + 51*c^3 - 59*c^2*d + 17*c*d^2 - d^3 - 2*(18*c^3 - 33*c^2*d + 12*c*d^2 - d^3)*cos(f*x + e)^2 + 2*(13*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e) + ((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^3 - 51*c^3 + 59*c^2*d - 17*c*d^2 + d^3 + (11*c^3 - 35*c^2*d + 17*c*d^2 - d^3)*cos(f*x + e)^2 - (25*c^3 - 31*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt(c/a) + (289*c^4 - 476*c^3*d + 230*c^2*d^2 - 28*c*d^3 + d^4)*cos(f*x + e) + ((c^4 - 28*c^3*d + 70*c^2*d^2 - 28*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 + 32*(c^4 - 7*c^3*d + 7*c^2*d^2 - c*d^3)*cos(f*x + e)^3 - 2*(65*c^4 - 140*c^3*d + 38*c^2*d^2 - 12*c*d^3 + d^4)*cos(f*x + e)^2 - 32*(9*c^4 - 15*c^3*d + 7*c^2*d^2 - c*d^3)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^5 + cos(f*x + e)^4 - 2*cos(f*x + e)^3 - 2*cos(f*x + e)^2 + (cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sin(f*x + e) + cos(f*x + e) + 1)))/f, 1/4*(sqrt(2)*sqrt((c - d)/a)*log(((c^2 - 14*c*d + 17*d^2)*cos(f*x + e)^3 + 4*sqrt(2)*((c - 3*d)*cos(f*x + e)^2 - (3*c - d)*cos(f*x + e) + ((c - 3*d)*cos(f*x + e) + 4*c - 4*d)*sin(f*x + e) - 4*c + 4*d)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt((c - d)/a) - (13*c^2 - 22*c*d - 3*d^2)*cos(f*x + e)^2 - 4*c^2 - 8*c*d - 4*d^2 - 2*(9*c^2 - 14*c*d + 9*d^2)*cos(f*x + e) + ((c^2 - 14*c*d + 17*d^2)*cos(f*x + e)^2 - 4*c^2 - 8*c*d - 4*d^2 + 2*(7*c^2 - 18*c*d + 7*d^2)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4)) + 2*sqrt(-c/a)*arctan(-1/4*((c^2 - 6*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 + 6*c*d - d^2 + 8*(c^2 - c*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt(-c/a)/((c^2*d - c*d^2)*cos(f*x + e)^3 - (c^3 - 3*c^2*d)*cos(f*x + e)*sin(f*x + e) + (2*c^3 - c^2*d + c*d^2)*cos(f*x + e))))/f, 1/4*(2*sqrt(2)*sqrt(-(c - d)/a)*arctan(1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*((c - 3*d)*sin(f*x + e) - 3*c + d)*sqrt(d*sin(f*x + e) + c)*sqrt(-(c - d)/a)/((c*d - d^2)*cos(f*x + e)*sin(f*x + e) + (c^2 - c*d)*cos(f*x + e))) + sqrt(c/a)*log(((c^4 - 28*c^3*d + 70*c^2*d^2 - 28*c*d^3 + d^4)*cos(f*x + e)^5 - (31*c^4 - 196*c^3*d + 154*c^2*d^2 - 4*c*d^3 - d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 - 2*(81*c^4 - 252*c^3*d + 150*c^2*d^2 - 28*c*d^3 + d^4)*cos(f*x + e)^3 + 2*(79*c^4 - 100*c^3*d + 74*c^2*d^2 - 4*c*d^3 - d^4)*cos(f*x + e)^2 - 8*((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^4 - 2*(5*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e)^3 + 51*c^3 - 59*c^2*d + 17*c*d^2 - d^3 - 2*(18*c^3 - 33*c^2*d + 12*c*d^2 - d^3)*cos(f*x + e)^2 + 2*(13*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e) + ((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^3 - 51*c^3 + 59*c^2*d - 17*c*d^2 + d^3 + (11*c^3 - 35*c^2*d + 17*c*d^2 - d^3)*cos(f*x + e)^2 - (25*c^3 - 31*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt(c/a) + (289*c^4 - 476*c^3*d + 230*c^2*d^2 - 28*c*d^3 + d^4)*cos(f*x + e) + ((c^4 - 28*c^3*d + 70*c^2*d^2 - 28*c*d^3 + d^4)*cos(f*x + e)^4 + c^4 + 4*c^3*d + 6*c^2*d^2 + 4*c*d^3 + d^4 + 32*(c^4 - 7*c^3*d + 7*c^2*d^2 - c*d^3)*cos(f*x + e)^3 - 2*(65*c^4 - 140*c^3*d + 38*c^2*d^2 - 12*c*d^3 + d^4)*cos(f*x + e)^2 - 32*(9*c^4 - 15*c^3*d + 7*c^2*d^2 - c*d^3)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^5 + cos(f*x + e)^4 - 2*cos(f*x + e)^3 - 2*cos(f*x + e)^2 + (cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sin(f*x + e) + cos(f*x + e) + 1)))/f, 1/2*(sqrt(2)*sqrt(-(c - d)/a)*arctan(1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*((c - 3*d)*sin(f*x + e) - 3*c + d)*sqrt(d*sin(f*x + e) + c)*sqrt(-(c - d)/a)/((c*d - d^2)*cos(f*x + e)*sin(f*x + e) + (c^2 - c*d)*cos(f*x + e))) + sqrt(-c/a)*arctan(-1/4*((c^2 - 6*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 + 6*c*d - d^2 + 8*(c^2 - c*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)*sqrt(-c/a)/((c^2*d - c*d^2)*cos(f*x + e)^3 - (c^3 - 3*c^2*d)*cos(f*x + e)*sin(f*x + e) + (2*c^3 - c^2*d + c*d^2)*cos(f*x + e))))/f]","B",0
38,1,3005,0,2.373385," ","integrate(1/sin(f*x+e)/(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\frac{\sqrt{2} a c \log\left(\frac{{\left(c^{2} - 14 \, c d + 17 \, d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(13 \, c^{2} - 22 \, c d - 3 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + \frac{4 \, \sqrt{2} {\left({\left(c^{2} - 4 \, c d + 3 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 4 \, c^{2} + 8 \, c d - 4 \, d^{2} - {\left(3 \, c^{2} - 4 \, c d + d^{2}\right)} \cos\left(f x + e\right) + {\left(4 \, c^{2} - 8 \, c d + 4 \, d^{2} + {\left(c^{2} - 4 \, c d + 3 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{a c - a d}} - 4 \, c^{2} - 8 \, c d - 4 \, d^{2} - 2 \, {\left(9 \, c^{2} - 14 \, c d + 9 \, d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{2} - 14 \, c d + 17 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 4 \, c^{2} - 8 \, c d - 4 \, d^{2} + 2 \, {\left(7 \, c^{2} - 18 \, c d + 7 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right)}{\sqrt{a c - a d}} + \sqrt{a c} \log\left(\frac{{\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - {\left(31 \, a c^{4} - 196 \, a c^{3} d + 154 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(81 \, a c^{4} - 252 \, a c^{3} d + 150 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(79 \, a c^{4} - 100 \, a c^{3} d + 74 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(5 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + 51 \, c^{3} - 59 \, c^{2} d + 17 \, c d^{2} - d^{3} - 2 \, {\left(18 \, c^{3} - 33 \, c^{2} d + 12 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - 51 \, c^{3} + 59 \, c^{2} d - 17 \, c d^{2} + d^{3} + {\left(11 \, c^{3} - 35 \, c^{2} d + 17 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(25 \, c^{3} - 31 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} + {\left(289 \, a c^{4} - 476 \, a c^{3} d + 230 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + {\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{4} + 32 \, {\left(a c^{4} - 7 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(65 \, a c^{4} - 140 \, a c^{3} d + 38 \, a c^{2} d^{2} - 12 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{2} - 32 \, {\left(9 \, a c^{4} - 15 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right) + 1}\right)}{4 \, a c f}, \frac{\frac{\sqrt{2} a c \log\left(\frac{{\left(c^{2} - 14 \, c d + 17 \, d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(13 \, c^{2} - 22 \, c d - 3 \, d^{2}\right)} \cos\left(f x + e\right)^{2} + \frac{4 \, \sqrt{2} {\left({\left(c^{2} - 4 \, c d + 3 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 4 \, c^{2} + 8 \, c d - 4 \, d^{2} - {\left(3 \, c^{2} - 4 \, c d + d^{2}\right)} \cos\left(f x + e\right) + {\left(4 \, c^{2} - 8 \, c d + 4 \, d^{2} + {\left(c^{2} - 4 \, c d + 3 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{\sqrt{a c - a d}} - 4 \, c^{2} - 8 \, c d - 4 \, d^{2} - 2 \, {\left(9 \, c^{2} - 14 \, c d + 9 \, d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{2} - 14 \, c d + 17 \, d^{2}\right)} \cos\left(f x + e\right)^{2} - 4 \, c^{2} - 8 \, c d - 4 \, d^{2} + 2 \, {\left(7 \, c^{2} - 18 \, c d + 7 \, d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3} + 3 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{2} - 2 \, \cos\left(f x + e\right) - 4\right)} \sin\left(f x + e\right) - 2 \, \cos\left(f x + e\right) - 4}\right)}{\sqrt{a c - a d}} + 2 \, \sqrt{-a c} \arctan\left(-\frac{{\left({\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} + 6 \, c d - d^{2} + 8 \, {\left(c^{2} - c d\right)} \sin\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{4 \, {\left({\left(a c^{2} d - a c d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(a c^{3} - 3 \, a c^{2} d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, a c^{3} - a c^{2} d + a c d^{2}\right)} \cos\left(f x + e\right)\right)}}\right)}{4 \, a c f}, -\frac{2 \, \sqrt{2} a c \sqrt{-\frac{1}{a c - a d}} \arctan\left(-\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left({\left(c - 3 \, d\right)} \sin\left(f x + e\right) - 3 \, c + d\right)} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{1}{a c - a d}}}{4 \, {\left(d \cos\left(f x + e\right) \sin\left(f x + e\right) + c \cos\left(f x + e\right)\right)}}\right) - \sqrt{a c} \log\left(\frac{{\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{5} + a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} - {\left(31 \, a c^{4} - 196 \, a c^{3} d + 154 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(81 \, a c^{4} - 252 \, a c^{3} d + 150 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(79 \, a c^{4} - 100 \, a c^{3} d + 74 \, a c^{2} d^{2} - 4 \, a c d^{3} - a d^{4}\right)} \cos\left(f x + e\right)^{2} - 8 \, {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(5 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right)^{3} + 51 \, c^{3} - 59 \, c^{2} d + 17 \, c d^{2} - d^{3} - 2 \, {\left(18 \, c^{3} - 33 \, c^{2} d + 12 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(13 \, c^{3} - 14 \, c^{2} d + 5 \, c d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(c^{3} - 7 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{3} - 51 \, c^{3} + 59 \, c^{2} d - 17 \, c d^{2} + d^{3} + {\left(11 \, c^{3} - 35 \, c^{2} d + 17 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(25 \, c^{3} - 31 \, c^{2} d + 7 \, c d^{2} - d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c} + {\left(289 \, a c^{4} - 476 \, a c^{3} d + 230 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right) + {\left(a c^{4} + 4 \, a c^{3} d + 6 \, a c^{2} d^{2} + 4 \, a c d^{3} + a d^{4} + {\left(a c^{4} - 28 \, a c^{3} d + 70 \, a c^{2} d^{2} - 28 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{4} + 32 \, {\left(a c^{4} - 7 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(65 \, a c^{4} - 140 \, a c^{3} d + 38 \, a c^{2} d^{2} - 12 \, a c d^{3} + a d^{4}\right)} \cos\left(f x + e\right)^{2} - 32 \, {\left(9 \, a c^{4} - 15 \, a c^{3} d + 7 \, a c^{2} d^{2} - a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{5} + \cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{3} - 2 \, \cos\left(f x + e\right)^{2} + {\left(\cos\left(f x + e\right)^{4} - 2 \, \cos\left(f x + e\right)^{2} + 1\right)} \sin\left(f x + e\right) + \cos\left(f x + e\right) + 1}\right)}{4 \, a c f}, -\frac{\sqrt{2} a c \sqrt{-\frac{1}{a c - a d}} \arctan\left(-\frac{\sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} {\left({\left(c - 3 \, d\right)} \sin\left(f x + e\right) - 3 \, c + d\right)} \sqrt{d \sin\left(f x + e\right) + c} \sqrt{-\frac{1}{a c - a d}}}{4 \, {\left(d \cos\left(f x + e\right) \sin\left(f x + e\right) + c \cos\left(f x + e\right)\right)}}\right) - \sqrt{-a c} \arctan\left(-\frac{{\left({\left(c^{2} - 6 \, c d + d^{2}\right)} \cos\left(f x + e\right)^{2} - 9 \, c^{2} + 6 \, c d - d^{2} + 8 \, {\left(c^{2} - c d\right)} \sin\left(f x + e\right)\right)} \sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{4 \, {\left({\left(a c^{2} d - a c d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(a c^{3} - 3 \, a c^{2} d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, a c^{3} - a c^{2} d + a c d^{2}\right)} \cos\left(f x + e\right)\right)}}\right)}{2 \, a c f}\right]"," ",0,"[1/4*(sqrt(2)*a*c*log(((c^2 - 14*c*d + 17*d^2)*cos(f*x + e)^3 - (13*c^2 - 22*c*d - 3*d^2)*cos(f*x + e)^2 + 4*sqrt(2)*((c^2 - 4*c*d + 3*d^2)*cos(f*x + e)^2 - 4*c^2 + 8*c*d - 4*d^2 - (3*c^2 - 4*c*d + d^2)*cos(f*x + e) + (4*c^2 - 8*c*d + 4*d^2 + (c^2 - 4*c*d + 3*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/sqrt(a*c - a*d) - 4*c^2 - 8*c*d - 4*d^2 - 2*(9*c^2 - 14*c*d + 9*d^2)*cos(f*x + e) + ((c^2 - 14*c*d + 17*d^2)*cos(f*x + e)^2 - 4*c^2 - 8*c*d - 4*d^2 + 2*(7*c^2 - 18*c*d + 7*d^2)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4))/sqrt(a*c - a*d) + sqrt(a*c)*log(((a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - (31*a*c^4 - 196*a*c^3*d + 154*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 2*(81*a*c^4 - 252*a*c^3*d + 150*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^3 + 2*(79*a*c^4 - 100*a*c^3*d + 74*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^2 - 8*((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^4 - 2*(5*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e)^3 + 51*c^3 - 59*c^2*d + 17*c*d^2 - d^3 - 2*(18*c^3 - 33*c^2*d + 12*c*d^2 - d^3)*cos(f*x + e)^2 + 2*(13*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e) + ((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^3 - 51*c^3 + 59*c^2*d - 17*c*d^2 + d^3 + (11*c^3 - 35*c^2*d + 17*c*d^2 - d^3)*cos(f*x + e)^2 - (25*c^3 - 31*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c) + (289*a*c^4 - 476*a*c^3*d + 230*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + (a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^4 + 32*(a*c^4 - 7*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e)^3 - 2*(65*a*c^4 - 140*a*c^3*d + 38*a*c^2*d^2 - 12*a*c*d^3 + a*d^4)*cos(f*x + e)^2 - 32*(9*a*c^4 - 15*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^5 + cos(f*x + e)^4 - 2*cos(f*x + e)^3 - 2*cos(f*x + e)^2 + (cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sin(f*x + e) + cos(f*x + e) + 1)))/(a*c*f), 1/4*(sqrt(2)*a*c*log(((c^2 - 14*c*d + 17*d^2)*cos(f*x + e)^3 - (13*c^2 - 22*c*d - 3*d^2)*cos(f*x + e)^2 + 4*sqrt(2)*((c^2 - 4*c*d + 3*d^2)*cos(f*x + e)^2 - 4*c^2 + 8*c*d - 4*d^2 - (3*c^2 - 4*c*d + d^2)*cos(f*x + e) + (4*c^2 - 8*c*d + 4*d^2 + (c^2 - 4*c*d + 3*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/sqrt(a*c - a*d) - 4*c^2 - 8*c*d - 4*d^2 - 2*(9*c^2 - 14*c*d + 9*d^2)*cos(f*x + e) + ((c^2 - 14*c*d + 17*d^2)*cos(f*x + e)^2 - 4*c^2 - 8*c*d - 4*d^2 + 2*(7*c^2 - 18*c*d + 7*d^2)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^3 + 3*cos(f*x + e)^2 + (cos(f*x + e)^2 - 2*cos(f*x + e) - 4)*sin(f*x + e) - 2*cos(f*x + e) - 4))/sqrt(a*c - a*d) + 2*sqrt(-a*c)*arctan(-1/4*((c^2 - 6*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 + 6*c*d - d^2 + 8*(c^2 - c*d)*sin(f*x + e))*sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/((a*c^2*d - a*c*d^2)*cos(f*x + e)^3 - (a*c^3 - 3*a*c^2*d)*cos(f*x + e)*sin(f*x + e) + (2*a*c^3 - a*c^2*d + a*c*d^2)*cos(f*x + e))))/(a*c*f), -1/4*(2*sqrt(2)*a*c*sqrt(-1/(a*c - a*d))*arctan(-1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*((c - 3*d)*sin(f*x + e) - 3*c + d)*sqrt(d*sin(f*x + e) + c)*sqrt(-1/(a*c - a*d))/(d*cos(f*x + e)*sin(f*x + e) + c*cos(f*x + e))) - sqrt(a*c)*log(((a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^5 + a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 - (31*a*c^4 - 196*a*c^3*d + 154*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^4 - 2*(81*a*c^4 - 252*a*c^3*d + 150*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^3 + 2*(79*a*c^4 - 100*a*c^3*d + 74*a*c^2*d^2 - 4*a*c*d^3 - a*d^4)*cos(f*x + e)^2 - 8*((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^4 - 2*(5*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e)^3 + 51*c^3 - 59*c^2*d + 17*c*d^2 - d^3 - 2*(18*c^3 - 33*c^2*d + 12*c*d^2 - d^3)*cos(f*x + e)^2 + 2*(13*c^3 - 14*c^2*d + 5*c*d^2)*cos(f*x + e) + ((c^3 - 7*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e)^3 - 51*c^3 + 59*c^2*d - 17*c*d^2 + d^3 + (11*c^3 - 35*c^2*d + 17*c*d^2 - d^3)*cos(f*x + e)^2 - (25*c^3 - 31*c^2*d + 7*c*d^2 - d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c) + (289*a*c^4 - 476*a*c^3*d + 230*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e) + (a*c^4 + 4*a*c^3*d + 6*a*c^2*d^2 + 4*a*c*d^3 + a*d^4 + (a*c^4 - 28*a*c^3*d + 70*a*c^2*d^2 - 28*a*c*d^3 + a*d^4)*cos(f*x + e)^4 + 32*(a*c^4 - 7*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e)^3 - 2*(65*a*c^4 - 140*a*c^3*d + 38*a*c^2*d^2 - 12*a*c*d^3 + a*d^4)*cos(f*x + e)^2 - 32*(9*a*c^4 - 15*a*c^3*d + 7*a*c^2*d^2 - a*c*d^3)*cos(f*x + e))*sin(f*x + e))/(cos(f*x + e)^5 + cos(f*x + e)^4 - 2*cos(f*x + e)^3 - 2*cos(f*x + e)^2 + (cos(f*x + e)^4 - 2*cos(f*x + e)^2 + 1)*sin(f*x + e) + cos(f*x + e) + 1)))/(a*c*f), -1/2*(sqrt(2)*a*c*sqrt(-1/(a*c - a*d))*arctan(-1/4*sqrt(2)*sqrt(a*sin(f*x + e) + a)*((c - 3*d)*sin(f*x + e) - 3*c + d)*sqrt(d*sin(f*x + e) + c)*sqrt(-1/(a*c - a*d))/(d*cos(f*x + e)*sin(f*x + e) + c*cos(f*x + e))) - sqrt(-a*c)*arctan(-1/4*((c^2 - 6*c*d + d^2)*cos(f*x + e)^2 - 9*c^2 + 6*c*d - d^2 + 8*(c^2 - c*d)*sin(f*x + e))*sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/((a*c^2*d - a*c*d^2)*cos(f*x + e)^3 - (a*c^3 - 3*a*c^2*d)*cos(f*x + e)*sin(f*x + e) + (2*a*c^3 - a*c^2*d + a*c*d^2)*cos(f*x + e))))/(a*c*f)]","B",0
39,-1,0,0,0.000000," ","integrate(sin(f*x+e)^2/(a+b*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)/sin(f*x+e)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate(1/sin(f*x+e)/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)*(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(g*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,0,0,0,3.404626," ","integrate((g*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))/(a+b*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{b d \cos\left(f x + e\right)^{2} - a c - b d - {\left(b c + a d\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/(b*d*cos(f*x + e)^2 - a*c - b*d - (b*c + a*d)*sin(f*x + e)), x)","F",0
45,0,0,0,13.140445," ","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=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{g \sin\left(f x + e\right)}}{{\left(b c + a d\right)} g \cos\left(f x + e\right)^{2} - {\left(b c + a d\right)} g + {\left(b d g \cos\left(f x + e\right)^{2} - {\left(a c + b d\right)} g\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)*sqrt(g*sin(f*x + e))/((b*c + a*d)*g*cos(f*x + e)^2 - (b*c + a*d)*g + (b*d*g*cos(f*x + e)^2 - (a*c + b*d)*g)*sin(f*x + e)), x)","F",0
46,-1,0,0,0.000000," ","integrate((c+d*sin(f*x+e))^(1/2)*(g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
47,-1,0,0,0.000000," ","integrate((g*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate((a+b*sin(f*x+e))^(1/2)*(c+d*sin(f*x+e))^(1/2)/sin(f*x+e),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,0,0,0,1.264746," ","integrate((a+b*sin(f*x+e))^(1/2)/sin(f*x+e)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{d \cos\left(f x + e\right)^{2} - c \sin\left(f x + e\right) - d}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(d*cos(f*x + e)^2 - c*sin(f*x + e) - d), x)","F",0
50,0,0,0,2.592065," ","integrate(1/sin(f*x+e)/(a+b*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{{\left(b c + a d\right)} \cos\left(f x + e\right)^{2} - b c - a d + {\left(b d \cos\left(f x + e\right)^{2} - a c - b d\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/((b*c + a*d)*cos(f*x + e)^2 - b*c - a*d + (b*d*cos(f*x + e)^2 - a*c - b*d)*sin(f*x + e)), x)","F",0
51,0,0,0,1.324756," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))^p*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\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}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)^p*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
