1,0,0,0,1.159285," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^3*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B a^{3} \cos\left(f x + e\right)^{4} - {\left(3 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(A + B\right)} a^{3} - {\left({\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((B*a^3*cos(f*x + e)^4 - (3*A + 5*B)*a^3*cos(f*x + e)^2 + 4*(A + B)*a^3 - ((A + 3*B)*a^3*cos(f*x + e)^2 - 4*(A + B)*a^3)*sin(f*x + e))*(d*sin(f*x + e))^n, x)","F",0
2,0,0,0,0.940023," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^2*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left({\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2} + {\left(B a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-((A + 2*B)*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2 + (B*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2)*sin(f*x + e))*(d*sin(f*x + e))^n, x)","F",0
3,0,0,0,1.184842," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(B a \cos\left(f x + e\right)^{2} - {\left(A + B\right)} a \sin\left(f x + e\right) - {\left(A + B\right)} a\right)} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(B*a*cos(f*x + e)^2 - (A + B)*a*sin(f*x + e) - (A + B)*a)*(d*sin(f*x + e))^n, x)","F",0
4,0,0,0,0.814700," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(d \sin\left(f x + e\right)\right)^{n}}{a \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/(a*sin(f*x + e) + a), x)","F",0
5,0,0,0,0.928319," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(d \sin\left(f x + e\right)\right)^{n}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
6,0,0,0,1.040264," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(d \sin\left(f x + e\right)\right)^{n}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
7,0,0,0,0.980036," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left({\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2} + {\left(B a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-((A + 2*B)*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2 + (B*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e))^n, x)","F",0
8,0,0,0,0.949601," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(B a \cos\left(f x + e\right)^{2} - {\left(A + B\right)} a \sin\left(f x + e\right) - {\left(A + B\right)} a\right)} \sqrt{a \sin\left(f x + e\right) + a} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(B*a*cos(f*x + e)^2 - (A + B)*a*sin(f*x + e) - (A + B)*a)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e))^n, x)","F",0
9,0,0,0,0.947121," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e))^n, x)","F",0
10,0,0,0,0.898170," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} \left(d \sin\left(f x + e\right)\right)^{n}}{\sqrt{a \sin\left(f x + e\right) + a}}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(d*sin(f*x + e))^n/sqrt(a*sin(f*x + e) + a), x)","F",0
11,0,0,0,1.028383," ","integrate((d*sin(f*x+e))^n*(A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} \left(d \sin\left(f x + e\right)\right)^{n}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e))^n/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
12,0,0,0,0.880701," ","integrate((d*sin(f*x+e))^n*(a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
13,0,0,0,0.943902," ","integrate((d*sin(f*x+e))^n*(a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a \sin\left(f x + e\right) - a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} \left(d \sin\left(f x + e\right)\right)^{n}, x\right)"," ",0,"integral(-(a*sin(f*x + e) - a)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e))^n, x)","F",0
14,1,41,0,0.998115," ","integrate(sin(d*x+c)^n*(a+a*sin(d*x+c))^(-2-n)*(-1-n-(-2-n)*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{-n - 2} \sin\left(d x + c\right)^{n} \cos\left(d x + c\right) \sin\left(d x + c\right)}{d}"," ",0,"-(a*sin(d*x + c) + a)^(-n - 2)*sin(d*x + c)^n*cos(d*x + c)*sin(d*x + c)/d","A",0
15,1,41,0,1.048019," ","integrate(sin(d*x+c)^(-2-m)*(a+a*sin(d*x+c))^m*(1+m-m*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{{\left(a \sin\left(d x + c\right) + a\right)}^{m} \sin\left(d x + c\right)^{-m - 2} \cos\left(d x + c\right) \sin\left(d x + c\right)}{d}"," ",0,"-(a*sin(d*x + c) + a)^m*sin(d*x + c)^(-m - 2)*cos(d*x + c)*sin(d*x + c)/d","A",0
16,1,804,0,0.986551," ","integrate(sin(f*x+e)^2*(A+B*sin(f*x+e))/(a+b*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, B a^{6} - A a^{5} b - 4 \, B a^{4} b^{2} + 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5}\right)} f x + {\left(2 \, B a^{5} - A a^{4} b - 3 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3} + {\left(2 \, B a^{4} b - A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}} \log\left(\frac{{\left(2 \, a^{2} - b^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, a b \sin\left(f x + e\right) - a^{2} - b^{2} + 2 \, {\left(a \cos\left(f x + e\right) \sin\left(f x + e\right) + b \cos\left(f x + e\right)\right)} \sqrt{-a^{2} + b^{2}}}{b^{2} \cos\left(f x + e\right)^{2} - 2 \, a b \sin\left(f x + e\right) - a^{2} - b^{2}}\right) + 2 \, {\left(2 \, B a^{5} b - A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} + B a b^{5}\right)} \cos\left(f x + e\right) + 2 \, {\left({\left(2 \, B a^{5} b - A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} f x + {\left(B a^{4} b^{2} - 2 \, B a^{2} b^{4} + B b^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} f \sin\left(f x + e\right) + {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} f\right)}}, -\frac{{\left(2 \, B a^{6} - A a^{5} b - 4 \, B a^{4} b^{2} + 2 \, A a^{3} b^{3} + 2 \, B a^{2} b^{4} - A a b^{5}\right)} f x + {\left(2 \, B a^{5} - A a^{4} b - 3 \, B a^{3} b^{2} + 2 \, A a^{2} b^{3} + {\left(2 \, B a^{4} b - A a^{3} b^{2} - 3 \, B a^{2} b^{3} + 2 \, A a b^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{a^{2} - b^{2}} \arctan\left(-\frac{a \sin\left(f x + e\right) + b}{\sqrt{a^{2} - b^{2}} \cos\left(f x + e\right)}\right) + {\left(2 \, B a^{5} b - A a^{4} b^{2} - 3 \, B a^{3} b^{3} + A a^{2} b^{4} + B a b^{5}\right)} \cos\left(f x + e\right) + {\left({\left(2 \, B a^{5} b - A a^{4} b^{2} - 4 \, B a^{3} b^{3} + 2 \, A a^{2} b^{4} + 2 \, B a b^{5} - A b^{6}\right)} f x + {\left(B a^{4} b^{2} - 2 \, B a^{2} b^{4} + B b^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{{\left(a^{4} b^{4} - 2 \, a^{2} b^{6} + b^{8}\right)} f \sin\left(f x + e\right) + {\left(a^{5} b^{3} - 2 \, a^{3} b^{5} + a b^{7}\right)} f}\right]"," ",0,"[-1/2*(2*(2*B*a^6 - A*a^5*b - 4*B*a^4*b^2 + 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5)*f*x + (2*B*a^5 - A*a^4*b - 3*B*a^3*b^2 + 2*A*a^2*b^3 + (2*B*a^4*b - A*a^3*b^2 - 3*B*a^2*b^3 + 2*A*a*b^4)*sin(f*x + e))*sqrt(-a^2 + b^2)*log(((2*a^2 - b^2)*cos(f*x + e)^2 - 2*a*b*sin(f*x + e) - a^2 - b^2 + 2*(a*cos(f*x + e)*sin(f*x + e) + b*cos(f*x + e))*sqrt(-a^2 + b^2))/(b^2*cos(f*x + e)^2 - 2*a*b*sin(f*x + e) - a^2 - b^2)) + 2*(2*B*a^5*b - A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 + B*a*b^5)*cos(f*x + e) + 2*((2*B*a^5*b - A*a^4*b^2 - 4*B*a^3*b^3 + 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*f*x + (B*a^4*b^2 - 2*B*a^2*b^4 + B*b^6)*cos(f*x + e))*sin(f*x + e))/((a^4*b^4 - 2*a^2*b^6 + b^8)*f*sin(f*x + e) + (a^5*b^3 - 2*a^3*b^5 + a*b^7)*f), -((2*B*a^6 - A*a^5*b - 4*B*a^4*b^2 + 2*A*a^3*b^3 + 2*B*a^2*b^4 - A*a*b^5)*f*x + (2*B*a^5 - A*a^4*b - 3*B*a^3*b^2 + 2*A*a^2*b^3 + (2*B*a^4*b - A*a^3*b^2 - 3*B*a^2*b^3 + 2*A*a*b^4)*sin(f*x + e))*sqrt(a^2 - b^2)*arctan(-(a*sin(f*x + e) + b)/(sqrt(a^2 - b^2)*cos(f*x + e))) + (2*B*a^5*b - A*a^4*b^2 - 3*B*a^3*b^3 + A*a^2*b^4 + B*a*b^5)*cos(f*x + e) + ((2*B*a^5*b - A*a^4*b^2 - 4*B*a^3*b^3 + 2*A*a^2*b^4 + 2*B*a*b^5 - A*b^6)*f*x + (B*a^4*b^2 - 2*B*a^2*b^4 + B*b^6)*cos(f*x + e))*sin(f*x + e))/((a^4*b^4 - 2*a^2*b^6 + b^8)*f*sin(f*x + e) + (a^5*b^3 - 2*a^3*b^5 + a*b^7)*f)]","B",0
17,1,123,0,0.809688," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","-\frac{48 \, {\left(A - 3 \, B\right)} a c^{4} \cos\left(f x + e\right)^{5} - 320 \, {\left(A - B\right)} a c^{4} \cos\left(f x + e\right)^{3} - 105 \, {\left(2 \, A - B\right)} a c^{4} f x + 5 \, {\left(8 \, B a c^{4} \cos\left(f x + e\right)^{5} + 2 \, {\left(18 \, A - 25 \, B\right)} a c^{4} \cos\left(f x + e\right)^{3} - 21 \, {\left(2 \, A - B\right)} a c^{4} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f}"," ",0,"-1/240*(48*(A - 3*B)*a*c^4*cos(f*x + e)^5 - 320*(A - B)*a*c^4*cos(f*x + e)^3 - 105*(2*A - B)*a*c^4*f*x + 5*(8*B*a*c^4*cos(f*x + e)^5 + 2*(18*A - 25*B)*a*c^4*cos(f*x + e)^3 - 21*(2*A - B)*a*c^4*cos(f*x + e))*sin(f*x + e))/f","A",0
18,1,102,0,1.007423," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{24 \, B a c^{3} \cos\left(f x + e\right)^{5} + 80 \, {\left(A - B\right)} a c^{3} \cos\left(f x + e\right)^{3} + 15 \, {\left(5 \, A - 2 \, B\right)} a c^{3} f x - 15 \, {\left(2 \, {\left(A - 2 \, B\right)} a c^{3} \cos\left(f x + e\right)^{3} - {\left(5 \, A - 2 \, B\right)} a c^{3} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{120 \, f}"," ",0,"1/120*(24*B*a*c^3*cos(f*x + e)^5 + 80*(A - B)*a*c^3*cos(f*x + e)^3 + 15*(5*A - 2*B)*a*c^3*f*x - 15*(2*(A - 2*B)*a*c^3*cos(f*x + e)^3 - (5*A - 2*B)*a*c^3*cos(f*x + e))*sin(f*x + e))/f","A",0
19,1,82,0,0.893753," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{8 \, {\left(A - B\right)} a c^{2} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, A - B\right)} a c^{2} f x + 3 \, {\left(2 \, B a c^{2} \cos\left(f x + e\right)^{3} + {\left(4 \, A - B\right)} a c^{2} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, f}"," ",0,"1/24*(8*(A - B)*a*c^2*cos(f*x + e)^3 + 3*(4*A - B)*a*c^2*f*x + 3*(2*B*a*c^2*cos(f*x + e)^3 + (4*A - B)*a*c^2*cos(f*x + e))*sin(f*x + e))/f","A",0
20,1,43,0,0.858927," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, B a c \cos\left(f x + e\right)^{3} - 3 \, A a c f x - 3 \, A a c \cos\left(f x + e\right) \sin\left(f x + e\right)}{6 \, f}"," ",0,"-1/6*(2*B*a*c*cos(f*x + e)^3 - 3*A*a*c*f*x - 3*A*a*c*cos(f*x + e)*sin(f*x + e))/f","A",0
21,1,116,0,0.794595," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(A + 2 \, B\right)} a f x - B a \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a + {\left({\left(A + 2 \, B\right)} a f x - {\left(2 \, A + 3 \, B\right)} a\right)} \cos\left(f x + e\right) - {\left({\left(A + 2 \, B\right)} a f x - B a \cos\left(f x + e\right) + 2 \, {\left(A + B\right)} a\right)} \sin\left(f x + e\right)}{c f \cos\left(f x + e\right) - c f \sin\left(f x + e\right) + c f}"," ",0,"-((A + 2*B)*a*f*x - B*a*cos(f*x + e)^2 - 2*(A + B)*a + ((A + 2*B)*a*f*x - (2*A + 3*B)*a)*cos(f*x + e) - ((A + 2*B)*a*f*x - B*a*cos(f*x + e) + 2*(A + B)*a)*sin(f*x + e))/(c*f*cos(f*x + e) - c*f*sin(f*x + e) + c*f)","B",0
22,1,162,0,0.862934," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{6 \, B a f x - {\left(3 \, B a f x + {\left(A + 7 \, B\right)} a\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(A + B\right)} a + {\left(3 \, B a f x + {\left(A - 5 \, B\right)} a\right)} \cos\left(f x + e\right) - {\left(6 \, B a f x - 2 \, {\left(A + B\right)} a + {\left(3 \, B a f x - {\left(A + 7 \, B\right)} a\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right) - 2 \, c^{2} f + {\left(c^{2} f \cos\left(f x + e\right) + 2 \, c^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/3*(6*B*a*f*x - (3*B*a*f*x + (A + 7*B)*a)*cos(f*x + e)^2 + 2*(A + B)*a + (3*B*a*f*x + (A - 5*B)*a)*cos(f*x + e) - (6*B*a*f*x - 2*(A + B)*a + (3*B*a*f*x - (A + 7*B)*a)*cos(f*x + e))*sin(f*x + e))/(c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e) - 2*c^2*f + (c^2*f*cos(f*x + e) + 2*c^2*f)*sin(f*x + e))","B",0
23,1,183,0,0.633946," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(A - 4 \, B\right)} a \cos\left(f x + e\right)^{3} - {\left(2 \, A + 7 \, B\right)} a \cos\left(f x + e\right)^{2} + 3 \, {\left(A + B\right)} a \cos\left(f x + e\right) + 6 \, {\left(A + B\right)} a + {\left({\left(A - 4 \, B\right)} a \cos\left(f x + e\right)^{2} + 3 \, {\left(A + B\right)} a \cos\left(f x + e\right) + 6 \, {\left(A + B\right)} a\right)} \sin\left(f x + e\right)}{15 \, {\left(c^{3} f \cos\left(f x + e\right)^{3} + 3 \, c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f - {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/15*((A - 4*B)*a*cos(f*x + e)^3 - (2*A + 7*B)*a*cos(f*x + e)^2 + 3*(A + B)*a*cos(f*x + e) + 6*(A + B)*a + ((A - 4*B)*a*cos(f*x + e)^2 + 3*(A + B)*a*cos(f*x + e) + 6*(A + B)*a)*sin(f*x + e))/(c^3*f*cos(f*x + e)^3 + 3*c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f - (c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f)*sin(f*x + e))","A",0
24,1,251,0,0.891868," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","\frac{{\left(2 \, A - 5 \, B\right)} a \cos\left(f x + e\right)^{4} + 4 \, {\left(2 \, A - 5 \, B\right)} a \cos\left(f x + e\right)^{3} - 3 \, {\left(3 \, A + 10 \, B\right)} a \cos\left(f x + e\right)^{2} + 15 \, {\left(A + B\right)} a \cos\left(f x + e\right) + 30 \, {\left(A + B\right)} a - {\left({\left(2 \, A - 5 \, B\right)} a \cos\left(f x + e\right)^{3} - 3 \, {\left(2 \, A - 5 \, B\right)} a \cos\left(f x + e\right)^{2} - 15 \, {\left(A + B\right)} a \cos\left(f x + e\right) - 30 \, {\left(A + B\right)} a\right)} \sin\left(f x + e\right)}{105 \, {\left(c^{4} f \cos\left(f x + e\right)^{4} - 3 \, c^{4} f \cos\left(f x + e\right)^{3} - 8 \, c^{4} f \cos\left(f x + e\right)^{2} + 4 \, c^{4} f \cos\left(f x + e\right) + 8 \, c^{4} f + {\left(c^{4} f \cos\left(f x + e\right)^{3} + 4 \, c^{4} f \cos\left(f x + e\right)^{2} - 4 \, c^{4} f \cos\left(f x + e\right) - 8 \, c^{4} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/105*((2*A - 5*B)*a*cos(f*x + e)^4 + 4*(2*A - 5*B)*a*cos(f*x + e)^3 - 3*(3*A + 10*B)*a*cos(f*x + e)^2 + 15*(A + B)*a*cos(f*x + e) + 30*(A + B)*a - ((2*A - 5*B)*a*cos(f*x + e)^3 - 3*(2*A - 5*B)*a*cos(f*x + e)^2 - 15*(A + B)*a*cos(f*x + e) - 30*(A + B)*a)*sin(f*x + e))/(c^4*f*cos(f*x + e)^4 - 3*c^4*f*cos(f*x + e)^3 - 8*c^4*f*cos(f*x + e)^2 + 4*c^4*f*cos(f*x + e) + 8*c^4*f + (c^4*f*cos(f*x + e)^3 + 4*c^4*f*cos(f*x + e)^2 - 4*c^4*f*cos(f*x + e) - 8*c^4*f)*sin(f*x + e))","A",0
25,1,305,0,0.919284," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x, algorithm=""fricas"")","-\frac{2 \, {\left(A - 2 \, B\right)} a \cos\left(f x + e\right)^{5} - 8 \, {\left(A - 2 \, B\right)} a \cos\left(f x + e\right)^{4} - 25 \, {\left(A - 2 \, B\right)} a \cos\left(f x + e\right)^{3} + 5 \, {\left(4 \, A + 13 \, B\right)} a \cos\left(f x + e\right)^{2} - 35 \, {\left(A + B\right)} a \cos\left(f x + e\right) - 70 \, {\left(A + B\right)} a + {\left(2 \, {\left(A - 2 \, B\right)} a \cos\left(f x + e\right)^{4} + 10 \, {\left(A - 2 \, B\right)} a \cos\left(f x + e\right)^{3} - 15 \, {\left(A - 2 \, B\right)} a \cos\left(f x + e\right)^{2} - 35 \, {\left(A + B\right)} a \cos\left(f x + e\right) - 70 \, {\left(A + B\right)} a\right)} \sin\left(f x + e\right)}{315 \, {\left(c^{5} f \cos\left(f x + e\right)^{5} + 5 \, c^{5} f \cos\left(f x + e\right)^{4} - 8 \, c^{5} f \cos\left(f x + e\right)^{3} - 20 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f - {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} - 12 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/315*(2*(A - 2*B)*a*cos(f*x + e)^5 - 8*(A - 2*B)*a*cos(f*x + e)^4 - 25*(A - 2*B)*a*cos(f*x + e)^3 + 5*(4*A + 13*B)*a*cos(f*x + e)^2 - 35*(A + B)*a*cos(f*x + e) - 70*(A + B)*a + (2*(A - 2*B)*a*cos(f*x + e)^4 + 10*(A - 2*B)*a*cos(f*x + e)^3 - 15*(A - 2*B)*a*cos(f*x + e)^2 - 35*(A + B)*a*cos(f*x + e) - 70*(A + B)*a)*sin(f*x + e))/(c^5*f*cos(f*x + e)^5 + 5*c^5*f*cos(f*x + e)^4 - 8*c^5*f*cos(f*x + e)^3 - 20*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f - (c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 - 12*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f)*sin(f*x + e))","A",0
26,1,158,0,0.965624," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5,x, algorithm=""fricas"")","-\frac{640 \, {\left(A - 3 \, B\right)} a^{2} c^{5} \cos\left(f x + e\right)^{7} - 3584 \, {\left(A - B\right)} a^{2} c^{5} \cos\left(f x + e\right)^{5} - 315 \, {\left(8 \, A - 3 \, B\right)} a^{2} c^{5} f x + 35 \, {\left(16 \, B a^{2} c^{5} \cos\left(f x + e\right)^{7} + 8 \, {\left(8 \, A - 11 \, B\right)} a^{2} c^{5} \cos\left(f x + e\right)^{5} - 6 \, {\left(8 \, A - 3 \, B\right)} a^{2} c^{5} \cos\left(f x + e\right)^{3} - 9 \, {\left(8 \, A - 3 \, B\right)} a^{2} c^{5} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4480 \, f}"," ",0,"-1/4480*(640*(A - 3*B)*a^2*c^5*cos(f*x + e)^7 - 3584*(A - B)*a^2*c^5*cos(f*x + e)^5 - 315*(8*A - 3*B)*a^2*c^5*f*x + 35*(16*B*a^2*c^5*cos(f*x + e)^7 + 8*(8*A - 11*B)*a^2*c^5*cos(f*x + e)^5 - 6*(8*A - 3*B)*a^2*c^5*cos(f*x + e)^3 - 9*(8*A - 3*B)*a^2*c^5*cos(f*x + e))*sin(f*x + e))/f","A",0
27,1,135,0,0.839147," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","\frac{240 \, B a^{2} c^{4} \cos\left(f x + e\right)^{7} + 672 \, {\left(A - B\right)} a^{2} c^{4} \cos\left(f x + e\right)^{5} + 105 \, {\left(7 \, A - 2 \, B\right)} a^{2} c^{4} f x - 35 \, {\left(8 \, {\left(A - 2 \, B\right)} a^{2} c^{4} \cos\left(f x + e\right)^{5} - 2 \, {\left(7 \, A - 2 \, B\right)} a^{2} c^{4} \cos\left(f x + e\right)^{3} - 3 \, {\left(7 \, A - 2 \, B\right)} a^{2} c^{4} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{1680 \, f}"," ",0,"1/1680*(240*B*a^2*c^4*cos(f*x + e)^7 + 672*(A - B)*a^2*c^4*cos(f*x + e)^5 + 105*(7*A - 2*B)*a^2*c^4*f*x - 35*(8*(A - 2*B)*a^2*c^4*cos(f*x + e)^5 - 2*(7*A - 2*B)*a^2*c^4*cos(f*x + e)^3 - 3*(7*A - 2*B)*a^2*c^4*cos(f*x + e))*sin(f*x + e))/f","A",0
28,1,114,0,0.928597," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{48 \, {\left(A - B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{5} + 15 \, {\left(6 \, A - B\right)} a^{2} c^{3} f x + 5 \, {\left(8 \, B a^{2} c^{3} \cos\left(f x + e\right)^{5} + 2 \, {\left(6 \, A - B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{3} + 3 \, {\left(6 \, A - B\right)} a^{2} c^{3} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f}"," ",0,"1/240*(48*(A - B)*a^2*c^3*cos(f*x + e)^5 + 15*(6*A - B)*a^2*c^3*f*x + 5*(8*B*a^2*c^3*cos(f*x + e)^5 + 2*(6*A - B)*a^2*c^3*cos(f*x + e)^3 + 3*(6*A - B)*a^2*c^3*cos(f*x + e))*sin(f*x + e))/f","A",0
29,1,75,0,0.848000," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{8 \, B a^{2} c^{2} \cos\left(f x + e\right)^{5} - 15 \, A a^{2} c^{2} f x - 5 \, {\left(2 \, A a^{2} c^{2} \cos\left(f x + e\right)^{3} + 3 \, A a^{2} c^{2} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{40 \, f}"," ",0,"-1/40*(8*B*a^2*c^2*cos(f*x + e)^5 - 15*A*a^2*c^2*f*x - 5*(2*A*a^2*c^2*cos(f*x + e)^3 + 3*A*a^2*c^2*cos(f*x + e))*sin(f*x + e))/f","A",0
30,1,77,0,0.708645," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{8 \, {\left(A + B\right)} a^{2} c \cos\left(f x + e\right)^{3} - 3 \, {\left(4 \, A + B\right)} a^{2} c f x + 3 \, {\left(2 \, B a^{2} c \cos\left(f x + e\right)^{3} - {\left(4 \, A + B\right)} a^{2} c \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, f}"," ",0,"-1/24*(8*(A + B)*a^2*c*cos(f*x + e)^3 - 3*(4*A + B)*a^2*c*f*x + 3*(2*B*a^2*c*cos(f*x + e)^3 - (4*A + B)*a^2*c*cos(f*x + e))*sin(f*x + e))/f","A",0
31,1,177,0,0.690902," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{B a^{2} \cos\left(f x + e\right)^{3} - 3 \, {\left(2 \, A + 3 \, B\right)} a^{2} f x + 2 \, {\left(A + 3 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 8 \, {\left(A + B\right)} a^{2} - {\left(3 \, {\left(2 \, A + 3 \, B\right)} a^{2} f x - {\left(10 \, A + 13 \, B\right)} a^{2}\right)} \cos\left(f x + e\right) + {\left(3 \, {\left(2 \, A + 3 \, B\right)} a^{2} f x + B a^{2} \cos\left(f x + e\right)^{2} - {\left(2 \, A + 5 \, B\right)} a^{2} \cos\left(f x + e\right) + 8 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left(c f \cos\left(f x + e\right) - c f \sin\left(f x + e\right) + c f\right)}}"," ",0,"1/2*(B*a^2*cos(f*x + e)^3 - 3*(2*A + 3*B)*a^2*f*x + 2*(A + 3*B)*a^2*cos(f*x + e)^2 + 8*(A + B)*a^2 - (3*(2*A + 3*B)*a^2*f*x - (10*A + 13*B)*a^2)*cos(f*x + e) + (3*(2*A + 3*B)*a^2*f*x + B*a^2*cos(f*x + e)^2 - (2*A + 5*B)*a^2*cos(f*x + e) + 8*(A + B)*a^2)*sin(f*x + e))/(c*f*cos(f*x + e) - c*f*sin(f*x + e) + c*f)","A",0
32,1,237,0,0.933625," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{3 \, B a^{2} \cos\left(f x + e\right)^{3} + 6 \, {\left(A + 4 \, B\right)} a^{2} f x + 4 \, {\left(A + B\right)} a^{2} - {\left(3 \, {\left(A + 4 \, B\right)} a^{2} f x + {\left(8 \, A + 23 \, B\right)} a^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, {\left(A + 4 \, B\right)} a^{2} f x - 2 \, {\left(2 \, A + 11 \, B\right)} a^{2}\right)} \cos\left(f x + e\right) - {\left(6 \, {\left(A + 4 \, B\right)} a^{2} f x - 3 \, B a^{2} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + B\right)} a^{2} + {\left(3 \, {\left(A + 4 \, B\right)} a^{2} f x - 2 \, {\left(4 \, A + 13 \, B\right)} a^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right) - 2 \, c^{2} f + {\left(c^{2} f \cos\left(f x + e\right) + 2 \, c^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/3*(3*B*a^2*cos(f*x + e)^3 + 6*(A + 4*B)*a^2*f*x + 4*(A + B)*a^2 - (3*(A + 4*B)*a^2*f*x + (8*A + 23*B)*a^2)*cos(f*x + e)^2 + (3*(A + 4*B)*a^2*f*x - 2*(2*A + 11*B)*a^2)*cos(f*x + e) - (6*(A + 4*B)*a^2*f*x - 3*B*a^2*cos(f*x + e)^2 - 4*(A + B)*a^2 + (3*(A + 4*B)*a^2*f*x - 2*(4*A + 13*B)*a^2)*cos(f*x + e))*sin(f*x + e))/(c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e) - 2*c^2*f + (c^2*f*cos(f*x + e) + 2*c^2*f)*sin(f*x + e))","B",0
33,1,277,0,0.783101," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{60 \, B a^{2} f x - {\left(15 \, B a^{2} f x - {\left(3 \, A + 43 \, B\right)} a^{2}\right)} \cos\left(f x + e\right)^{3} - 12 \, {\left(A + B\right)} a^{2} - {\left(45 \, B a^{2} f x - {\left(9 \, A - 11 \, B\right)} a^{2}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(5 \, B a^{2} f x - {\left(A + 11 \, B\right)} a^{2}\right)} \cos\left(f x + e\right) - {\left(60 \, B a^{2} f x + 12 \, {\left(A + B\right)} a^{2} - {\left(15 \, B a^{2} f x + {\left(3 \, A + 43 \, B\right)} a^{2}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(5 \, B a^{2} f x + {\left(A - 9 \, B\right)} a^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left(c^{3} f \cos\left(f x + e\right)^{3} + 3 \, c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f - {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/15*(60*B*a^2*f*x - (15*B*a^2*f*x - (3*A + 43*B)*a^2)*cos(f*x + e)^3 - 12*(A + B)*a^2 - (45*B*a^2*f*x - (9*A - 11*B)*a^2)*cos(f*x + e)^2 + 6*(5*B*a^2*f*x - (A + 11*B)*a^2)*cos(f*x + e) - (60*B*a^2*f*x + 12*(A + B)*a^2 - (15*B*a^2*f*x + (3*A + 43*B)*a^2)*cos(f*x + e)^2 + 6*(5*B*a^2*f*x + (A - 9*B)*a^2)*cos(f*x + e))*sin(f*x + e))/(c^3*f*cos(f*x + e)^3 + 3*c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f - (c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f)*sin(f*x + e))","B",0
34,1,263,0,0.755493," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","-\frac{{\left(A - 6 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} + {\left(4 \, A + 11 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} + {\left(13 \, A + 27 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 10 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right) - 20 \, {\left(A + B\right)} a^{2} - {\left({\left(A - 6 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - {\left(3 \, A + 17 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 10 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right) + 20 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)}{35 \, {\left(c^{4} f \cos\left(f x + e\right)^{4} - 3 \, c^{4} f \cos\left(f x + e\right)^{3} - 8 \, c^{4} f \cos\left(f x + e\right)^{2} + 4 \, c^{4} f \cos\left(f x + e\right) + 8 \, c^{4} f + {\left(c^{4} f \cos\left(f x + e\right)^{3} + 4 \, c^{4} f \cos\left(f x + e\right)^{2} - 4 \, c^{4} f \cos\left(f x + e\right) - 8 \, c^{4} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/35*((A - 6*B)*a^2*cos(f*x + e)^4 + (4*A + 11*B)*a^2*cos(f*x + e)^3 + (13*A + 27*B)*a^2*cos(f*x + e)^2 - 10*(A + B)*a^2*cos(f*x + e) - 20*(A + B)*a^2 - ((A - 6*B)*a^2*cos(f*x + e)^3 - (3*A + 17*B)*a^2*cos(f*x + e)^2 + 10*(A + B)*a^2*cos(f*x + e) + 20*(A + B)*a^2)*sin(f*x + e))/(c^4*f*cos(f*x + e)^4 - 3*c^4*f*cos(f*x + e)^3 - 8*c^4*f*cos(f*x + e)^2 + 4*c^4*f*cos(f*x + e) + 8*c^4*f + (c^4*f*cos(f*x + e)^3 + 4*c^4*f*cos(f*x + e)^2 - 4*c^4*f*cos(f*x + e) - 8*c^4*f)*sin(f*x + e))","B",0
35,1,335,0,0.827502," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x, algorithm=""fricas"")","\frac{{\left(2 \, A - 7 \, B\right)} a^{2} \cos\left(f x + e\right)^{5} - 4 \, {\left(2 \, A - 7 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} - 5 \, {\left(5 \, A + 14 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - 5 \, {\left(17 \, A + 35 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 70 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right) + 140 \, {\left(A + B\right)} a^{2} + {\left({\left(2 \, A - 7 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} + 5 \, {\left(2 \, A - 7 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - 15 \, {\left(A + 7 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 70 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right) + 140 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)}{315 \, {\left(c^{5} f \cos\left(f x + e\right)^{5} + 5 \, c^{5} f \cos\left(f x + e\right)^{4} - 8 \, c^{5} f \cos\left(f x + e\right)^{3} - 20 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f - {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} - 12 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/315*((2*A - 7*B)*a^2*cos(f*x + e)^5 - 4*(2*A - 7*B)*a^2*cos(f*x + e)^4 - 5*(5*A + 14*B)*a^2*cos(f*x + e)^3 - 5*(17*A + 35*B)*a^2*cos(f*x + e)^2 + 70*(A + B)*a^2*cos(f*x + e) + 140*(A + B)*a^2 + ((2*A - 7*B)*a^2*cos(f*x + e)^4 + 5*(2*A - 7*B)*a^2*cos(f*x + e)^3 - 15*(A + 7*B)*a^2*cos(f*x + e)^2 + 70*(A + B)*a^2*cos(f*x + e) + 140*(A + B)*a^2)*sin(f*x + e))/(c^5*f*cos(f*x + e)^5 + 5*c^5*f*cos(f*x + e)^4 - 8*c^5*f*cos(f*x + e)^3 - 20*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f - (c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 - 12*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f)*sin(f*x + e))","B",0
36,1,407,0,0.820847," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^6,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A - 8 \, B\right)} a^{2} \cos\left(f x + e\right)^{6} + 12 \, {\left(3 \, A - 8 \, B\right)} a^{2} \cos\left(f x + e\right)^{5} - 25 \, {\left(3 \, A - 8 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} - 35 \, {\left(6 \, A + 17 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - 35 \, {\left(21 \, A + 43 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 630 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right) + 1260 \, {\left(A + B\right)} a^{2} - {\left(2 \, {\left(3 \, A - 8 \, B\right)} a^{2} \cos\left(f x + e\right)^{5} - 10 \, {\left(3 \, A - 8 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} - 35 \, {\left(3 \, A - 8 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} + 35 \, {\left(3 \, A + 25 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 630 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right) - 1260 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)}{3465 \, {\left(c^{6} f \cos\left(f x + e\right)^{6} - 5 \, c^{6} f \cos\left(f x + e\right)^{5} - 18 \, c^{6} f \cos\left(f x + e\right)^{4} + 20 \, c^{6} f \cos\left(f x + e\right)^{3} + 48 \, c^{6} f \cos\left(f x + e\right)^{2} - 16 \, c^{6} f \cos\left(f x + e\right) - 32 \, c^{6} f + {\left(c^{6} f \cos\left(f x + e\right)^{5} + 6 \, c^{6} f \cos\left(f x + e\right)^{4} - 12 \, c^{6} f \cos\left(f x + e\right)^{3} - 32 \, c^{6} f \cos\left(f x + e\right)^{2} + 16 \, c^{6} f \cos\left(f x + e\right) + 32 \, c^{6} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/3465*(2*(3*A - 8*B)*a^2*cos(f*x + e)^6 + 12*(3*A - 8*B)*a^2*cos(f*x + e)^5 - 25*(3*A - 8*B)*a^2*cos(f*x + e)^4 - 35*(6*A + 17*B)*a^2*cos(f*x + e)^3 - 35*(21*A + 43*B)*a^2*cos(f*x + e)^2 + 630*(A + B)*a^2*cos(f*x + e) + 1260*(A + B)*a^2 - (2*(3*A - 8*B)*a^2*cos(f*x + e)^5 - 10*(3*A - 8*B)*a^2*cos(f*x + e)^4 - 35*(3*A - 8*B)*a^2*cos(f*x + e)^3 + 35*(3*A + 25*B)*a^2*cos(f*x + e)^2 - 630*(A + B)*a^2*cos(f*x + e) - 1260*(A + B)*a^2)*sin(f*x + e))/(c^6*f*cos(f*x + e)^6 - 5*c^6*f*cos(f*x + e)^5 - 18*c^6*f*cos(f*x + e)^4 + 20*c^6*f*cos(f*x + e)^3 + 48*c^6*f*cos(f*x + e)^2 - 16*c^6*f*cos(f*x + e) - 32*c^6*f + (c^6*f*cos(f*x + e)^5 + 6*c^6*f*cos(f*x + e)^4 - 12*c^6*f*cos(f*x + e)^3 - 32*c^6*f*cos(f*x + e)^2 + 16*c^6*f*cos(f*x + e) + 32*c^6*f)*sin(f*x + e))","B",0
37,1,475,0,0.664053," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^7,x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, A - 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{7} - 12 \, {\left(4 \, A - 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{6} - 49 \, {\left(4 \, A - 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{5} + 70 \, {\left(4 \, A - 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} + 105 \, {\left(7 \, A + 20 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} + 105 \, {\left(25 \, A + 51 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2310 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right) - 4620 \, {\left(A + B\right)} a^{2} + {\left(2 \, {\left(4 \, A - 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{6} + 14 \, {\left(4 \, A - 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{5} - 35 \, {\left(4 \, A - 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} - 105 \, {\left(4 \, A - 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} + 105 \, {\left(3 \, A + 29 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2310 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right) - 4620 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)}{15015 \, {\left(c^{7} f \cos\left(f x + e\right)^{7} + 7 \, c^{7} f \cos\left(f x + e\right)^{6} - 18 \, c^{7} f \cos\left(f x + e\right)^{5} - 56 \, c^{7} f \cos\left(f x + e\right)^{4} + 48 \, c^{7} f \cos\left(f x + e\right)^{3} + 112 \, c^{7} f \cos\left(f x + e\right)^{2} - 32 \, c^{7} f \cos\left(f x + e\right) - 64 \, c^{7} f - {\left(c^{7} f \cos\left(f x + e\right)^{6} - 6 \, c^{7} f \cos\left(f x + e\right)^{5} - 24 \, c^{7} f \cos\left(f x + e\right)^{4} + 32 \, c^{7} f \cos\left(f x + e\right)^{3} + 80 \, c^{7} f \cos\left(f x + e\right)^{2} - 32 \, c^{7} f \cos\left(f x + e\right) - 64 \, c^{7} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/15015*(2*(4*A - 9*B)*a^2*cos(f*x + e)^7 - 12*(4*A - 9*B)*a^2*cos(f*x + e)^6 - 49*(4*A - 9*B)*a^2*cos(f*x + e)^5 + 70*(4*A - 9*B)*a^2*cos(f*x + e)^4 + 105*(7*A + 20*B)*a^2*cos(f*x + e)^3 + 105*(25*A + 51*B)*a^2*cos(f*x + e)^2 - 2310*(A + B)*a^2*cos(f*x + e) - 4620*(A + B)*a^2 + (2*(4*A - 9*B)*a^2*cos(f*x + e)^6 + 14*(4*A - 9*B)*a^2*cos(f*x + e)^5 - 35*(4*A - 9*B)*a^2*cos(f*x + e)^4 - 105*(4*A - 9*B)*a^2*cos(f*x + e)^3 + 105*(3*A + 29*B)*a^2*cos(f*x + e)^2 - 2310*(A + B)*a^2*cos(f*x + e) - 4620*(A + B)*a^2)*sin(f*x + e))/(c^7*f*cos(f*x + e)^7 + 7*c^7*f*cos(f*x + e)^6 - 18*c^7*f*cos(f*x + e)^5 - 56*c^7*f*cos(f*x + e)^4 + 48*c^7*f*cos(f*x + e)^3 + 112*c^7*f*cos(f*x + e)^2 - 32*c^7*f*cos(f*x + e) - 64*c^7*f - (c^7*f*cos(f*x + e)^6 - 6*c^7*f*cos(f*x + e)^5 - 24*c^7*f*cos(f*x + e)^4 + 32*c^7*f*cos(f*x + e)^3 + 80*c^7*f*cos(f*x + e)^2 - 32*c^7*f*cos(f*x + e) - 64*c^7*f)*sin(f*x + e))","B",0
38,1,181,0,0.923379," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^6,x, algorithm=""fricas"")","-\frac{8960 \, {\left(A - 3 \, B\right)} a^{3} c^{6} \cos\left(f x + e\right)^{9} - 46080 \, {\left(A - B\right)} a^{3} c^{6} \cos\left(f x + e\right)^{7} - 3465 \, {\left(10 \, A - 3 \, B\right)} a^{3} c^{6} f x + 21 \, {\left(384 \, B a^{3} c^{6} \cos\left(f x + e\right)^{9} + 48 \, {\left(30 \, A - 41 \, B\right)} a^{3} c^{6} \cos\left(f x + e\right)^{7} - 88 \, {\left(10 \, A - 3 \, B\right)} a^{3} c^{6} \cos\left(f x + e\right)^{5} - 110 \, {\left(10 \, A - 3 \, B\right)} a^{3} c^{6} \cos\left(f x + e\right)^{3} - 165 \, {\left(10 \, A - 3 \, B\right)} a^{3} c^{6} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{80640 \, f}"," ",0,"-1/80640*(8960*(A - 3*B)*a^3*c^6*cos(f*x + e)^9 - 46080*(A - B)*a^3*c^6*cos(f*x + e)^7 - 3465*(10*A - 3*B)*a^3*c^6*f*x + 21*(384*B*a^3*c^6*cos(f*x + e)^9 + 48*(30*A - 41*B)*a^3*c^6*cos(f*x + e)^7 - 88*(10*A - 3*B)*a^3*c^6*cos(f*x + e)^5 - 110*(10*A - 3*B)*a^3*c^6*cos(f*x + e)^3 - 165*(10*A - 3*B)*a^3*c^6*cos(f*x + e))*sin(f*x + e))/f","A",0
39,1,158,0,1.010424," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5,x, algorithm=""fricas"")","\frac{896 \, B a^{3} c^{5} \cos\left(f x + e\right)^{9} + 2304 \, {\left(A - B\right)} a^{3} c^{5} \cos\left(f x + e\right)^{7} + 315 \, {\left(9 \, A - 2 \, B\right)} a^{3} c^{5} f x - 21 \, {\left(48 \, {\left(A - 2 \, B\right)} a^{3} c^{5} \cos\left(f x + e\right)^{7} - 8 \, {\left(9 \, A - 2 \, B\right)} a^{3} c^{5} \cos\left(f x + e\right)^{5} - 10 \, {\left(9 \, A - 2 \, B\right)} a^{3} c^{5} \cos\left(f x + e\right)^{3} - 15 \, {\left(9 \, A - 2 \, B\right)} a^{3} c^{5} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{8064 \, f}"," ",0,"1/8064*(896*B*a^3*c^5*cos(f*x + e)^9 + 2304*(A - B)*a^3*c^5*cos(f*x + e)^7 + 315*(9*A - 2*B)*a^3*c^5*f*x - 21*(48*(A - 2*B)*a^3*c^5*cos(f*x + e)^7 - 8*(9*A - 2*B)*a^3*c^5*cos(f*x + e)^5 - 10*(9*A - 2*B)*a^3*c^5*cos(f*x + e)^3 - 15*(9*A - 2*B)*a^3*c^5*cos(f*x + e))*sin(f*x + e))/f","A",0
40,1,137,0,0.960495," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","\frac{384 \, {\left(A - B\right)} a^{3} c^{4} \cos\left(f x + e\right)^{7} + 105 \, {\left(8 \, A - B\right)} a^{3} c^{4} f x + 7 \, {\left(48 \, B a^{3} c^{4} \cos\left(f x + e\right)^{7} + 8 \, {\left(8 \, A - B\right)} a^{3} c^{4} \cos\left(f x + e\right)^{5} + 10 \, {\left(8 \, A - B\right)} a^{3} c^{4} \cos\left(f x + e\right)^{3} + 15 \, {\left(8 \, A - B\right)} a^{3} c^{4} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2688 \, f}"," ",0,"1/2688*(384*(A - B)*a^3*c^4*cos(f*x + e)^7 + 105*(8*A - B)*a^3*c^4*f*x + 7*(48*B*a^3*c^4*cos(f*x + e)^7 + 8*(8*A - B)*a^3*c^4*cos(f*x + e)^5 + 10*(8*A - B)*a^3*c^4*cos(f*x + e)^3 + 15*(8*A - B)*a^3*c^4*cos(f*x + e))*sin(f*x + e))/f","A",0
41,1,92,0,0.954311," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{48 \, B a^{3} c^{3} \cos\left(f x + e\right)^{7} - 105 \, A a^{3} c^{3} f x - 7 \, {\left(8 \, A a^{3} c^{3} \cos\left(f x + e\right)^{5} + 10 \, A a^{3} c^{3} \cos\left(f x + e\right)^{3} + 15 \, A a^{3} c^{3} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{336 \, f}"," ",0,"-1/336*(48*B*a^3*c^3*cos(f*x + e)^7 - 105*A*a^3*c^3*f*x - 7*(8*A*a^3*c^3*cos(f*x + e)^5 + 10*A*a^3*c^3*cos(f*x + e)^3 + 15*A*a^3*c^3*cos(f*x + e))*sin(f*x + e))/f","A",0
42,1,106,0,0.951969," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{48 \, {\left(A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{5} - 15 \, {\left(6 \, A + B\right)} a^{3} c^{2} f x + 5 \, {\left(8 \, B a^{3} c^{2} \cos\left(f x + e\right)^{5} - 2 \, {\left(6 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{3} - 3 \, {\left(6 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f}"," ",0,"-1/240*(48*(A + B)*a^3*c^2*cos(f*x + e)^5 - 15*(6*A + B)*a^3*c^2*f*x + 5*(8*B*a^3*c^2*cos(f*x + e)^5 - 2*(6*A + B)*a^3*c^2*cos(f*x + e)^3 - 3*(6*A + B)*a^3*c^2*cos(f*x + e))*sin(f*x + e))/f","A",0
43,1,100,0,0.737751," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{24 \, B a^{3} c \cos\left(f x + e\right)^{5} - 80 \, {\left(A + B\right)} a^{3} c \cos\left(f x + e\right)^{3} + 15 \, {\left(5 \, A + 2 \, B\right)} a^{3} c f x - 15 \, {\left(2 \, {\left(A + 2 \, B\right)} a^{3} c \cos\left(f x + e\right)^{3} - {\left(5 \, A + 2 \, B\right)} a^{3} c \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{120 \, f}"," ",0,"1/120*(24*B*a^3*c*cos(f*x + e)^5 - 80*(A + B)*a^3*c*cos(f*x + e)^3 + 15*(5*A + 2*B)*a^3*c*f*x - 15*(2*(A + 2*B)*a^3*c*cos(f*x + e)^3 - (5*A + 2*B)*a^3*c*cos(f*x + e))*sin(f*x + e))/f","A",0
44,1,218,0,0.969154," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, B a^{3} \cos\left(f x + e\right)^{4} - {\left(3 \, A + 10 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 15 \, {\left(3 \, A + 4 \, B\right)} a^{3} f x - 24 \, {\left(A + 2 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 48 \, {\left(A + B\right)} a^{3} + 3 \, {\left(5 \, {\left(3 \, A + 4 \, B\right)} a^{3} f x - {\left(23 \, A + 28 \, B\right)} a^{3}\right)} \cos\left(f x + e\right) - {\left(2 \, B a^{3} \cos\left(f x + e\right)^{3} + 15 \, {\left(3 \, A + 4 \, B\right)} a^{3} f x + 3 \, {\left(A + 4 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 3 \, {\left(7 \, A + 12 \, B\right)} a^{3} \cos\left(f x + e\right) + 48 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)}{6 \, {\left(c f \cos\left(f x + e\right) - c f \sin\left(f x + e\right) + c f\right)}}"," ",0,"-1/6*(2*B*a^3*cos(f*x + e)^4 - (3*A + 10*B)*a^3*cos(f*x + e)^3 + 15*(3*A + 4*B)*a^3*f*x - 24*(A + 2*B)*a^3*cos(f*x + e)^2 - 48*(A + B)*a^3 + 3*(5*(3*A + 4*B)*a^3*f*x - (23*A + 28*B)*a^3)*cos(f*x + e) - (2*B*a^3*cos(f*x + e)^3 + 15*(3*A + 4*B)*a^3*f*x + 3*(A + 4*B)*a^3*cos(f*x + e)^2 - 3*(7*A + 12*B)*a^3*cos(f*x + e) + 48*(A + B)*a^3)*sin(f*x + e))/(c*f*cos(f*x + e) - c*f*sin(f*x + e) + c*f)","A",0
45,1,286,0,0.933247," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, B a^{3} \cos\left(f x + e\right)^{4} - 6 \, {\left(A + 4 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 30 \, {\left(2 \, A + 5 \, B\right)} a^{3} f x - 16 \, {\left(A + B\right)} a^{3} + {\left(15 \, {\left(2 \, A + 5 \, B\right)} a^{3} f x + {\left(62 \, A + 131 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(15 \, {\left(2 \, A + 5 \, B\right)} a^{3} f x - 2 \, {\left(26 \, A + 71 \, B\right)} a^{3}\right)} \cos\left(f x + e\right) - {\left(3 \, B a^{3} \cos\left(f x + e\right)^{3} - 30 \, {\left(2 \, A + 5 \, B\right)} a^{3} f x + 3 \, {\left(2 \, A + 9 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 16 \, {\left(A + B\right)} a^{3} - {\left(15 \, {\left(2 \, A + 5 \, B\right)} a^{3} f x - 2 \, {\left(34 \, A + 79 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right) - 2 \, c^{2} f + {\left(c^{2} f \cos\left(f x + e\right) + 2 \, c^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/6*(3*B*a^3*cos(f*x + e)^4 - 6*(A + 4*B)*a^3*cos(f*x + e)^3 - 30*(2*A + 5*B)*a^3*f*x - 16*(A + B)*a^3 + (15*(2*A + 5*B)*a^3*f*x + (62*A + 131*B)*a^3)*cos(f*x + e)^2 - (15*(2*A + 5*B)*a^3*f*x - 2*(26*A + 71*B)*a^3)*cos(f*x + e) - (3*B*a^3*cos(f*x + e)^3 - 30*(2*A + 5*B)*a^3*f*x + 3*(2*A + 9*B)*a^3*cos(f*x + e)^2 + 16*(A + B)*a^3 - (15*(2*A + 5*B)*a^3*f*x - 2*(34*A + 79*B)*a^3)*cos(f*x + e))*sin(f*x + e))/(c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e) - 2*c^2*f + (c^2*f*cos(f*x + e) + 2*c^2*f)*sin(f*x + e))","A",0
46,1,337,0,0.919727," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, B a^{3} \cos\left(f x + e\right)^{4} + 60 \, {\left(A + 6 \, B\right)} a^{3} f x - 24 \, {\left(A + B\right)} a^{3} - {\left(15 \, {\left(A + 6 \, B\right)} a^{3} f x - {\left(46 \, A + 231 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(45 \, {\left(A + 6 \, B\right)} a^{3} f x + 2 \, {\left(A + 66 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(5 \, {\left(A + 6 \, B\right)} a^{3} f x - 2 \, {\left(6 \, A + 31 \, B\right)} a^{3}\right)} \cos\left(f x + e\right) - {\left(15 \, B a^{3} \cos\left(f x + e\right)^{3} + 60 \, {\left(A + 6 \, B\right)} a^{3} f x + 24 \, {\left(A + B\right)} a^{3} - {\left(15 \, {\left(A + 6 \, B\right)} a^{3} f x + 2 \, {\left(23 \, A + 108 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(5 \, {\left(A + 6 \, B\right)} a^{3} f x - 2 \, {\left(4 \, A + 29 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left(c^{3} f \cos\left(f x + e\right)^{3} + 3 \, c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f - {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/15*(15*B*a^3*cos(f*x + e)^4 + 60*(A + 6*B)*a^3*f*x - 24*(A + B)*a^3 - (15*(A + 6*B)*a^3*f*x - (46*A + 231*B)*a^3)*cos(f*x + e)^3 - (45*(A + 6*B)*a^3*f*x + 2*(A + 66*B)*a^3)*cos(f*x + e)^2 + 6*(5*(A + 6*B)*a^3*f*x - 2*(6*A + 31*B)*a^3)*cos(f*x + e) - (15*B*a^3*cos(f*x + e)^3 + 60*(A + 6*B)*a^3*f*x + 24*(A + B)*a^3 - (15*(A + 6*B)*a^3*f*x + 2*(23*A + 108*B)*a^3)*cos(f*x + e)^2 + 6*(5*(A + 6*B)*a^3*f*x - 2*(4*A + 29*B)*a^3)*cos(f*x + e))*sin(f*x + e))/(c^3*f*cos(f*x + e)^3 + 3*c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f - (c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f)*sin(f*x + e))","B",0
47,1,363,0,0.844382," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","\frac{840 \, B a^{3} f x + {\left(105 \, B a^{3} f x + {\left(15 \, A + 337 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{4} + 120 \, {\left(A + B\right)} a^{3} - {\left(315 \, B a^{3} f x + {\left(45 \, A - 613 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{3} - 24 \, {\left(35 \, B a^{3} f x + {\left(5 \, A + 26 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{2} + 60 \, {\left(7 \, B a^{3} f x + {\left(A - 13 \, B\right)} a^{3}\right)} \cos\left(f x + e\right) - {\left(840 \, B a^{3} f x - 120 \, {\left(A + B\right)} a^{3} - {\left(105 \, B a^{3} f x - {\left(15 \, A + 337 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{3} - 12 \, {\left(35 \, B a^{3} f x - {\left(5 \, A - 23 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)^{2} + 60 \, {\left(7 \, B a^{3} f x - {\left(A + 15 \, B\right)} a^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{105 \, {\left(c^{4} f \cos\left(f x + e\right)^{4} - 3 \, c^{4} f \cos\left(f x + e\right)^{3} - 8 \, c^{4} f \cos\left(f x + e\right)^{2} + 4 \, c^{4} f \cos\left(f x + e\right) + 8 \, c^{4} f + {\left(c^{4} f \cos\left(f x + e\right)^{3} + 4 \, c^{4} f \cos\left(f x + e\right)^{2} - 4 \, c^{4} f \cos\left(f x + e\right) - 8 \, c^{4} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/105*(840*B*a^3*f*x + (105*B*a^3*f*x + (15*A + 337*B)*a^3)*cos(f*x + e)^4 + 120*(A + B)*a^3 - (315*B*a^3*f*x + (45*A - 613*B)*a^3)*cos(f*x + e)^3 - 24*(35*B*a^3*f*x + (5*A + 26*B)*a^3)*cos(f*x + e)^2 + 60*(7*B*a^3*f*x + (A - 13*B)*a^3)*cos(f*x + e) - (840*B*a^3*f*x - 120*(A + B)*a^3 - (105*B*a^3*f*x - (15*A + 337*B)*a^3)*cos(f*x + e)^3 - 12*(35*B*a^3*f*x - (5*A - 23*B)*a^3)*cos(f*x + e)^2 + 60*(7*B*a^3*f*x - (A + 15*B)*a^3)*cos(f*x + e))*sin(f*x + e))/(c^4*f*cos(f*x + e)^4 - 3*c^4*f*cos(f*x + e)^3 - 8*c^4*f*cos(f*x + e)^2 + 4*c^4*f*cos(f*x + e) + 8*c^4*f + (c^4*f*cos(f*x + e)^3 + 4*c^4*f*cos(f*x + e)^2 - 4*c^4*f*cos(f*x + e) - 8*c^4*f)*sin(f*x + e))","B",0
48,1,331,0,0.850337," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^5,x, algorithm=""fricas"")","-\frac{{\left(A - 8 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} - {\left(4 \, A + 31 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} + {\left(19 \, A + 37 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 4 \, {\left(13 \, A + 22 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 28 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) - 56 \, {\left(A + B\right)} a^{3} + {\left({\left(A - 8 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} + {\left(5 \, A + 23 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 12 \, {\left(2 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 28 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) - 56 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)}{63 \, {\left(c^{5} f \cos\left(f x + e\right)^{5} + 5 \, c^{5} f \cos\left(f x + e\right)^{4} - 8 \, c^{5} f \cos\left(f x + e\right)^{3} - 20 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f - {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} - 12 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/63*((A - 8*B)*a^3*cos(f*x + e)^5 - (4*A + 31*B)*a^3*cos(f*x + e)^4 + (19*A + 37*B)*a^3*cos(f*x + e)^3 + 4*(13*A + 22*B)*a^3*cos(f*x + e)^2 - 28*(A + B)*a^3*cos(f*x + e) - 56*(A + B)*a^3 + ((A - 8*B)*a^3*cos(f*x + e)^4 + (5*A + 23*B)*a^3*cos(f*x + e)^3 + 12*(2*A + 5*B)*a^3*cos(f*x + e)^2 - 28*(A + B)*a^3*cos(f*x + e) - 56*(A + B)*a^3)*sin(f*x + e))/(c^5*f*cos(f*x + e)^5 + 5*c^5*f*cos(f*x + e)^4 - 8*c^5*f*cos(f*x + e)^3 - 20*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f - (c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 - 12*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f)*sin(f*x + e))","B",0
49,1,405,0,0.767188," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^6,x, algorithm=""fricas"")","\frac{{\left(2 \, A - 9 \, B\right)} a^{3} \cos\left(f x + e\right)^{6} + 6 \, {\left(2 \, A - 9 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} - {\left(25 \, A + 234 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} + 7 \, {\left(23 \, A + 45 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 28 \, {\left(16 \, A + 27 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 252 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) - 504 \, {\left(A + B\right)} a^{3} - {\left({\left(2 \, A - 9 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} - 5 \, {\left(2 \, A - 9 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 7 \, {\left(5 \, A + 27 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 28 \, {\left(7 \, A + 18 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 252 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) + 504 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)}{693 \, {\left(c^{6} f \cos\left(f x + e\right)^{6} - 5 \, c^{6} f \cos\left(f x + e\right)^{5} - 18 \, c^{6} f \cos\left(f x + e\right)^{4} + 20 \, c^{6} f \cos\left(f x + e\right)^{3} + 48 \, c^{6} f \cos\left(f x + e\right)^{2} - 16 \, c^{6} f \cos\left(f x + e\right) - 32 \, c^{6} f + {\left(c^{6} f \cos\left(f x + e\right)^{5} + 6 \, c^{6} f \cos\left(f x + e\right)^{4} - 12 \, c^{6} f \cos\left(f x + e\right)^{3} - 32 \, c^{6} f \cos\left(f x + e\right)^{2} + 16 \, c^{6} f \cos\left(f x + e\right) + 32 \, c^{6} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/693*((2*A - 9*B)*a^3*cos(f*x + e)^6 + 6*(2*A - 9*B)*a^3*cos(f*x + e)^5 - (25*A + 234*B)*a^3*cos(f*x + e)^4 + 7*(23*A + 45*B)*a^3*cos(f*x + e)^3 + 28*(16*A + 27*B)*a^3*cos(f*x + e)^2 - 252*(A + B)*a^3*cos(f*x + e) - 504*(A + B)*a^3 - ((2*A - 9*B)*a^3*cos(f*x + e)^5 - 5*(2*A - 9*B)*a^3*cos(f*x + e)^4 - 7*(5*A + 27*B)*a^3*cos(f*x + e)^3 - 28*(7*A + 18*B)*a^3*cos(f*x + e)^2 + 252*(A + B)*a^3*cos(f*x + e) + 504*(A + B)*a^3)*sin(f*x + e))/(c^6*f*cos(f*x + e)^6 - 5*c^6*f*cos(f*x + e)^5 - 18*c^6*f*cos(f*x + e)^4 + 20*c^6*f*cos(f*x + e)^3 + 48*c^6*f*cos(f*x + e)^2 - 16*c^6*f*cos(f*x + e) - 32*c^6*f + (c^6*f*cos(f*x + e)^5 + 6*c^6*f*cos(f*x + e)^4 - 12*c^6*f*cos(f*x + e)^3 - 32*c^6*f*cos(f*x + e)^2 + 16*c^6*f*cos(f*x + e) + 32*c^6*f)*sin(f*x + e))","B",0
50,1,475,0,0.881083," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^7,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, A - 10 \, B\right)} a^{3} \cos\left(f x + e\right)^{7} - 12 \, {\left(3 \, A - 10 \, B\right)} a^{3} \cos\left(f x + e\right)^{6} - 49 \, {\left(3 \, A - 10 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} + 7 \, {\left(30 \, A + 329 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 63 \, {\left(27 \, A + 53 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 252 \, {\left(19 \, A + 32 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 2772 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) + 5544 \, {\left(A + B\right)} a^{3} + {\left(2 \, {\left(3 \, A - 10 \, B\right)} a^{3} \cos\left(f x + e\right)^{6} + 14 \, {\left(3 \, A - 10 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} - 35 \, {\left(3 \, A - 10 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 63 \, {\left(5 \, A + 31 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 252 \, {\left(8 \, A + 21 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 2772 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) + 5544 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)}{9009 \, {\left(c^{7} f \cos\left(f x + e\right)^{7} + 7 \, c^{7} f \cos\left(f x + e\right)^{6} - 18 \, c^{7} f \cos\left(f x + e\right)^{5} - 56 \, c^{7} f \cos\left(f x + e\right)^{4} + 48 \, c^{7} f \cos\left(f x + e\right)^{3} + 112 \, c^{7} f \cos\left(f x + e\right)^{2} - 32 \, c^{7} f \cos\left(f x + e\right) - 64 \, c^{7} f - {\left(c^{7} f \cos\left(f x + e\right)^{6} - 6 \, c^{7} f \cos\left(f x + e\right)^{5} - 24 \, c^{7} f \cos\left(f x + e\right)^{4} + 32 \, c^{7} f \cos\left(f x + e\right)^{3} + 80 \, c^{7} f \cos\left(f x + e\right)^{2} - 32 \, c^{7} f \cos\left(f x + e\right) - 64 \, c^{7} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/9009*(2*(3*A - 10*B)*a^3*cos(f*x + e)^7 - 12*(3*A - 10*B)*a^3*cos(f*x + e)^6 - 49*(3*A - 10*B)*a^3*cos(f*x + e)^5 + 7*(30*A + 329*B)*a^3*cos(f*x + e)^4 - 63*(27*A + 53*B)*a^3*cos(f*x + e)^3 - 252*(19*A + 32*B)*a^3*cos(f*x + e)^2 + 2772*(A + B)*a^3*cos(f*x + e) + 5544*(A + B)*a^3 + (2*(3*A - 10*B)*a^3*cos(f*x + e)^6 + 14*(3*A - 10*B)*a^3*cos(f*x + e)^5 - 35*(3*A - 10*B)*a^3*cos(f*x + e)^4 - 63*(5*A + 31*B)*a^3*cos(f*x + e)^3 - 252*(8*A + 21*B)*a^3*cos(f*x + e)^2 + 2772*(A + B)*a^3*cos(f*x + e) + 5544*(A + B)*a^3)*sin(f*x + e))/(c^7*f*cos(f*x + e)^7 + 7*c^7*f*cos(f*x + e)^6 - 18*c^7*f*cos(f*x + e)^5 - 56*c^7*f*cos(f*x + e)^4 + 48*c^7*f*cos(f*x + e)^3 + 112*c^7*f*cos(f*x + e)^2 - 32*c^7*f*cos(f*x + e) - 64*c^7*f - (c^7*f*cos(f*x + e)^6 - 6*c^7*f*cos(f*x + e)^5 - 24*c^7*f*cos(f*x + e)^4 + 32*c^7*f*cos(f*x + e)^3 + 80*c^7*f*cos(f*x + e)^2 - 32*c^7*f*cos(f*x + e) - 64*c^7*f)*sin(f*x + e))","B",0
51,1,541,0,0.870852," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^8,x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, A - 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{8} + 16 \, {\left(4 \, A - 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{7} - 49 \, {\left(4 \, A - 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{6} - 168 \, {\left(4 \, A - 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} + 105 \, {\left(7 \, A + 88 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 231 \, {\left(31 \, A + 61 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 924 \, {\left(22 \, A + 37 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 12012 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) + 24024 \, {\left(A + B\right)} a^{3} - {\left(2 \, {\left(4 \, A - 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{7} - 14 \, {\left(4 \, A - 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{6} - 63 \, {\left(4 \, A - 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} + 105 \, {\left(4 \, A - 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} + 1155 \, {\left(A + 7 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 2772 \, {\left(3 \, A + 8 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 12012 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) - 24024 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)}{45045 \, {\left(c^{8} f \cos\left(f x + e\right)^{8} - 7 \, c^{8} f \cos\left(f x + e\right)^{7} - 32 \, c^{8} f \cos\left(f x + e\right)^{6} + 56 \, c^{8} f \cos\left(f x + e\right)^{5} + 160 \, c^{8} f \cos\left(f x + e\right)^{4} - 112 \, c^{8} f \cos\left(f x + e\right)^{3} - 256 \, c^{8} f \cos\left(f x + e\right)^{2} + 64 \, c^{8} f \cos\left(f x + e\right) + 128 \, c^{8} f + {\left(c^{8} f \cos\left(f x + e\right)^{7} + 8 \, c^{8} f \cos\left(f x + e\right)^{6} - 24 \, c^{8} f \cos\left(f x + e\right)^{5} - 80 \, c^{8} f \cos\left(f x + e\right)^{4} + 80 \, c^{8} f \cos\left(f x + e\right)^{3} + 192 \, c^{8} f \cos\left(f x + e\right)^{2} - 64 \, c^{8} f \cos\left(f x + e\right) - 128 \, c^{8} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/45045*(2*(4*A - 11*B)*a^3*cos(f*x + e)^8 + 16*(4*A - 11*B)*a^3*cos(f*x + e)^7 - 49*(4*A - 11*B)*a^3*cos(f*x + e)^6 - 168*(4*A - 11*B)*a^3*cos(f*x + e)^5 + 105*(7*A + 88*B)*a^3*cos(f*x + e)^4 - 231*(31*A + 61*B)*a^3*cos(f*x + e)^3 - 924*(22*A + 37*B)*a^3*cos(f*x + e)^2 + 12012*(A + B)*a^3*cos(f*x + e) + 24024*(A + B)*a^3 - (2*(4*A - 11*B)*a^3*cos(f*x + e)^7 - 14*(4*A - 11*B)*a^3*cos(f*x + e)^6 - 63*(4*A - 11*B)*a^3*cos(f*x + e)^5 + 105*(4*A - 11*B)*a^3*cos(f*x + e)^4 + 1155*(A + 7*B)*a^3*cos(f*x + e)^3 + 2772*(3*A + 8*B)*a^3*cos(f*x + e)^2 - 12012*(A + B)*a^3*cos(f*x + e) - 24024*(A + B)*a^3)*sin(f*x + e))/(c^8*f*cos(f*x + e)^8 - 7*c^8*f*cos(f*x + e)^7 - 32*c^8*f*cos(f*x + e)^6 + 56*c^8*f*cos(f*x + e)^5 + 160*c^8*f*cos(f*x + e)^4 - 112*c^8*f*cos(f*x + e)^3 - 256*c^8*f*cos(f*x + e)^2 + 64*c^8*f*cos(f*x + e) + 128*c^8*f + (c^8*f*cos(f*x + e)^7 + 8*c^8*f*cos(f*x + e)^6 - 24*c^8*f*cos(f*x + e)^5 - 80*c^8*f*cos(f*x + e)^4 + 80*c^8*f*cos(f*x + e)^3 + 192*c^8*f*cos(f*x + e)^2 - 64*c^8*f*cos(f*x + e) - 128*c^8*f)*sin(f*x + e))","B",0
52,1,261,0,0.912654," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{6 \, B c^{4} \cos\left(f x + e\right)^{5} - 8 \, {\left(A - 5 \, B\right)} c^{4} \cos\left(f x + e\right)^{4} + {\left(52 \, A - 113 \, B\right)} c^{4} \cos\left(f x + e\right)^{3} + 105 \, {\left(4 \, A - 5 \, B\right)} c^{4} f x + 96 \, {\left(3 \, A - 5 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} + 384 \, {\left(A - B\right)} c^{4} + 3 \, {\left(35 \, {\left(4 \, A - 5 \, B\right)} c^{4} f x + {\left(204 \, A - 239 \, B\right)} c^{4}\right)} \cos\left(f x + e\right) - {\left(6 \, B c^{4} \cos\left(f x + e\right)^{4} + 2 \, {\left(4 \, A - 17 \, B\right)} c^{4} \cos\left(f x + e\right)^{3} - 105 \, {\left(4 \, A - 5 \, B\right)} c^{4} f x + 3 \, {\left(20 \, A - 49 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} - 3 \, {\left(76 \, A - 111 \, B\right)} c^{4} \cos\left(f x + e\right) + 384 \, {\left(A - B\right)} c^{4}\right)} \sin\left(f x + e\right)}{24 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"-1/24*(6*B*c^4*cos(f*x + e)^5 - 8*(A - 5*B)*c^4*cos(f*x + e)^4 + (52*A - 113*B)*c^4*cos(f*x + e)^3 + 105*(4*A - 5*B)*c^4*f*x + 96*(3*A - 5*B)*c^4*cos(f*x + e)^2 + 384*(A - B)*c^4 + 3*(35*(4*A - 5*B)*c^4*f*x + (204*A - 239*B)*c^4)*cos(f*x + e) - (6*B*c^4*cos(f*x + e)^4 + 2*(4*A - 17*B)*c^4*cos(f*x + e)^3 - 105*(4*A - 5*B)*c^4*f*x + 3*(20*A - 49*B)*c^4*cos(f*x + e)^2 - 3*(76*A - 111*B)*c^4*cos(f*x + e) + 384*(A - B)*c^4)*sin(f*x + e))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","A",0
53,1,218,0,0.689745," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, B c^{3} \cos\left(f x + e\right)^{4} + {\left(3 \, A - 10 \, B\right)} c^{3} \cos\left(f x + e\right)^{3} + 15 \, {\left(3 \, A - 4 \, B\right)} c^{3} f x + 24 \, {\left(A - 2 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} + 48 \, {\left(A - B\right)} c^{3} + 3 \, {\left(5 \, {\left(3 \, A - 4 \, B\right)} c^{3} f x + {\left(23 \, A - 28 \, B\right)} c^{3}\right)} \cos\left(f x + e\right) + {\left(2 \, B c^{3} \cos\left(f x + e\right)^{3} + 15 \, {\left(3 \, A - 4 \, B\right)} c^{3} f x - 3 \, {\left(A - 4 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} + 3 \, {\left(7 \, A - 12 \, B\right)} c^{3} \cos\left(f x + e\right) - 48 \, {\left(A - B\right)} c^{3}\right)} \sin\left(f x + e\right)}{6 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"-1/6*(2*B*c^3*cos(f*x + e)^4 + (3*A - 10*B)*c^3*cos(f*x + e)^3 + 15*(3*A - 4*B)*c^3*f*x + 24*(A - 2*B)*c^3*cos(f*x + e)^2 + 48*(A - B)*c^3 + 3*(5*(3*A - 4*B)*c^3*f*x + (23*A - 28*B)*c^3)*cos(f*x + e) + (2*B*c^3*cos(f*x + e)^3 + 15*(3*A - 4*B)*c^3*f*x - 3*(A - 4*B)*c^3*cos(f*x + e)^2 + 3*(7*A - 12*B)*c^3*cos(f*x + e) - 48*(A - B)*c^3)*sin(f*x + e))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","A",0
54,1,179,0,0.879607," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{B c^{2} \cos\left(f x + e\right)^{3} - 3 \, {\left(2 \, A - 3 \, B\right)} c^{2} f x - 2 \, {\left(A - 3 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} - 8 \, {\left(A - B\right)} c^{2} - {\left(3 \, {\left(2 \, A - 3 \, B\right)} c^{2} f x + {\left(10 \, A - 13 \, B\right)} c^{2}\right)} \cos\left(f x + e\right) - {\left(3 \, {\left(2 \, A - 3 \, B\right)} c^{2} f x + B c^{2} \cos\left(f x + e\right)^{2} + {\left(2 \, A - 5 \, B\right)} c^{2} \cos\left(f x + e\right) - 8 \, {\left(A - B\right)} c^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"1/2*(B*c^2*cos(f*x + e)^3 - 3*(2*A - 3*B)*c^2*f*x - 2*(A - 3*B)*c^2*cos(f*x + e)^2 - 8*(A - B)*c^2 - (3*(2*A - 3*B)*c^2*f*x + (10*A - 13*B)*c^2)*cos(f*x + e) - (3*(2*A - 3*B)*c^2*f*x + B*c^2*cos(f*x + e)^2 + (2*A - 5*B)*c^2*cos(f*x + e) - 8*(A - B)*c^2)*sin(f*x + e))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","A",0
55,1,117,0,0.603475," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(A - 2 \, B\right)} c f x - B c \cos\left(f x + e\right)^{2} + 2 \, {\left(A - B\right)} c + {\left({\left(A - 2 \, B\right)} c f x + {\left(2 \, A - 3 \, B\right)} c\right)} \cos\left(f x + e\right) + {\left({\left(A - 2 \, B\right)} c f x - B c \cos\left(f x + e\right) - 2 \, {\left(A - B\right)} c\right)} \sin\left(f x + e\right)}{a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f}"," ",0,"-((A - 2*B)*c*f*x - B*c*cos(f*x + e)^2 + 2*(A - B)*c + ((A - 2*B)*c*f*x + (2*A - 3*B)*c)*cos(f*x + e) + ((A - 2*B)*c*f*x - B*c*cos(f*x + e) - 2*(A - B)*c)*sin(f*x + e))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","B",0
56,1,28,0,0.937529," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{A \sin\left(f x + e\right) + B}{a c f \cos\left(f x + e\right)}"," ",0,"(A*sin(f*x + e) + B)/(a*c*f*cos(f*x + e))","A",0
57,1,73,0,0.797463," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{{\left(2 \, A - B\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, A - B\right)} \sin\left(f x + e\right) - A + 2 \, B}{3 \, {\left(a c^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) - a c^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"-1/3*((2*A - B)*cos(f*x + e)^2 + (2*A - B)*sin(f*x + e) - A + 2*B)/(a*c^2*f*cos(f*x + e)*sin(f*x + e) - a*c^2*f*cos(f*x + e))","A",0
58,1,107,0,0.565911," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{4 \, {\left(3 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, {\left(3 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{2} - 9 \, A + 6 \, B\right)} \sin\left(f x + e\right) - 6 \, A + 9 \, B}{15 \, {\left(a c^{3} f \cos\left(f x + e\right)^{3} + 2 \, a c^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a c^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"-1/15*(4*(3*A - 2*B)*cos(f*x + e)^2 - (2*(3*A - 2*B)*cos(f*x + e)^2 - 9*A + 6*B)*sin(f*x + e) - 6*A + 9*B)/(a*c^3*f*cos(f*x + e)^3 + 2*a*c^3*f*cos(f*x + e)*sin(f*x + e) - 2*a*c^3*f*cos(f*x + e))","A",0
59,1,141,0,0.804922," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","\frac{2 \, {\left(4 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{4} - 9 \, {\left(4 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, {\left(4 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{2} - 20 \, A + 15 \, B\right)} \sin\left(f x + e\right) + 15 \, A - 20 \, B}{35 \, {\left(3 \, a c^{4} f \cos\left(f x + e\right)^{3} - 4 \, a c^{4} f \cos\left(f x + e\right) - {\left(a c^{4} f \cos\left(f x + e\right)^{3} - 4 \, a c^{4} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/35*(2*(4*A - 3*B)*cos(f*x + e)^4 - 9*(4*A - 3*B)*cos(f*x + e)^2 + (6*(4*A - 3*B)*cos(f*x + e)^2 - 20*A + 15*B)*sin(f*x + e) + 15*A - 20*B)/(3*a*c^4*f*cos(f*x + e)^3 - 4*a*c^4*f*cos(f*x + e) - (a*c^4*f*cos(f*x + e)^3 - 4*a*c^4*f*cos(f*x + e))*sin(f*x + e))","A",0
60,1,370,0,0.795522," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{6 \, B c^{5} \cos\left(f x + e\right)^{6} + 4 \, {\left(2 \, A - 11 \, B\right)} c^{5} \cos\left(f x + e\right)^{5} + {\left(76 \, A - 241 \, B\right)} c^{5} \cos\left(f x + e\right)^{4} - 2 \, {\left(212 \, A - 431 \, B\right)} c^{5} \cos\left(f x + e\right)^{3} + 630 \, {\left(4 \, A - 7 \, B\right)} c^{5} f x - 256 \, {\left(A - B\right)} c^{5} - {\left(315 \, {\left(4 \, A - 7 \, B\right)} c^{5} f x - {\left(2156 \, A - 3485 \, B\right)} c^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(315 \, {\left(4 \, A - 7 \, B\right)} c^{5} f x + 2 \, {\left(1196 \, A - 2141 \, B\right)} c^{5}\right)} \cos\left(f x + e\right) + {\left(6 \, B c^{5} \cos\left(f x + e\right)^{5} - 2 \, {\left(4 \, A - 25 \, B\right)} c^{5} \cos\left(f x + e\right)^{4} + {\left(68 \, A - 191 \, B\right)} c^{5} \cos\left(f x + e\right)^{3} + 630 \, {\left(4 \, A - 7 \, B\right)} c^{5} f x + 3 \, {\left(164 \, A - 351 \, B\right)} c^{5} \cos\left(f x + e\right)^{2} + 256 \, {\left(A - B\right)} c^{5} + {\left(315 \, {\left(4 \, A - 7 \, B\right)} c^{5} f x + 2 \, {\left(1324 \, A - 2269 \, B\right)} c^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/24*(6*B*c^5*cos(f*x + e)^6 + 4*(2*A - 11*B)*c^5*cos(f*x + e)^5 + (76*A - 241*B)*c^5*cos(f*x + e)^4 - 2*(212*A - 431*B)*c^5*cos(f*x + e)^3 + 630*(4*A - 7*B)*c^5*f*x - 256*(A - B)*c^5 - (315*(4*A - 7*B)*c^5*f*x - (2156*A - 3485*B)*c^5)*cos(f*x + e)^2 + (315*(4*A - 7*B)*c^5*f*x + 2*(1196*A - 2141*B)*c^5)*cos(f*x + e) + (6*B*c^5*cos(f*x + e)^5 - 2*(4*A - 25*B)*c^5*cos(f*x + e)^4 + (68*A - 191*B)*c^5*cos(f*x + e)^3 + 630*(4*A - 7*B)*c^5*f*x + 3*(164*A - 351*B)*c^5*cos(f*x + e)^2 + 256*(A - B)*c^5 + (315*(4*A - 7*B)*c^5*f*x + 2*(1324*A - 2269*B)*c^5)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","A",0
61,1,322,0,0.925674," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, B c^{4} \cos\left(f x + e\right)^{5} - {\left(3 \, A - 16 \, B\right)} c^{4} \cos\left(f x + e\right)^{4} + 2 \, {\left(15 \, A - 38 \, B\right)} c^{4} \cos\left(f x + e\right)^{3} - 210 \, {\left(A - 2 \, B\right)} c^{4} f x + 32 \, {\left(A - B\right)} c^{4} + {\left(105 \, {\left(A - 2 \, B\right)} c^{4} f x - {\left(193 \, A - 346 \, B\right)} c^{4}\right)} \cos\left(f x + e\right)^{2} - {\left(105 \, {\left(A - 2 \, B\right)} c^{4} f x + 2 \, {\left(97 \, A - 202 \, B\right)} c^{4}\right)} \cos\left(f x + e\right) - {\left(2 \, B c^{4} \cos\left(f x + e\right)^{4} + {\left(3 \, A - 14 \, B\right)} c^{4} \cos\left(f x + e\right)^{3} + 210 \, {\left(A - 2 \, B\right)} c^{4} f x + 3 \, {\left(11 \, A - 30 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} + 32 \, {\left(A - B\right)} c^{4} + {\left(105 \, {\left(A - 2 \, B\right)} c^{4} f x + 2 \, {\left(113 \, A - 218 \, B\right)} c^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/6*(2*B*c^4*cos(f*x + e)^5 - (3*A - 16*B)*c^4*cos(f*x + e)^4 + 2*(15*A - 38*B)*c^4*cos(f*x + e)^3 - 210*(A - 2*B)*c^4*f*x + 32*(A - B)*c^4 + (105*(A - 2*B)*c^4*f*x - (193*A - 346*B)*c^4)*cos(f*x + e)^2 - (105*(A - 2*B)*c^4*f*x + 2*(97*A - 202*B)*c^4)*cos(f*x + e) - (2*B*c^4*cos(f*x + e)^4 + (3*A - 14*B)*c^4*cos(f*x + e)^3 + 210*(A - 2*B)*c^4*f*x + 3*(11*A - 30*B)*c^4*cos(f*x + e)^2 + 32*(A - B)*c^4 + (105*(A - 2*B)*c^4*f*x + 2*(113*A - 218*B)*c^4)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","A",0
62,1,291,0,0.710964," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{3 \, B c^{3} \cos\left(f x + e\right)^{4} + 6 \, {\left(A - 4 \, B\right)} c^{3} \cos\left(f x + e\right)^{3} - 30 \, {\left(2 \, A - 5 \, B\right)} c^{3} f x + 16 \, {\left(A - B\right)} c^{3} + {\left(15 \, {\left(2 \, A - 5 \, B\right)} c^{3} f x - {\left(62 \, A - 131 \, B\right)} c^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(15 \, {\left(2 \, A - 5 \, B\right)} c^{3} f x + 2 \, {\left(26 \, A - 71 \, B\right)} c^{3}\right)} \cos\left(f x + e\right) + {\left(3 \, B c^{3} \cos\left(f x + e\right)^{3} - 30 \, {\left(2 \, A - 5 \, B\right)} c^{3} f x - 3 \, {\left(2 \, A - 9 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 16 \, {\left(A - B\right)} c^{3} - {\left(15 \, {\left(2 \, A - 5 \, B\right)} c^{3} f x + 2 \, {\left(34 \, A - 79 \, B\right)} c^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/6*(3*B*c^3*cos(f*x + e)^4 + 6*(A - 4*B)*c^3*cos(f*x + e)^3 - 30*(2*A - 5*B)*c^3*f*x + 16*(A - B)*c^3 + (15*(2*A - 5*B)*c^3*f*x - (62*A - 131*B)*c^3)*cos(f*x + e)^2 - (15*(2*A - 5*B)*c^3*f*x + 2*(26*A - 71*B)*c^3)*cos(f*x + e) + (3*B*c^3*cos(f*x + e)^3 - 30*(2*A - 5*B)*c^3*f*x - 3*(2*A - 9*B)*c^3*cos(f*x + e)^2 - 16*(A - B)*c^3 - (15*(2*A - 5*B)*c^3*f*x + 2*(34*A - 79*B)*c^3)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","A",0
63,1,242,0,0.881162," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{3 \, B c^{2} \cos\left(f x + e\right)^{3} + 6 \, {\left(A - 4 \, B\right)} c^{2} f x - 4 \, {\left(A - B\right)} c^{2} - {\left(3 \, {\left(A - 4 \, B\right)} c^{2} f x - {\left(8 \, A - 23 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, {\left(A - 4 \, B\right)} c^{2} f x + 2 \, {\left(2 \, A - 11 \, B\right)} c^{2}\right)} \cos\left(f x + e\right) + {\left(6 \, {\left(A - 4 \, B\right)} c^{2} f x - 3 \, B c^{2} \cos\left(f x + e\right)^{2} + 4 \, {\left(A - B\right)} c^{2} + {\left(3 \, {\left(A - 4 \, B\right)} c^{2} f x + 2 \, {\left(4 \, A - 13 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/3*(3*B*c^2*cos(f*x + e)^3 + 6*(A - 4*B)*c^2*f*x - 4*(A - B)*c^2 - (3*(A - 4*B)*c^2*f*x - (8*A - 23*B)*c^2)*cos(f*x + e)^2 + (3*(A - 4*B)*c^2*f*x + 2*(2*A - 11*B)*c^2)*cos(f*x + e) + (6*(A - 4*B)*c^2*f*x - 3*B*c^2*cos(f*x + e)^2 + 4*(A - B)*c^2 + (3*(A - 4*B)*c^2*f*x + 2*(4*A - 13*B)*c^2)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
64,1,166,0,0.932516," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{6 \, B c f x - {\left(3 \, B c f x + {\left(A - 7 \, B\right)} c\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(A - B\right)} c + {\left(3 \, B c f x + {\left(A + 5 \, B\right)} c\right)} \cos\left(f x + e\right) + {\left(6 \, B c f x - 2 \, {\left(A - B\right)} c + {\left(3 \, B c f x - {\left(A - 7 \, B\right)} c\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/3*(6*B*c*f*x - (3*B*c*f*x + (A - 7*B)*c)*cos(f*x + e)^2 + 2*(A - B)*c + (3*B*c*f*x + (A + 5*B)*c)*cos(f*x + e) + (6*B*c*f*x - 2*(A - B)*c + (3*B*c*f*x - (A - 7*B)*c)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
65,1,69,0,0.837966," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(2 \, A + B\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, A + B\right)} \sin\left(f x + e\right) - A - 2 \, B}{3 \, {\left(a^{2} c f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} c f \cos\left(f x + e\right)\right)}}"," ",0,"-1/3*((2*A + B)*cos(f*x + e)^2 - (2*A + B)*sin(f*x + e) - A - 2*B)/(a^2*c*f*cos(f*x + e)*sin(f*x + e) + a^2*c*f*cos(f*x + e))","A",0
66,1,41,0,0.808947," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(2 \, A \cos\left(f x + e\right)^{2} + A\right)} \sin\left(f x + e\right) + B}{3 \, a^{2} c^{2} f \cos\left(f x + e\right)^{3}}"," ",0,"1/3*((2*A*cos(f*x + e)^2 + A)*sin(f*x + e) + B)/(a^2*c^2*f*cos(f*x + e)^3)","A",0
67,1,116,0,0.850424," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, A - B\right)} \cos\left(f x + e\right)^{4} - {\left(4 \, A - B\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, {\left(4 \, A - B\right)} \cos\left(f x + e\right)^{2} + 4 \, A - B\right)} \sin\left(f x + e\right) - A + 4 \, B}{15 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - a^{2} c^{3} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"-1/15*(2*(4*A - B)*cos(f*x + e)^4 - (4*A - B)*cos(f*x + e)^2 + (2*(4*A - B)*cos(f*x + e)^2 + 4*A - B)*sin(f*x + e) - A + 4*B)/(a^2*c^3*f*cos(f*x + e)^3*sin(f*x + e) - a^2*c^3*f*cos(f*x + e)^3)","A",0
68,1,151,0,0.719854," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","-\frac{16 \, {\left(5 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{4} - 8 \, {\left(5 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{2} - {\left(8 \, {\left(5 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{4} - 12 \, {\left(5 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{2} - 25 \, A + 10 \, B\right)} \sin\left(f x + e\right) - 10 \, A + 25 \, B}{105 \, {\left(a^{2} c^{4} f \cos\left(f x + e\right)^{5} + 2 \, a^{2} c^{4} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - 2 \, a^{2} c^{4} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"-1/105*(16*(5*A - 2*B)*cos(f*x + e)^4 - 8*(5*A - 2*B)*cos(f*x + e)^2 - (8*(5*A - 2*B)*cos(f*x + e)^4 - 12*(5*A - 2*B)*cos(f*x + e)^2 - 25*A + 10*B)*sin(f*x + e) - 10*A + 25*B)/(a^2*c^4*f*cos(f*x + e)^5 + 2*a^2*c^4*f*cos(f*x + e)^3*sin(f*x + e) - 2*a^2*c^4*f*cos(f*x + e)^3)","A",0
69,1,187,0,0.937068," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^5,x, algorithm=""fricas"")","\frac{8 \, {\left(2 \, A - B\right)} \cos\left(f x + e\right)^{6} - 36 \, {\left(2 \, A - B\right)} \cos\left(f x + e\right)^{4} + 15 \, {\left(2 \, A - B\right)} \cos\left(f x + e\right)^{2} + {\left(24 \, {\left(2 \, A - B\right)} \cos\left(f x + e\right)^{4} - 20 \, {\left(2 \, A - B\right)} \cos\left(f x + e\right)^{2} - 14 \, A + 7 \, B\right)} \sin\left(f x + e\right) + 7 \, A - 14 \, B}{63 \, {\left(3 \, a^{2} c^{5} f \cos\left(f x + e\right)^{5} - 4 \, a^{2} c^{5} f \cos\left(f x + e\right)^{3} - {\left(a^{2} c^{5} f \cos\left(f x + e\right)^{5} - 4 \, a^{2} c^{5} f \cos\left(f x + e\right)^{3}\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/63*(8*(2*A - B)*cos(f*x + e)^6 - 36*(2*A - B)*cos(f*x + e)^4 + 15*(2*A - B)*cos(f*x + e)^2 + (24*(2*A - B)*cos(f*x + e)^4 - 20*(2*A - B)*cos(f*x + e)^2 - 14*A + 7*B)*sin(f*x + e) + 7*A - 14*B)/(3*a^2*c^5*f*cos(f*x + e)^5 - 4*a^2*c^5*f*cos(f*x + e)^3 - (a^2*c^5*f*cos(f*x + e)^5 - 4*a^2*c^5*f*cos(f*x + e)^3)*sin(f*x + e))","A",0
70,1,429,0,0.941838," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^5/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{10 \, B c^{5} \cos\left(f x + e\right)^{6} + 15 \, {\left(A - 6 \, B\right)} c^{5} \cos\left(f x + e\right)^{5} + 10 \, {\left(21 \, A - 74 \, B\right)} c^{5} \cos\left(f x + e\right)^{4} - 1260 \, {\left(3 \, A - 8 \, B\right)} c^{5} f x - 192 \, {\left(A - B\right)} c^{5} + {\left(315 \, {\left(3 \, A - 8 \, B\right)} c^{5} f x + {\left(2373 \, A - 6128 \, B\right)} c^{5}\right)} \cos\left(f x + e\right)^{3} + {\left(945 \, {\left(3 \, A - 8 \, B\right)} c^{5} f x - 2 \, {\left(753 \, A - 2248 \, B\right)} c^{5}\right)} \cos\left(f x + e\right)^{2} - 6 \, {\left(105 \, {\left(3 \, A - 8 \, B\right)} c^{5} f x + 2 \, {\left(323 \, A - 848 \, B\right)} c^{5}\right)} \cos\left(f x + e\right) + {\left(10 \, B c^{5} \cos\left(f x + e\right)^{5} - 5 \, {\left(3 \, A - 20 \, B\right)} c^{5} \cos\left(f x + e\right)^{4} + 5 \, {\left(39 \, A - 128 \, B\right)} c^{5} \cos\left(f x + e\right)^{3} - 1260 \, {\left(3 \, A - 8 \, B\right)} c^{5} f x + 192 \, {\left(A - B\right)} c^{5} + {\left(315 \, {\left(3 \, A - 8 \, B\right)} c^{5} f x - 2 \, {\left(1089 \, A - 2744 \, B\right)} c^{5}\right)} \cos\left(f x + e\right)^{2} - 6 \, {\left(105 \, {\left(3 \, A - 8 \, B\right)} c^{5} f x + 2 \, {\left(307 \, A - 832 \, B\right)} c^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/30*(10*B*c^5*cos(f*x + e)^6 + 15*(A - 6*B)*c^5*cos(f*x + e)^5 + 10*(21*A - 74*B)*c^5*cos(f*x + e)^4 - 1260*(3*A - 8*B)*c^5*f*x - 192*(A - B)*c^5 + (315*(3*A - 8*B)*c^5*f*x + (2373*A - 6128*B)*c^5)*cos(f*x + e)^3 + (945*(3*A - 8*B)*c^5*f*x - 2*(753*A - 2248*B)*c^5)*cos(f*x + e)^2 - 6*(105*(3*A - 8*B)*c^5*f*x + 2*(323*A - 848*B)*c^5)*cos(f*x + e) + (10*B*c^5*cos(f*x + e)^5 - 5*(3*A - 20*B)*c^5*cos(f*x + e)^4 + 5*(39*A - 128*B)*c^5*cos(f*x + e)^3 - 1260*(3*A - 8*B)*c^5*f*x + 192*(A - B)*c^5 + (315*(3*A - 8*B)*c^5*f*x - 2*(1089*A - 2744*B)*c^5)*cos(f*x + e)^2 - 6*(105*(3*A - 8*B)*c^5*f*x + 2*(307*A - 832*B)*c^5)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","A",0
71,1,392,0,0.960089," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^4/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, B c^{4} \cos\left(f x + e\right)^{5} - 30 \, {\left(A - 6 \, B\right)} c^{4} \cos\left(f x + e\right)^{4} + 420 \, {\left(2 \, A - 7 \, B\right)} c^{4} f x + 96 \, {\left(A - B\right)} c^{4} - {\left(105 \, {\left(2 \, A - 7 \, B\right)} c^{4} f x + {\left(554 \, A - 1819 \, B\right)} c^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(315 \, {\left(2 \, A - 7 \, B\right)} c^{4} f x - 2 \, {\left(134 \, A - 619 \, B\right)} c^{4}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(35 \, {\left(2 \, A - 7 \, B\right)} c^{4} f x + 2 \, {\left(74 \, A - 249 \, B\right)} c^{4}\right)} \cos\left(f x + e\right) - {\left(15 \, B c^{4} \cos\left(f x + e\right)^{4} + 15 \, {\left(2 \, A - 11 \, B\right)} c^{4} \cos\left(f x + e\right)^{3} - 420 \, {\left(2 \, A - 7 \, B\right)} c^{4} f x + 96 \, {\left(A - B\right)} c^{4} + {\left(105 \, {\left(2 \, A - 7 \, B\right)} c^{4} f x - 2 \, {\left(262 \, A - 827 \, B\right)} c^{4}\right)} \cos\left(f x + e\right)^{2} - 6 \, {\left(35 \, {\left(2 \, A - 7 \, B\right)} c^{4} f x + 2 \, {\left(66 \, A - 241 \, B\right)} c^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/30*(15*B*c^4*cos(f*x + e)^5 - 30*(A - 6*B)*c^4*cos(f*x + e)^4 + 420*(2*A - 7*B)*c^4*f*x + 96*(A - B)*c^4 - (105*(2*A - 7*B)*c^4*f*x + (554*A - 1819*B)*c^4)*cos(f*x + e)^3 - (315*(2*A - 7*B)*c^4*f*x - 2*(134*A - 619*B)*c^4)*cos(f*x + e)^2 + 6*(35*(2*A - 7*B)*c^4*f*x + 2*(74*A - 249*B)*c^4)*cos(f*x + e) - (15*B*c^4*cos(f*x + e)^4 + 15*(2*A - 11*B)*c^4*cos(f*x + e)^3 - 420*(2*A - 7*B)*c^4*f*x + 96*(A - B)*c^4 + (105*(2*A - 7*B)*c^4*f*x - 2*(262*A - 827*B)*c^4)*cos(f*x + e)^2 - 6*(35*(2*A - 7*B)*c^4*f*x + 2*(66*A - 241*B)*c^4)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
72,1,338,0,0.983073," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{15 \, B c^{3} \cos\left(f x + e\right)^{4} + 60 \, {\left(A - 6 \, B\right)} c^{3} f x + 24 \, {\left(A - B\right)} c^{3} - {\left(15 \, {\left(A - 6 \, B\right)} c^{3} f x + {\left(46 \, A - 231 \, B\right)} c^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(45 \, {\left(A - 6 \, B\right)} c^{3} f x - 2 \, {\left(A - 66 \, B\right)} c^{3}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(5 \, {\left(A - 6 \, B\right)} c^{3} f x + 2 \, {\left(6 \, A - 31 \, B\right)} c^{3}\right)} \cos\left(f x + e\right) + {\left(15 \, B c^{3} \cos\left(f x + e\right)^{3} + 60 \, {\left(A - 6 \, B\right)} c^{3} f x - 24 \, {\left(A - B\right)} c^{3} - {\left(15 \, {\left(A - 6 \, B\right)} c^{3} f x - 2 \, {\left(23 \, A - 108 \, B\right)} c^{3}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(5 \, {\left(A - 6 \, B\right)} c^{3} f x + 2 \, {\left(4 \, A - 29 \, B\right)} c^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/15*(15*B*c^3*cos(f*x + e)^4 + 60*(A - 6*B)*c^3*f*x + 24*(A - B)*c^3 - (15*(A - 6*B)*c^3*f*x + (46*A - 231*B)*c^3)*cos(f*x + e)^3 - (45*(A - 6*B)*c^3*f*x - 2*(A - 66*B)*c^3)*cos(f*x + e)^2 + 6*(5*(A - 6*B)*c^3*f*x + 2*(6*A - 31*B)*c^3)*cos(f*x + e) + (15*B*c^3*cos(f*x + e)^3 + 60*(A - 6*B)*c^3*f*x - 24*(A - B)*c^3 - (15*(A - 6*B)*c^3*f*x - 2*(23*A - 108*B)*c^3)*cos(f*x + e)^2 + 6*(5*(A - 6*B)*c^3*f*x + 2*(4*A - 29*B)*c^3)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
73,1,279,0,0.758137," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{60 \, B c^{2} f x - {\left(15 \, B c^{2} f x - {\left(3 \, A - 43 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)^{3} - 12 \, {\left(A - B\right)} c^{2} - {\left(45 \, B c^{2} f x - {\left(9 \, A + 11 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(5 \, B c^{2} f x - {\left(A - 11 \, B\right)} c^{2}\right)} \cos\left(f x + e\right) + {\left(60 \, B c^{2} f x + 12 \, {\left(A - B\right)} c^{2} - {\left(15 \, B c^{2} f x + {\left(3 \, A - 43 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} + 6 \, {\left(5 \, B c^{2} f x + {\left(A + 9 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/15*(60*B*c^2*f*x - (15*B*c^2*f*x - (3*A - 43*B)*c^2)*cos(f*x + e)^3 - 12*(A - B)*c^2 - (45*B*c^2*f*x - (9*A + 11*B)*c^2)*cos(f*x + e)^2 + 6*(5*B*c^2*f*x - (A - 11*B)*c^2)*cos(f*x + e) + (60*B*c^2*f*x + 12*(A - B)*c^2 - (15*B*c^2*f*x + (3*A - 43*B)*c^2)*cos(f*x + e)^2 + 6*(5*B*c^2*f*x + (A + 9*B)*c^2)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
74,1,191,0,0.861865," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(A + 4 \, B\right)} c \cos\left(f x + e\right)^{3} - {\left(2 \, A - 7 \, B\right)} c \cos\left(f x + e\right)^{2} + 3 \, {\left(A - B\right)} c \cos\left(f x + e\right) + 6 \, {\left(A - B\right)} c - {\left({\left(A + 4 \, B\right)} c \cos\left(f x + e\right)^{2} + 3 \, {\left(A - B\right)} c \cos\left(f x + e\right) + 6 \, {\left(A - B\right)} c\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/15*((A + 4*B)*c*cos(f*x + e)^3 - (2*A - 7*B)*c*cos(f*x + e)^2 + 3*(A - B)*c*cos(f*x + e) + 6*(A - B)*c - ((A + 4*B)*c*cos(f*x + e)^2 + 3*(A - B)*c*cos(f*x + e) + 6*(A - B)*c)*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","A",0
75,1,106,0,0.774078," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, A + 2 \, B\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, {\left(3 \, A + 2 \, B\right)} \cos\left(f x + e\right)^{2} - 9 \, A - 6 \, B\right)} \sin\left(f x + e\right) - 6 \, A - 9 \, B}{15 \, {\left(a^{3} c f \cos\left(f x + e\right)^{3} - 2 \, a^{3} c f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} c f \cos\left(f x + e\right)\right)}}"," ",0,"1/15*(4*(3*A + 2*B)*cos(f*x + e)^2 + (2*(3*A + 2*B)*cos(f*x + e)^2 - 9*A - 6*B)*sin(f*x + e) - 6*A - 9*B)/(a^3*c*f*cos(f*x + e)^3 - 2*a^3*c*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*c*f*cos(f*x + e))","A",0
76,1,108,0,0.544373," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(4 \, A + B\right)} \cos\left(f x + e\right)^{4} - {\left(4 \, A + B\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, {\left(4 \, A + B\right)} \cos\left(f x + e\right)^{2} + 4 \, A + B\right)} \sin\left(f x + e\right) - A - 4 \, B}{15 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + a^{3} c^{2} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"-1/15*(2*(4*A + B)*cos(f*x + e)^4 - (4*A + B)*cos(f*x + e)^2 - (2*(4*A + B)*cos(f*x + e)^2 + 4*A + B)*sin(f*x + e) - A - 4*B)/(a^3*c^2*f*cos(f*x + e)^3*sin(f*x + e) + a^3*c^2*f*cos(f*x + e)^3)","A",0
77,1,56,0,0.862125," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{{\left(8 \, A \cos\left(f x + e\right)^{4} + 4 \, A \cos\left(f x + e\right)^{2} + 3 \, A\right)} \sin\left(f x + e\right) + 3 \, B}{15 \, a^{3} c^{3} f \cos\left(f x + e\right)^{5}}"," ",0,"1/15*((8*A*cos(f*x + e)^4 + 4*A*cos(f*x + e)^2 + 3*A)*sin(f*x + e) + 3*B)/(a^3*c^3*f*cos(f*x + e)^5)","A",0
78,1,150,0,0.862917," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^4,x, algorithm=""fricas"")","-\frac{8 \, {\left(6 \, A - B\right)} \cos\left(f x + e\right)^{6} - 4 \, {\left(6 \, A - B\right)} \cos\left(f x + e\right)^{4} - {\left(6 \, A - B\right)} \cos\left(f x + e\right)^{2} + {\left(8 \, {\left(6 \, A - B\right)} \cos\left(f x + e\right)^{4} + 4 \, {\left(6 \, A - B\right)} \cos\left(f x + e\right)^{2} + 18 \, A - 3 \, B\right)} \sin\left(f x + e\right) - 3 \, A + 18 \, B}{105 \, {\left(a^{3} c^{4} f \cos\left(f x + e\right)^{5} \sin\left(f x + e\right) - a^{3} c^{4} f \cos\left(f x + e\right)^{5}\right)}}"," ",0,"-1/105*(8*(6*A - B)*cos(f*x + e)^6 - 4*(6*A - B)*cos(f*x + e)^4 - (6*A - B)*cos(f*x + e)^2 + (8*(6*A - B)*cos(f*x + e)^4 + 4*(6*A - B)*cos(f*x + e)^2 + 18*A - 3*B)*sin(f*x + e) - 3*A + 18*B)/(a^3*c^4*f*cos(f*x + e)^5*sin(f*x + e) - a^3*c^4*f*cos(f*x + e)^5)","A",0
79,1,185,0,0.859405," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^5,x, algorithm=""fricas"")","-\frac{32 \, {\left(7 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{6} - 16 \, {\left(7 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{4} - 4 \, {\left(7 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{2} - {\left(16 \, {\left(7 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{6} - 24 \, {\left(7 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{4} - 10 \, {\left(7 \, A - 2 \, B\right)} \cos\left(f x + e\right)^{2} - 49 \, A + 14 \, B\right)} \sin\left(f x + e\right) - 14 \, A + 49 \, B}{315 \, {\left(a^{3} c^{5} f \cos\left(f x + e\right)^{7} + 2 \, a^{3} c^{5} f \cos\left(f x + e\right)^{5} \sin\left(f x + e\right) - 2 \, a^{3} c^{5} f \cos\left(f x + e\right)^{5}\right)}}"," ",0,"-1/315*(32*(7*A - 2*B)*cos(f*x + e)^6 - 16*(7*A - 2*B)*cos(f*x + e)^4 - 4*(7*A - 2*B)*cos(f*x + e)^2 - (16*(7*A - 2*B)*cos(f*x + e)^6 - 24*(7*A - 2*B)*cos(f*x + e)^4 - 10*(7*A - 2*B)*cos(f*x + e)^2 - 49*A + 14*B)*sin(f*x + e) - 14*A + 49*B)/(a^3*c^5*f*cos(f*x + e)^7 + 2*a^3*c^5*f*cos(f*x + e)^5*sin(f*x + e) - 2*a^3*c^5*f*cos(f*x + e)^5)","A",0
80,1,221,0,0.714339," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^6,x, algorithm=""fricas"")","\frac{16 \, {\left(8 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{8} - 72 \, {\left(8 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{6} + 30 \, {\left(8 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{4} + 7 \, {\left(8 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{2} + {\left(48 \, {\left(8 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{6} - 40 \, {\left(8 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{4} - 14 \, {\left(8 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{2} - 72 \, A + 27 \, B\right)} \sin\left(f x + e\right) + 27 \, A - 72 \, B}{495 \, {\left(3 \, a^{3} c^{6} f \cos\left(f x + e\right)^{7} - 4 \, a^{3} c^{6} f \cos\left(f x + e\right)^{5} - {\left(a^{3} c^{6} f \cos\left(f x + e\right)^{7} - 4 \, a^{3} c^{6} f \cos\left(f x + e\right)^{5}\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/495*(16*(8*A - 3*B)*cos(f*x + e)^8 - 72*(8*A - 3*B)*cos(f*x + e)^6 + 30*(8*A - 3*B)*cos(f*x + e)^4 + 7*(8*A - 3*B)*cos(f*x + e)^2 + (48*(8*A - 3*B)*cos(f*x + e)^6 - 40*(8*A - 3*B)*cos(f*x + e)^4 - 14*(8*A - 3*B)*cos(f*x + e)^2 - 72*A + 27*B)*sin(f*x + e) + 27*A - 72*B)/(3*a^3*c^6*f*cos(f*x + e)^7 - 4*a^3*c^6*f*cos(f*x + e)^5 - (a^3*c^6*f*cos(f*x + e)^7 - 4*a^3*c^6*f*cos(f*x + e)^5)*sin(f*x + e))","A",0
81,1,287,0,0.926831," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(315 \, B a c^{3} \cos\left(f x + e\right)^{6} - 35 \, {\left(11 \, A - 32 \, B\right)} a c^{3} \cos\left(f x + e\right)^{5} + 5 \, {\left(209 \, A - 221 \, B\right)} a c^{3} \cos\left(f x + e\right)^{4} + 2 \, {\left(1243 \, A - 1195 \, B\right)} a c^{3} \cos\left(f x + e\right)^{3} - 32 \, {\left(11 \, A - 5 \, B\right)} a c^{3} \cos\left(f x + e\right)^{2} + 128 \, {\left(11 \, A - 5 \, B\right)} a c^{3} \cos\left(f x + e\right) + 256 \, {\left(11 \, A - 5 \, B\right)} a c^{3} - {\left(315 \, B a c^{3} \cos\left(f x + e\right)^{5} + 35 \, {\left(11 \, A - 23 \, B\right)} a c^{3} \cos\left(f x + e\right)^{4} + 10 \, {\left(143 \, A - 191 \, B\right)} a c^{3} \cos\left(f x + e\right)^{3} - 96 \, {\left(11 \, A - 5 \, B\right)} a c^{3} \cos\left(f x + e\right)^{2} - 128 \, {\left(11 \, A - 5 \, B\right)} a c^{3} \cos\left(f x + e\right) - 256 \, {\left(11 \, A - 5 \, B\right)} a c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{3465 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/3465*(315*B*a*c^3*cos(f*x + e)^6 - 35*(11*A - 32*B)*a*c^3*cos(f*x + e)^5 + 5*(209*A - 221*B)*a*c^3*cos(f*x + e)^4 + 2*(1243*A - 1195*B)*a*c^3*cos(f*x + e)^3 - 32*(11*A - 5*B)*a*c^3*cos(f*x + e)^2 + 128*(11*A - 5*B)*a*c^3*cos(f*x + e) + 256*(11*A - 5*B)*a*c^3 - (315*B*a*c^3*cos(f*x + e)^5 + 35*(11*A - 23*B)*a*c^3*cos(f*x + e)^4 + 10*(143*A - 191*B)*a*c^3*cos(f*x + e)^3 - 96*(11*A - 5*B)*a*c^3*cos(f*x + e)^2 - 128*(11*A - 5*B)*a*c^3*cos(f*x + e) - 256*(11*A - 5*B)*a*c^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","A",0
82,1,243,0,0.951883," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(35 \, B a c^{2} \cos\left(f x + e\right)^{5} + 5 \, {\left(9 \, A - 10 \, B\right)} a c^{2} \cos\left(f x + e\right)^{4} + {\left(117 \, A - 109 \, B\right)} a c^{2} \cos\left(f x + e\right)^{3} - 8 \, {\left(3 \, A - B\right)} a c^{2} \cos\left(f x + e\right)^{2} + 32 \, {\left(3 \, A - B\right)} a c^{2} \cos\left(f x + e\right) + 64 \, {\left(3 \, A - B\right)} a c^{2} + {\left(35 \, B a c^{2} \cos\left(f x + e\right)^{4} - 5 \, {\left(9 \, A - 17 \, B\right)} a c^{2} \cos\left(f x + e\right)^{3} + 24 \, {\left(3 \, A - B\right)} a c^{2} \cos\left(f x + e\right)^{2} + 32 \, {\left(3 \, A - B\right)} a c^{2} \cos\left(f x + e\right) + 64 \, {\left(3 \, A - B\right)} a c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{315 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/315*(35*B*a*c^2*cos(f*x + e)^5 + 5*(9*A - 10*B)*a*c^2*cos(f*x + e)^4 + (117*A - 109*B)*a*c^2*cos(f*x + e)^3 - 8*(3*A - B)*a*c^2*cos(f*x + e)^2 + 32*(3*A - B)*a*c^2*cos(f*x + e) + 64*(3*A - B)*a*c^2 + (35*B*a*c^2*cos(f*x + e)^4 - 5*(9*A - 17*B)*a*c^2*cos(f*x + e)^3 + 24*(3*A - B)*a*c^2*cos(f*x + e)^2 + 32*(3*A - B)*a*c^2*cos(f*x + e) + 64*(3*A - B)*a*c^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","A",0
83,1,184,0,0.935456," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, B a c \cos\left(f x + e\right)^{4} - 3 \, {\left(7 \, A - 6 \, B\right)} a c \cos\left(f x + e\right)^{3} + {\left(7 \, A - B\right)} a c \cos\left(f x + e\right)^{2} - 4 \, {\left(7 \, A - B\right)} a c \cos\left(f x + e\right) - 8 \, {\left(7 \, A - B\right)} a c - {\left(15 \, B a c \cos\left(f x + e\right)^{3} + 3 \, {\left(7 \, A - B\right)} a c \cos\left(f x + e\right)^{2} + 4 \, {\left(7 \, A - B\right)} a c \cos\left(f x + e\right) + 8 \, {\left(7 \, A - B\right)} a c\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{105 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/105*(15*B*a*c*cos(f*x + e)^4 - 3*(7*A - 6*B)*a*c*cos(f*x + e)^3 + (7*A - B)*a*c*cos(f*x + e)^2 - 4*(7*A - B)*a*c*cos(f*x + e) - 8*(7*A - B)*a*c - (15*B*a*c*cos(f*x + e)^3 + 3*(7*A - B)*a*c*cos(f*x + e)^2 + 4*(7*A - B)*a*c*cos(f*x + e) + 8*(7*A - B)*a*c)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","A",0
84,1,130,0,0.967269," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, B a \cos\left(f x + e\right)^{3} + {\left(5 \, A + 4 \, B\right)} a \cos\left(f x + e\right)^{2} - {\left(5 \, A + B\right)} a \cos\left(f x + e\right) - 2 \, {\left(5 \, A + B\right)} a + {\left(3 \, B a \cos\left(f x + e\right)^{2} - {\left(5 \, A + B\right)} a \cos\left(f x + e\right) - 2 \, {\left(5 \, A + B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/15*(3*B*a*cos(f*x + e)^3 + (5*A + 4*B)*a*cos(f*x + e)^2 - (5*A + B)*a*cos(f*x + e) - 2*(5*A + B)*a + (3*B*a*cos(f*x + e)^2 - (5*A + B)*a*cos(f*x + e) - 2*(5*A + B)*a)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","A",0
85,1,254,0,0.973723," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\frac{3 \, \sqrt{2} {\left({\left(A + B\right)} a c \cos\left(f x + e\right) - {\left(A + B\right)} a c \sin\left(f x + e\right) + {\left(A + B\right)} a c\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{-c \sin\left(f x + e\right) + c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)}}{\sqrt{c}} + 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{c}} + 2 \, {\left(B a \cos\left(f x + e\right)^{2} - {\left(3 \, A + 4 \, B\right)} a \cos\left(f x + e\right) - {\left(3 \, A + 5 \, B\right)} a - {\left(B a \cos\left(f x + e\right) + {\left(3 \, A + 5 \, B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, {\left(c f \cos\left(f x + e\right) - c f \sin\left(f x + e\right) + c f\right)}}"," ",0,"1/3*(3*sqrt(2)*((A + B)*a*c*cos(f*x + e) - (A + B)*a*c*sin(f*x + e) + (A + B)*a*c)*log(-(cos(f*x + e)^2 + (cos(f*x + e) - 2)*sin(f*x + e) + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*(cos(f*x + e) + sin(f*x + e) + 1)/sqrt(c) + 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(c) + 2*(B*a*cos(f*x + e)^2 - (3*A + 4*B)*a*cos(f*x + e) - (3*A + 5*B)*a - (B*a*cos(f*x + e) + (3*A + 5*B)*a)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c*f*cos(f*x + e) - c*f*sin(f*x + e) + c*f)","B",0
86,1,318,0,0.863118," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\frac{\sqrt{2} {\left({\left(A + 5 \, B\right)} a c \cos\left(f x + e\right)^{2} - {\left(A + 5 \, B\right)} a c \cos\left(f x + e\right) - 2 \, {\left(A + 5 \, B\right)} a c + {\left({\left(A + 5 \, B\right)} a c \cos\left(f x + e\right) + 2 \, {\left(A + 5 \, B\right)} a c\right)} \sin\left(f x + e\right)\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{-c \sin\left(f x + e\right) + c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)}}{\sqrt{c}} + 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{c}} - 4 \, {\left(2 \, B a \cos\left(f x + e\right)^{2} + {\left(A + 3 \, B\right)} a \cos\left(f x + e\right) + {\left(A + B\right)} a - {\left(2 \, B a \cos\left(f x + e\right) - {\left(A + B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{4 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right) - 2 \, c^{2} f + {\left(c^{2} f \cos\left(f x + e\right) + 2 \, c^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/4*(sqrt(2)*((A + 5*B)*a*c*cos(f*x + e)^2 - (A + 5*B)*a*c*cos(f*x + e) - 2*(A + 5*B)*a*c + ((A + 5*B)*a*c*cos(f*x + e) + 2*(A + 5*B)*a*c)*sin(f*x + e))*log(-(cos(f*x + e)^2 + (cos(f*x + e) - 2)*sin(f*x + e) - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*(cos(f*x + e) + sin(f*x + e) + 1)/sqrt(c) + 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(c) - 4*(2*B*a*cos(f*x + e)^2 + (A + 3*B)*a*cos(f*x + e) + (A + B)*a - (2*B*a*cos(f*x + e) - (A + B)*a)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e) - 2*c^2*f + (c^2*f*cos(f*x + e) + 2*c^2*f)*sin(f*x + e))","B",0
87,1,394,0,0.912070," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(A - 7 \, B\right)} a \cos\left(f x + e\right)^{3} + 3 \, {\left(A - 7 \, B\right)} a \cos\left(f x + e\right)^{2} - 2 \, {\left(A - 7 \, B\right)} a \cos\left(f x + e\right) - 4 \, {\left(A - 7 \, B\right)} a - {\left({\left(A - 7 \, B\right)} a \cos\left(f x + e\right)^{2} - 2 \, {\left(A - 7 \, B\right)} a \cos\left(f x + e\right) - 4 \, {\left(A - 7 \, B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left({\left(A + 9 \, B\right)} a \cos\left(f x + e\right)^{2} - {\left(3 \, A - 5 \, B\right)} a \cos\left(f x + e\right) - 4 \, {\left(A + B\right)} a - {\left({\left(A + 9 \, B\right)} a \cos\left(f x + e\right) + 4 \, {\left(A + B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{32 \, {\left(c^{3} f \cos\left(f x + e\right)^{3} + 3 \, c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f - {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/32*(sqrt(2)*((A - 7*B)*a*cos(f*x + e)^3 + 3*(A - 7*B)*a*cos(f*x + e)^2 - 2*(A - 7*B)*a*cos(f*x + e) - 4*(A - 7*B)*a - ((A - 7*B)*a*cos(f*x + e)^2 - 2*(A - 7*B)*a*cos(f*x + e) - 4*(A - 7*B)*a)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*((A + 9*B)*a*cos(f*x + e)^2 - (3*A - 5*B)*a*cos(f*x + e) - 4*(A + B)*a - ((A + 9*B)*a*cos(f*x + e) + 4*(A + B)*a)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^3*f*cos(f*x + e)^3 + 3*c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f - (c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f)*sin(f*x + e))","B",0
88,1,490,0,0.974203," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(A - 3 \, B\right)} a \cos\left(f x + e\right)^{4} - 3 \, {\left(A - 3 \, B\right)} a \cos\left(f x + e\right)^{3} - 8 \, {\left(A - 3 \, B\right)} a \cos\left(f x + e\right)^{2} + 4 \, {\left(A - 3 \, B\right)} a \cos\left(f x + e\right) + 8 \, {\left(A - 3 \, B\right)} a + {\left({\left(A - 3 \, B\right)} a \cos\left(f x + e\right)^{3} + 4 \, {\left(A - 3 \, B\right)} a \cos\left(f x + e\right)^{2} - 4 \, {\left(A - 3 \, B\right)} a \cos\left(f x + e\right) - 8 \, {\left(A - 3 \, B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(3 \, {\left(A - 3 \, B\right)} a \cos\left(f x + e\right)^{3} - {\left(7 \, A + 43 \, B\right)} a \cos\left(f x + e\right)^{2} + 2 \, {\left(11 \, A - B\right)} a \cos\left(f x + e\right) + 32 \, {\left(A + B\right)} a + {\left(3 \, {\left(A - 3 \, B\right)} a \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, A + 17 \, B\right)} a \cos\left(f x + e\right) + 32 \, {\left(A + B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{384 \, {\left(c^{4} f \cos\left(f x + e\right)^{4} - 3 \, c^{4} f \cos\left(f x + e\right)^{3} - 8 \, c^{4} f \cos\left(f x + e\right)^{2} + 4 \, c^{4} f \cos\left(f x + e\right) + 8 \, c^{4} f + {\left(c^{4} f \cos\left(f x + e\right)^{3} + 4 \, c^{4} f \cos\left(f x + e\right)^{2} - 4 \, c^{4} f \cos\left(f x + e\right) - 8 \, c^{4} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/384*(3*sqrt(2)*((A - 3*B)*a*cos(f*x + e)^4 - 3*(A - 3*B)*a*cos(f*x + e)^3 - 8*(A - 3*B)*a*cos(f*x + e)^2 + 4*(A - 3*B)*a*cos(f*x + e) + 8*(A - 3*B)*a + ((A - 3*B)*a*cos(f*x + e)^3 + 4*(A - 3*B)*a*cos(f*x + e)^2 - 4*(A - 3*B)*a*cos(f*x + e) - 8*(A - 3*B)*a)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(3*(A - 3*B)*a*cos(f*x + e)^3 - (7*A + 43*B)*a*cos(f*x + e)^2 + 2*(11*A - B)*a*cos(f*x + e) + 32*(A + B)*a + (3*(A - 3*B)*a*cos(f*x + e)^2 + 2*(5*A + 17*B)*a*cos(f*x + e) + 32*(A + B)*a)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^4*f*cos(f*x + e)^4 - 3*c^4*f*cos(f*x + e)^3 - 8*c^4*f*cos(f*x + e)^2 + 4*c^4*f*cos(f*x + e) + 8*c^4*f + (c^4*f*cos(f*x + e)^3 + 4*c^4*f*cos(f*x + e)^2 - 4*c^4*f*cos(f*x + e) - 8*c^4*f)*sin(f*x + e))","B",0
89,1,358,0,0.828059," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{2 \, {\left(1155 \, B a^{2} c^{3} \cos\left(f x + e\right)^{7} + 105 \, {\left(13 \, A - 14 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{6} + 35 \, {\left(91 \, A - 87 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{5} - 20 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{4} + 32 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{3} - 64 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{2} + 256 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right) + 512 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} + {\left(1155 \, B a^{2} c^{3} \cos\left(f x + e\right)^{6} - 105 \, {\left(13 \, A - 25 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{5} + 140 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{4} + 160 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{3} + 192 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{2} + 256 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3} \cos\left(f x + e\right) + 512 \, {\left(13 \, A - 3 \, B\right)} a^{2} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15015 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/15015*(1155*B*a^2*c^3*cos(f*x + e)^7 + 105*(13*A - 14*B)*a^2*c^3*cos(f*x + e)^6 + 35*(91*A - 87*B)*a^2*c^3*cos(f*x + e)^5 - 20*(13*A - 3*B)*a^2*c^3*cos(f*x + e)^4 + 32*(13*A - 3*B)*a^2*c^3*cos(f*x + e)^3 - 64*(13*A - 3*B)*a^2*c^3*cos(f*x + e)^2 + 256*(13*A - 3*B)*a^2*c^3*cos(f*x + e) + 512*(13*A - 3*B)*a^2*c^3 + (1155*B*a^2*c^3*cos(f*x + e)^6 - 105*(13*A - 25*B)*a^2*c^3*cos(f*x + e)^5 + 140*(13*A - 3*B)*a^2*c^3*cos(f*x + e)^4 + 160*(13*A - 3*B)*a^2*c^3*cos(f*x + e)^3 + 192*(13*A - 3*B)*a^2*c^3*cos(f*x + e)^2 + 256*(13*A - 3*B)*a^2*c^3*cos(f*x + e) + 512*(13*A - 3*B)*a^2*c^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","A",0
90,1,313,0,0.921520," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, B a^{2} c^{2} \cos\left(f x + e\right)^{6} - 35 \, {\left(11 \, A - 10 \, B\right)} a^{2} c^{2} \cos\left(f x + e\right)^{5} + 5 \, {\left(11 \, A - B\right)} a^{2} c^{2} \cos\left(f x + e\right)^{4} - 8 \, {\left(11 \, A - B\right)} a^{2} c^{2} \cos\left(f x + e\right)^{3} + 16 \, {\left(11 \, A - B\right)} a^{2} c^{2} \cos\left(f x + e\right)^{2} - 64 \, {\left(11 \, A - B\right)} a^{2} c^{2} \cos\left(f x + e\right) - 128 \, {\left(11 \, A - B\right)} a^{2} c^{2} - {\left(315 \, B a^{2} c^{2} \cos\left(f x + e\right)^{5} + 35 \, {\left(11 \, A - B\right)} a^{2} c^{2} \cos\left(f x + e\right)^{4} + 40 \, {\left(11 \, A - B\right)} a^{2} c^{2} \cos\left(f x + e\right)^{3} + 48 \, {\left(11 \, A - B\right)} a^{2} c^{2} \cos\left(f x + e\right)^{2} + 64 \, {\left(11 \, A - B\right)} a^{2} c^{2} \cos\left(f x + e\right) + 128 \, {\left(11 \, A - B\right)} a^{2} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{3465 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/3465*(315*B*a^2*c^2*cos(f*x + e)^6 - 35*(11*A - 10*B)*a^2*c^2*cos(f*x + e)^5 + 5*(11*A - B)*a^2*c^2*cos(f*x + e)^4 - 8*(11*A - B)*a^2*c^2*cos(f*x + e)^3 + 16*(11*A - B)*a^2*c^2*cos(f*x + e)^2 - 64*(11*A - B)*a^2*c^2*cos(f*x + e) - 128*(11*A - B)*a^2*c^2 - (315*B*a^2*c^2*cos(f*x + e)^5 + 35*(11*A - B)*a^2*c^2*cos(f*x + e)^4 + 40*(11*A - B)*a^2*c^2*cos(f*x + e)^3 + 48*(11*A - B)*a^2*c^2*cos(f*x + e)^2 + 64*(11*A - B)*a^2*c^2*cos(f*x + e) + 128*(11*A - B)*a^2*c^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","B",0
91,1,228,0,0.850954," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, B a^{2} c \cos\left(f x + e\right)^{5} + 5 \, {\left(9 \, A + 8 \, B\right)} a^{2} c \cos\left(f x + e\right)^{4} - {\left(9 \, A + B\right)} a^{2} c \cos\left(f x + e\right)^{3} + 2 \, {\left(9 \, A + B\right)} a^{2} c \cos\left(f x + e\right)^{2} - 8 \, {\left(9 \, A + B\right)} a^{2} c \cos\left(f x + e\right) - 16 \, {\left(9 \, A + B\right)} a^{2} c + {\left(35 \, B a^{2} c \cos\left(f x + e\right)^{4} - 5 \, {\left(9 \, A + B\right)} a^{2} c \cos\left(f x + e\right)^{3} - 6 \, {\left(9 \, A + B\right)} a^{2} c \cos\left(f x + e\right)^{2} - 8 \, {\left(9 \, A + B\right)} a^{2} c \cos\left(f x + e\right) - 16 \, {\left(9 \, A + B\right)} a^{2} c\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{315 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/315*(35*B*a^2*c*cos(f*x + e)^5 + 5*(9*A + 8*B)*a^2*c*cos(f*x + e)^4 - (9*A + B)*a^2*c*cos(f*x + e)^3 + 2*(9*A + B)*a^2*c*cos(f*x + e)^2 - 8*(9*A + B)*a^2*c*cos(f*x + e) - 16*(9*A + B)*a^2*c + (35*B*a^2*c*cos(f*x + e)^4 - 5*(9*A + B)*a^2*c*cos(f*x + e)^3 - 6*(9*A + B)*a^2*c*cos(f*x + e)^2 - 8*(9*A + B)*a^2*c*cos(f*x + e) - 16*(9*A + B)*a^2*c)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","B",0
92,1,193,0,0.903987," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B a^{2} \cos\left(f x + e\right)^{4} - {\left(7 \, A + 8 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - {\left(21 \, A + 19 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(7 \, A + 3 \, B\right)} a^{2} \cos\left(f x + e\right) + 4 \, {\left(7 \, A + 3 \, B\right)} a^{2} - {\left(5 \, B a^{2} \cos\left(f x + e\right)^{3} + {\left(7 \, A + 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(7 \, A + 3 \, B\right)} a^{2} \cos\left(f x + e\right) - 4 \, {\left(7 \, A + 3 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{35 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/35*(5*B*a^2*cos(f*x + e)^4 - (7*A + 8*B)*a^2*cos(f*x + e)^3 - (21*A + 19*B)*a^2*cos(f*x + e)^2 + 2*(7*A + 3*B)*a^2*cos(f*x + e) + 4*(7*A + 3*B)*a^2 - (5*B*a^2*cos(f*x + e)^3 + (7*A + 13*B)*a^2*cos(f*x + e)^2 - 2*(7*A + 3*B)*a^2*cos(f*x + e) - 4*(7*A + 3*B)*a^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","B",0
93,1,310,0,0.876309," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\frac{15 \, \sqrt{2} {\left({\left(A + B\right)} a^{2} c \cos\left(f x + e\right) - {\left(A + B\right)} a^{2} c \sin\left(f x + e\right) + {\left(A + B\right)} a^{2} c\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{-c \sin\left(f x + e\right) + c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)}}{\sqrt{c}} + 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{c}} + {\left(3 \, B a^{2} \cos\left(f x + e\right)^{3} + {\left(5 \, A + 14 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - {\left(35 \, A + 41 \, B\right)} a^{2} \cos\left(f x + e\right) - 4 \, {\left(10 \, A + 13 \, B\right)} a^{2} + {\left(3 \, B a^{2} \cos\left(f x + e\right)^{2} - {\left(5 \, A + 11 \, B\right)} a^{2} \cos\left(f x + e\right) - 4 \, {\left(10 \, A + 13 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}\right)}}{15 \, {\left(c f \cos\left(f x + e\right) - c f \sin\left(f x + e\right) + c f\right)}}"," ",0,"2/15*(15*sqrt(2)*((A + B)*a^2*c*cos(f*x + e) - (A + B)*a^2*c*sin(f*x + e) + (A + B)*a^2*c)*log(-(cos(f*x + e)^2 + (cos(f*x + e) - 2)*sin(f*x + e) + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*(cos(f*x + e) + sin(f*x + e) + 1)/sqrt(c) + 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(c) + (3*B*a^2*cos(f*x + e)^3 + (5*A + 14*B)*a^2*cos(f*x + e)^2 - (35*A + 41*B)*a^2*cos(f*x + e) - 4*(10*A + 13*B)*a^2 + (3*B*a^2*cos(f*x + e)^2 - (5*A + 11*B)*a^2*cos(f*x + e) - 4*(10*A + 13*B)*a^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c*f*cos(f*x + e) - c*f*sin(f*x + e) + c*f)","B",0
94,1,385,0,0.700124," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\frac{3 \, \sqrt{2} {\left({\left(3 \, A + 7 \, B\right)} a^{2} c \cos\left(f x + e\right)^{2} - {\left(3 \, A + 7 \, B\right)} a^{2} c \cos\left(f x + e\right) - 2 \, {\left(3 \, A + 7 \, B\right)} a^{2} c + {\left({\left(3 \, A + 7 \, B\right)} a^{2} c \cos\left(f x + e\right) + 2 \, {\left(3 \, A + 7 \, B\right)} a^{2} c\right)} \sin\left(f x + e\right)\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{-c \sin\left(f x + e\right) + c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)}}{\sqrt{c}} + 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{c}} - 4 \, {\left(B a^{2} \cos\left(f x + e\right)^{3} + {\left(3 \, A + 10 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 6 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right) + 3 \, {\left(A + B\right)} a^{2} + {\left(B a^{2} \cos\left(f x + e\right)^{2} - 3 \, {\left(A + 3 \, B\right)} a^{2} \cos\left(f x + e\right) + 3 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{6 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right) - 2 \, c^{2} f + {\left(c^{2} f \cos\left(f x + e\right) + 2 \, c^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/6*(3*sqrt(2)*((3*A + 7*B)*a^2*c*cos(f*x + e)^2 - (3*A + 7*B)*a^2*c*cos(f*x + e) - 2*(3*A + 7*B)*a^2*c + ((3*A + 7*B)*a^2*c*cos(f*x + e) + 2*(3*A + 7*B)*a^2*c)*sin(f*x + e))*log(-(cos(f*x + e)^2 + (cos(f*x + e) - 2)*sin(f*x + e) - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*(cos(f*x + e) + sin(f*x + e) + 1)/sqrt(c) + 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(c) - 4*(B*a^2*cos(f*x + e)^3 + (3*A + 10*B)*a^2*cos(f*x + e)^2 + 6*(A + 2*B)*a^2*cos(f*x + e) + 3*(A + B)*a^2 + (B*a^2*cos(f*x + e)^2 - 3*(A + 3*B)*a^2*cos(f*x + e) + 3*(A + B)*a^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e) - 2*c^2*f + (c^2*f*cos(f*x + e) + 2*c^2*f)*sin(f*x + e))","B",0
95,1,449,0,0.916665," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(A + 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} + 3 \, {\left(A + 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + 9 \, B\right)} a^{2} \cos\left(f x + e\right) - 4 \, {\left(A + 9 \, B\right)} a^{2} - {\left({\left(A + 9 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + 9 \, B\right)} a^{2} \cos\left(f x + e\right) - 4 \, {\left(A + 9 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(8 \, B a^{2} \cos\left(f x + e\right)^{3} - {\left(5 \, A + 21 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - {\left(A + 25 \, B\right)} a^{2} \cos\left(f x + e\right) + 4 \, {\left(A + B\right)} a^{2} + {\left(8 \, B a^{2} \cos\left(f x + e\right)^{2} + {\left(5 \, A + 29 \, B\right)} a^{2} \cos\left(f x + e\right) + 4 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{16 \, {\left(c^{3} f \cos\left(f x + e\right)^{3} + 3 \, c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f - {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/16*(3*sqrt(2)*((A + 9*B)*a^2*cos(f*x + e)^3 + 3*(A + 9*B)*a^2*cos(f*x + e)^2 - 2*(A + 9*B)*a^2*cos(f*x + e) - 4*(A + 9*B)*a^2 - ((A + 9*B)*a^2*cos(f*x + e)^2 - 2*(A + 9*B)*a^2*cos(f*x + e) - 4*(A + 9*B)*a^2)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(8*B*a^2*cos(f*x + e)^3 - (5*A + 21*B)*a^2*cos(f*x + e)^2 - (A + 25*B)*a^2*cos(f*x + e) + 4*(A + B)*a^2 + (8*B*a^2*cos(f*x + e)^2 + (5*A + 29*B)*a^2*cos(f*x + e) + 4*(A + B)*a^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^3*f*cos(f*x + e)^3 + 3*c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f - (c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f)*sin(f*x + e))","B",0
96,1,521,0,0.982854," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(A - 11 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} - 3 \, {\left(A - 11 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - 8 \, {\left(A - 11 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 4 \, {\left(A - 11 \, B\right)} a^{2} \cos\left(f x + e\right) + 8 \, {\left(A - 11 \, B\right)} a^{2} + {\left({\left(A - 11 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} + 4 \, {\left(A - 11 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - 11 \, B\right)} a^{2} \cos\left(f x + e\right) - 8 \, {\left(A - 11 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) + 4 \, {\left(3 \, {\left(A + 21 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} + {\left(25 \, A + 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, A + 41 \, B\right)} a^{2} \cos\left(f x + e\right) - 32 \, {\left(A + B\right)} a^{2} + {\left(3 \, {\left(A + 21 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(11 \, A - 25 \, B\right)} a^{2} \cos\left(f x + e\right) - 32 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{192 \, {\left(c^{4} f \cos\left(f x + e\right)^{4} - 3 \, c^{4} f \cos\left(f x + e\right)^{3} - 8 \, c^{4} f \cos\left(f x + e\right)^{2} + 4 \, c^{4} f \cos\left(f x + e\right) + 8 \, c^{4} f + {\left(c^{4} f \cos\left(f x + e\right)^{3} + 4 \, c^{4} f \cos\left(f x + e\right)^{2} - 4 \, c^{4} f \cos\left(f x + e\right) - 8 \, c^{4} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/192*(3*sqrt(2)*((A - 11*B)*a^2*cos(f*x + e)^4 - 3*(A - 11*B)*a^2*cos(f*x + e)^3 - 8*(A - 11*B)*a^2*cos(f*x + e)^2 + 4*(A - 11*B)*a^2*cos(f*x + e) + 8*(A - 11*B)*a^2 + ((A - 11*B)*a^2*cos(f*x + e)^3 + 4*(A - 11*B)*a^2*cos(f*x + e)^2 - 4*(A - 11*B)*a^2*cos(f*x + e) - 8*(A - 11*B)*a^2)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(3*(A + 21*B)*a^2*cos(f*x + e)^3 + (25*A + 13*B)*a^2*cos(f*x + e)^2 - 2*(5*A + 41*B)*a^2*cos(f*x + e) - 32*(A + B)*a^2 + (3*(A + 21*B)*a^2*cos(f*x + e)^2 - 2*(11*A - 25*B)*a^2*cos(f*x + e) - 32*(A + B)*a^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^4*f*cos(f*x + e)^4 - 3*c^4*f*cos(f*x + e)^3 - 8*c^4*f*cos(f*x + e)^2 + 4*c^4*f*cos(f*x + e) + 8*c^4*f + (c^4*f*cos(f*x + e)^3 + 4*c^4*f*cos(f*x + e)^2 - 4*c^4*f*cos(f*x + e) - 8*c^4*f)*sin(f*x + e))","B",0
97,1,654,0,0.957381," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{5} + 5 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} - 8 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - 20 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 8 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right) + 16 \, {\left(3 \, A - 13 \, B\right)} a^{2} - {\left({\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} - 4 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - 12 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 8 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right) + 16 \, {\left(3 \, A - 13 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) + 4 \, {\left(3 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{4} + {\left(39 \, A + 343 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} + 2 \, {\left(129 \, A + 209 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 12 \, {\left(13 \, A + 29 \, B\right)} a^{2} \cos\left(f x + e\right) - 384 \, {\left(A + B\right)} a^{2} - {\left(3 \, {\left(3 \, A - 13 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - 2 \, {\left(15 \, A + 191 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} + 12 \, {\left(19 \, A + 3 \, B\right)} a^{2} \cos\left(f x + e\right) + 384 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{3072 \, {\left(c^{5} f \cos\left(f x + e\right)^{5} + 5 \, c^{5} f \cos\left(f x + e\right)^{4} - 8 \, c^{5} f \cos\left(f x + e\right)^{3} - 20 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f - {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} - 12 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/3072*(3*sqrt(2)*((3*A - 13*B)*a^2*cos(f*x + e)^5 + 5*(3*A - 13*B)*a^2*cos(f*x + e)^4 - 8*(3*A - 13*B)*a^2*cos(f*x + e)^3 - 20*(3*A - 13*B)*a^2*cos(f*x + e)^2 + 8*(3*A - 13*B)*a^2*cos(f*x + e) + 16*(3*A - 13*B)*a^2 - ((3*A - 13*B)*a^2*cos(f*x + e)^4 - 4*(3*A - 13*B)*a^2*cos(f*x + e)^3 - 12*(3*A - 13*B)*a^2*cos(f*x + e)^2 + 8*(3*A - 13*B)*a^2*cos(f*x + e) + 16*(3*A - 13*B)*a^2)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(3*(3*A - 13*B)*a^2*cos(f*x + e)^4 + (39*A + 343*B)*a^2*cos(f*x + e)^3 + 2*(129*A + 209*B)*a^2*cos(f*x + e)^2 - 12*(13*A + 29*B)*a^2*cos(f*x + e) - 384*(A + B)*a^2 - (3*(3*A - 13*B)*a^2*cos(f*x + e)^3 - 2*(15*A + 191*B)*a^2*cos(f*x + e)^2 + 12*(19*A + 3*B)*a^2*cos(f*x + e) + 384*(A + B)*a^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^5*f*cos(f*x + e)^5 + 5*c^5*f*cos(f*x + e)^4 - 8*c^5*f*cos(f*x + e)^3 - 20*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f - (c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 - 12*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f)*sin(f*x + e))","B",0
98,1,405,0,0.895480," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(3003 \, B a^{3} c^{3} \cos\left(f x + e\right)^{8} - 231 \, {\left(15 \, A - 14 \, B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{7} + 21 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{6} - 28 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{5} + 40 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{4} - 64 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{3} + 128 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{2} - 512 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right) - 1024 \, {\left(15 \, A - B\right)} a^{3} c^{3} - {\left(3003 \, B a^{3} c^{3} \cos\left(f x + e\right)^{7} + 231 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{6} + 252 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{5} + 280 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{4} + 320 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{3} + 384 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right)^{2} + 512 \, {\left(15 \, A - B\right)} a^{3} c^{3} \cos\left(f x + e\right) + 1024 \, {\left(15 \, A - B\right)} a^{3} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{45045 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/45045*(3003*B*a^3*c^3*cos(f*x + e)^8 - 231*(15*A - 14*B)*a^3*c^3*cos(f*x + e)^7 + 21*(15*A - B)*a^3*c^3*cos(f*x + e)^6 - 28*(15*A - B)*a^3*c^3*cos(f*x + e)^5 + 40*(15*A - B)*a^3*c^3*cos(f*x + e)^4 - 64*(15*A - B)*a^3*c^3*cos(f*x + e)^3 + 128*(15*A - B)*a^3*c^3*cos(f*x + e)^2 - 512*(15*A - B)*a^3*c^3*cos(f*x + e) - 1024*(15*A - B)*a^3*c^3 - (3003*B*a^3*c^3*cos(f*x + e)^7 + 231*(15*A - B)*a^3*c^3*cos(f*x + e)^6 + 252*(15*A - B)*a^3*c^3*cos(f*x + e)^5 + 280*(15*A - B)*a^3*c^3*cos(f*x + e)^4 + 320*(15*A - B)*a^3*c^3*cos(f*x + e)^3 + 384*(15*A - B)*a^3*c^3*cos(f*x + e)^2 + 512*(15*A - B)*a^3*c^3*cos(f*x + e) + 1024*(15*A - B)*a^3*c^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","B",0
99,1,334,0,0.693731," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(693 \, B a^{3} c^{2} \cos\left(f x + e\right)^{7} + 63 \, {\left(13 \, A + 12 \, B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{6} - 7 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{5} + 10 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{4} - 16 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{3} + 32 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{2} - 128 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right) - 256 \, {\left(13 \, A + B\right)} a^{3} c^{2} + {\left(693 \, B a^{3} c^{2} \cos\left(f x + e\right)^{6} - 63 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{5} - 70 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{4} - 80 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{3} - 96 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{2} - 128 \, {\left(13 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right) - 256 \, {\left(13 \, A + B\right)} a^{3} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{9009 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/9009*(693*B*a^3*c^2*cos(f*x + e)^7 + 63*(13*A + 12*B)*a^3*c^2*cos(f*x + e)^6 - 7*(13*A + B)*a^3*c^2*cos(f*x + e)^5 + 10*(13*A + B)*a^3*c^2*cos(f*x + e)^4 - 16*(13*A + B)*a^3*c^2*cos(f*x + e)^3 + 32*(13*A + B)*a^3*c^2*cos(f*x + e)^2 - 128*(13*A + B)*a^3*c^2*cos(f*x + e) - 256*(13*A + B)*a^3*c^2 + (693*B*a^3*c^2*cos(f*x + e)^6 - 63*(13*A + B)*a^3*c^2*cos(f*x + e)^5 - 70*(13*A + B)*a^3*c^2*cos(f*x + e)^4 - 80*(13*A + B)*a^3*c^2*cos(f*x + e)^3 - 96*(13*A + B)*a^3*c^2*cos(f*x + e)^2 - 128*(13*A + B)*a^3*c^2*cos(f*x + e) - 256*(13*A + B)*a^3*c^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","B",0
100,1,287,0,0.761997," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(63 \, B a^{3} c \cos\left(f x + e\right)^{6} - 7 \, {\left(11 \, A + 12 \, B\right)} a^{3} c \cos\left(f x + e\right)^{5} - {\left(187 \, A + 177 \, B\right)} a^{3} c \cos\left(f x + e\right)^{4} + 2 \, {\left(11 \, A + 3 \, B\right)} a^{3} c \cos\left(f x + e\right)^{3} - 4 \, {\left(11 \, A + 3 \, B\right)} a^{3} c \cos\left(f x + e\right)^{2} + 16 \, {\left(11 \, A + 3 \, B\right)} a^{3} c \cos\left(f x + e\right) + 32 \, {\left(11 \, A + 3 \, B\right)} a^{3} c - {\left(63 \, B a^{3} c \cos\left(f x + e\right)^{5} + 7 \, {\left(11 \, A + 21 \, B\right)} a^{3} c \cos\left(f x + e\right)^{4} - 10 \, {\left(11 \, A + 3 \, B\right)} a^{3} c \cos\left(f x + e\right)^{3} - 12 \, {\left(11 \, A + 3 \, B\right)} a^{3} c \cos\left(f x + e\right)^{2} - 16 \, {\left(11 \, A + 3 \, B\right)} a^{3} c \cos\left(f x + e\right) - 32 \, {\left(11 \, A + 3 \, B\right)} a^{3} c\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{693 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/693*(63*B*a^3*c*cos(f*x + e)^6 - 7*(11*A + 12*B)*a^3*c*cos(f*x + e)^5 - (187*A + 177*B)*a^3*c*cos(f*x + e)^4 + 2*(11*A + 3*B)*a^3*c*cos(f*x + e)^3 - 4*(11*A + 3*B)*a^3*c*cos(f*x + e)^2 + 16*(11*A + 3*B)*a^3*c*cos(f*x + e) + 32*(11*A + 3*B)*a^3*c - (63*B*a^3*c*cos(f*x + e)^5 + 7*(11*A + 21*B)*a^3*c*cos(f*x + e)^4 - 10*(11*A + 3*B)*a^3*c*cos(f*x + e)^3 - 12*(11*A + 3*B)*a^3*c*cos(f*x + e)^2 - 16*(11*A + 3*B)*a^3*c*cos(f*x + e) - 32*(11*A + 3*B)*a^3*c)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","B",0
101,1,232,0,0.895075," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(7 \, B a^{3} \cos\left(f x + e\right)^{5} + {\left(9 \, A + 26 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - {\left(27 \, A + 29 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 4 \, {\left(18 \, A + 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(9 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right) + 8 \, {\left(9 \, A + 5 \, B\right)} a^{3} + {\left(7 \, B a^{3} \cos\left(f x + e\right)^{4} - {\left(9 \, A + 19 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 12 \, {\left(3 \, A + 4 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(9 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right) + 8 \, {\left(9 \, A + 5 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{63 \, {\left(f \cos\left(f x + e\right) - f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/63*(7*B*a^3*cos(f*x + e)^5 + (9*A + 26*B)*a^3*cos(f*x + e)^4 - (27*A + 29*B)*a^3*cos(f*x + e)^3 - 4*(18*A + 17*B)*a^3*cos(f*x + e)^2 + 4*(9*A + 5*B)*a^3*cos(f*x + e) + 8*(9*A + 5*B)*a^3 + (7*B*a^3*cos(f*x + e)^4 - (9*A + 19*B)*a^3*cos(f*x + e)^3 - 12*(3*A + 4*B)*a^3*cos(f*x + e)^2 + 4*(9*A + 5*B)*a^3*cos(f*x + e) + 8*(9*A + 5*B)*a^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e) - f*sin(f*x + e) + f)","B",0
102,1,353,0,0.912266," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\frac{210 \, \sqrt{2} {\left({\left(A + B\right)} a^{3} c \cos\left(f x + e\right) - {\left(A + B\right)} a^{3} c \sin\left(f x + e\right) + {\left(A + B\right)} a^{3} c\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{-c \sin\left(f x + e\right) + c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)}}{\sqrt{c}} + 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{c}} - {\left(15 \, B a^{3} \cos\left(f x + e\right)^{4} - 3 \, {\left(7 \, A + 22 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - {\left(133 \, A + 253 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(133 \, A + 148 \, B\right)} a^{3} \cos\left(f x + e\right) + 4 \, {\left(161 \, A + 191 \, B\right)} a^{3} - {\left(15 \, B a^{3} \cos\left(f x + e\right)^{3} + 3 \, {\left(7 \, A + 27 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(28 \, A + 43 \, B\right)} a^{3} \cos\left(f x + e\right) - 4 \, {\left(161 \, A + 191 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}\right)}}{105 \, {\left(c f \cos\left(f x + e\right) - c f \sin\left(f x + e\right) + c f\right)}}"," ",0,"2/105*(210*sqrt(2)*((A + B)*a^3*c*cos(f*x + e) - (A + B)*a^3*c*sin(f*x + e) + (A + B)*a^3*c)*log(-(cos(f*x + e)^2 + (cos(f*x + e) - 2)*sin(f*x + e) + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*(cos(f*x + e) + sin(f*x + e) + 1)/sqrt(c) + 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(c) - (15*B*a^3*cos(f*x + e)^4 - 3*(7*A + 22*B)*a^3*cos(f*x + e)^3 - (133*A + 253*B)*a^3*cos(f*x + e)^2 + 4*(133*A + 148*B)*a^3*cos(f*x + e) + 4*(161*A + 191*B)*a^3 - (15*B*a^3*cos(f*x + e)^3 + 3*(7*A + 27*B)*a^3*cos(f*x + e)^2 - 4*(28*A + 43*B)*a^3*cos(f*x + e) - 4*(161*A + 191*B)*a^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c*f*cos(f*x + e) - c*f*sin(f*x + e) + c*f)","A",0
103,1,430,0,0.805789," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\frac{15 \, \sqrt{2} {\left({\left(5 \, A + 9 \, B\right)} a^{3} c \cos\left(f x + e\right)^{2} - {\left(5 \, A + 9 \, B\right)} a^{3} c \cos\left(f x + e\right) - 2 \, {\left(5 \, A + 9 \, B\right)} a^{3} c + {\left({\left(5 \, A + 9 \, B\right)} a^{3} c \cos\left(f x + e\right) + 2 \, {\left(5 \, A + 9 \, B\right)} a^{3} c\right)} \sin\left(f x + e\right)\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{-c \sin\left(f x + e\right) + c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)}}{\sqrt{c}} + 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{c}} + 2 \, {\left(3 \, B a^{3} \cos\left(f x + e\right)^{4} - {\left(5 \, A + 18 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - {\left(65 \, A + 141 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 30 \, {\left(3 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right) - 30 \, {\left(A + B\right)} a^{3} - {\left(3 \, B a^{3} \cos\left(f x + e\right)^{3} + {\left(5 \, A + 21 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 60 \, {\left(A + 2 \, B\right)} a^{3} \cos\left(f x + e\right) + 30 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, {\left(c^{2} f \cos\left(f x + e\right)^{2} - c^{2} f \cos\left(f x + e\right) - 2 \, c^{2} f + {\left(c^{2} f \cos\left(f x + e\right) + 2 \, c^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/15*(15*sqrt(2)*((5*A + 9*B)*a^3*c*cos(f*x + e)^2 - (5*A + 9*B)*a^3*c*cos(f*x + e) - 2*(5*A + 9*B)*a^3*c + ((5*A + 9*B)*a^3*c*cos(f*x + e) + 2*(5*A + 9*B)*a^3*c)*sin(f*x + e))*log(-(cos(f*x + e)^2 + (cos(f*x + e) - 2)*sin(f*x + e) - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*(cos(f*x + e) + sin(f*x + e) + 1)/sqrt(c) + 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(c) + 2*(3*B*a^3*cos(f*x + e)^4 - (5*A + 18*B)*a^3*cos(f*x + e)^3 - (65*A + 141*B)*a^3*cos(f*x + e)^2 - 30*(3*A + 5*B)*a^3*cos(f*x + e) - 30*(A + B)*a^3 - (3*B*a^3*cos(f*x + e)^3 + (5*A + 21*B)*a^3*cos(f*x + e)^2 - 60*(A + 2*B)*a^3*cos(f*x + e) + 30*(A + B)*a^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^2*f*cos(f*x + e)^2 - c^2*f*cos(f*x + e) - 2*c^2*f + (c^2*f*cos(f*x + e) + 2*c^2*f)*sin(f*x + e))","B",0
104,1,505,0,0.850131," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(3 \, A + 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 3 \, {\left(3 \, A + 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, A + 11 \, B\right)} a^{3} \cos\left(f x + e\right) - 4 \, {\left(3 \, A + 11 \, B\right)} a^{3} - {\left({\left(3 \, A + 11 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, A + 11 \, B\right)} a^{3} \cos\left(f x + e\right) - 4 \, {\left(3 \, A + 11 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) + 4 \, {\left(4 \, B a^{3} \cos\left(f x + e\right)^{4} - 4 \, {\left(3 \, A + 14 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 3 \, {\left(13 \, A + 37 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 3 \, {\left(13 \, A + 53 \, B\right)} a^{3} \cos\left(f x + e\right) - 12 \, {\left(A + B\right)} a^{3} - {\left(4 \, B a^{3} \cos\left(f x + e\right)^{3} + 12 \, {\left(A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 3 \, {\left(17 \, A + 57 \, B\right)} a^{3} \cos\left(f x + e\right) + 12 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{24 \, {\left(c^{3} f \cos\left(f x + e\right)^{3} + 3 \, c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f - {\left(c^{3} f \cos\left(f x + e\right)^{2} - 2 \, c^{3} f \cos\left(f x + e\right) - 4 \, c^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/24*(15*sqrt(2)*((3*A + 11*B)*a^3*cos(f*x + e)^3 + 3*(3*A + 11*B)*a^3*cos(f*x + e)^2 - 2*(3*A + 11*B)*a^3*cos(f*x + e) - 4*(3*A + 11*B)*a^3 - ((3*A + 11*B)*a^3*cos(f*x + e)^2 - 2*(3*A + 11*B)*a^3*cos(f*x + e) - 4*(3*A + 11*B)*a^3)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(4*B*a^3*cos(f*x + e)^4 - 4*(3*A + 14*B)*a^3*cos(f*x + e)^3 + 3*(13*A + 37*B)*a^3*cos(f*x + e)^2 + 3*(13*A + 53*B)*a^3*cos(f*x + e) - 12*(A + B)*a^3 - (4*B*a^3*cos(f*x + e)^3 + 12*(A + 5*B)*a^3*cos(f*x + e)^2 + 3*(17*A + 57*B)*a^3*cos(f*x + e) + 12*(A + B)*a^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^3*f*cos(f*x + e)^3 + 3*c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f - (c^3*f*cos(f*x + e)^2 - 2*c^3*f*cos(f*x + e) - 4*c^3*f)*sin(f*x + e))","B",0
105,1,554,0,0.917022," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(A + 13 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 3 \, {\left(A + 13 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 8 \, {\left(A + 13 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(A + 13 \, B\right)} a^{3} \cos\left(f x + e\right) + 8 \, {\left(A + 13 \, B\right)} a^{3} + {\left({\left(A + 13 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 4 \, {\left(A + 13 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + 13 \, B\right)} a^{3} \cos\left(f x + e\right) - 8 \, {\left(A + 13 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(48 \, B a^{3} \cos\left(f x + e\right)^{4} + 3 \, {\left(11 \, A + 95 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + {\left(19 \, A - 137 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 2 \, {\left(23 \, A + 203 \, B\right)} a^{3} \cos\left(f x + e\right) - 32 \, {\left(A + B\right)} a^{3} - {\left(48 \, B a^{3} \cos\left(f x + e\right)^{3} - 3 \, {\left(11 \, A + 79 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 2 \, {\left(7 \, A + 187 \, B\right)} a^{3} \cos\left(f x + e\right) + 32 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{96 \, {\left(c^{4} f \cos\left(f x + e\right)^{4} - 3 \, c^{4} f \cos\left(f x + e\right)^{3} - 8 \, c^{4} f \cos\left(f x + e\right)^{2} + 4 \, c^{4} f \cos\left(f x + e\right) + 8 \, c^{4} f + {\left(c^{4} f \cos\left(f x + e\right)^{3} + 4 \, c^{4} f \cos\left(f x + e\right)^{2} - 4 \, c^{4} f \cos\left(f x + e\right) - 8 \, c^{4} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/96*(15*sqrt(2)*((A + 13*B)*a^3*cos(f*x + e)^4 - 3*(A + 13*B)*a^3*cos(f*x + e)^3 - 8*(A + 13*B)*a^3*cos(f*x + e)^2 + 4*(A + 13*B)*a^3*cos(f*x + e) + 8*(A + 13*B)*a^3 + ((A + 13*B)*a^3*cos(f*x + e)^3 + 4*(A + 13*B)*a^3*cos(f*x + e)^2 - 4*(A + 13*B)*a^3*cos(f*x + e) - 8*(A + 13*B)*a^3)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(48*B*a^3*cos(f*x + e)^4 + 3*(11*A + 95*B)*a^3*cos(f*x + e)^3 + (19*A - 137*B)*a^3*cos(f*x + e)^2 - 2*(23*A + 203*B)*a^3*cos(f*x + e) - 32*(A + B)*a^3 - (48*B*a^3*cos(f*x + e)^3 - 3*(11*A + 79*B)*a^3*cos(f*x + e)^2 - 2*(7*A + 187*B)*a^3*cos(f*x + e) + 32*(A + B)*a^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^4*f*cos(f*x + e)^4 - 3*c^4*f*cos(f*x + e)^3 - 8*c^4*f*cos(f*x + e)^2 + 4*c^4*f*cos(f*x + e) + 8*c^4*f + (c^4*f*cos(f*x + e)^3 + 4*c^4*f*cos(f*x + e)^2 - 4*c^4*f*cos(f*x + e) - 8*c^4*f)*sin(f*x + e))","B",0
106,1,633,0,0.944505," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} {\left({\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} + 5 \, {\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 8 \, {\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 20 \, {\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 8 \, {\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right) + 16 \, {\left(A - 15 \, B\right)} a^{3} - {\left({\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 4 \, {\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 12 \, {\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 8 \, {\left(A - 15 \, B\right)} a^{3} \cos\left(f x + e\right) + 16 \, {\left(A - 15 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(3 \, {\left(5 \, A + 181 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - {\left(191 \, A - 561 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 2 \, {\left(169 \, A + 537 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 12 \, {\left(21 \, A - 59 \, B\right)} a^{3} \cos\left(f x + e\right) + 384 \, {\left(A + B\right)} a^{3} - {\left(3 \, {\left(5 \, A + 181 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 2 \, {\left(103 \, A - 9 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 12 \, {\left(11 \, A + 91 \, B\right)} a^{3} \cos\left(f x + e\right) - 384 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{1536 \, {\left(c^{5} f \cos\left(f x + e\right)^{5} + 5 \, c^{5} f \cos\left(f x + e\right)^{4} - 8 \, c^{5} f \cos\left(f x + e\right)^{3} - 20 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f - {\left(c^{5} f \cos\left(f x + e\right)^{4} - 4 \, c^{5} f \cos\left(f x + e\right)^{3} - 12 \, c^{5} f \cos\left(f x + e\right)^{2} + 8 \, c^{5} f \cos\left(f x + e\right) + 16 \, c^{5} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/1536*(15*sqrt(2)*((A - 15*B)*a^3*cos(f*x + e)^5 + 5*(A - 15*B)*a^3*cos(f*x + e)^4 - 8*(A - 15*B)*a^3*cos(f*x + e)^3 - 20*(A - 15*B)*a^3*cos(f*x + e)^2 + 8*(A - 15*B)*a^3*cos(f*x + e) + 16*(A - 15*B)*a^3 - ((A - 15*B)*a^3*cos(f*x + e)^4 - 4*(A - 15*B)*a^3*cos(f*x + e)^3 - 12*(A - 15*B)*a^3*cos(f*x + e)^2 + 8*(A - 15*B)*a^3*cos(f*x + e) + 16*(A - 15*B)*a^3)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(3*(5*A + 181*B)*a^3*cos(f*x + e)^4 - (191*A - 561*B)*a^3*cos(f*x + e)^3 - 2*(169*A + 537*B)*a^3*cos(f*x + e)^2 + 12*(21*A - 59*B)*a^3*cos(f*x + e) + 384*(A + B)*a^3 - (3*(5*A + 181*B)*a^3*cos(f*x + e)^3 + 2*(103*A - 9*B)*a^3*cos(f*x + e)^2 - 12*(11*A + 91*B)*a^3*cos(f*x + e) - 384*(A + B)*a^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^5*f*cos(f*x + e)^5 + 5*c^5*f*cos(f*x + e)^4 - 8*c^5*f*cos(f*x + e)^3 - 20*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f - (c^5*f*cos(f*x + e)^4 - 4*c^5*f*cos(f*x + e)^3 - 12*c^5*f*cos(f*x + e)^2 + 8*c^5*f*cos(f*x + e) + 16*c^5*f)*sin(f*x + e))","B",0
107,1,760,0,0.996290," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} {\left({\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{6} - 5 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} - 18 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} + 20 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 48 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 16 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right) - 32 \, {\left(3 \, A - 17 \, B\right)} a^{3} + {\left({\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} + 6 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 12 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} - 32 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 16 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right) + 32 \, {\left(3 \, A - 17 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(15 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{5} - 5 \, {\left(39 \, A + 803 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} + 4 \, {\left(609 \, A + 389 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 12 \, {\left(449 \, A + 869 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 24 \, {\left(143 \, A + 43 \, B\right)} a^{3} \cos\left(f x + e\right) - 6144 \, {\left(A + B\right)} a^{3} + {\left(15 \, {\left(3 \, A - 17 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} + 80 \, {\left(3 \, A + 47 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 12 \, {\left(223 \, A + 443 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 24 \, {\left(113 \, A + 213 \, B\right)} a^{3} \cos\left(f x + e\right) - 6144 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{30720 \, {\left(c^{6} f \cos\left(f x + e\right)^{6} - 5 \, c^{6} f \cos\left(f x + e\right)^{5} - 18 \, c^{6} f \cos\left(f x + e\right)^{4} + 20 \, c^{6} f \cos\left(f x + e\right)^{3} + 48 \, c^{6} f \cos\left(f x + e\right)^{2} - 16 \, c^{6} f \cos\left(f x + e\right) - 32 \, c^{6} f + {\left(c^{6} f \cos\left(f x + e\right)^{5} + 6 \, c^{6} f \cos\left(f x + e\right)^{4} - 12 \, c^{6} f \cos\left(f x + e\right)^{3} - 32 \, c^{6} f \cos\left(f x + e\right)^{2} + 16 \, c^{6} f \cos\left(f x + e\right) + 32 \, c^{6} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/30720*(15*sqrt(2)*((3*A - 17*B)*a^3*cos(f*x + e)^6 - 5*(3*A - 17*B)*a^3*cos(f*x + e)^5 - 18*(3*A - 17*B)*a^3*cos(f*x + e)^4 + 20*(3*A - 17*B)*a^3*cos(f*x + e)^3 + 48*(3*A - 17*B)*a^3*cos(f*x + e)^2 - 16*(3*A - 17*B)*a^3*cos(f*x + e) - 32*(3*A - 17*B)*a^3 + ((3*A - 17*B)*a^3*cos(f*x + e)^5 + 6*(3*A - 17*B)*a^3*cos(f*x + e)^4 - 12*(3*A - 17*B)*a^3*cos(f*x + e)^3 - 32*(3*A - 17*B)*a^3*cos(f*x + e)^2 + 16*(3*A - 17*B)*a^3*cos(f*x + e) + 32*(3*A - 17*B)*a^3)*sin(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(15*(3*A - 17*B)*a^3*cos(f*x + e)^5 - 5*(39*A + 803*B)*a^3*cos(f*x + e)^4 + 4*(609*A + 389*B)*a^3*cos(f*x + e)^3 + 12*(449*A + 869*B)*a^3*cos(f*x + e)^2 - 24*(143*A + 43*B)*a^3*cos(f*x + e) - 6144*(A + B)*a^3 + (15*(3*A - 17*B)*a^3*cos(f*x + e)^4 + 80*(3*A + 47*B)*a^3*cos(f*x + e)^3 + 12*(223*A + 443*B)*a^3*cos(f*x + e)^2 - 24*(113*A + 213*B)*a^3*cos(f*x + e) - 6144*(A + B)*a^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c))/(c^6*f*cos(f*x + e)^6 - 5*c^6*f*cos(f*x + e)^5 - 18*c^6*f*cos(f*x + e)^4 + 20*c^6*f*cos(f*x + e)^3 + 48*c^6*f*cos(f*x + e)^2 - 16*c^6*f*cos(f*x + e) - 32*c^6*f + (c^6*f*cos(f*x + e)^5 + 6*c^6*f*cos(f*x + e)^4 - 12*c^6*f*cos(f*x + e)^3 - 32*c^6*f*cos(f*x + e)^2 + 16*c^6*f*cos(f*x + e) + 32*c^6*f)*sin(f*x + e))","B",0
108,1,115,0,0.888198," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, B c^{3} \cos\left(f x + e\right)^{4} + {\left(49 \, A - 103 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(147 \, A - 179 \, B\right)} c^{3} - {\left({\left(7 \, A - 29 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(77 \, A - 109 \, B\right)} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{35 \, a f \cos\left(f x + e\right)}"," ",0,"-2/35*(5*B*c^3*cos(f*x + e)^4 + (49*A - 103*B)*c^3*cos(f*x + e)^2 + 4*(147*A - 179*B)*c^3 - ((7*A - 29*B)*c^3*cos(f*x + e)^2 - 4*(77*A - 109*B)*c^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(a*f*cos(f*x + e))","A",0
109,1,95,0,0.841568," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(5 \, A - 16 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(55 \, A - 71 \, B\right)} c^{2} + {\left(3 \, B c^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(25 \, A - 41 \, B\right)} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, a f \cos\left(f x + e\right)}"," ",0,"-2/15*((5*A - 16*B)*c^2*cos(f*x + e)^2 + 2*(55*A - 71*B)*c^2 + (3*B*c^2*cos(f*x + e)^2 + 2*(25*A - 41*B)*c^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(a*f*cos(f*x + e))","A",0
110,1,67,0,0.894949," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(B c \cos\left(f x + e\right)^{2} - {\left(3 \, A - 7 \, B\right)} c \sin\left(f x + e\right) - {\left(9 \, A - 13 \, B\right)} c\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a f \cos\left(f x + e\right)}"," ",0,"2/3*(B*c*cos(f*x + e)^2 - (3*A - 7*B)*c*sin(f*x + e) - (9*A - 13*B)*c)*sqrt(-c*sin(f*x + e) + c)/(a*f*cos(f*x + e))","A",0
111,1,44,0,0.654357," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(B \sin\left(f x + e\right) - A + 2 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{a f \cos\left(f x + e\right)}"," ",0,"2*(B*sin(f*x + e) - A + 2*B)*sqrt(-c*sin(f*x + e) + c)/(a*f*cos(f*x + e))","A",0
112,1,162,0,0.668377," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(A + B\right)} \sqrt{c} \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{-c \sin\left(f x + e\right) + c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)}}{\sqrt{c}} + 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) - 4 \, \sqrt{-c \sin\left(f x + e\right) + c} {\left(A - B\right)}}{4 \, a c f \cos\left(f x + e\right)}"," ",0,"1/4*(sqrt(2)*(A + B)*sqrt(c)*cos(f*x + e)*log(-(cos(f*x + e)^2 + (cos(f*x + e) - 2)*sin(f*x + e) + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*(cos(f*x + e) + sin(f*x + e) + 1)/sqrt(c) + 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)) - 4*sqrt(-c*sin(f*x + e) + c)*(A - B))/(a*c*f*cos(f*x + e))","A",0
113,1,231,0,0.921623," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left(3 \, A - B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(3 \, A - B\right)} \cos\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) + 4 \, {\left({\left(3 \, A - B\right)} \sin\left(f x + e\right) - A + 3 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{16 \, {\left(a c^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) - a c^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"-1/16*(sqrt(2)*((3*A - B)*cos(f*x + e)*sin(f*x + e) - (3*A - B)*cos(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*((3*A - B)*sin(f*x + e) - A + 3*B)*sqrt(-c*sin(f*x + e) + c))/(a*c^2*f*cos(f*x + e)*sin(f*x + e) - a*c^2*f*cos(f*x + e))","A",0
114,1,282,0,0.949194," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left({\left(5 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(5 \, A - 3 \, B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, {\left(5 \, A - 3 \, B\right)} \cos\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) + 4 \, {\left(3 \, {\left(5 \, A - 3 \, B\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(5 \, A - 3 \, B\right)} \sin\left(f x + e\right) - 12 \, A + 20 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{128 \, {\left(a c^{3} f \cos\left(f x + e\right)^{3} + 2 \, a c^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a c^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"-1/128*(3*sqrt(2)*((5*A - 3*B)*cos(f*x + e)^3 + 2*(5*A - 3*B)*cos(f*x + e)*sin(f*x + e) - 2*(5*A - 3*B)*cos(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(3*(5*A - 3*B)*cos(f*x + e)^2 + 4*(5*A - 3*B)*sin(f*x + e) - 12*A + 20*B)*sqrt(-c*sin(f*x + e) + c))/(a*c^3*f*cos(f*x + e)^3 + 2*a*c^3*f*cos(f*x + e)*sin(f*x + e) - 2*a*c^3*f*cos(f*x + e))","A",0
115,1,153,0,1.024433," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, {\left(7 \, A - 38 \, B\right)} c^{4} \cos\left(f x + e\right)^{4} - 12 \, {\left(154 \, A - 311 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} + 24 \, {\left(287 \, A - 543 \, B\right)} c^{4} + {\left(15 \, B c^{4} \cos\left(f x + e\right)^{4} + 4 \, {\left(49 \, A - 136 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} + 8 \, {\left(931 \, A - 1699 \, B\right)} c^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{105 \, {\left(a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"2/105*(3*(7*A - 38*B)*c^4*cos(f*x + e)^4 - 12*(154*A - 311*B)*c^4*cos(f*x + e)^2 + 24*(287*A - 543*B)*c^4 + (15*B*c^4*cos(f*x + e)^4 + 4*(49*A - 136*B)*c^4*cos(f*x + e)^2 + 8*(931*A - 1699*B)*c^4)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f*cos(f*x + e))","A",0
116,1,133,0,0.830761," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, B c^{3} \cos\left(f x + e\right)^{4} + 3 \, {\left(25 \, A - 63 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 12 \, {\left(25 \, A - 57 \, B\right)} c^{3} - {\left({\left(5 \, A - 23 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(85 \, A - 181 \, B\right)} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, {\left(a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"-2/15*(3*B*c^3*cos(f*x + e)^4 + 3*(25*A - 63*B)*c^3*cos(f*x + e)^2 - 12*(25*A - 57*B)*c^3 - ((5*A - 23*B)*c^3*cos(f*x + e)^2 + 4*(85*A - 181*B)*c^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f*cos(f*x + e))","A",0
117,1,110,0,0.679120," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, {\left(A - 4 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(7 \, A - 23 \, B\right)} c^{2} + {\left(B c^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(9 \, A - 25 \, B\right)} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, {\left(a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"-2/3*(3*(A - 4*B)*c^2*cos(f*x + e)^2 - 2*(7*A - 23*B)*c^2 + (B*c^2*cos(f*x + e)^2 - 2*(9*A - 25*B)*c^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f*cos(f*x + e))","A",0
118,1,80,0,0.954698," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B c \cos\left(f x + e\right)^{2} + 3 \, {\left(A - 5 \, B\right)} c \sin\left(f x + e\right) + {\left(A - 13 \, B\right)} c\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, {\left(a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"2/3*(3*B*c*cos(f*x + e)^2 + 3*(A - 5*B)*c*sin(f*x + e) + (A - 13*B)*c)*sqrt(-c*sin(f*x + e) + c)/(a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f*cos(f*x + e))","A",0
119,1,60,0,0.868579," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(3 \, B \sin\left(f x + e\right) + A + 2 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, {\left(a^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} f \cos\left(f x + e\right)\right)}}"," ",0,"-2/3*(3*B*sin(f*x + e) + A + 2*B)*sqrt(-c*sin(f*x + e) + c)/(a^2*f*cos(f*x + e)*sin(f*x + e) + a^2*f*cos(f*x + e))","A",0
120,1,217,0,0.796691," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left({\left(A + B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(A + B\right)} \cos\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(3 \, {\left(A + B\right)} \sin\left(f x + e\right) + 5 \, A + B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{24 \, {\left(a^{2} c f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} c f \cos\left(f x + e\right)\right)}}"," ",0,"1/24*(3*sqrt(2)*((A + B)*cos(f*x + e)*sin(f*x + e) + (A + B)*cos(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(3*(A + B)*sin(f*x + e) + 5*A + B)*sqrt(-c*sin(f*x + e) + c))/(a^2*c*f*cos(f*x + e)*sin(f*x + e) + a^2*c*f*cos(f*x + e))","A",0
121,1,206,0,0.831757," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{3 \, \sqrt{2} {\left(5 \, A + B\right)} \sqrt{c} \cos\left(f x + e\right)^{3} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(3 \, {\left(5 \, A + B\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, A + B\right)} \sin\left(f x + e\right) - 2 \, A - 10 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{96 \, a^{2} c^{2} f \cos\left(f x + e\right)^{3}}"," ",0,"1/96*(3*sqrt(2)*(5*A + B)*sqrt(c)*cos(f*x + e)^3*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(3*(5*A + B)*cos(f*x + e)^2 - 2*(5*A + B)*sin(f*x + e) - 2*A - 10*B)*sqrt(-c*sin(f*x + e) + c))/(a^2*c^2*f*cos(f*x + e)^3)","A",0
122,1,279,0,0.949456," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{15 \, \sqrt{2} {\left({\left(7 \, A - B\right)} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - {\left(7 \, A - B\right)} \cos\left(f x + e\right)^{3}\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(5 \, {\left(7 \, A - B\right)} \cos\left(f x + e\right)^{2} - {\left(15 \, {\left(7 \, A - B\right)} \cos\left(f x + e\right)^{2} + 56 \, A - 8 \, B\right)} \sin\left(f x + e\right) + 8 \, A - 56 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{768 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - a^{2} c^{3} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"-1/768*(15*sqrt(2)*((7*A - B)*cos(f*x + e)^3*sin(f*x + e) - (7*A - B)*cos(f*x + e)^3)*sqrt(c)*log(-(c*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(5*(7*A - B)*cos(f*x + e)^2 - (15*(7*A - B)*cos(f*x + e)^2 + 56*A - 8*B)*sin(f*x + e) + 8*A - 56*B)*sqrt(-c*sin(f*x + e) + c))/(a^2*c^3*f*cos(f*x + e)^3*sin(f*x + e) - a^2*c^3*f*cos(f*x + e)^3)","A",0
123,1,166,0,0.974278," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(5 \, {\left(A - 6 \, B\right)} c^{4} \cos\left(f x + e\right)^{4} + 20 \, {\left(34 \, A - 99 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} - 8 \, {\left(131 \, A - 387 \, B\right)} c^{4} + {\left(3 \, B c^{4} \cos\left(f x + e\right)^{4} + 4 \, {\left(25 \, A - 84 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} - 8 \, {\left(125 \, A - 381 \, B\right)} c^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} - 2 \, a^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"-2/15*(5*(A - 6*B)*c^4*cos(f*x + e)^4 + 20*(34*A - 99*B)*c^4*cos(f*x + e)^2 - 8*(131*A - 387*B)*c^4 + (3*B*c^4*cos(f*x + e)^4 + 4*(25*A - 84*B)*c^4*cos(f*x + e)^2 - 8*(125*A - 381*B)*c^4)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(a^3*f*cos(f*x + e)^3 - 2*a^3*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*f*cos(f*x + e))","A",0
124,1,148,0,0.849762," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B c^{3} \cos\left(f x + e\right)^{4} - 5 \, {\left(27 \, A - 109 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(51 \, A - 211 \, B\right)} c^{3} - 5 \, {\left({\left(3 \, A - 17 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(9 \, A - 41 \, B\right)} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} - 2 \, a^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"2/15*(5*B*c^3*cos(f*x + e)^4 - 5*(27*A - 109*B)*c^3*cos(f*x + e)^2 + 4*(51*A - 211*B)*c^3 - 5*((3*A - 17*B)*c^3*cos(f*x + e)^2 - 4*(9*A - 41*B)*c^3)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(a^3*f*cos(f*x + e)^3 - 2*a^3*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*f*cos(f*x + e))","A",0
125,1,125,0,0.808370," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, {\left(A - 8 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(11 \, A - 91 \, B\right)} c^{2} - 5 \, {\left(3 \, B c^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(A - 17 \, B\right)} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} - 2 \, a^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"-2/15*(15*(A - 8*B)*c^2*cos(f*x + e)^2 - 2*(11*A - 91*B)*c^2 - 5*(3*B*c^2*cos(f*x + e)^2 + 2*(A - 17*B)*c^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/(a^3*f*cos(f*x + e)^3 - 2*a^3*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*f*cos(f*x + e))","A",0
126,1,95,0,0.772778," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B c \cos\left(f x + e\right)^{2} - 5 \, {\left(A + 3 \, B\right)} c \sin\left(f x + e\right) + {\left(A - 21 \, B\right)} c\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} - 2 \, a^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"2/15*(15*B*c*cos(f*x + e)^2 - 5*(A + 3*B)*c*sin(f*x + e) + (A - 21*B)*c)*sqrt(-c*sin(f*x + e) + c)/(a^3*f*cos(f*x + e)^3 - 2*a^3*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*f*cos(f*x + e))","A",0
127,1,77,0,0.573589," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(5 \, B \sin\left(f x + e\right) + 3 \, A + 2 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} - 2 \, a^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"2/15*(5*B*sin(f*x + e) + 3*A + 2*B)*sqrt(-c*sin(f*x + e) + c)/(a^3*f*cos(f*x + e)^3 - 2*a^3*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*f*cos(f*x + e))","A",0
128,1,262,0,0.898898," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(A + B\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(A + B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, {\left(A + B\right)} \cos\left(f x + e\right)\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(15 \, {\left(A + B\right)} \cos\left(f x + e\right)^{2} - 40 \, {\left(A + B\right)} \sin\left(f x + e\right) - 52 \, A - 28 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{240 \, {\left(a^{3} c f \cos\left(f x + e\right)^{3} - 2 \, a^{3} c f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} c f \cos\left(f x + e\right)\right)}}"," ",0,"1/240*(15*sqrt(2)*((A + B)*cos(f*x + e)^3 - 2*(A + B)*cos(f*x + e)*sin(f*x + e) - 2*(A + B)*cos(f*x + e))*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(15*(A + B)*cos(f*x + e)^2 - 40*(A + B)*sin(f*x + e) - 52*A - 28*B)*sqrt(-c*sin(f*x + e) + c))/(a^3*c*f*cos(f*x + e)^3 - 2*a^3*c*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*c*f*cos(f*x + e))","A",0
129,1,277,0,0.977624," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left({\left(7 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + {\left(7 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{3}\right)} \sqrt{c} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(25 \, {\left(7 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(7 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{2} - 28 \, A - 12 \, B\right)} \sin\left(f x + e\right) - 36 \, A - 84 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{960 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + a^{3} c^{2} f \cos\left(f x + e\right)^{3}\right)}}"," ",0,"1/960*(15*sqrt(2)*((7*A + 3*B)*cos(f*x + e)^3*sin(f*x + e) + (7*A + 3*B)*cos(f*x + e)^3)*sqrt(c)*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(25*(7*A + 3*B)*cos(f*x + e)^2 + 3*(5*(7*A + 3*B)*cos(f*x + e)^2 - 28*A - 12*B)*sin(f*x + e) - 36*A - 84*B)*sqrt(-c*sin(f*x + e) + c))/(a^3*c^2*f*cos(f*x + e)^3*sin(f*x + e) + a^3*c^2*f*cos(f*x + e)^3)","A",0
130,1,238,0,1.029890," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{105 \, \sqrt{2} {\left(9 \, A + B\right)} \sqrt{c} \cos\left(f x + e\right)^{5} \log\left(-\frac{c \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{-c \sin\left(f x + e\right) + c} \sqrt{c} {\left(\cos\left(f x + e\right) + \sin\left(f x + e\right) + 1\right)} + 3 \, c \cos\left(f x + e\right) + {\left(c \cos\left(f x + e\right) - 2 \, c\right)} \sin\left(f x + e\right) + 2 \, c}{\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) - 4 \, {\left(105 \, {\left(9 \, A + B\right)} \cos\left(f x + e\right)^{4} - 14 \, {\left(9 \, A + B\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(35 \, {\left(9 \, A + B\right)} \cos\left(f x + e\right)^{2} + 216 \, A + 24 \, B\right)} \sin\left(f x + e\right) - 48 \, A - 432 \, B\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{7680 \, a^{3} c^{3} f \cos\left(f x + e\right)^{5}}"," ",0,"1/7680*(105*sqrt(2)*(9*A + B)*sqrt(c)*cos(f*x + e)^5*log(-(c*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(-c*sin(f*x + e) + c)*sqrt(c)*(cos(f*x + e) + sin(f*x + e) + 1) + 3*c*cos(f*x + e) + (c*cos(f*x + e) - 2*c)*sin(f*x + e) + 2*c)/(cos(f*x + e)^2 + (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(105*(9*A + B)*cos(f*x + e)^4 - 14*(9*A + B)*cos(f*x + e)^2 - 2*(35*(9*A + B)*cos(f*x + e)^2 + 216*A + 24*B)*sin(f*x + e) - 48*A - 432*B)*sqrt(-c*sin(f*x + e) + c))/(a^3*c^3*f*cos(f*x + e)^5)","A",0
131,1,140,0,1.058338," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(5 \, {\left(A - 3 \, B\right)} c^{3} \cos\left(f x + e\right)^{4} - 40 \, {\left(A - B\right)} c^{3} \cos\left(f x + e\right)^{2} + 5 \, {\left(7 \, A - 5 \, B\right)} c^{3} + 4 \, {\left(B c^{3} \cos\left(f x + e\right)^{4} + {\left(5 \, A - 7 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, A - 3 \, B\right)} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{20 \, f \cos\left(f x + e\right)}"," ",0,"-1/20*(5*(A - 3*B)*c^3*cos(f*x + e)^4 - 40*(A - B)*c^3*cos(f*x + e)^2 + 5*(7*A - 5*B)*c^3 + 4*(B*c^3*cos(f*x + e)^4 + (5*A - 7*B)*c^3*cos(f*x + e)^2 - 2*(5*A - 3*B)*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
132,1,121,0,0.739063," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B c^{2} \cos\left(f x + e\right)^{4} + 12 \, {\left(A - B\right)} c^{2} \cos\left(f x + e\right)^{2} - 3 \, {\left(4 \, A - 3 \, B\right)} c^{2} - 4 \, {\left({\left(A - 2 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(2 \, A - B\right)} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{12 \, f \cos\left(f x + e\right)}"," ",0,"1/12*(3*B*c^2*cos(f*x + e)^4 + 12*(A - B)*c^2*cos(f*x + e)^2 - 3*(4*A - 3*B)*c^2 - 4*((A - 2*B)*c^2*cos(f*x + e)^2 - 2*(2*A - B)*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
133,1,92,0,0.918167," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(A - B\right)} c \cos\left(f x + e\right)^{2} - 3 \, {\left(A - B\right)} c + 2 \, {\left(B c \cos\left(f x + e\right)^{2} + {\left(3 \, A - B\right)} c\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{6 \, f \cos\left(f x + e\right)}"," ",0,"1/6*(3*(A - B)*c*cos(f*x + e)^2 - 3*(A - B)*c + 2*(B*c*cos(f*x + e)^2 + (3*A - B)*c)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
134,1,61,0,1.015443," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(B \cos\left(f x + e\right)^{2} - 2 \, A \sin\left(f x + e\right) - B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, f \cos\left(f x + e\right)}"," ",0,"-1/2*(B*cos(f*x + e)^2 - 2*A*sin(f*x + e) - B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
135,0,0,0,1.764994," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*sin(f*x + e) - c), x)","F",0
136,0,0,0,2.342782," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
137,1,87,0,0.884967," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(2 \, B \sin\left(f x + e\right) + A - B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, {\left(c^{3} f \cos\left(f x + e\right)^{3} + 2 \, c^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, c^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"-1/2*(2*B*sin(f*x + e) + A - B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^3*f*cos(f*x + e)^3 + 2*c^3*f*cos(f*x + e)*sin(f*x + e) - 2*c^3*f*cos(f*x + e))","A",0
138,1,106,0,0.862836," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, B \sin\left(f x + e\right) + 2 \, A - B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{6 \, {\left(3 \, c^{4} f \cos\left(f x + e\right)^{3} - 4 \, c^{4} f \cos\left(f x + e\right) - {\left(c^{4} f \cos\left(f x + e\right)^{3} - 4 \, c^{4} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/6*(3*B*sin(f*x + e) + 2*A - B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^4*f*cos(f*x + e)^3 - 4*c^4*f*cos(f*x + e) - (c^4*f*cos(f*x + e)^3 - 4*c^4*f*cos(f*x + e))*sin(f*x + e))","A",0
139,1,148,0,0.614215," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(5 \, B a c^{3} \cos\left(f x + e\right)^{6} + 15 \, {\left(A - B\right)} a c^{3} \cos\left(f x + e\right)^{4} - 5 \, {\left(3 \, A - 2 \, B\right)} a c^{3} - 2 \, {\left(3 \, {\left(A - 2 \, B\right)} a c^{3} \cos\left(f x + e\right)^{4} - 2 \, {\left(3 \, A - B\right)} a c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(3 \, A - B\right)} a c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, f \cos\left(f x + e\right)}"," ",0,"1/30*(5*B*a*c^3*cos(f*x + e)^6 + 15*(A - B)*a*c^3*cos(f*x + e)^4 - 5*(3*A - 2*B)*a*c^3 - 2*(3*(A - 2*B)*a*c^3*cos(f*x + e)^4 - 2*(3*A - B)*a*c^3*cos(f*x + e)^2 - 4*(3*A - B)*a*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
140,1,126,0,0.794621," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(15 \, {\left(A - B\right)} a c^{2} \cos\left(f x + e\right)^{4} - 15 \, {\left(A - B\right)} a c^{2} + 4 \, {\left(3 \, B a c^{2} \cos\left(f x + e\right)^{4} + {\left(5 \, A - B\right)} a c^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, A - B\right)} a c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{60 \, f \cos\left(f x + e\right)}"," ",0,"1/60*(15*(A - B)*a*c^2*cos(f*x + e)^4 - 15*(A - B)*a*c^2 + 4*(3*B*a*c^2*cos(f*x + e)^4 + (5*A - B)*a*c^2*cos(f*x + e)^2 + 2*(5*A - B)*a*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
141,1,83,0,1.017430," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, B a c \cos\left(f x + e\right)^{4} - 3 \, B a c - 4 \, {\left(A a c \cos\left(f x + e\right)^{2} + 2 \, A a c\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{12 \, f \cos\left(f x + e\right)}"," ",0,"-1/12*(3*B*a*c*cos(f*x + e)^4 - 3*B*a*c - 4*(A*a*c*cos(f*x + e)^2 + 2*A*a*c)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
142,1,87,0,0.979206," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, {\left(A + B\right)} a \cos\left(f x + e\right)^{2} - 3 \, {\left(A + B\right)} a + 2 \, {\left(B a \cos\left(f x + e\right)^{2} - {\left(3 \, A + B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{6 \, f \cos\left(f x + e\right)}"," ",0,"-1/6*(3*(A + B)*a*cos(f*x + e)^2 - 3*(A + B)*a + 2*(B*a*cos(f*x + e)^2 - (3*A + B)*a)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
143,0,0,0,5.599662," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B a \cos\left(f x + e\right)^{2} - {\left(A + B\right)} a \sin\left(f x + e\right) - {\left(A + B\right)} a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral((B*a*cos(f*x + e)^2 - (A + B)*a*sin(f*x + e) - (A + B)*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*sin(f*x + e) - c), x)","F",0
144,0,0,0,11.952203," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B a \cos\left(f x + e\right)^{2} - {\left(A + B\right)} a \sin\left(f x + e\right) - {\left(A + B\right)} a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral((B*a*cos(f*x + e)^2 - (A + B)*a*sin(f*x + e) - (A + B)*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
145,0,0,0,5.959066," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B a \cos\left(f x + e\right)^{2} - {\left(A + B\right)} a \sin\left(f x + e\right) - {\left(A + B\right)} a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((B*a*cos(f*x + e)^2 - (A + B)*a*sin(f*x + e) - (A + B)*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
146,1,125,0,0.874837," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(6 \, B a \cos\left(f x + e\right)^{2} - 3 \, {\left(A - B\right)} a \sin\left(f x + e\right) - {\left(A + 7 \, B\right)} a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{6 \, {\left(3 \, c^{4} f \cos\left(f x + e\right)^{3} - 4 \, c^{4} f \cos\left(f x + e\right) - {\left(c^{4} f \cos\left(f x + e\right)^{3} - 4 \, c^{4} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/6*(6*B*a*cos(f*x + e)^2 - 3*(A - B)*a*sin(f*x + e) - (A + 7*B)*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^4*f*cos(f*x + e)^3 - 4*c^4*f*cos(f*x + e) - (c^4*f*cos(f*x + e)^3 - 4*c^4*f*cos(f*x + e))*sin(f*x + e))","A",0
147,1,134,0,0.654158," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, B a \cos\left(f x + e\right)^{2} - 2 \, A a \sin\left(f x + e\right) - {\left(A + 3 \, B\right)} a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{6 \, {\left(c^{5} f \cos\left(f x + e\right)^{5} - 8 \, c^{5} f \cos\left(f x + e\right)^{3} + 8 \, c^{5} f \cos\left(f x + e\right) + 4 \, {\left(c^{5} f \cos\left(f x + e\right)^{3} - 2 \, c^{5} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/6*(3*B*a*cos(f*x + e)^2 - 2*A*a*sin(f*x + e) - (A + 3*B)*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^5*f*cos(f*x + e)^5 - 8*c^5*f*cos(f*x + e)^3 + 8*c^5*f*cos(f*x + e) + 4*(c^5*f*cos(f*x + e)^3 - 2*c^5*f*cos(f*x + e))*sin(f*x + e))","A",0
148,1,155,0,0.856189," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x, algorithm=""fricas"")","-\frac{{\left(20 \, B a \cos\left(f x + e\right)^{2} - 5 \, {\left(3 \, A + B\right)} a \sin\left(f x + e\right) - {\left(9 \, A + 19 \, B\right)} a\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{60 \, {\left(5 \, c^{6} f \cos\left(f x + e\right)^{5} - 20 \, c^{6} f \cos\left(f x + e\right)^{3} + 16 \, c^{6} f \cos\left(f x + e\right) - {\left(c^{6} f \cos\left(f x + e\right)^{5} - 12 \, c^{6} f \cos\left(f x + e\right)^{3} + 16 \, c^{6} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/60*(20*B*a*cos(f*x + e)^2 - 5*(3*A + B)*a*sin(f*x + e) - (9*A + 19*B)*a)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^6*f*cos(f*x + e)^5 - 20*c^6*f*cos(f*x + e)^3 + 16*c^6*f*cos(f*x + e) - (c^6*f*cos(f*x + e)^5 - 12*c^6*f*cos(f*x + e)^3 + 16*c^6*f*cos(f*x + e))*sin(f*x + e))","A",0
149,1,160,0,0.816731," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","\frac{{\left(35 \, {\left(A - B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{6} - 35 \, {\left(A - B\right)} a^{2} c^{3} + 2 \, {\left(15 \, B a^{2} c^{3} \cos\left(f x + e\right)^{6} + 3 \, {\left(7 \, A - B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{4} + 4 \, {\left(7 \, A - B\right)} a^{2} c^{3} \cos\left(f x + e\right)^{2} + 8 \, {\left(7 \, A - B\right)} a^{2} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{210 \, f \cos\left(f x + e\right)}"," ",0,"1/210*(35*(A - B)*a^2*c^3*cos(f*x + e)^6 - 35*(A - B)*a^2*c^3 + 2*(15*B*a^2*c^3*cos(f*x + e)^6 + 3*(7*A - B)*a^2*c^3*cos(f*x + e)^4 + 4*(7*A - B)*a^2*c^3*cos(f*x + e)^2 + 8*(7*A - B)*a^2*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
150,1,117,0,0.913367," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(5 \, B a^{2} c^{2} \cos\left(f x + e\right)^{6} - 5 \, B a^{2} c^{2} - 2 \, {\left(3 \, A a^{2} c^{2} \cos\left(f x + e\right)^{4} + 4 \, A a^{2} c^{2} \cos\left(f x + e\right)^{2} + 8 \, A a^{2} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, f \cos\left(f x + e\right)}"," ",0,"-1/30*(5*B*a^2*c^2*cos(f*x + e)^6 - 5*B*a^2*c^2 - 2*(3*A*a^2*c^2*cos(f*x + e)^4 + 4*A*a^2*c^2*cos(f*x + e)^2 + 8*A*a^2*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
151,1,119,0,0.751907," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{{\left(15 \, {\left(A + B\right)} a^{2} c \cos\left(f x + e\right)^{4} - 15 \, {\left(A + B\right)} a^{2} c + 4 \, {\left(3 \, B a^{2} c \cos\left(f x + e\right)^{4} - {\left(5 \, A + B\right)} a^{2} c \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, A + B\right)} a^{2} c\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{60 \, f \cos\left(f x + e\right)}"," ",0,"-1/60*(15*(A + B)*a^2*c*cos(f*x + e)^4 - 15*(A + B)*a^2*c + 4*(3*B*a^2*c*cos(f*x + e)^4 - (5*A + B)*a^2*c*cos(f*x + e)^2 - 2*(5*A + B)*a^2*c)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
152,1,117,0,0.901213," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(3 \, B a^{2} \cos\left(f x + e\right)^{4} - 12 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right)^{2} + 3 \, {\left(4 \, A + 3 \, B\right)} a^{2} - 4 \, {\left({\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(2 \, A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{12 \, f \cos\left(f x + e\right)}"," ",0,"1/12*(3*B*a^2*cos(f*x + e)^4 - 12*(A + B)*a^2*cos(f*x + e)^2 + 3*(4*A + 3*B)*a^2 - 4*((A + 2*B)*a^2*cos(f*x + e)^2 - 2*(2*A + B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
153,0,0,0,9.263655," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2} + {\left(B a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(((A + 2*B)*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2 + (B*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*sin(f*x + e) - c), x)","F",0
154,0,0,0,22.897896," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2} + {\left(B a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(((A + 2*B)*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2 + (B*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
155,0,0,0,1.768905," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2} + {\left(B a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(((A + 2*B)*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2 + (B*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
156,0,0,0,8.457114," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2} + {\left(B a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-((A + 2*B)*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2 + (B*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
157,1,165,0,0.566411," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, {\left(A - B\right)} a^{2} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - B\right)} a^{2} + 2 \, {\left(3 \, B a^{2} \cos\left(f x + e\right)^{2} - {\left(A + 5 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{6 \, {\left(c^{5} f \cos\left(f x + e\right)^{5} - 8 \, c^{5} f \cos\left(f x + e\right)^{3} + 8 \, c^{5} f \cos\left(f x + e\right) + 4 \, {\left(c^{5} f \cos\left(f x + e\right)^{3} - 2 \, c^{5} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/6*(3*(A - B)*a^2*cos(f*x + e)^2 - 4*(A - B)*a^2 + 2*(3*B*a^2*cos(f*x + e)^2 - (A + 5*B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^5*f*cos(f*x + e)^5 - 8*c^5*f*cos(f*x + e)^3 + 8*c^5*f*cos(f*x + e) + 4*(c^5*f*cos(f*x + e)^3 - 2*c^5*f*cos(f*x + e))*sin(f*x + e))","A",0
158,1,182,0,0.775830," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x, algorithm=""fricas"")","-\frac{{\left(5 \, {\left(2 \, A + B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(7 \, A + 2 \, B\right)} a^{2} + 5 \, {\left(3 \, B a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + 2 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, {\left(5 \, c^{6} f \cos\left(f x + e\right)^{5} - 20 \, c^{6} f \cos\left(f x + e\right)^{3} + 16 \, c^{6} f \cos\left(f x + e\right) - {\left(c^{6} f \cos\left(f x + e\right)^{5} - 12 \, c^{6} f \cos\left(f x + e\right)^{3} + 16 \, c^{6} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/30*(5*(2*A + B)*a^2*cos(f*x + e)^2 - 2*(7*A + 2*B)*a^2 + 5*(3*B*a^2*cos(f*x + e)^2 - 2*(A + 2*B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^6*f*cos(f*x + e)^5 - 20*c^6*f*cos(f*x + e)^3 + 16*c^6*f*cos(f*x + e) - (c^6*f*cos(f*x + e)^5 - 12*c^6*f*cos(f*x + e)^3 + 16*c^6*f*cos(f*x + e))*sin(f*x + e))","A",0
159,1,196,0,0.667567," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(13/2),x, algorithm=""fricas"")","\frac{{\left(15 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(11 \, A + 7 \, B\right)} a^{2} + 2 \, {\left(10 \, B a^{2} \cos\left(f x + e\right)^{2} - {\left(9 \, A + 13 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{60 \, {\left(c^{7} f \cos\left(f x + e\right)^{7} - 18 \, c^{7} f \cos\left(f x + e\right)^{5} + 48 \, c^{7} f \cos\left(f x + e\right)^{3} - 32 \, c^{7} f \cos\left(f x + e\right) + 2 \, {\left(3 \, c^{7} f \cos\left(f x + e\right)^{5} - 16 \, c^{7} f \cos\left(f x + e\right)^{3} + 16 \, c^{7} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/60*(15*(A + B)*a^2*cos(f*x + e)^2 - 2*(11*A + 7*B)*a^2 + 2*(10*B*a^2*cos(f*x + e)^2 - (9*A + 13*B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^7*f*cos(f*x + e)^7 - 18*c^7*f*cos(f*x + e)^5 + 48*c^7*f*cos(f*x + e)^3 - 32*c^7*f*cos(f*x + e) + 2*(3*c^7*f*cos(f*x + e)^5 - 16*c^7*f*cos(f*x + e)^3 + 16*c^7*f*cos(f*x + e))*sin(f*x + e))","A",0
160,1,183,0,0.722275," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","\frac{{\left(315 \, {\left(A - B\right)} a^{3} c^{4} \cos\left(f x + e\right)^{8} - 315 \, {\left(A - B\right)} a^{3} c^{4} + 8 \, {\left(35 \, B a^{3} c^{4} \cos\left(f x + e\right)^{8} + 5 \, {\left(9 \, A - B\right)} a^{3} c^{4} \cos\left(f x + e\right)^{6} + 6 \, {\left(9 \, A - B\right)} a^{3} c^{4} \cos\left(f x + e\right)^{4} + 8 \, {\left(9 \, A - B\right)} a^{3} c^{4} \cos\left(f x + e\right)^{2} + 16 \, {\left(9 \, A - B\right)} a^{3} c^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2520 \, f \cos\left(f x + e\right)}"," ",0,"1/2520*(315*(A - B)*a^3*c^4*cos(f*x + e)^8 - 315*(A - B)*a^3*c^4 + 8*(35*B*a^3*c^4*cos(f*x + e)^8 + 5*(9*A - B)*a^3*c^4*cos(f*x + e)^6 + 6*(9*A - B)*a^3*c^4*cos(f*x + e)^4 + 8*(9*A - B)*a^3*c^4*cos(f*x + e)^2 + 16*(9*A - B)*a^3*c^4)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
161,1,134,0,0.694458," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","-\frac{{\left(35 \, B a^{3} c^{3} \cos\left(f x + e\right)^{8} - 35 \, B a^{3} c^{3} - 8 \, {\left(5 \, A a^{3} c^{3} \cos\left(f x + e\right)^{6} + 6 \, A a^{3} c^{3} \cos\left(f x + e\right)^{4} + 8 \, A a^{3} c^{3} \cos\left(f x + e\right)^{2} + 16 \, A a^{3} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{280 \, f \cos\left(f x + e\right)}"," ",0,"-1/280*(35*B*a^3*c^3*cos(f*x + e)^8 - 35*B*a^3*c^3 - 8*(5*A*a^3*c^3*cos(f*x + e)^6 + 6*A*a^3*c^3*cos(f*x + e)^4 + 8*A*a^3*c^3*cos(f*x + e)^2 + 16*A*a^3*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
162,1,150,0,0.774273," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{{\left(35 \, {\left(A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{6} - 35 \, {\left(A + B\right)} a^{3} c^{2} + 2 \, {\left(15 \, B a^{3} c^{2} \cos\left(f x + e\right)^{6} - 3 \, {\left(7 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{4} - 4 \, {\left(7 \, A + B\right)} a^{3} c^{2} \cos\left(f x + e\right)^{2} - 8 \, {\left(7 \, A + B\right)} a^{3} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{210 \, f \cos\left(f x + e\right)}"," ",0,"-1/210*(35*(A + B)*a^3*c^2*cos(f*x + e)^6 - 35*(A + B)*a^3*c^2 + 2*(15*B*a^3*c^2*cos(f*x + e)^6 - 3*(7*A + B)*a^3*c^2*cos(f*x + e)^4 - 4*(7*A + B)*a^3*c^2*cos(f*x + e)^2 - 8*(7*A + B)*a^3*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
163,1,142,0,0.637357," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{{\left(5 \, B a^{3} c \cos\left(f x + e\right)^{6} - 15 \, {\left(A + B\right)} a^{3} c \cos\left(f x + e\right)^{4} + 5 \, {\left(3 \, A + 2 \, B\right)} a^{3} c - 2 \, {\left(3 \, {\left(A + 2 \, B\right)} a^{3} c \cos\left(f x + e\right)^{4} - 2 \, {\left(3 \, A + B\right)} a^{3} c \cos\left(f x + e\right)^{2} - 4 \, {\left(3 \, A + B\right)} a^{3} c\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, f \cos\left(f x + e\right)}"," ",0,"1/30*(5*B*a^3*c*cos(f*x + e)^6 - 15*(A + B)*a^3*c*cos(f*x + e)^4 + 5*(3*A + 2*B)*a^3*c - 2*(3*(A + 2*B)*a^3*c*cos(f*x + e)^4 - 2*(3*A + B)*a^3*c*cos(f*x + e)^2 - 4*(3*A + B)*a^3*c)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
164,1,139,0,0.778495," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{{\left(5 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{4} - 40 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right)^{2} + 5 \, {\left(7 \, A + 5 \, B\right)} a^{3} + 4 \, {\left(B a^{3} \cos\left(f x + e\right)^{4} - {\left(5 \, A + 7 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, A + 3 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{20 \, f \cos\left(f x + e\right)}"," ",0,"1/20*(5*(A + 3*B)*a^3*cos(f*x + e)^4 - 40*(A + B)*a^3*cos(f*x + e)^2 + 5*(7*A + 5*B)*a^3 + 4*(B*a^3*cos(f*x + e)^4 - (5*A + 7*B)*a^3*cos(f*x + e)^2 + 2*(5*A + 3*B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(f*cos(f*x + e))","A",0
165,0,0,0,1.905093," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B a^{3} \cos\left(f x + e\right)^{4} - {\left(3 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(A + B\right)} a^{3} - {\left({\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(B*a^3*cos(f*x + e)^4 - (3*A + 5*B)*a^3*cos(f*x + e)^2 + 4*(A + B)*a^3 - ((A + 3*B)*a^3*cos(f*x + e)^2 - 4*(A + B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c*sin(f*x + e) - c), x)","F",0
166,0,0,0,1.777612," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B a^{3} \cos\left(f x + e\right)^{4} - {\left(3 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(A + B\right)} a^{3} - {\left({\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-(B*a^3*cos(f*x + e)^4 - (3*A + 5*B)*a^3*cos(f*x + e)^2 + 4*(A + B)*a^3 - ((A + 3*B)*a^3*cos(f*x + e)^2 - 4*(A + B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
167,0,0,0,38.518452," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B a^{3} \cos\left(f x + e\right)^{4} - {\left(3 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(A + B\right)} a^{3} - {\left({\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(B*a^3*cos(f*x + e)^4 - (3*A + 5*B)*a^3*cos(f*x + e)^2 + 4*(A + B)*a^3 - ((A + 3*B)*a^3*cos(f*x + e)^2 - 4*(A + B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
168,0,0,0,66.147786," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B a^{3} \cos\left(f x + e\right)^{4} - {\left(3 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(A + B\right)} a^{3} - {\left({\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{c^{4} \cos\left(f x + e\right)^{4} - 8 \, c^{4} \cos\left(f x + e\right)^{2} + 8 \, c^{4} + 4 \, {\left(c^{4} \cos\left(f x + e\right)^{2} - 2 \, c^{4}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((B*a^3*cos(f*x + e)^4 - (3*A + 5*B)*a^3*cos(f*x + e)^2 + 4*(A + B)*a^3 - ((A + 3*B)*a^3*cos(f*x + e)^2 - 4*(A + B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^4*cos(f*x + e)^4 - 8*c^4*cos(f*x + e)^2 + 8*c^4 + 4*(c^4*cos(f*x + e)^2 - 2*c^4)*sin(f*x + e)), x)","F",0
169,0,0,0,1.487138," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B a^{3} \cos\left(f x + e\right)^{4} - {\left(3 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(A + B\right)} a^{3} - {\left({\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A + B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{5 \, c^{5} \cos\left(f x + e\right)^{4} - 20 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5} - {\left(c^{5} \cos\left(f x + e\right)^{4} - 12 \, c^{5} \cos\left(f x + e\right)^{2} + 16 \, c^{5}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((B*a^3*cos(f*x + e)^4 - (3*A + 5*B)*a^3*cos(f*x + e)^2 + 4*(A + B)*a^3 - ((A + 3*B)*a^3*cos(f*x + e)^2 - 4*(A + B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^5*cos(f*x + e)^4 - 20*c^5*cos(f*x + e)^2 + 16*c^5 - (c^5*cos(f*x + e)^4 - 12*c^5*cos(f*x + e)^2 + 16*c^5)*sin(f*x + e)), x)","F",0
170,1,199,0,0.649364," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(11/2),x, algorithm=""fricas"")","\frac{{\left(10 \, B a^{3} \cos\left(f x + e\right)^{4} - 5 \, {\left(A + 7 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, A + 13 \, B\right)} a^{3} - 5 \, {\left({\left(A - B\right)} a^{3} \cos\left(f x + e\right)^{2} - 2 \, {\left(A - B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{10 \, {\left(5 \, c^{6} f \cos\left(f x + e\right)^{5} - 20 \, c^{6} f \cos\left(f x + e\right)^{3} + 16 \, c^{6} f \cos\left(f x + e\right) - {\left(c^{6} f \cos\left(f x + e\right)^{5} - 12 \, c^{6} f \cos\left(f x + e\right)^{3} + 16 \, c^{6} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/10*(10*B*a^3*cos(f*x + e)^4 - 5*(A + 7*B)*a^3*cos(f*x + e)^2 + 2*(3*A + 13*B)*a^3 - 5*((A - B)*a^3*cos(f*x + e)^2 - 2*(A - B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(5*c^6*f*cos(f*x + e)^5 - 20*c^6*f*cos(f*x + e)^3 + 16*c^6*f*cos(f*x + e) - (c^6*f*cos(f*x + e)^5 - 12*c^6*f*cos(f*x + e)^3 + 16*c^6*f*cos(f*x + e))*sin(f*x + e))","B",0
171,1,214,0,0.717291," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(13/2),x, algorithm=""fricas"")","-\frac{{\left(15 \, B a^{3} \cos\left(f x + e\right)^{4} - 15 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 6 \, {\left(3 \, A + 5 \, B\right)} a^{3} - 2 \, {\left(5 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right)^{2} - {\left(11 \, A + 5 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{30 \, {\left(c^{7} f \cos\left(f x + e\right)^{7} - 18 \, c^{7} f \cos\left(f x + e\right)^{5} + 48 \, c^{7} f \cos\left(f x + e\right)^{3} - 32 \, c^{7} f \cos\left(f x + e\right) + 2 \, {\left(3 \, c^{7} f \cos\left(f x + e\right)^{5} - 16 \, c^{7} f \cos\left(f x + e\right)^{3} + 16 \, c^{7} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/30*(15*B*a^3*cos(f*x + e)^4 - 15*(A + 3*B)*a^3*cos(f*x + e)^2 + 6*(3*A + 5*B)*a^3 - 2*(5*(A + B)*a^3*cos(f*x + e)^2 - (11*A + 5*B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^7*f*cos(f*x + e)^7 - 18*c^7*f*cos(f*x + e)^5 + 48*c^7*f*cos(f*x + e)^3 - 32*c^7*f*cos(f*x + e) + 2*(3*c^7*f*cos(f*x + e)^5 - 16*c^7*f*cos(f*x + e)^3 + 16*c^7*f*cos(f*x + e))*sin(f*x + e))","A",0
172,1,234,0,0.845777," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(15/2),x, algorithm=""fricas"")","-\frac{{\left(140 \, B a^{3} \cos\left(f x + e\right)^{4} - 7 \, {\left(27 \, A + 61 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(57 \, A + 71 \, B\right)} a^{3} - 7 \, {\left(5 \, {\left(3 \, A + 5 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(9 \, A + 7 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{420 \, {\left(7 \, c^{8} f \cos\left(f x + e\right)^{7} - 56 \, c^{8} f \cos\left(f x + e\right)^{5} + 112 \, c^{8} f \cos\left(f x + e\right)^{3} - 64 \, c^{8} f \cos\left(f x + e\right) - {\left(c^{8} f \cos\left(f x + e\right)^{7} - 24 \, c^{8} f \cos\left(f x + e\right)^{5} + 80 \, c^{8} f \cos\left(f x + e\right)^{3} - 64 \, c^{8} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/420*(140*B*a^3*cos(f*x + e)^4 - 7*(27*A + 61*B)*a^3*cos(f*x + e)^2 + 4*(57*A + 71*B)*a^3 - 7*(5*(3*A + 5*B)*a^3*cos(f*x + e)^2 - 4*(9*A + 7*B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(7*c^8*f*cos(f*x + e)^7 - 56*c^8*f*cos(f*x + e)^5 + 112*c^8*f*cos(f*x + e)^3 - 64*c^8*f*cos(f*x + e) - (c^8*f*cos(f*x + e)^7 - 24*c^8*f*cos(f*x + e)^5 + 80*c^8*f*cos(f*x + e)^3 - 64*c^8*f*cos(f*x + e))*sin(f*x + e))","A",0
173,1,243,0,0.804594," ","integrate((a+a*sin(f*x+e))^(7/2)*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(17/2),x, algorithm=""fricas"")","\frac{{\left(35 \, B a^{3} \cos\left(f x + e\right)^{4} - 56 \, {\left(A + 2 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} + 4 \, {\left(17 \, A + 19 \, B\right)} a^{3} - 4 \, {\left(7 \, {\left(A + 2 \, B\right)} a^{3} \cos\left(f x + e\right)^{2} - 2 \, {\left(9 \, A + 8 \, B\right)} a^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{140 \, {\left(c^{9} f \cos\left(f x + e\right)^{9} - 32 \, c^{9} f \cos\left(f x + e\right)^{7} + 160 \, c^{9} f \cos\left(f x + e\right)^{5} - 256 \, c^{9} f \cos\left(f x + e\right)^{3} + 128 \, c^{9} f \cos\left(f x + e\right) + 8 \, {\left(c^{9} f \cos\left(f x + e\right)^{7} - 10 \, c^{9} f \cos\left(f x + e\right)^{5} + 24 \, c^{9} f \cos\left(f x + e\right)^{3} - 16 \, c^{9} f \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/140*(35*B*a^3*cos(f*x + e)^4 - 56*(A + 2*B)*a^3*cos(f*x + e)^2 + 4*(17*A + 19*B)*a^3 - 4*(7*(A + 2*B)*a^3*cos(f*x + e)^2 - 2*(9*A + 8*B)*a^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(c^9*f*cos(f*x + e)^9 - 32*c^9*f*cos(f*x + e)^7 + 160*c^9*f*cos(f*x + e)^5 - 256*c^9*f*cos(f*x + e)^3 + 128*c^9*f*cos(f*x + e) + 8*(c^9*f*cos(f*x + e)^7 - 10*c^9*f*cos(f*x + e)^5 + 24*c^9*f*cos(f*x + e)^3 - 16*c^9*f*cos(f*x + e))*sin(f*x + e))","A",0
174,0,0,0,6.189487," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A - 2 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A - B\right)} c^{2} + {\left(B c^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(A - B\right)} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a}}, x\right)"," ",0,"integral(-((A - 2*B)*c^2*cos(f*x + e)^2 - 2*(A - B)*c^2 + (B*c^2*cos(f*x + e)^2 + 2*(A - B)*c^2)*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
175,0,0,0,4.199294," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(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\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a}}, x\right)"," ",0,"integral((B*c*cos(f*x + e)^2 - (A - B)*c*sin(f*x + e) + (A - B)*c)*sqrt(-c*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
176,0,0,0,2.300149," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{-c \sin\left(f x + e\right) + c}}{\sqrt{a \sin\left(f x + e\right) + a}}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*sqrt(-c*sin(f*x + e) + c)/sqrt(a*sin(f*x + e) + a), x)","F",0
177,0,0,0,1.938517," ","integrate((A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right)^{2}}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)^2), x)","F",0
178,1,337,0,0.821128," ","integrate((A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(A - B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(A - B\right)} \cos\left(f x + e\right)\right)} \sqrt{a c} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) + 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) + 2 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} {\left(A + B\right)}}{4 \, {\left(a c^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) - a c^{2} f \cos\left(f x + e\right)\right)}}, -\frac{{\left({\left(A - B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(A - B\right)} \cos\left(f x + e\right)\right)} \sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) + \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} {\left(A + B\right)}}{2 \, {\left(a c^{2} f \cos\left(f x + e\right) \sin\left(f x + e\right) - a c^{2} f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*(((A - B)*cos(f*x + e)*sin(f*x + e) - (A - B)*cos(f*x + e))*sqrt(a*c)*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) + 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) + 2*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*(A + B))/(a*c^2*f*cos(f*x + e)*sin(f*x + e) - a*c^2*f*cos(f*x + e)), -1/2*(((A - B)*cos(f*x + e)*sin(f*x + e) - (A - B)*cos(f*x + e))*sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e))) + sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*(A + B))/(a*c^2*f*cos(f*x + e)*sin(f*x + e) - a*c^2*f*cos(f*x + e))]","A",0
179,1,424,0,0.774545," ","integrate((A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(A - B\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(A - B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, {\left(A - B\right)} \cos\left(f x + e\right)\right)} \sqrt{a c} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) + 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) - 2 \, {\left({\left(A - B\right)} \sin\left(f x + e\right) - 2 \, A\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{8 \, {\left(a c^{3} f \cos\left(f x + e\right)^{3} + 2 \, a c^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a c^{3} f \cos\left(f x + e\right)\right)}}, -\frac{{\left({\left(A - B\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(A - B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, {\left(A - B\right)} \cos\left(f x + e\right)\right)} \sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) - {\left({\left(A - B\right)} \sin\left(f x + e\right) - 2 \, A\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{4 \, {\left(a c^{3} f \cos\left(f x + e\right)^{3} + 2 \, a c^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a c^{3} f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[-1/8*(((A - B)*cos(f*x + e)^3 + 2*(A - B)*cos(f*x + e)*sin(f*x + e) - 2*(A - B)*cos(f*x + e))*sqrt(a*c)*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) + 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) - 2*((A - B)*sin(f*x + e) - 2*A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a*c^3*f*cos(f*x + e)^3 + 2*a*c^3*f*cos(f*x + e)*sin(f*x + e) - 2*a*c^3*f*cos(f*x + e)), -1/4*(((A - B)*cos(f*x + e)^3 + 2*(A - B)*cos(f*x + e)*sin(f*x + e) - 2*(A - B)*cos(f*x + e))*sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e))) - ((A - B)*sin(f*x + e) - 2*A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a*c^3*f*cos(f*x + e)^3 + 2*a*c^3*f*cos(f*x + e)*sin(f*x + e) - 2*a*c^3*f*cos(f*x + e))]","A",0
180,0,0,0,23.632484," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c^{3} \cos\left(f x + e\right)^{4} + {\left(3 \, A - 5 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - B\right)} c^{3} - {\left({\left(A - 3 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - B\right)} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral((B*c^3*cos(f*x + e)^4 + (3*A - 5*B)*c^3*cos(f*x + e)^2 - 4*(A - B)*c^3 - ((A - 3*B)*c^3*cos(f*x + e)^2 - 4*(A - B)*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
181,0,0,0,14.971818," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - 2 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A - B\right)} c^{2} + {\left(B c^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(A - B\right)} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(((A - 2*B)*c^2*cos(f*x + e)^2 - 2*(A - B)*c^2 + (B*c^2*cos(f*x + e)^2 + 2*(A - B)*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
182,0,0,0,1.481037," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(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\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(B*c*cos(f*x + e)^2 - (A - B)*c*sin(f*x + e) + (A - B)*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
183,0,0,0,1.815063," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
184,1,329,0,0.753371," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(A + B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(A + B\right)} \cos\left(f x + e\right)\right)} \sqrt{a c} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) - 2 \, \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} {\left(A - B\right)}}{4 \, {\left(a^{2} c f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} c f \cos\left(f x + e\right)\right)}}, -\frac{{\left({\left(A + B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(A + B\right)} \cos\left(f x + e\right)\right)} \sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) + \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} {\left(A - B\right)}}{2 \, {\left(a^{2} c f \cos\left(f x + e\right) \sin\left(f x + e\right) + a^{2} c f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(((A + B)*cos(f*x + e)*sin(f*x + e) + (A + B)*cos(f*x + e))*sqrt(a*c)*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) - 2*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*(A - B))/(a^2*c*f*cos(f*x + e)*sin(f*x + e) + a^2*c*f*cos(f*x + e)), -1/2*(((A + B)*cos(f*x + e)*sin(f*x + e) + (A + B)*cos(f*x + e))*sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e))) + sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*(A - B))/(a^2*c*f*cos(f*x + e)*sin(f*x + e) + a^2*c*f*cos(f*x + e))]","A",0
185,1,272,0,0.859972," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c} A \cos\left(f x + e\right)^{3} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) + 2 \, {\left(A \sin\left(f x + e\right) + B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{4 \, a^{2} c^{2} f \cos\left(f x + e\right)^{3}}, -\frac{\sqrt{-a c} A \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) \cos\left(f x + e\right)^{3} - {\left(A \sin\left(f x + e\right) + B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, a^{2} c^{2} f \cos\left(f x + e\right)^{3}}\right]"," ",0,"[1/4*(sqrt(a*c)*A*cos(f*x + e)^3*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) + 2*(A*sin(f*x + e) + B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^2*c^2*f*cos(f*x + e)^3), -1/2*(sqrt(-a*c)*A*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e)))*cos(f*x + e)^3 - (A*sin(f*x + e) + B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^2*c^2*f*cos(f*x + e)^3)]","A",0
186,1,437,0,0.773174," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, A - B\right)} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - {\left(3 \, A - B\right)} \cos\left(f x + e\right)^{3}\right)} \sqrt{a c} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) + 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) + 2 \, {\left({\left(3 \, A - B\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, A - B\right)} \sin\left(f x + e\right) - A + 3 \, B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{16 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - a^{2} c^{3} f \cos\left(f x + e\right)^{3}\right)}}, -\frac{{\left({\left(3 \, A - B\right)} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - {\left(3 \, A - B\right)} \cos\left(f x + e\right)^{3}\right)} \sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) + {\left({\left(3 \, A - B\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, A - B\right)} \sin\left(f x + e\right) - A + 3 \, B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{8 \, {\left(a^{2} c^{3} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) - a^{2} c^{3} f \cos\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[-1/16*(((3*A - B)*cos(f*x + e)^3*sin(f*x + e) - (3*A - B)*cos(f*x + e)^3)*sqrt(a*c)*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) + 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) + 2*((3*A - B)*cos(f*x + e)^2 + (3*A - B)*sin(f*x + e) - A + 3*B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^2*c^3*f*cos(f*x + e)^3*sin(f*x + e) - a^2*c^3*f*cos(f*x + e)^3), -1/8*(((3*A - B)*cos(f*x + e)^3*sin(f*x + e) - (3*A - B)*cos(f*x + e)^3)*sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e))) + ((3*A - B)*cos(f*x + e)^2 + (3*A - B)*sin(f*x + e) - A + 3*B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^2*c^3*f*cos(f*x + e)^3*sin(f*x + e) - a^2*c^3*f*cos(f*x + e)^3)]","A",0
187,0,0,0,68.398380," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(9/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left({\left(A - 4 \, B\right)} c^{4} \cos\left(f x + e\right)^{4} - 4 \, {\left(2 \, A - 3 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} + 8 \, {\left(A - B\right)} c^{4} + {\left(B c^{4} \cos\left(f x + e\right)^{4} + 4 \, {\left(A - 2 \, B\right)} c^{4} \cos\left(f x + e\right)^{2} - 8 \, {\left(A - B\right)} c^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-((A - 4*B)*c^4*cos(f*x + e)^4 - 4*(2*A - 3*B)*c^4*cos(f*x + e)^2 + 8*(A - B)*c^4 + (B*c^4*cos(f*x + e)^4 + 4*(A - 2*B)*c^4*cos(f*x + e)^2 - 8*(A - B)*c^4)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
188,0,0,0,1.886704," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(7/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B c^{3} \cos\left(f x + e\right)^{4} + {\left(3 \, A - 5 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - B\right)} c^{3} - {\left({\left(A - 3 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - B\right)} c^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((B*c^3*cos(f*x + e)^4 + (3*A - 5*B)*c^3*cos(f*x + e)^2 - 4*(A - B)*c^3 - ((A - 3*B)*c^3*cos(f*x + e)^2 - 4*(A - B)*c^3)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
189,0,0,0,2.200209," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left({\left(A - 2 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A - B\right)} c^{2} + {\left(B c^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(A - B\right)} c^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(((A - 2*B)*c^2*cos(f*x + e)^2 - 2*(A - B)*c^2 + (B*c^2*cos(f*x + e)^2 + 2*(A - B)*c^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
190,0,0,0,4.566207," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(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\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{3 \, a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3} + {\left(a^{3} \cos\left(f x + e\right)^{2} - 4 \, a^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(B*c*cos(f*x + e)^2 - (A - B)*c*sin(f*x + e) + (A - B)*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(3*a^3*cos(f*x + e)^2 - 4*a^3 + (a^3*cos(f*x + e)^2 - 4*a^3)*sin(f*x + e)), x)","F",0
191,1,85,0,0.815457," ","integrate((A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2)/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{{\left(2 \, B \sin\left(f x + e\right) + A + B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{2 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} - 2 \, a^{3} f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} f \cos\left(f x + e\right)\right)}}"," ",0,"1/2*(2*B*sin(f*x + e) + A + B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a^3*f*cos(f*x + e)^3 - 2*a^3*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*f*cos(f*x + e))","A",0
192,1,408,0,0.891668," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(A + B\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(A + B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, {\left(A + B\right)} \cos\left(f x + e\right)\right)} \sqrt{a c} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) + 2 \, {\left({\left(A + B\right)} \sin\left(f x + e\right) + 2 \, A\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{8 \, {\left(a^{3} c f \cos\left(f x + e\right)^{3} - 2 \, a^{3} c f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} c f \cos\left(f x + e\right)\right)}}, -\frac{{\left({\left(A + B\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(A + B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, {\left(A + B\right)} \cos\left(f x + e\right)\right)} \sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) - {\left({\left(A + B\right)} \sin\left(f x + e\right) + 2 \, A\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{4 \, {\left(a^{3} c f \cos\left(f x + e\right)^{3} - 2 \, a^{3} c f \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, a^{3} c f \cos\left(f x + e\right)\right)}}\right]"," ",0,"[1/8*(((A + B)*cos(f*x + e)^3 - 2*(A + B)*cos(f*x + e)*sin(f*x + e) - 2*(A + B)*cos(f*x + e))*sqrt(a*c)*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) + 2*((A + B)*sin(f*x + e) + 2*A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^3*c*f*cos(f*x + e)^3 - 2*a^3*c*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*c*f*cos(f*x + e)), -1/4*(((A + B)*cos(f*x + e)^3 - 2*(A + B)*cos(f*x + e)*sin(f*x + e) - 2*(A + B)*cos(f*x + e))*sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e))) - ((A + B)*sin(f*x + e) + 2*A)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^3*c*f*cos(f*x + e)^3 - 2*a^3*c*f*cos(f*x + e)*sin(f*x + e) - 2*a^3*c*f*cos(f*x + e))]","A",0
193,1,419,0,0.976094," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(3 \, A + B\right)} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + {\left(3 \, A + B\right)} \cos\left(f x + e\right)^{3}\right)} \sqrt{a c} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) - 2 \, {\left({\left(3 \, A + B\right)} \cos\left(f x + e\right)^{2} - {\left(3 \, A + B\right)} \sin\left(f x + e\right) - A - 3 \, B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{16 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + a^{3} c^{2} f \cos\left(f x + e\right)^{3}\right)}}, -\frac{{\left({\left(3 \, A + B\right)} \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + {\left(3 \, A + B\right)} \cos\left(f x + e\right)^{3}\right)} \sqrt{-a c} \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) + {\left({\left(3 \, A + B\right)} \cos\left(f x + e\right)^{2} - {\left(3 \, A + B\right)} \sin\left(f x + e\right) - A - 3 \, B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{8 \, {\left(a^{3} c^{2} f \cos\left(f x + e\right)^{3} \sin\left(f x + e\right) + a^{3} c^{2} f \cos\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[1/16*(((3*A + B)*cos(f*x + e)^3*sin(f*x + e) + (3*A + B)*cos(f*x + e)^3)*sqrt(a*c)*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) - 2*((3*A + B)*cos(f*x + e)^2 - (3*A + B)*sin(f*x + e) - A - 3*B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^3*c^2*f*cos(f*x + e)^3*sin(f*x + e) + a^3*c^2*f*cos(f*x + e)^3), -1/8*(((3*A + B)*cos(f*x + e)^3*sin(f*x + e) + (3*A + B)*cos(f*x + e)^3)*sqrt(-a*c)*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e))) + ((3*A + B)*cos(f*x + e)^2 - (3*A + B)*sin(f*x + e) - A - 3*B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^3*c^2*f*cos(f*x + e)^3*sin(f*x + e) + a^3*c^2*f*cos(f*x + e)^3)]","A",0
194,1,306,0,0.924259," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{a c} A \cos\left(f x + e\right)^{5} \log\left(-\frac{a c \cos\left(f x + e\right)^{3} - 2 \, a c \cos\left(f x + e\right) - 2 \, \sqrt{a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c} \sin\left(f x + e\right)}{\cos\left(f x + e\right)^{3}}\right) + 2 \, {\left({\left(3 \, A \cos\left(f x + e\right)^{2} + 2 \, A\right)} \sin\left(f x + e\right) + 2 \, B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{16 \, a^{3} c^{3} f \cos\left(f x + e\right)^{5}}, -\frac{3 \, \sqrt{-a c} A \arctan\left(\frac{\sqrt{-a c} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{a c \cos\left(f x + e\right) \sin\left(f x + e\right)}\right) \cos\left(f x + e\right)^{5} - {\left({\left(3 \, A \cos\left(f x + e\right)^{2} + 2 \, A\right)} \sin\left(f x + e\right) + 2 \, B\right)} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{-c \sin\left(f x + e\right) + c}}{8 \, a^{3} c^{3} f \cos\left(f x + e\right)^{5}}\right]"," ",0,"[1/16*(3*sqrt(a*c)*A*cos(f*x + e)^5*log(-(a*c*cos(f*x + e)^3 - 2*a*c*cos(f*x + e) - 2*sqrt(a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)*sin(f*x + e))/cos(f*x + e)^3) + 2*((3*A*cos(f*x + e)^2 + 2*A)*sin(f*x + e) + 2*B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^3*c^3*f*cos(f*x + e)^5), -1/8*(3*sqrt(-a*c)*A*arctan(sqrt(-a*c)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c)/(a*c*cos(f*x + e)*sin(f*x + e)))*cos(f*x + e)^5 - ((3*A*cos(f*x + e)^2 + 2*A)*sin(f*x + e) + 2*B)*sqrt(a*sin(f*x + e) + a)*sqrt(-c*sin(f*x + e) + c))/(a^3*c^3*f*cos(f*x + e)^5)]","A",0
195,0,0,0,0.758967," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\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)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n, x)","F",0
196,0,0,0,0.783832," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(B c^{3} \cos\left(f x + e\right)^{4} + {\left(3 \, A - 5 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - B\right)} c^{3} - {\left({\left(A - 3 \, B\right)} c^{3} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - B\right)} c^{3}\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(B*c^3*cos(f*x + e)^4 + (3*A - 5*B)*c^3*cos(f*x + e)^2 - 4*(A - B)*c^3 - ((A - 3*B)*c^3*cos(f*x + e)^2 - 4*(A - B)*c^3)*sin(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
197,0,0,0,0.676075," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-{\left({\left(A - 2 \, B\right)} c^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A - B\right)} c^{2} + {\left(B c^{2} \cos\left(f x + e\right)^{2} + 2 \, {\left(A - B\right)} c^{2}\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-((A - 2*B)*c^2*cos(f*x + e)^2 - 2*(A - B)*c^2 + (B*c^2*cos(f*x + e)^2 + 2*(A - B)*c^2)*sin(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
198,0,0,0,0.824929," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(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\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*c*cos(f*x + e)^2 - (A - B)*c*sin(f*x + e) + (A - B)*c)*(a*sin(f*x + e) + a)^m, x)","F",0
199,0,0,0,0.859721," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m, x)","F",0
200,0,0,0,0.649654," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
201,0,0,0,1.012691," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
202,0,0,0,0.718879," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
203,0,0,0,0.739188," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
204,0,0,0,0.648971," ","integrate((A+B*sin(f*x+e))*(c+c*sin(f*x+e))^m/(a-a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{-a \sin\left(f x + e\right) + a} {\left(c \sin\left(f x + e\right) + c\right)}^{m}}{a \sin\left(f x + e\right) - a}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(-a*sin(f*x + e) + a)*(c*sin(f*x + e) + c)^m/(a*sin(f*x + e) - a), x)","F",0
205,1,562,0,0.719562," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(8 \, B c^{2} m^{3} + 36 \, B c^{2} m^{2} + 46 \, B c^{2} m + 15 \, B c^{2}\right)} \cos\left(f x + e\right)^{4} + 64 \, {\left(A + B\right)} c^{2} m - {\left(8 \, {\left(A - 2 \, B\right)} c^{2} m^{3} + 4 \, {\left(11 \, A - 28 \, B\right)} c^{2} m^{2} + 2 \, {\left(31 \, A - 86 \, B\right)} c^{2} m + 3 \, {\left(7 \, A - 20 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)^{3} + 32 \, {\left(7 \, A - 5 \, B\right)} c^{2} + {\left(8 \, {\left(A - B\right)} c^{2} m^{3} + 4 \, {\left(19 \, A - 11 \, B\right)} c^{2} m^{2} + 190 \, {\left(A - B\right)} c^{2} m + {\left(77 \, A - 85 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(8 \, {\left(A - B\right)} c^{2} m^{3} + 60 \, {\left(A - B\right)} c^{2} m^{2} + 2 \, {\left(79 \, A - 63 \, B\right)} c^{2} m + {\left(161 \, A - 145 \, B\right)} c^{2}\right)} \cos\left(f x + e\right) + {\left(64 \, {\left(A + B\right)} c^{2} m - {\left(8 \, B c^{2} m^{3} + 36 \, B c^{2} m^{2} + 46 \, B c^{2} m + 15 \, B c^{2}\right)} \cos\left(f x + e\right)^{3} + 32 \, {\left(7 \, A - 5 \, B\right)} c^{2} - {\left(8 \, {\left(A - B\right)} c^{2} m^{3} + 4 \, {\left(11 \, A - 19 \, B\right)} c^{2} m^{2} + 2 \, {\left(31 \, A - 63 \, B\right)} c^{2} m + 3 \, {\left(7 \, A - 15 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(8 \, {\left(A - B\right)} c^{2} m^{3} + 60 \, {\left(A - B\right)} c^{2} m^{2} + 2 \, {\left(63 \, A - 79 \, B\right)} c^{2} m + {\left(49 \, A - 65 \, B\right)} c^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + {\left(16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + 105 \, f\right)} \cos\left(f x + e\right) - {\left(16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + 105 \, f\right)} \sin\left(f x + e\right) + 105 \, f}"," ",0,"2*((8*B*c^2*m^3 + 36*B*c^2*m^2 + 46*B*c^2*m + 15*B*c^2)*cos(f*x + e)^4 + 64*(A + B)*c^2*m - (8*(A - 2*B)*c^2*m^3 + 4*(11*A - 28*B)*c^2*m^2 + 2*(31*A - 86*B)*c^2*m + 3*(7*A - 20*B)*c^2)*cos(f*x + e)^3 + 32*(7*A - 5*B)*c^2 + (8*(A - B)*c^2*m^3 + 4*(19*A - 11*B)*c^2*m^2 + 190*(A - B)*c^2*m + (77*A - 85*B)*c^2)*cos(f*x + e)^2 + 2*(8*(A - B)*c^2*m^3 + 60*(A - B)*c^2*m^2 + 2*(79*A - 63*B)*c^2*m + (161*A - 145*B)*c^2)*cos(f*x + e) + (64*(A + B)*c^2*m - (8*B*c^2*m^3 + 36*B*c^2*m^2 + 46*B*c^2*m + 15*B*c^2)*cos(f*x + e)^3 + 32*(7*A - 5*B)*c^2 - (8*(A - B)*c^2*m^3 + 4*(11*A - 19*B)*c^2*m^2 + 2*(31*A - 63*B)*c^2*m + 3*(7*A - 15*B)*c^2)*cos(f*x + e)^2 - 2*(8*(A - B)*c^2*m^3 + 60*(A - B)*c^2*m^2 + 2*(63*A - 79*B)*c^2*m + (49*A - 65*B)*c^2)*cos(f*x + e))*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + (16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + 105*f)*cos(f*x + e) - (16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + 105*f)*sin(f*x + e) + 105*f)","B",0
206,1,313,0,0.814395," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left({\left(4 \, B c m^{2} + 8 \, B c m + 3 \, B c\right)} \cos\left(f x + e\right)^{3} + 8 \, {\left(A + B\right)} c m + {\left(4 \, A c m^{2} + 12 \, {\left(A - B\right)} c m + {\left(5 \, A - 6 \, B\right)} c\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(5 \, A - 3 \, B\right)} c + {\left(4 \, {\left(A - B\right)} c m^{2} + 4 \, {\left(5 \, A - 3 \, B\right)} c m + {\left(25 \, A - 21 \, B\right)} c\right)} \cos\left(f x + e\right) + {\left(8 \, {\left(A + B\right)} c m + {\left(4 \, B c m^{2} + 8 \, B c m + 3 \, B c\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(5 \, A - 3 \, B\right)} c - {\left(4 \, {\left(A - B\right)} c m^{2} + 4 \, {\left(3 \, A - 5 \, B\right)} c m + {\left(5 \, A - 9 \, B\right)} c\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + {\left(8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f\right)} \cos\left(f x + e\right) - {\left(8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f\right)} \sin\left(f x + e\right) + 15 \, f}"," ",0,"2*((4*B*c*m^2 + 8*B*c*m + 3*B*c)*cos(f*x + e)^3 + 8*(A + B)*c*m + (4*A*c*m^2 + 12*(A - B)*c*m + (5*A - 6*B)*c)*cos(f*x + e)^2 + 4*(5*A - 3*B)*c + (4*(A - B)*c*m^2 + 4*(5*A - 3*B)*c*m + (25*A - 21*B)*c)*cos(f*x + e) + (8*(A + B)*c*m + (4*B*c*m^2 + 8*B*c*m + 3*B*c)*cos(f*x + e)^2 + 4*(5*A - 3*B)*c - (4*(A - B)*c*m^2 + 4*(3*A - 5*B)*c*m + (5*A - 9*B)*c)*cos(f*x + e))*sin(f*x + e))*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(8*f*m^3 + 36*f*m^2 + 46*f*m + (8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)*cos(f*x + e) - (8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)*sin(f*x + e) + 15*f)","A",0
207,1,165,0,0.836577," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(2 \, B m + B\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} m - {\left(2 \, A m + 3 \, A - 2 \, B\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(A + B\right)} m + {\left(2 \, B m + B\right)} \cos\left(f x + e\right) + 3 \, A - B\right)} \sin\left(f x + e\right) - 3 \, A + B\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{4 \, f m^{2} + 8 \, f m + {\left(4 \, f m^{2} + 8 \, f m + 3 \, f\right)} \cos\left(f x + e\right) - {\left(4 \, f m^{2} + 8 \, f m + 3 \, f\right)} \sin\left(f x + e\right) + 3 \, f}"," ",0,"-2*((2*B*m + B)*cos(f*x + e)^2 - 2*(A + B)*m - (2*A*m + 3*A - 2*B)*cos(f*x + e) - (2*(A + B)*m + (2*B*m + B)*cos(f*x + e) + 3*A - B)*sin(f*x + e) - 3*A + B)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(4*f*m^2 + 8*f*m + (4*f*m^2 + 8*f*m + 3*f)*cos(f*x + e) - (4*f*m^2 + 8*f*m + 3*f)*sin(f*x + e) + 3*f)","A",0
208,0,0,0,0.782034," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c \sin\left(f x + e\right) - c}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(c*sin(f*x + e) - c), x)","F",0
209,0,0,0,0.690934," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{c^{2} \cos\left(f x + e\right)^{2} + 2 \, c^{2} \sin\left(f x + e\right) - 2 \, c^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(c^2*cos(f*x + e)^2 + 2*c^2*sin(f*x + e) - 2*c^2), x)","F",0
210,0,0,0,0.666355," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c-c*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{-c \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{3 \, c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3} - {\left(c^{3} \cos\left(f x + e\right)^{2} - 4 \, c^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(-c*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(3*c^3*cos(f*x + e)^2 - 4*c^3 - (c^3*cos(f*x + e)^2 - 4*c^3)*sin(f*x + e)), x)","F",0
211,1,205,0,0.729680," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-4-m),x, algorithm=""fricas"")","\frac{{\left(4 \, {\left(2 \, B m^{2} - {\left(3 \, A - 8 \, B\right)} m - 6 \, A + 8 \, B\right)} \cos\left(f x + e\right)^{3} + {\left(8 \, A m^{3} + 12 \, {\left(4 \, A - B\right)} m^{2} + 2 \, {\left(47 \, A - 24 \, B\right)} m + 60 \, A - 45 \, B\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(2 \, B m - 3 \, A + 4 \, B\right)} \cos\left(f x + e\right)^{3} - {\left(8 \, B m^{3} - 12 \, {\left(A - 4 \, B\right)} m^{2} - 2 \, {\left(24 \, A - 47 \, B\right)} m - 45 \, A + 60 \, B\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 4}}{16 \, f m^{4} + 128 \, f m^{3} + 344 \, f m^{2} + 352 \, f m + 105 \, f}"," ",0,"(4*(2*B*m^2 - (3*A - 8*B)*m - 6*A + 8*B)*cos(f*x + e)^3 + (8*A*m^3 + 12*(4*A - B)*m^2 + 2*(47*A - 24*B)*m + 60*A - 45*B)*cos(f*x + e) - (2*(2*B*m - 3*A + 4*B)*cos(f*x + e)^3 - (8*B*m^3 - 12*(A - 4*B)*m^2 - 2*(24*A - 47*B)*m - 45*A + 60*B)*cos(f*x + e))*sin(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 4)/(16*f*m^4 + 128*f*m^3 + 344*f*m^2 + 352*f*m + 105*f)","A",0
212,1,137,0,0.684047," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-3-m),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, B m - 2 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{3} + {\left(4 \, B m^{2} - 4 \, {\left(A - 3 \, B\right)} m - 6 \, A + 9 \, B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(4 \, A m^{2} + 4 \, {\left(3 \, A - B\right)} m + 9 \, A - 6 \, B\right)} \cos\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 3}}{8 \, f m^{3} + 36 \, f m^{2} + 46 \, f m + 15 \, f}"," ",0,"((2*B*m - 2*A + 3*B)*cos(f*x + e)^3 + (4*B*m^2 - 4*(A - 3*B)*m - 6*A + 9*B)*cos(f*x + e)*sin(f*x + e) + (4*A*m^2 + 4*(3*A - B)*m + 9*A - 6*B)*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 3)/(8*f*m^3 + 36*f*m^2 + 46*f*m + 15*f)","A",0
213,1,89,0,0.576441," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-2-m),x, algorithm=""fricas"")","\frac{{\left({\left(2 \, B m - A + 2 \, B\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(2 \, A m + 2 \, A - B\right)} \cos\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 2}}{4 \, f m^{2} + 8 \, f m + 3 \, f}"," ",0,"((2*B*m - A + 2*B)*cos(f*x + e)*sin(f*x + e) + (2*A*m + 2*A - B)*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 2)/(4*f*m^2 + 8*f*m + 3*f)","A",0
214,0,0,0,0.779375," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(-1-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m - 1}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m - 1), x)","F",0
215,0,0,0,0.627569," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/((c-c*sin(f*x+e))^m),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{{\left(-c \sin\left(f x + e\right) + c\right)}^{m}}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(-c*sin(f*x + e) + c)^m, x)","F",0
216,0,0,0,0.753911," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(1-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 1}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 1), x)","F",0
217,0,0,0,0.837718," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c-c*sin(f*x+e))^(2-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{-m + 2}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^(-m + 2), x)","F",0
218,1,78,0,0.672599," ","integrate((a+a*sin(f*x+e))^3*(c-c*sin(f*x+e))^n*(B*(3-n)-B*(4+n)*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(3 \, B a^{3} \cos\left(f x + e\right)^{3} - 4 \, B a^{3} \cos\left(f x + e\right) + {\left(B a^{3} \cos\left(f x + e\right)^{3} - 4 \, B a^{3} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} {\left(-c \sin\left(f x + e\right) + c\right)}^{n}}{f}"," ",0,"-(3*B*a^3*cos(f*x + e)^3 - 4*B*a^3*cos(f*x + e) + (B*a^3*cos(f*x + e)^3 - 4*B*a^3*cos(f*x + e))*sin(f*x + e))*(-c*sin(f*x + e) + c)^n/f","B",0
219,1,77,0,0.624272," ","integrate((a-a*sin(f*x+e))^3*(c+c*sin(f*x+e))^n*(B*(3-n)+B*(4+n)*sin(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(3 \, B a^{3} \cos\left(f x + e\right)^{3} - 4 \, B a^{3} \cos\left(f x + e\right) - {\left(B a^{3} \cos\left(f x + e\right)^{3} - 4 \, B a^{3} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} {\left(c \sin\left(f x + e\right) + c\right)}^{n}}{f}"," ",0,"(3*B*a^3*cos(f*x + e)^3 - 4*B*a^3*cos(f*x + e) - (B*a^3*cos(f*x + e)^3 - 4*B*a^3*cos(f*x + e))*sin(f*x + e))*(c*sin(f*x + e) + c)^n/f","B",0
220,1,78,0,0.699626," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^3*(B*(-3+m)-B*(4+m)*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(3 \, B c^{3} \cos\left(f x + e\right)^{3} - 4 \, B c^{3} \cos\left(f x + e\right) - {\left(B c^{3} \cos\left(f x + e\right)^{3} - 4 \, B c^{3} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{f}"," ",0,"-(3*B*c^3*cos(f*x + e)^3 - 4*B*c^3*cos(f*x + e) - (B*c^3*cos(f*x + e)^3 - 4*B*c^3*cos(f*x + e))*sin(f*x + e))*(a*sin(f*x + e) + a)^m/f","B",0
221,1,77,0,0.817348," ","integrate((a-a*sin(f*x+e))^m*(c+c*sin(f*x+e))^3*(B*(-3+m)+B*(4+m)*sin(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(3 \, B c^{3} \cos\left(f x + e\right)^{3} - 4 \, B c^{3} \cos\left(f x + e\right) + {\left(B c^{3} \cos\left(f x + e\right)^{3} - 4 \, B c^{3} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} {\left(-a \sin\left(f x + e\right) + a\right)}^{m}}{f}"," ",0,"(3*B*c^3*cos(f*x + e)^3 - 4*B*c^3*cos(f*x + e) + (B*c^3*cos(f*x + e)^3 - 4*B*c^3*cos(f*x + e))*sin(f*x + e))*(-a*sin(f*x + e) + a)^m/f","B",0
222,1,36,0,0.774350," ","integrate((a+a*sin(f*x+e))^m*(c-c*sin(f*x+e))^n*(B*(m-n)-B*(1+m+n)*sin(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(-c \sin\left(f x + e\right) + c\right)}^{n} B \cos\left(f x + e\right)}{f}"," ",0,"(a*sin(f*x + e) + a)^m*(-c*sin(f*x + e) + c)^n*B*cos(f*x + e)/f","A",0
223,1,37,0,0.652844," ","integrate((a-a*sin(f*x+e))^m*(c+c*sin(f*x+e))^n*(B*(m-n)+B*(1+m+n)*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(-a \sin\left(f x + e\right) + a\right)}^{m} {\left(c \sin\left(f x + e\right) + c\right)}^{n} B \cos\left(f x + e\right)}{f}"," ",0,"-(-a*sin(f*x + e) + a)^m*(c*sin(f*x + e) + c)^n*B*cos(f*x + e)/f","A",0
224,1,105,0,0.668331," ","integrate(sin(d*x+c)^3*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{120 \, A a^{3} \cos\left(d x + c\right)^{7} - 504 \, A a^{3} \cos\left(d x + c\right)^{5} + 560 \, A a^{3} \cos\left(d x + c\right)^{3} - 105 \, A a^{3} d x - 35 \, {\left(8 \, A a^{3} \cos\left(d x + c\right)^{5} - 14 \, A a^{3} \cos\left(d x + c\right)^{3} + 3 \, A a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{840 \, d}"," ",0,"-1/840*(120*A*a^3*cos(d*x + c)^7 - 504*A*a^3*cos(d*x + c)^5 + 560*A*a^3*cos(d*x + c)^3 - 105*A*a^3*d*x - 35*(8*A*a^3*cos(d*x + c)^5 - 14*A*a^3*cos(d*x + c)^3 + 3*A*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
225,1,91,0,0.571349," ","integrate(sin(d*x+c)^2*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","\frac{96 \, A a^{3} \cos\left(d x + c\right)^{5} - 160 \, A a^{3} \cos\left(d x + c\right)^{3} + 45 \, A a^{3} d x + 5 \, {\left(8 \, A a^{3} \cos\left(d x + c\right)^{5} - 26 \, A a^{3} \cos\left(d x + c\right)^{3} + 9 \, A a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(96*A*a^3*cos(d*x + c)^5 - 160*A*a^3*cos(d*x + c)^3 + 45*A*a^3*d*x + 5*(8*A*a^3*cos(d*x + c)^5 - 26*A*a^3*cos(d*x + c)^3 + 9*A*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
226,1,77,0,0.696931," ","integrate(sin(d*x+c)*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","\frac{12 \, A a^{3} \cos\left(d x + c\right)^{5} - 40 \, A a^{3} \cos\left(d x + c\right)^{3} + 15 \, A a^{3} d x - 15 \, {\left(2 \, A a^{3} \cos\left(d x + c\right)^{3} - A a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{60 \, d}"," ",0,"1/60*(12*A*a^3*cos(d*x + c)^5 - 40*A*a^3*cos(d*x + c)^3 + 15*A*a^3*d*x - 15*(2*A*a^3*cos(d*x + c)^3 - A*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
227,1,63,0,0.588855," ","integrate((a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{16 \, A a^{3} \cos\left(d x + c\right)^{3} - 15 \, A a^{3} d x + 3 \, {\left(2 \, A a^{3} \cos\left(d x + c\right)^{3} - 5 \, A a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{24 \, d}"," ",0,"-1/24*(16*A*a^3*cos(d*x + c)^3 - 15*A*a^3*d*x + 3*(2*A*a^3*cos(d*x + c)^3 - 5*A*a^3*cos(d*x + c))*sin(d*x + c))/d","A",0
228,1,92,0,0.624532," ","integrate(csc(d*x+c)*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{2 \, A a^{3} \cos\left(d x + c\right)^{3} - 6 \, A a^{3} d x - 6 \, A a^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) - 6 \, A a^{3} \cos\left(d x + c\right) + 3 \, A a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 3 \, A a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{6 \, d}"," ",0,"-1/6*(2*A*a^3*cos(d*x + c)^3 - 6*A*a^3*d*x - 6*A*a^3*cos(d*x + c)*sin(d*x + c) - 6*A*a^3*cos(d*x + c) + 3*A*a^3*log(1/2*cos(d*x + c) + 1/2) - 3*A*a^3*log(-1/2*cos(d*x + c) + 1/2))/d","A",0
229,1,111,0,0.609148," ","integrate(csc(d*x+c)^2*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{A a^{3} \cos\left(d x + c\right)^{3} + 2 \, A a^{3} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 2 \, A a^{3} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + A a^{3} \cos\left(d x + c\right) + {\left(A a^{3} d x - 4 \, A a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{2 \, d \sin\left(d x + c\right)}"," ",0,"-1/2*(A*a^3*cos(d*x + c)^3 + 2*A*a^3*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 2*A*a^3*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + A*a^3*cos(d*x + c) + (A*a^3*d*x - 4*A*a^3*cos(d*x + c))*sin(d*x + c))/(d*sin(d*x + c))","A",0
230,1,152,0,0.839047," ","integrate(csc(d*x+c)^3*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{8 \, A a^{3} d x \cos\left(d x + c\right)^{2} - 4 \, A a^{3} \cos\left(d x + c\right)^{3} - 8 \, A a^{3} d x - 8 \, A a^{3} \cos\left(d x + c\right) \sin\left(d x + c\right) + 2 \, A a^{3} \cos\left(d x + c\right) + {\left(A a^{3} \cos\left(d x + c\right)^{2} - A a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - {\left(A a^{3} \cos\left(d x + c\right)^{2} - A a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{4 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/4*(8*A*a^3*d*x*cos(d*x + c)^2 - 4*A*a^3*cos(d*x + c)^3 - 8*A*a^3*d*x - 8*A*a^3*cos(d*x + c)*sin(d*x + c) + 2*A*a^3*cos(d*x + c) + (A*a^3*cos(d*x + c)^2 - A*a^3)*log(1/2*cos(d*x + c) + 1/2) - (A*a^3*cos(d*x + c)^2 - A*a^3)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^2 - d)","B",0
231,1,175,0,0.532354," ","integrate(csc(d*x+c)^4*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{4 \, A a^{3} \cos\left(d x + c\right)^{3} - 6 \, A a^{3} \cos\left(d x + c\right) - 3 \, {\left(A a^{3} \cos\left(d x + c\right)^{2} - A a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 3 \, {\left(A a^{3} \cos\left(d x + c\right)^{2} - A a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) + 6 \, {\left(A a^{3} d x \cos\left(d x + c\right)^{2} - A a^{3} d x - A a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{6 \, {\left(d \cos\left(d x + c\right)^{2} - d\right)} \sin\left(d x + c\right)}"," ",0,"-1/6*(4*A*a^3*cos(d*x + c)^3 - 6*A*a^3*cos(d*x + c) - 3*(A*a^3*cos(d*x + c)^2 - A*a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 3*(A*a^3*cos(d*x + c)^2 - A*a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) + 6*(A*a^3*d*x*cos(d*x + c)^2 - A*a^3*d*x - A*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^2 - d)*sin(d*x + c))","B",0
232,1,166,0,0.926389," ","integrate(csc(d*x+c)^5*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{32 \, A a^{3} \cos\left(d x + c\right)^{3} \sin\left(d x + c\right) - 18 \, A a^{3} \cos\left(d x + c\right)^{3} + 30 \, A a^{3} \cos\left(d x + c\right) - 15 \, {\left(A a^{3} \cos\left(d x + c\right)^{4} - 2 \, A a^{3} \cos\left(d x + c\right)^{2} + A a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 15 \, {\left(A a^{3} \cos\left(d x + c\right)^{4} - 2 \, A a^{3} \cos\left(d x + c\right)^{2} + A a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right)}{48 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)}}"," ",0,"-1/48*(32*A*a^3*cos(d*x + c)^3*sin(d*x + c) - 18*A*a^3*cos(d*x + c)^3 + 30*A*a^3*cos(d*x + c) - 15*(A*a^3*cos(d*x + c)^4 - 2*A*a^3*cos(d*x + c)^2 + A*a^3)*log(1/2*cos(d*x + c) + 1/2) + 15*(A*a^3*cos(d*x + c)^4 - 2*A*a^3*cos(d*x + c)^2 + A*a^3)*log(-1/2*cos(d*x + c) + 1/2))/(d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)","B",0
233,1,201,0,0.903310," ","integrate(csc(d*x+c)^6*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","\frac{56 \, A a^{3} \cos\left(d x + c\right)^{5} - 80 \, A a^{3} \cos\left(d x + c\right)^{3} + 15 \, {\left(A a^{3} \cos\left(d x + c\right)^{4} - 2 \, A a^{3} \cos\left(d x + c\right)^{2} + A a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 15 \, {\left(A a^{3} \cos\left(d x + c\right)^{4} - 2 \, A a^{3} \cos\left(d x + c\right)^{2} + A a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) \sin\left(d x + c\right) - 30 \, {\left(A a^{3} \cos\left(d x + c\right)^{3} + A a^{3} \cos\left(d x + c\right)\right)} \sin\left(d x + c\right)}{120 \, {\left(d \cos\left(d x + c\right)^{4} - 2 \, d \cos\left(d x + c\right)^{2} + d\right)} \sin\left(d x + c\right)}"," ",0,"1/120*(56*A*a^3*cos(d*x + c)^5 - 80*A*a^3*cos(d*x + c)^3 + 15*(A*a^3*cos(d*x + c)^4 - 2*A*a^3*cos(d*x + c)^2 + A*a^3)*log(1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 15*(A*a^3*cos(d*x + c)^4 - 2*A*a^3*cos(d*x + c)^2 + A*a^3)*log(-1/2*cos(d*x + c) + 1/2)*sin(d*x + c) - 30*(A*a^3*cos(d*x + c)^3 + A*a^3*cos(d*x + c))*sin(d*x + c))/((d*cos(d*x + c)^4 - 2*d*cos(d*x + c)^2 + d)*sin(d*x + c))","B",0
234,1,240,0,0.720535," ","integrate(csc(d*x+c)^7*(a+a*sin(d*x+c))^3*(A-A*sin(d*x+c)),x, algorithm=""fricas"")","-\frac{90 \, A a^{3} \cos\left(d x + c\right)^{5} - 80 \, A a^{3} \cos\left(d x + c\right)^{3} - 90 \, A a^{3} \cos\left(d x + c\right) - 45 \, {\left(A a^{3} \cos\left(d x + c\right)^{6} - 3 \, A a^{3} \cos\left(d x + c\right)^{4} + 3 \, A a^{3} \cos\left(d x + c\right)^{2} - A a^{3}\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 45 \, {\left(A a^{3} \cos\left(d x + c\right)^{6} - 3 \, A a^{3} \cos\left(d x + c\right)^{4} + 3 \, A a^{3} \cos\left(d x + c\right)^{2} - A a^{3}\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 64 \, {\left(2 \, A a^{3} \cos\left(d x + c\right)^{5} - 5 \, A a^{3} \cos\left(d x + c\right)^{3}\right)} \sin\left(d x + c\right)}{480 \, {\left(d \cos\left(d x + c\right)^{6} - 3 \, d \cos\left(d x + c\right)^{4} + 3 \, d \cos\left(d x + c\right)^{2} - d\right)}}"," ",0,"-1/480*(90*A*a^3*cos(d*x + c)^5 - 80*A*a^3*cos(d*x + c)^3 - 90*A*a^3*cos(d*x + c) - 45*(A*a^3*cos(d*x + c)^6 - 3*A*a^3*cos(d*x + c)^4 + 3*A*a^3*cos(d*x + c)^2 - A*a^3)*log(1/2*cos(d*x + c) + 1/2) + 45*(A*a^3*cos(d*x + c)^6 - 3*A*a^3*cos(d*x + c)^4 + 3*A*a^3*cos(d*x + c)^2 - A*a^3)*log(-1/2*cos(d*x + c) + 1/2) + 64*(2*A*a^3*cos(d*x + c)^5 - 5*A*a^3*cos(d*x + c)^3)*sin(d*x + c))/(d*cos(d*x + c)^6 - 3*d*cos(d*x + c)^4 + 3*d*cos(d*x + c)^2 - d)","B",0
235,1,248,0,0.741493," ","integrate(sin(d*x+c)^4*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{15 \, A \cos\left(d x + c\right)^{5} + 90 \, A \cos\left(d x + c\right)^{4} + {\left(285 \, A d x + 683 \, A\right)} \cos\left(d x + c\right)^{3} - 1140 \, A d x + {\left(855 \, A d x - 526 \, A\right)} \cos\left(d x + c\right)^{2} - 6 \, {\left(95 \, A d x + 191 \, A\right)} \cos\left(d x + c\right) - {\left(15 \, A \cos\left(d x + c\right)^{4} - 75 \, A \cos\left(d x + c\right)^{3} + 1140 \, A d x - 19 \, {\left(15 \, A d x - 32 \, A\right)} \cos\left(d x + c\right)^{2} + 6 \, {\left(95 \, A d x + 189 \, A\right)} \cos\left(d x + c\right) - 12 \, A\right)} \sin\left(d x + c\right) - 12 \, A}{30 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/30*(15*A*cos(d*x + c)^5 + 90*A*cos(d*x + c)^4 + (285*A*d*x + 683*A)*cos(d*x + c)^3 - 1140*A*d*x + (855*A*d*x - 526*A)*cos(d*x + c)^2 - 6*(95*A*d*x + 191*A)*cos(d*x + c) - (15*A*cos(d*x + c)^4 - 75*A*cos(d*x + c)^3 + 1140*A*d*x - 19*(15*A*d*x - 32*A)*cos(d*x + c)^2 + 6*(95*A*d*x + 189*A)*cos(d*x + c) - 12*A)*sin(d*x + c) - 12*A)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
236,1,225,0,0.762395," ","integrate(sin(d*x+c)^3*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{15 \, A \cos\left(d x + c\right)^{4} + {\left(60 \, A d x + 149 \, A\right)} \cos\left(d x + c\right)^{3} - 240 \, A d x + {\left(180 \, A d x - 103 \, A\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(40 \, A d x + 81 \, A\right)} \cos\left(d x + c\right) + {\left(15 \, A \cos\left(d x + c\right)^{3} - 240 \, A d x + 2 \, {\left(30 \, A d x - 67 \, A\right)} \cos\left(d x + c\right)^{2} - 3 \, {\left(40 \, A d x + 79 \, A\right)} \cos\left(d x + c\right) + 6 \, A\right)} \sin\left(d x + c\right) - 6 \, A}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/15*(15*A*cos(d*x + c)^4 + (60*A*d*x + 149*A)*cos(d*x + c)^3 - 240*A*d*x + (180*A*d*x - 103*A)*cos(d*x + c)^2 - 3*(40*A*d*x + 81*A)*cos(d*x + c) + (15*A*cos(d*x + c)^3 - 240*A*d*x + 2*(30*A*d*x - 67*A)*cos(d*x + c)^2 - 3*(40*A*d*x + 79*A)*cos(d*x + c) + 6*A)*sin(d*x + c) - 6*A)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
237,1,204,0,0.511187," ","integrate(sin(d*x+c)^2*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","-\frac{{\left(5 \, A d x + 13 \, A\right)} \cos\left(d x + c\right)^{3} - 20 \, A d x + 3 \, {\left(5 \, A d x - 2 \, A\right)} \cos\left(d x + c\right)^{2} - {\left(10 \, A d x + 21 \, A\right)} \cos\left(d x + c\right) - {\left(20 \, A d x - {\left(5 \, A d x - 13 \, A\right)} \cos\left(d x + c\right)^{2} + {\left(10 \, A d x + 19 \, A\right)} \cos\left(d x + c\right) - 2 \, A\right)} \sin\left(d x + c\right) - 2 \, A}{5 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"-1/5*((5*A*d*x + 13*A)*cos(d*x + c)^3 - 20*A*d*x + 3*(5*A*d*x - 2*A)*cos(d*x + c)^2 - (10*A*d*x + 21*A)*cos(d*x + c) - (20*A*d*x - (5*A*d*x - 13*A)*cos(d*x + c)^2 + (10*A*d*x + 19*A)*cos(d*x + c) - 2*A)*sin(d*x + c) - 2*A)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
238,1,156,0,0.764110," ","integrate(sin(d*x+c)*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{4 \, A \cos\left(d x + c\right)^{3} + 7 \, A \cos\left(d x + c\right)^{2} - 3 \, A \cos\left(d x + c\right) - {\left(4 \, A \cos\left(d x + c\right)^{2} - 3 \, A \cos\left(d x + c\right) - 6 \, A\right)} \sin\left(d x + c\right) - 6 \, A}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/15*(4*A*cos(d*x + c)^3 + 7*A*cos(d*x + c)^2 - 3*A*cos(d*x + c) - (4*A*cos(d*x + c)^2 - 3*A*cos(d*x + c) - 6*A)*sin(d*x + c) - 6*A)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
239,1,154,0,0.674844," ","integrate((A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{A \cos\left(d x + c\right)^{3} - 2 \, A \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) - {\left(A \cos\left(d x + c\right)^{2} + 3 \, A \cos\left(d x + c\right) + 6 \, A\right)} \sin\left(d x + c\right) + 6 \, A}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/15*(A*cos(d*x + c)^3 - 2*A*cos(d*x + c)^2 + 3*A*cos(d*x + c) - (A*cos(d*x + c)^2 + 3*A*cos(d*x + c) + 6*A)*sin(d*x + c) + 6*A)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
240,1,310,0,0.701771," ","integrate(csc(d*x+c)*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{16 \, A \cos\left(d x + c\right)^{3} - 22 \, A \cos\left(d x + c\right)^{2} - 42 \, A \cos\left(d x + c\right) - 5 \, {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) - 4 \, A\right)} \sin\left(d x + c\right) - 4 \, A\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 5 \, {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) + {\left(A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) - 4 \, A\right)} \sin\left(d x + c\right) - 4 \, A\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(8 \, A \cos\left(d x + c\right)^{2} + 19 \, A \cos\left(d x + c\right) - 2 \, A\right)} \sin\left(d x + c\right) - 4 \, A}{10 \, {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/10*(16*A*cos(d*x + c)^3 - 22*A*cos(d*x + c)^2 - 42*A*cos(d*x + c) - 5*(A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + (A*cos(d*x + c)^2 - 2*A*cos(d*x + c) - 4*A)*sin(d*x + c) - 4*A)*log(1/2*cos(d*x + c) + 1/2) + 5*(A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 - 2*A*cos(d*x + c) + (A*cos(d*x + c)^2 - 2*A*cos(d*x + c) - 4*A)*sin(d*x + c) - 4*A)*log(-1/2*cos(d*x + c) + 1/2) - 2*(8*A*cos(d*x + c)^2 + 19*A*cos(d*x + c) - 2*A)*sin(d*x + c) - 4*A)/(a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d + (a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
241,1,406,0,0.713433," ","integrate(csc(d*x+c)^2*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{94 \, A \cos\left(d x + c\right)^{4} + 222 \, A \cos\left(d x + c\right)^{3} - 115 \, A \cos\left(d x + c\right)^{2} - 237 \, A \cos\left(d x + c\right) + 30 \, {\left(A \cos\left(d x + c\right)^{4} - 2 \, A \cos\left(d x + c\right)^{3} - 5 \, A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) - {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) - 4 \, A\right)} \sin\left(d x + c\right) + 4 \, A\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 30 \, {\left(A \cos\left(d x + c\right)^{4} - 2 \, A \cos\left(d x + c\right)^{3} - 5 \, A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) - {\left(A \cos\left(d x + c\right)^{3} + 3 \, A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) - 4 \, A\right)} \sin\left(d x + c\right) + 4 \, A\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(94 \, A \cos\left(d x + c\right)^{3} - 128 \, A \cos\left(d x + c\right)^{2} - 243 \, A \cos\left(d x + c\right) - 6 \, A\right)} \sin\left(d x + c\right) + 6 \, A}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{3} - 5 \, a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d \cos\left(d x + c\right) + 4 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right)^{3} + 3 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/15*(94*A*cos(d*x + c)^4 + 222*A*cos(d*x + c)^3 - 115*A*cos(d*x + c)^2 - 237*A*cos(d*x + c) + 30*(A*cos(d*x + c)^4 - 2*A*cos(d*x + c)^3 - 5*A*cos(d*x + c)^2 + 2*A*cos(d*x + c) - (A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 - 2*A*cos(d*x + c) - 4*A)*sin(d*x + c) + 4*A)*log(1/2*cos(d*x + c) + 1/2) - 30*(A*cos(d*x + c)^4 - 2*A*cos(d*x + c)^3 - 5*A*cos(d*x + c)^2 + 2*A*cos(d*x + c) - (A*cos(d*x + c)^3 + 3*A*cos(d*x + c)^2 - 2*A*cos(d*x + c) - 4*A)*sin(d*x + c) + 4*A)*log(-1/2*cos(d*x + c) + 1/2) + (94*A*cos(d*x + c)^3 - 128*A*cos(d*x + c)^2 - 243*A*cos(d*x + c) - 6*A)*sin(d*x + c) + 6*A)/(a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^3 - 5*a^3*d*cos(d*x + c)^2 + 2*a^3*d*cos(d*x + c) + 4*a^3*d - (a^3*d*cos(d*x + c)^3 + 3*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d)*sin(d*x + c))","B",0
242,1,498,0,0.642073," ","integrate(csc(d*x+c)^3*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{896 \, A \cos\left(d x + c\right)^{5} - 1222 \, A \cos\left(d x + c\right)^{4} - 3218 \, A \cos\left(d x + c\right)^{3} + 1168 \, A \cos\left(d x + c\right)^{2} + 2292 \, A \cos\left(d x + c\right) - 285 \, {\left(A \cos\left(d x + c\right)^{5} + 3 \, A \cos\left(d x + c\right)^{4} - 3 \, A \cos\left(d x + c\right)^{3} - 7 \, A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + {\left(A \cos\left(d x + c\right)^{4} - 2 \, A \cos\left(d x + c\right)^{3} - 5 \, A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + 4 \, A\right)} \sin\left(d x + c\right) + 4 \, A\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + 285 \, {\left(A \cos\left(d x + c\right)^{5} + 3 \, A \cos\left(d x + c\right)^{4} - 3 \, A \cos\left(d x + c\right)^{3} - 7 \, A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + {\left(A \cos\left(d x + c\right)^{4} - 2 \, A \cos\left(d x + c\right)^{3} - 5 \, A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + 4 \, A\right)} \sin\left(d x + c\right) + 4 \, A\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 2 \, {\left(448 \, A \cos\left(d x + c\right)^{4} + 1059 \, A \cos\left(d x + c\right)^{3} - 550 \, A \cos\left(d x + c\right)^{2} - 1134 \, A \cos\left(d x + c\right) + 12 \, A\right)} \sin\left(d x + c\right) + 24 \, A}{60 \, {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} - 3 \, a^{3} d \cos\left(d x + c\right)^{3} - 7 \, a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d \cos\left(d x + c\right) + 4 \, a^{3} d + {\left(a^{3} d \cos\left(d x + c\right)^{4} - 2 \, a^{3} d \cos\left(d x + c\right)^{3} - 5 \, a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d \cos\left(d x + c\right) + 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/60*(896*A*cos(d*x + c)^5 - 1222*A*cos(d*x + c)^4 - 3218*A*cos(d*x + c)^3 + 1168*A*cos(d*x + c)^2 + 2292*A*cos(d*x + c) - 285*(A*cos(d*x + c)^5 + 3*A*cos(d*x + c)^4 - 3*A*cos(d*x + c)^3 - 7*A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + (A*cos(d*x + c)^4 - 2*A*cos(d*x + c)^3 - 5*A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + 4*A)*sin(d*x + c) + 4*A)*log(1/2*cos(d*x + c) + 1/2) + 285*(A*cos(d*x + c)^5 + 3*A*cos(d*x + c)^4 - 3*A*cos(d*x + c)^3 - 7*A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + (A*cos(d*x + c)^4 - 2*A*cos(d*x + c)^3 - 5*A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + 4*A)*sin(d*x + c) + 4*A)*log(-1/2*cos(d*x + c) + 1/2) - 2*(448*A*cos(d*x + c)^4 + 1059*A*cos(d*x + c)^3 - 550*A*cos(d*x + c)^2 - 1134*A*cos(d*x + c) + 12*A)*sin(d*x + c) + 24*A)/(a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 - 3*a^3*d*cos(d*x + c)^3 - 7*a^3*d*cos(d*x + c)^2 + 2*a^3*d*cos(d*x + c) + 4*a^3*d + (a^3*d*cos(d*x + c)^4 - 2*a^3*d*cos(d*x + c)^3 - 5*a^3*d*cos(d*x + c)^2 + 2*a^3*d*cos(d*x + c) + 4*a^3*d)*sin(d*x + c))","B",0
243,1,594,0,0.662235," ","integrate(csc(d*x+c)^4*(A-A*sin(d*x+c))/(a+a*sin(d*x+c))^3,x, algorithm=""fricas"")","\frac{424 \, A \cos\left(d x + c\right)^{6} + 1002 \, A \cos\left(d x + c\right)^{5} - 944 \, A \cos\left(d x + c\right)^{4} - 2074 \, A \cos\left(d x + c\right)^{3} + 531 \, A \cos\left(d x + c\right)^{2} + 1077 \, A \cos\left(d x + c\right) + 135 \, {\left(A \cos\left(d x + c\right)^{6} - 2 \, A \cos\left(d x + c\right)^{5} - 6 \, A \cos\left(d x + c\right)^{4} + 4 \, A \cos\left(d x + c\right)^{3} + 9 \, A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) - {\left(A \cos\left(d x + c\right)^{5} + 3 \, A \cos\left(d x + c\right)^{4} - 3 \, A \cos\left(d x + c\right)^{3} - 7 \, A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + 4 \, A\right)} \sin\left(d x + c\right) - 4 \, A\right)} \log\left(\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) - 135 \, {\left(A \cos\left(d x + c\right)^{6} - 2 \, A \cos\left(d x + c\right)^{5} - 6 \, A \cos\left(d x + c\right)^{4} + 4 \, A \cos\left(d x + c\right)^{3} + 9 \, A \cos\left(d x + c\right)^{2} - 2 \, A \cos\left(d x + c\right) - {\left(A \cos\left(d x + c\right)^{5} + 3 \, A \cos\left(d x + c\right)^{4} - 3 \, A \cos\left(d x + c\right)^{3} - 7 \, A \cos\left(d x + c\right)^{2} + 2 \, A \cos\left(d x + c\right) + 4 \, A\right)} \sin\left(d x + c\right) - 4 \, A\right)} \log\left(-\frac{1}{2} \, \cos\left(d x + c\right) + \frac{1}{2}\right) + {\left(424 \, A \cos\left(d x + c\right)^{5} - 578 \, A \cos\left(d x + c\right)^{4} - 1522 \, A \cos\left(d x + c\right)^{3} + 552 \, A \cos\left(d x + c\right)^{2} + 1083 \, A \cos\left(d x + c\right) + 6 \, A\right)} \sin\left(d x + c\right) - 6 \, A}{15 \, {\left(a^{3} d \cos\left(d x + c\right)^{6} - 2 \, a^{3} d \cos\left(d x + c\right)^{5} - 6 \, a^{3} d \cos\left(d x + c\right)^{4} + 4 \, a^{3} d \cos\left(d x + c\right)^{3} + 9 \, a^{3} d \cos\left(d x + c\right)^{2} - 2 \, a^{3} d \cos\left(d x + c\right) - 4 \, a^{3} d - {\left(a^{3} d \cos\left(d x + c\right)^{5} + 3 \, a^{3} d \cos\left(d x + c\right)^{4} - 3 \, a^{3} d \cos\left(d x + c\right)^{3} - 7 \, a^{3} d \cos\left(d x + c\right)^{2} + 2 \, a^{3} d \cos\left(d x + c\right) + 4 \, a^{3} d\right)} \sin\left(d x + c\right)\right)}}"," ",0,"1/15*(424*A*cos(d*x + c)^6 + 1002*A*cos(d*x + c)^5 - 944*A*cos(d*x + c)^4 - 2074*A*cos(d*x + c)^3 + 531*A*cos(d*x + c)^2 + 1077*A*cos(d*x + c) + 135*(A*cos(d*x + c)^6 - 2*A*cos(d*x + c)^5 - 6*A*cos(d*x + c)^4 + 4*A*cos(d*x + c)^3 + 9*A*cos(d*x + c)^2 - 2*A*cos(d*x + c) - (A*cos(d*x + c)^5 + 3*A*cos(d*x + c)^4 - 3*A*cos(d*x + c)^3 - 7*A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + 4*A)*sin(d*x + c) - 4*A)*log(1/2*cos(d*x + c) + 1/2) - 135*(A*cos(d*x + c)^6 - 2*A*cos(d*x + c)^5 - 6*A*cos(d*x + c)^4 + 4*A*cos(d*x + c)^3 + 9*A*cos(d*x + c)^2 - 2*A*cos(d*x + c) - (A*cos(d*x + c)^5 + 3*A*cos(d*x + c)^4 - 3*A*cos(d*x + c)^3 - 7*A*cos(d*x + c)^2 + 2*A*cos(d*x + c) + 4*A)*sin(d*x + c) - 4*A)*log(-1/2*cos(d*x + c) + 1/2) + (424*A*cos(d*x + c)^5 - 578*A*cos(d*x + c)^4 - 1522*A*cos(d*x + c)^3 + 552*A*cos(d*x + c)^2 + 1083*A*cos(d*x + c) + 6*A)*sin(d*x + c) - 6*A)/(a^3*d*cos(d*x + c)^6 - 2*a^3*d*cos(d*x + c)^5 - 6*a^3*d*cos(d*x + c)^4 + 4*a^3*d*cos(d*x + c)^3 + 9*a^3*d*cos(d*x + c)^2 - 2*a^3*d*cos(d*x + c) - 4*a^3*d - (a^3*d*cos(d*x + c)^5 + 3*a^3*d*cos(d*x + c)^4 - 3*a^3*d*cos(d*x + c)^3 - 7*a^3*d*cos(d*x + c)^2 + 2*a^3*d*cos(d*x + c) + 4*a^3*d)*sin(d*x + c))","B",0
244,1,239,0,0.857831," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{24 \, B a d^{3} \cos\left(f x + e\right)^{5} - 40 \, {\left(3 \, B a c^{2} d + 3 \, {\left(A + B\right)} a c d^{2} + {\left(A + 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{3} - 15 \, {\left(4 \, {\left(2 \, A + B\right)} a c^{3} + 12 \, {\left(A + B\right)} a c^{2} d + 3 \, {\left(4 \, A + 3 \, B\right)} a c d^{2} + 3 \, {\left(A + B\right)} a d^{3}\right)} f x + 120 \, {\left({\left(A + B\right)} a c^{3} + 3 \, {\left(A + B\right)} a c^{2} d + 3 \, {\left(A + B\right)} a c d^{2} + {\left(A + B\right)} a d^{3}\right)} \cos\left(f x + e\right) - 15 \, {\left(2 \, {\left(3 \, B a c d^{2} + {\left(A + B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(4 \, B a c^{3} + 12 \, {\left(A + B\right)} a c^{2} d + 3 \, {\left(4 \, A + 5 \, B\right)} a c d^{2} + 5 \, {\left(A + B\right)} a d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{120 \, f}"," ",0,"-1/120*(24*B*a*d^3*cos(f*x + e)^5 - 40*(3*B*a*c^2*d + 3*(A + B)*a*c*d^2 + (A + 2*B)*a*d^3)*cos(f*x + e)^3 - 15*(4*(2*A + B)*a*c^3 + 12*(A + B)*a*c^2*d + 3*(4*A + 3*B)*a*c*d^2 + 3*(A + B)*a*d^3)*f*x + 120*((A + B)*a*c^3 + 3*(A + B)*a*c^2*d + 3*(A + B)*a*c*d^2 + (A + B)*a*d^3)*cos(f*x + e) - 15*(2*(3*B*a*c*d^2 + (A + B)*a*d^3)*cos(f*x + e)^3 - (4*B*a*c^3 + 12*(A + B)*a*c^2*d + 3*(4*A + 5*B)*a*c*d^2 + 5*(A + B)*a*d^3)*cos(f*x + e))*sin(f*x + e))/f","A",0
245,1,160,0,0.894202," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{8 \, {\left(2 \, B a c d + {\left(A + B\right)} a d^{2}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, {\left(2 \, A + B\right)} a c^{2} + 8 \, {\left(A + B\right)} a c d + {\left(4 \, A + 3 \, B\right)} a d^{2}\right)} f x - 24 \, {\left({\left(A + B\right)} a c^{2} + 2 \, {\left(A + B\right)} a c d + {\left(A + B\right)} a d^{2}\right)} \cos\left(f x + e\right) + 3 \, {\left(2 \, B a d^{2} \cos\left(f x + e\right)^{3} - {\left(4 \, B a c^{2} + 8 \, {\left(A + B\right)} a c d + {\left(4 \, A + 5 \, B\right)} a d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, f}"," ",0,"1/24*(8*(2*B*a*c*d + (A + B)*a*d^2)*cos(f*x + e)^3 + 3*(4*(2*A + B)*a*c^2 + 8*(A + B)*a*c*d + (4*A + 3*B)*a*d^2)*f*x - 24*((A + B)*a*c^2 + 2*(A + B)*a*c*d + (A + B)*a*d^2)*cos(f*x + e) + 3*(2*B*a*d^2*cos(f*x + e)^3 - (4*B*a*c^2 + 8*(A + B)*a*c*d + (4*A + 5*B)*a*d^2)*cos(f*x + e))*sin(f*x + e))/f","A",0
246,1,84,0,0.895420," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, B a d \cos\left(f x + e\right)^{3} + 3 \, {\left({\left(2 \, A + B\right)} a c + {\left(A + B\right)} a d\right)} f x - 3 \, {\left(B a c + {\left(A + B\right)} a d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - 6 \, {\left({\left(A + B\right)} a c + {\left(A + B\right)} a d\right)} \cos\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(2*B*a*d*cos(f*x + e)^3 + 3*((2*A + B)*a*c + (A + B)*a*d)*f*x - 3*(B*a*c + (A + B)*a*d)*cos(f*x + e)*sin(f*x + e) - 6*((A + B)*a*c + (A + B)*a*d)*cos(f*x + e))/f","A",0
247,1,43,0,0.764360," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","\frac{{\left(2 \, A + B\right)} a f x - B a \cos\left(f x + e\right) \sin\left(f x + e\right) - 2 \, {\left(A + B\right)} a \cos\left(f x + e\right)}{2 \, f}"," ",0,"1/2*((2*A + B)*a*f*x - B*a*cos(f*x + e)*sin(f*x + e) - 2*(A + B)*a*cos(f*x + e))/f","A",0
248,1,292,0,0.556174," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{2 \, B a d \cos\left(f x + e\right) + 2 \, {\left(B a c - {\left(A + B\right)} a d\right)} f x - {\left(B a c - A a d\right)} \sqrt{-\frac{c - d}{c + d}} \log\left(-\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} - 2 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right)}{2 \, d^{2} f}, -\frac{B a d \cos\left(f x + e\right) + {\left(B a c - {\left(A + B\right)} a d\right)} f x + {\left(B a c - A a d\right)} \sqrt{\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(c \sin\left(f x + e\right) + d\right)} \sqrt{\frac{c - d}{c + d}}}{{\left(c - d\right)} \cos\left(f x + e\right)}\right)}{d^{2} f}\right]"," ",0,"[-1/2*(2*B*a*d*cos(f*x + e) + 2*(B*a*c - (A + B)*a*d)*f*x - (B*a*c - A*a*d)*sqrt(-(c - d)/(c + d))*log(-((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 - 2*((c^2 + c*d)*cos(f*x + e)*sin(f*x + e) + (c*d + d^2)*cos(f*x + e))*sqrt(-(c - d)/(c + d)))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)))/(d^2*f), -(B*a*d*cos(f*x + e) + (B*a*c - (A + B)*a*d)*f*x + (B*a*c - A*a*d)*sqrt((c - d)/(c + d))*arctan(-(c*sin(f*x + e) + d)*sqrt((c - d)/(c + d))/((c - d)*cos(f*x + e))))/(d^2*f)]","A",0
249,1,655,0,0.766516," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a c^{3} d + B a c^{2} d^{2} - B a c d^{3} - B a d^{4}\right)} f x \sin\left(f x + e\right) + 2 \, {\left(B a c^{4} + B a c^{3} d - B a c^{2} d^{2} - B a c d^{3}\right)} f x + {\left(B a c^{3} + B a c^{2} d - {\left(A + B\right)} a c d^{2} + {\left(B a c^{2} d + B a c d^{2} - {\left(A + B\right)} a d^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left(B a c^{3} d - A a c^{2} d^{2} - B a c d^{3} + A a d^{4}\right)} \cos\left(f x + e\right)}{2 \, {\left({\left(c^{3} d^{3} + c^{2} d^{4} - c d^{5} - d^{6}\right)} f \sin\left(f x + e\right) + {\left(c^{4} d^{2} + c^{3} d^{3} - c^{2} d^{4} - c d^{5}\right)} f\right)}}, \frac{{\left(B a c^{3} d + B a c^{2} d^{2} - B a c d^{3} - B a d^{4}\right)} f x \sin\left(f x + e\right) + {\left(B a c^{4} + B a c^{3} d - B a c^{2} d^{2} - B a c d^{3}\right)} f x + {\left(B a c^{3} + B a c^{2} d - {\left(A + B\right)} a c d^{2} + {\left(B a c^{2} d + B a c d^{2} - {\left(A + B\right)} a d^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + {\left(B a c^{3} d - A a c^{2} d^{2} - B a c d^{3} + A a d^{4}\right)} \cos\left(f x + e\right)}{{\left(c^{3} d^{3} + c^{2} d^{4} - c d^{5} - d^{6}\right)} f \sin\left(f x + e\right) + {\left(c^{4} d^{2} + c^{3} d^{3} - c^{2} d^{4} - c d^{5}\right)} f}\right]"," ",0,"[1/2*(2*(B*a*c^3*d + B*a*c^2*d^2 - B*a*c*d^3 - B*a*d^4)*f*x*sin(f*x + e) + 2*(B*a*c^4 + B*a*c^3*d - B*a*c^2*d^2 - B*a*c*d^3)*f*x + (B*a*c^3 + B*a*c^2*d - (A + B)*a*c*d^2 + (B*a*c^2*d + B*a*c*d^2 - (A + B)*a*d^3)*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*(B*a*c^3*d - A*a*c^2*d^2 - B*a*c*d^3 + A*a*d^4)*cos(f*x + e))/((c^3*d^3 + c^2*d^4 - c*d^5 - d^6)*f*sin(f*x + e) + (c^4*d^2 + c^3*d^3 - c^2*d^4 - c*d^5)*f), ((B*a*c^3*d + B*a*c^2*d^2 - B*a*c*d^3 - B*a*d^4)*f*x*sin(f*x + e) + (B*a*c^4 + B*a*c^3*d - B*a*c^2*d^2 - B*a*c*d^3)*f*x + (B*a*c^3 + B*a*c^2*d - (A + B)*a*c*d^2 + (B*a*c^2*d + B*a*c*d^2 - (A + B)*a*d^3)*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + (B*a*c^3*d - A*a*c^2*d^2 - B*a*c*d^3 + A*a*d^4)*cos(f*x + e))/((c^3*d^3 + c^2*d^4 - c*d^5 - d^6)*f*sin(f*x + e) + (c^4*d^2 + c^3*d^3 - c^2*d^4 - c*d^5)*f)]","B",0
250,1,967,0,0.688064," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(B a c^{4} + {\left(A + 2 \, B\right)} a c^{3} d - {\left(2 \, A + 3 \, B\right)} a c^{2} d^{2} - {\left(A + 2 \, B\right)} a c d^{3} + 2 \, {\left(A + B\right)} a d^{4}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left({\left(2 \, A + B\right)} a c^{3} - {\left(A + 2 \, B\right)} a c^{2} d + {\left(2 \, A + B\right)} a c d^{2} - {\left(A + 2 \, B\right)} a d^{3} - {\left({\left(2 \, A + B\right)} a c d^{2} - {\left(A + 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(2 \, A + B\right)} a c^{2} d - {\left(A + 2 \, B\right)} a c d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left(2 \, {\left(A + B\right)} a c^{4} - {\left(2 \, A + B\right)} a c^{3} d - {\left(3 \, A + 2 \, B\right)} a c^{2} d^{2} + {\left(2 \, A + B\right)} a c d^{3} + A a d^{4}\right)} \cos\left(f x + e\right)}{4 \, {\left({\left(c^{5} d^{2} + c^{4} d^{3} - 2 \, c^{3} d^{4} - 2 \, c^{2} d^{5} + c d^{6} + d^{7}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{6} d + c^{5} d^{2} - 2 \, c^{4} d^{3} - 2 \, c^{3} d^{4} + c^{2} d^{5} + c d^{6}\right)} f \sin\left(f x + e\right) - {\left(c^{7} + c^{6} d - c^{5} d^{2} - c^{4} d^{3} - c^{3} d^{4} - c^{2} d^{5} + c d^{6} + d^{7}\right)} f\right)}}, \frac{{\left(B a c^{4} + {\left(A + 2 \, B\right)} a c^{3} d - {\left(2 \, A + 3 \, B\right)} a c^{2} d^{2} - {\left(A + 2 \, B\right)} a c d^{3} + 2 \, {\left(A + B\right)} a d^{4}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left({\left(2 \, A + B\right)} a c^{3} - {\left(A + 2 \, B\right)} a c^{2} d + {\left(2 \, A + B\right)} a c d^{2} - {\left(A + 2 \, B\right)} a d^{3} - {\left({\left(2 \, A + B\right)} a c d^{2} - {\left(A + 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(2 \, A + B\right)} a c^{2} d - {\left(A + 2 \, B\right)} a c d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + {\left(2 \, {\left(A + B\right)} a c^{4} - {\left(2 \, A + B\right)} a c^{3} d - {\left(3 \, A + 2 \, B\right)} a c^{2} d^{2} + {\left(2 \, A + B\right)} a c d^{3} + A a d^{4}\right)} \cos\left(f x + e\right)}{2 \, {\left({\left(c^{5} d^{2} + c^{4} d^{3} - 2 \, c^{3} d^{4} - 2 \, c^{2} d^{5} + c d^{6} + d^{7}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{6} d + c^{5} d^{2} - 2 \, c^{4} d^{3} - 2 \, c^{3} d^{4} + c^{2} d^{5} + c d^{6}\right)} f \sin\left(f x + e\right) - {\left(c^{7} + c^{6} d - c^{5} d^{2} - c^{4} d^{3} - c^{3} d^{4} - c^{2} d^{5} + c d^{6} + d^{7}\right)} f\right)}}\right]"," ",0,"[1/4*(2*(B*a*c^4 + (A + 2*B)*a*c^3*d - (2*A + 3*B)*a*c^2*d^2 - (A + 2*B)*a*c*d^3 + 2*(A + B)*a*d^4)*cos(f*x + e)*sin(f*x + e) + ((2*A + B)*a*c^3 - (A + 2*B)*a*c^2*d + (2*A + B)*a*c*d^2 - (A + 2*B)*a*d^3 - ((2*A + B)*a*c*d^2 - (A + 2*B)*a*d^3)*cos(f*x + e)^2 + 2*((2*A + B)*a*c^2*d - (A + 2*B)*a*c*d^2)*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*(2*(A + B)*a*c^4 - (2*A + B)*a*c^3*d - (3*A + 2*B)*a*c^2*d^2 + (2*A + B)*a*c*d^3 + A*a*d^4)*cos(f*x + e))/((c^5*d^2 + c^4*d^3 - 2*c^3*d^4 - 2*c^2*d^5 + c*d^6 + d^7)*f*cos(f*x + e)^2 - 2*(c^6*d + c^5*d^2 - 2*c^4*d^3 - 2*c^3*d^4 + c^2*d^5 + c*d^6)*f*sin(f*x + e) - (c^7 + c^6*d - c^5*d^2 - c^4*d^3 - c^3*d^4 - c^2*d^5 + c*d^6 + d^7)*f), 1/2*((B*a*c^4 + (A + 2*B)*a*c^3*d - (2*A + 3*B)*a*c^2*d^2 - (A + 2*B)*a*c*d^3 + 2*(A + B)*a*d^4)*cos(f*x + e)*sin(f*x + e) + ((2*A + B)*a*c^3 - (A + 2*B)*a*c^2*d + (2*A + B)*a*c*d^2 - (A + 2*B)*a*d^3 - ((2*A + B)*a*c*d^2 - (A + 2*B)*a*d^3)*cos(f*x + e)^2 + 2*((2*A + B)*a*c^2*d - (A + 2*B)*a*c*d^2)*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + (2*(A + B)*a*c^4 - (2*A + B)*a*c^3*d - (3*A + 2*B)*a*c^2*d^2 + (2*A + B)*a*c*d^3 + A*a*d^4)*cos(f*x + e))/((c^5*d^2 + c^4*d^3 - 2*c^3*d^4 - 2*c^2*d^5 + c*d^6 + d^7)*f*cos(f*x + e)^2 - 2*(c^6*d + c^5*d^2 - 2*c^4*d^3 - 2*c^3*d^4 + c^2*d^5 + c*d^6)*f*sin(f*x + e) - (c^7 + c^6*d - c^5*d^2 - c^4*d^3 - c^3*d^4 - c^2*d^5 + c*d^6 + d^7)*f)]","B",0
251,1,364,0,0.705521," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{48 \, {\left(3 \, B a^{2} c d^{2} + {\left(A + 2 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{5} - 80 \, {\left(B a^{2} c^{3} + 3 \, {\left(A + 2 \, B\right)} a^{2} c^{2} d + 3 \, {\left(2 \, A + 3 \, B\right)} a^{2} c d^{2} + {\left(3 \, A + 4 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} - 15 \, {\left(8 \, {\left(3 \, A + 2 \, B\right)} a^{2} c^{3} + 6 \, {\left(8 \, A + 7 \, B\right)} a^{2} c^{2} d + 6 \, {\left(7 \, A + 6 \, B\right)} a^{2} c d^{2} + {\left(12 \, A + 11 \, B\right)} a^{2} d^{3}\right)} f x + 480 \, {\left({\left(A + B\right)} a^{2} c^{3} + 3 \, {\left(A + B\right)} a^{2} c^{2} d + 3 \, {\left(A + B\right)} a^{2} c d^{2} + {\left(A + B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right) + 5 \, {\left(8 \, B a^{2} d^{3} \cos\left(f x + e\right)^{5} - 2 \, {\left(18 \, B a^{2} c^{2} d + 18 \, {\left(A + 2 \, B\right)} a^{2} c d^{2} + {\left(12 \, A + 19 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(8 \, {\left(A + 2 \, B\right)} a^{2} c^{3} + 6 \, {\left(8 \, A + 9 \, B\right)} a^{2} c^{2} d + 6 \, {\left(9 \, A + 10 \, B\right)} a^{2} c d^{2} + {\left(20 \, A + 21 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f}"," ",0,"-1/240*(48*(3*B*a^2*c*d^2 + (A + 2*B)*a^2*d^3)*cos(f*x + e)^5 - 80*(B*a^2*c^3 + 3*(A + 2*B)*a^2*c^2*d + 3*(2*A + 3*B)*a^2*c*d^2 + (3*A + 4*B)*a^2*d^3)*cos(f*x + e)^3 - 15*(8*(3*A + 2*B)*a^2*c^3 + 6*(8*A + 7*B)*a^2*c^2*d + 6*(7*A + 6*B)*a^2*c*d^2 + (12*A + 11*B)*a^2*d^3)*f*x + 480*((A + B)*a^2*c^3 + 3*(A + B)*a^2*c^2*d + 3*(A + B)*a^2*c*d^2 + (A + B)*a^2*d^3)*cos(f*x + e) + 5*(8*B*a^2*d^3*cos(f*x + e)^5 - 2*(18*B*a^2*c^2*d + 18*(A + 2*B)*a^2*c*d^2 + (12*A + 19*B)*a^2*d^3)*cos(f*x + e)^3 + 3*(8*(A + 2*B)*a^2*c^3 + 6*(8*A + 9*B)*a^2*c^2*d + 6*(9*A + 10*B)*a^2*c*d^2 + (20*A + 21*B)*a^2*d^3)*cos(f*x + e))*sin(f*x + e))/f","A",0
252,1,245,0,0.516231," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{24 \, B a^{2} d^{2} \cos\left(f x + e\right)^{5} - 40 \, {\left(B a^{2} c^{2} + 2 \, {\left(A + 2 \, B\right)} a^{2} c d + {\left(2 \, A + 3 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} - 15 \, {\left(4 \, {\left(3 \, A + 2 \, B\right)} a^{2} c^{2} + 2 \, {\left(8 \, A + 7 \, B\right)} a^{2} c d + {\left(7 \, A + 6 \, B\right)} a^{2} d^{2}\right)} f x + 240 \, {\left({\left(A + B\right)} a^{2} c^{2} + 2 \, {\left(A + B\right)} a^{2} c d + {\left(A + B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right) - 15 \, {\left(2 \, {\left(2 \, B a^{2} c d + {\left(A + 2 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} - {\left(4 \, {\left(A + 2 \, B\right)} a^{2} c^{2} + 2 \, {\left(8 \, A + 9 \, B\right)} a^{2} c d + {\left(9 \, A + 10 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{120 \, f}"," ",0,"-1/120*(24*B*a^2*d^2*cos(f*x + e)^5 - 40*(B*a^2*c^2 + 2*(A + 2*B)*a^2*c*d + (2*A + 3*B)*a^2*d^2)*cos(f*x + e)^3 - 15*(4*(3*A + 2*B)*a^2*c^2 + 2*(8*A + 7*B)*a^2*c*d + (7*A + 6*B)*a^2*d^2)*f*x + 240*((A + B)*a^2*c^2 + 2*(A + B)*a^2*c*d + (A + B)*a^2*d^2)*cos(f*x + e) - 15*(2*(2*B*a^2*c*d + (A + 2*B)*a^2*d^2)*cos(f*x + e)^3 - (4*(A + 2*B)*a^2*c^2 + 2*(8*A + 9*B)*a^2*c*d + (9*A + 10*B)*a^2*d^2)*cos(f*x + e))*sin(f*x + e))/f","A",0
253,1,144,0,0.798631," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\frac{8 \, {\left(B a^{2} c + {\left(A + 2 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(4 \, {\left(3 \, A + 2 \, B\right)} a^{2} c + {\left(8 \, A + 7 \, B\right)} a^{2} d\right)} f x - 48 \, {\left({\left(A + B\right)} a^{2} c + {\left(A + B\right)} a^{2} d\right)} \cos\left(f x + e\right) + 3 \, {\left(2 \, B a^{2} d \cos\left(f x + e\right)^{3} - {\left(4 \, {\left(A + 2 \, B\right)} a^{2} c + {\left(8 \, A + 9 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, f}"," ",0,"1/24*(8*(B*a^2*c + (A + 2*B)*a^2*d)*cos(f*x + e)^3 + 3*(4*(3*A + 2*B)*a^2*c + (8*A + 7*B)*a^2*d)*f*x - 48*((A + B)*a^2*c + (A + B)*a^2*d)*cos(f*x + e) + 3*(2*B*a^2*d*cos(f*x + e)^3 - (4*(A + 2*B)*a^2*c + (8*A + 9*B)*a^2*d)*cos(f*x + e))*sin(f*x + e))/f","A",0
254,1,70,0,0.763087," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, B a^{2} \cos\left(f x + e\right)^{3} + 3 \, {\left(3 \, A + 2 \, B\right)} a^{2} f x - 3 \, {\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - 12 \, {\left(A + B\right)} a^{2} \cos\left(f x + e\right)}{6 \, f}"," ",0,"1/6*(2*B*a^2*cos(f*x + e)^3 + 3*(3*A + 2*B)*a^2*f*x - 3*(A + 2*B)*a^2*cos(f*x + e)*sin(f*x + e) - 12*(A + B)*a^2*cos(f*x + e))/f","A",0
255,1,452,0,0.699661," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{B a^{2} d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(2 \, B a^{2} c^{2} - 2 \, {\left(A + 2 \, B\right)} a^{2} c d + {\left(4 \, A + 3 \, B\right)} a^{2} d^{2}\right)} f x + {\left(B a^{2} c^{2} - {\left(A + B\right)} a^{2} c d + A a^{2} d^{2}\right)} \sqrt{-\frac{c - d}{c + d}} \log\left(-\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} - 2 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) - 2 \, {\left(B a^{2} c d - {\left(A + 2 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)}{2 \, d^{3} f}, -\frac{B a^{2} d^{2} \cos\left(f x + e\right) \sin\left(f x + e\right) - {\left(2 \, B a^{2} c^{2} - 2 \, {\left(A + 2 \, B\right)} a^{2} c d + {\left(4 \, A + 3 \, B\right)} a^{2} d^{2}\right)} f x - 2 \, {\left(B a^{2} c^{2} - {\left(A + B\right)} a^{2} c d + A a^{2} d^{2}\right)} \sqrt{\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(c \sin\left(f x + e\right) + d\right)} \sqrt{\frac{c - d}{c + d}}}{{\left(c - d\right)} \cos\left(f x + e\right)}\right) - 2 \, {\left(B a^{2} c d - {\left(A + 2 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)}{2 \, d^{3} f}\right]"," ",0,"[-1/2*(B*a^2*d^2*cos(f*x + e)*sin(f*x + e) - (2*B*a^2*c^2 - 2*(A + 2*B)*a^2*c*d + (4*A + 3*B)*a^2*d^2)*f*x + (B*a^2*c^2 - (A + B)*a^2*c*d + A*a^2*d^2)*sqrt(-(c - d)/(c + d))*log(-((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 - 2*((c^2 + c*d)*cos(f*x + e)*sin(f*x + e) + (c*d + d^2)*cos(f*x + e))*sqrt(-(c - d)/(c + d)))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) - 2*(B*a^2*c*d - (A + 2*B)*a^2*d^2)*cos(f*x + e))/(d^3*f), -1/2*(B*a^2*d^2*cos(f*x + e)*sin(f*x + e) - (2*B*a^2*c^2 - 2*(A + 2*B)*a^2*c*d + (4*A + 3*B)*a^2*d^2)*f*x - 2*(B*a^2*c^2 - (A + B)*a^2*c*d + A*a^2*d^2)*sqrt((c - d)/(c + d))*arctan(-(c*sin(f*x + e) + d)*sqrt((c - d)/(c + d))/((c - d)*cos(f*x + e))) - 2*(B*a^2*c*d - (A + 2*B)*a^2*d^2)*cos(f*x + e))/(d^3*f)]","A",0
256,1,731,0,1.030858," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, B a^{2} c^{3} - A a^{2} c^{2} d - {\left(A + 2 \, B\right)} a^{2} c d^{2}\right)} f x + {\left(2 \, B a^{2} c^{3} - {\left(A - 2 \, B\right)} a^{2} c^{2} d - {\left(2 \, A + B\right)} a^{2} c d^{2} + {\left(2 \, B a^{2} c^{2} d - {\left(A - 2 \, B\right)} a^{2} c d^{2} - {\left(2 \, A + B\right)} a^{2} d^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left(2 \, B a^{2} c^{2} d - A a^{2} c d^{2} + A a^{2} d^{3}\right)} \cos\left(f x + e\right) + 2 \, {\left({\left(2 \, B a^{2} c^{2} d - A a^{2} c d^{2} - {\left(A + 2 \, B\right)} a^{2} d^{3}\right)} f x + {\left(B a^{2} c d^{2} + B a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c d^{4} + d^{5}\right)} f \sin\left(f x + e\right) + {\left(c^{2} d^{3} + c d^{4}\right)} f\right)}}, -\frac{{\left(2 \, B a^{2} c^{3} - A a^{2} c^{2} d - {\left(A + 2 \, B\right)} a^{2} c d^{2}\right)} f x + {\left(2 \, B a^{2} c^{3} - {\left(A - 2 \, B\right)} a^{2} c^{2} d - {\left(2 \, A + B\right)} a^{2} c d^{2} + {\left(2 \, B a^{2} c^{2} d - {\left(A - 2 \, B\right)} a^{2} c d^{2} - {\left(2 \, A + B\right)} a^{2} d^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(c \sin\left(f x + e\right) + d\right)} \sqrt{\frac{c - d}{c + d}}}{{\left(c - d\right)} \cos\left(f x + e\right)}\right) + {\left(2 \, B a^{2} c^{2} d - A a^{2} c d^{2} + A a^{2} d^{3}\right)} \cos\left(f x + e\right) + {\left({\left(2 \, B a^{2} c^{2} d - A a^{2} c d^{2} - {\left(A + 2 \, B\right)} a^{2} d^{3}\right)} f x + {\left(B a^{2} c d^{2} + B a^{2} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{{\left(c d^{4} + d^{5}\right)} f \sin\left(f x + e\right) + {\left(c^{2} d^{3} + c d^{4}\right)} f}\right]"," ",0,"[-1/2*(2*(2*B*a^2*c^3 - A*a^2*c^2*d - (A + 2*B)*a^2*c*d^2)*f*x + (2*B*a^2*c^3 - (A - 2*B)*a^2*c^2*d - (2*A + B)*a^2*c*d^2 + (2*B*a^2*c^2*d - (A - 2*B)*a^2*c*d^2 - (2*A + B)*a^2*d^3)*sin(f*x + e))*sqrt(-(c - d)/(c + d))*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*((c^2 + c*d)*cos(f*x + e)*sin(f*x + e) + (c*d + d^2)*cos(f*x + e))*sqrt(-(c - d)/(c + d)))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*(2*B*a^2*c^2*d - A*a^2*c*d^2 + A*a^2*d^3)*cos(f*x + e) + 2*((2*B*a^2*c^2*d - A*a^2*c*d^2 - (A + 2*B)*a^2*d^3)*f*x + (B*a^2*c*d^2 + B*a^2*d^3)*cos(f*x + e))*sin(f*x + e))/((c*d^4 + d^5)*f*sin(f*x + e) + (c^2*d^3 + c*d^4)*f), -((2*B*a^2*c^3 - A*a^2*c^2*d - (A + 2*B)*a^2*c*d^2)*f*x + (2*B*a^2*c^3 - (A - 2*B)*a^2*c^2*d - (2*A + B)*a^2*c*d^2 + (2*B*a^2*c^2*d - (A - 2*B)*a^2*c*d^2 - (2*A + B)*a^2*d^3)*sin(f*x + e))*sqrt((c - d)/(c + d))*arctan(-(c*sin(f*x + e) + d)*sqrt((c - d)/(c + d))/((c - d)*cos(f*x + e))) + (2*B*a^2*c^2*d - A*a^2*c*d^2 + A*a^2*d^3)*cos(f*x + e) + ((2*B*a^2*c^2*d - A*a^2*c*d^2 - (A + 2*B)*a^2*d^3)*f*x + (B*a^2*c*d^2 + B*a^2*d^3)*cos(f*x + e))*sin(f*x + e))/((c*d^4 + d^5)*f*sin(f*x + e) + (c^2*d^3 + c*d^4)*f)]","A",0
257,1,1483,0,0.631418," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(B a^{2} c^{4} d^{2} + 2 \, B a^{2} c^{3} d^{3} - 2 \, B a^{2} c d^{5} - B a^{2} d^{6}\right)} f x \cos\left(f x + e\right)^{2} - 4 \, {\left(B a^{2} c^{6} + 2 \, B a^{2} c^{5} d + B a^{2} c^{4} d^{2} - B a^{2} c^{2} d^{4} - 2 \, B a^{2} c d^{5} - B a^{2} d^{6}\right)} f x - {\left(2 \, B a^{2} c^{5} + 4 \, B a^{2} c^{4} d + 3 \, B a^{2} c^{3} d^{2} - 3 \, A a^{2} c^{2} d^{3} + B a^{2} c d^{4} - {\left(3 \, A + 4 \, B\right)} a^{2} d^{5} - {\left(2 \, B a^{2} c^{3} d^{2} + 4 \, B a^{2} c^{2} d^{3} + B a^{2} c d^{4} - {\left(3 \, A + 4 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, B a^{2} c^{4} d + 4 \, B a^{2} c^{3} d^{2} + B a^{2} c^{2} d^{3} - {\left(3 \, A + 4 \, B\right)} a^{2} c d^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) - 2 \, {\left(2 \, B a^{2} c^{5} d + 4 \, B a^{2} c^{4} d^{2} - {\left(4 \, A + 3 \, B\right)} a^{2} c^{3} d^{3} - {\left(A + 4 \, B\right)} a^{2} c^{2} d^{4} + {\left(4 \, A + B\right)} a^{2} c d^{5} + A a^{2} d^{6}\right)} \cos\left(f x + e\right) - 2 \, {\left(4 \, {\left(B a^{2} c^{5} d + 2 \, B a^{2} c^{4} d^{2} - 2 \, B a^{2} c^{2} d^{4} - B a^{2} c d^{5}\right)} f x + {\left(3 \, B a^{2} c^{4} d^{2} - {\left(A - 4 \, B\right)} a^{2} c^{3} d^{3} - {\left(4 \, A + 5 \, B\right)} a^{2} c^{2} d^{4} + {\left(A - 4 \, B\right)} a^{2} c d^{5} + 2 \, {\left(2 \, A + B\right)} a^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{4} d^{5} + 2 \, c^{3} d^{6} - 2 \, c d^{8} - d^{9}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{5} d^{4} + 2 \, c^{4} d^{5} - 2 \, c^{2} d^{7} - c d^{8}\right)} f \sin\left(f x + e\right) - {\left(c^{6} d^{3} + 2 \, c^{5} d^{4} + c^{4} d^{5} - c^{2} d^{7} - 2 \, c d^{8} - d^{9}\right)} f\right)}}, \frac{2 \, {\left(B a^{2} c^{4} d^{2} + 2 \, B a^{2} c^{3} d^{3} - 2 \, B a^{2} c d^{5} - B a^{2} d^{6}\right)} f x \cos\left(f x + e\right)^{2} - 2 \, {\left(B a^{2} c^{6} + 2 \, B a^{2} c^{5} d + B a^{2} c^{4} d^{2} - B a^{2} c^{2} d^{4} - 2 \, B a^{2} c d^{5} - B a^{2} d^{6}\right)} f x - {\left(2 \, B a^{2} c^{5} + 4 \, B a^{2} c^{4} d + 3 \, B a^{2} c^{3} d^{2} - 3 \, A a^{2} c^{2} d^{3} + B a^{2} c d^{4} - {\left(3 \, A + 4 \, B\right)} a^{2} d^{5} - {\left(2 \, B a^{2} c^{3} d^{2} + 4 \, B a^{2} c^{2} d^{3} + B a^{2} c d^{4} - {\left(3 \, A + 4 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, B a^{2} c^{4} d + 4 \, B a^{2} c^{3} d^{2} + B a^{2} c^{2} d^{3} - {\left(3 \, A + 4 \, B\right)} a^{2} c d^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) - {\left(2 \, B a^{2} c^{5} d + 4 \, B a^{2} c^{4} d^{2} - {\left(4 \, A + 3 \, B\right)} a^{2} c^{3} d^{3} - {\left(A + 4 \, B\right)} a^{2} c^{2} d^{4} + {\left(4 \, A + B\right)} a^{2} c d^{5} + A a^{2} d^{6}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(B a^{2} c^{5} d + 2 \, B a^{2} c^{4} d^{2} - 2 \, B a^{2} c^{2} d^{4} - B a^{2} c d^{5}\right)} f x + {\left(3 \, B a^{2} c^{4} d^{2} - {\left(A - 4 \, B\right)} a^{2} c^{3} d^{3} - {\left(4 \, A + 5 \, B\right)} a^{2} c^{2} d^{4} + {\left(A - 4 \, B\right)} a^{2} c d^{5} + 2 \, {\left(2 \, A + B\right)} a^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{4} d^{5} + 2 \, c^{3} d^{6} - 2 \, c d^{8} - d^{9}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{5} d^{4} + 2 \, c^{4} d^{5} - 2 \, c^{2} d^{7} - c d^{8}\right)} f \sin\left(f x + e\right) - {\left(c^{6} d^{3} + 2 \, c^{5} d^{4} + c^{4} d^{5} - c^{2} d^{7} - 2 \, c d^{8} - d^{9}\right)} f\right)}}\right]"," ",0,"[1/4*(4*(B*a^2*c^4*d^2 + 2*B*a^2*c^3*d^3 - 2*B*a^2*c*d^5 - B*a^2*d^6)*f*x*cos(f*x + e)^2 - 4*(B*a^2*c^6 + 2*B*a^2*c^5*d + B*a^2*c^4*d^2 - B*a^2*c^2*d^4 - 2*B*a^2*c*d^5 - B*a^2*d^6)*f*x - (2*B*a^2*c^5 + 4*B*a^2*c^4*d + 3*B*a^2*c^3*d^2 - 3*A*a^2*c^2*d^3 + B*a^2*c*d^4 - (3*A + 4*B)*a^2*d^5 - (2*B*a^2*c^3*d^2 + 4*B*a^2*c^2*d^3 + B*a^2*c*d^4 - (3*A + 4*B)*a^2*d^5)*cos(f*x + e)^2 + 2*(2*B*a^2*c^4*d + 4*B*a^2*c^3*d^2 + B*a^2*c^2*d^3 - (3*A + 4*B)*a^2*c*d^4)*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) - 2*(2*B*a^2*c^5*d + 4*B*a^2*c^4*d^2 - (4*A + 3*B)*a^2*c^3*d^3 - (A + 4*B)*a^2*c^2*d^4 + (4*A + B)*a^2*c*d^5 + A*a^2*d^6)*cos(f*x + e) - 2*(4*(B*a^2*c^5*d + 2*B*a^2*c^4*d^2 - 2*B*a^2*c^2*d^4 - B*a^2*c*d^5)*f*x + (3*B*a^2*c^4*d^2 - (A - 4*B)*a^2*c^3*d^3 - (4*A + 5*B)*a^2*c^2*d^4 + (A - 4*B)*a^2*c*d^5 + 2*(2*A + B)*a^2*d^6)*cos(f*x + e))*sin(f*x + e))/((c^4*d^5 + 2*c^3*d^6 - 2*c*d^8 - d^9)*f*cos(f*x + e)^2 - 2*(c^5*d^4 + 2*c^4*d^5 - 2*c^2*d^7 - c*d^8)*f*sin(f*x + e) - (c^6*d^3 + 2*c^5*d^4 + c^4*d^5 - c^2*d^7 - 2*c*d^8 - d^9)*f), 1/2*(2*(B*a^2*c^4*d^2 + 2*B*a^2*c^3*d^3 - 2*B*a^2*c*d^5 - B*a^2*d^6)*f*x*cos(f*x + e)^2 - 2*(B*a^2*c^6 + 2*B*a^2*c^5*d + B*a^2*c^4*d^2 - B*a^2*c^2*d^4 - 2*B*a^2*c*d^5 - B*a^2*d^6)*f*x - (2*B*a^2*c^5 + 4*B*a^2*c^4*d + 3*B*a^2*c^3*d^2 - 3*A*a^2*c^2*d^3 + B*a^2*c*d^4 - (3*A + 4*B)*a^2*d^5 - (2*B*a^2*c^3*d^2 + 4*B*a^2*c^2*d^3 + B*a^2*c*d^4 - (3*A + 4*B)*a^2*d^5)*cos(f*x + e)^2 + 2*(2*B*a^2*c^4*d + 4*B*a^2*c^3*d^2 + B*a^2*c^2*d^3 - (3*A + 4*B)*a^2*c*d^4)*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) - (2*B*a^2*c^5*d + 4*B*a^2*c^4*d^2 - (4*A + 3*B)*a^2*c^3*d^3 - (A + 4*B)*a^2*c^2*d^4 + (4*A + B)*a^2*c*d^5 + A*a^2*d^6)*cos(f*x + e) - (4*(B*a^2*c^5*d + 2*B*a^2*c^4*d^2 - 2*B*a^2*c^2*d^4 - B*a^2*c*d^5)*f*x + (3*B*a^2*c^4*d^2 - (A - 4*B)*a^2*c^3*d^3 - (4*A + 5*B)*a^2*c^2*d^4 + (A - 4*B)*a^2*c*d^5 + 2*(2*A + B)*a^2*d^6)*cos(f*x + e))*sin(f*x + e))/((c^4*d^5 + 2*c^3*d^6 - 2*c*d^8 - d^9)*f*cos(f*x + e)^2 - 2*(c^5*d^4 + 2*c^4*d^5 - 2*c^2*d^7 - c*d^8)*f*sin(f*x + e) - (c^6*d^3 + 2*c^5*d^4 + c^4*d^5 - c^2*d^7 - 2*c*d^8 - d^9)*f)]","B",0
258,1,432,0,0.945685," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{240 \, B a^{3} d^{3} \cos\left(f x + e\right)^{7} - 1008 \, {\left(B a^{3} c^{2} d + {\left(A + 3 \, B\right)} a^{3} c d^{2} + {\left(A + 2 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right)^{5} + 560 \, {\left({\left(A + 3 \, B\right)} a^{3} c^{3} + 3 \, {\left(3 \, A + 5 \, B\right)} a^{3} c^{2} d + 3 \, {\left(5 \, A + 7 \, B\right)} a^{3} c d^{2} + {\left(7 \, A + 9 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right)^{3} + 105 \, {\left(10 \, {\left(4 \, A + 3 \, B\right)} a^{3} c^{3} + 6 \, {\left(15 \, A + 13 \, B\right)} a^{3} c^{2} d + 3 \, {\left(26 \, A + 23 \, B\right)} a^{3} c d^{2} + {\left(23 \, A + 21 \, B\right)} a^{3} d^{3}\right)} f x - 6720 \, {\left({\left(A + B\right)} a^{3} c^{3} + 3 \, {\left(A + B\right)} a^{3} c^{2} d + 3 \, {\left(A + B\right)} a^{3} c d^{2} + {\left(A + B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right) - 35 \, {\left(8 \, {\left(3 \, B a^{3} c d^{2} + {\left(A + 3 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right)^{5} - 2 \, {\left(6 \, B a^{3} c^{3} + 18 \, {\left(A + 3 \, B\right)} a^{3} c^{2} d + 3 \, {\left(18 \, A + 31 \, B\right)} a^{3} c d^{2} + {\left(31 \, A + 45 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(2 \, {\left(12 \, A + 17 \, B\right)} a^{3} c^{3} + 6 \, {\left(17 \, A + 19 \, B\right)} a^{3} c^{2} d + 3 \, {\left(38 \, A + 41 \, B\right)} a^{3} c d^{2} + {\left(41 \, A + 43 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{1680 \, f}"," ",0,"1/1680*(240*B*a^3*d^3*cos(f*x + e)^7 - 1008*(B*a^3*c^2*d + (A + 3*B)*a^3*c*d^2 + (A + 2*B)*a^3*d^3)*cos(f*x + e)^5 + 560*((A + 3*B)*a^3*c^3 + 3*(3*A + 5*B)*a^3*c^2*d + 3*(5*A + 7*B)*a^3*c*d^2 + (7*A + 9*B)*a^3*d^3)*cos(f*x + e)^3 + 105*(10*(4*A + 3*B)*a^3*c^3 + 6*(15*A + 13*B)*a^3*c^2*d + 3*(26*A + 23*B)*a^3*c*d^2 + (23*A + 21*B)*a^3*d^3)*f*x - 6720*((A + B)*a^3*c^3 + 3*(A + B)*a^3*c^2*d + 3*(A + B)*a^3*c*d^2 + (A + B)*a^3*d^3)*cos(f*x + e) - 35*(8*(3*B*a^3*c*d^2 + (A + 3*B)*a^3*d^3)*cos(f*x + e)^5 - 2*(6*B*a^3*c^3 + 18*(A + 3*B)*a^3*c^2*d + 3*(18*A + 31*B)*a^3*c*d^2 + (31*A + 45*B)*a^3*d^3)*cos(f*x + e)^3 + 3*(2*(12*A + 17*B)*a^3*c^3 + 6*(17*A + 19*B)*a^3*c^2*d + 3*(38*A + 41*B)*a^3*c*d^2 + (41*A + 43*B)*a^3*d^3)*cos(f*x + e))*sin(f*x + e))/f","A",0
259,1,299,0,0.857250," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{48 \, {\left(2 \, B a^{3} c d + {\left(A + 3 \, B\right)} a^{3} d^{2}\right)} \cos\left(f x + e\right)^{5} - 80 \, {\left({\left(A + 3 \, B\right)} a^{3} c^{2} + 2 \, {\left(3 \, A + 5 \, B\right)} a^{3} c d + {\left(5 \, A + 7 \, B\right)} a^{3} d^{2}\right)} \cos\left(f x + e\right)^{3} - 15 \, {\left(10 \, {\left(4 \, A + 3 \, B\right)} a^{3} c^{2} + 4 \, {\left(15 \, A + 13 \, B\right)} a^{3} c d + {\left(26 \, A + 23 \, B\right)} a^{3} d^{2}\right)} f x + 960 \, {\left({\left(A + B\right)} a^{3} c^{2} + 2 \, {\left(A + B\right)} a^{3} c d + {\left(A + B\right)} a^{3} d^{2}\right)} \cos\left(f x + e\right) + 5 \, {\left(8 \, B a^{3} d^{2} \cos\left(f x + e\right)^{5} - 2 \, {\left(6 \, B a^{3} c^{2} + 12 \, {\left(A + 3 \, B\right)} a^{3} c d + {\left(18 \, A + 31 \, B\right)} a^{3} d^{2}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(2 \, {\left(12 \, A + 17 \, B\right)} a^{3} c^{2} + 4 \, {\left(17 \, A + 19 \, B\right)} a^{3} c d + {\left(38 \, A + 41 \, B\right)} a^{3} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{240 \, f}"," ",0,"-1/240*(48*(2*B*a^3*c*d + (A + 3*B)*a^3*d^2)*cos(f*x + e)^5 - 80*((A + 3*B)*a^3*c^2 + 2*(3*A + 5*B)*a^3*c*d + (5*A + 7*B)*a^3*d^2)*cos(f*x + e)^3 - 15*(10*(4*A + 3*B)*a^3*c^2 + 4*(15*A + 13*B)*a^3*c*d + (26*A + 23*B)*a^3*d^2)*f*x + 960*((A + B)*a^3*c^2 + 2*(A + B)*a^3*c*d + (A + B)*a^3*d^2)*cos(f*x + e) + 5*(8*B*a^3*d^2*cos(f*x + e)^5 - 2*(6*B*a^3*c^2 + 12*(A + 3*B)*a^3*c*d + (18*A + 31*B)*a^3*d^2)*cos(f*x + e)^3 + 3*(2*(12*A + 17*B)*a^3*c^2 + 4*(17*A + 19*B)*a^3*c*d + (38*A + 41*B)*a^3*d^2)*cos(f*x + e))*sin(f*x + e))/f","A",0
260,1,178,0,0.554409," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{24 \, B a^{3} d \cos\left(f x + e\right)^{5} - 40 \, {\left({\left(A + 3 \, B\right)} a^{3} c + {\left(3 \, A + 5 \, B\right)} a^{3} d\right)} \cos\left(f x + e\right)^{3} - 15 \, {\left(5 \, {\left(4 \, A + 3 \, B\right)} a^{3} c + {\left(15 \, A + 13 \, B\right)} a^{3} d\right)} f x + 480 \, {\left({\left(A + B\right)} a^{3} c + {\left(A + B\right)} a^{3} d\right)} \cos\left(f x + e\right) - 15 \, {\left(2 \, {\left(B a^{3} c + {\left(A + 3 \, B\right)} a^{3} d\right)} \cos\left(f x + e\right)^{3} - {\left({\left(12 \, A + 17 \, B\right)} a^{3} c + {\left(17 \, A + 19 \, B\right)} a^{3} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{120 \, f}"," ",0,"-1/120*(24*B*a^3*d*cos(f*x + e)^5 - 40*((A + 3*B)*a^3*c + (3*A + 5*B)*a^3*d)*cos(f*x + e)^3 - 15*(5*(4*A + 3*B)*a^3*c + (15*A + 13*B)*a^3*d)*f*x + 480*((A + B)*a^3*c + (A + B)*a^3*d)*cos(f*x + e) - 15*(2*(B*a^3*c + (A + 3*B)*a^3*d)*cos(f*x + e)^3 - ((12*A + 17*B)*a^3*c + (17*A + 19*B)*a^3*d)*cos(f*x + e))*sin(f*x + e))/f","A",0
261,1,93,0,0.934487," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","\frac{8 \, {\left(A + 3 \, B\right)} a^{3} \cos\left(f x + e\right)^{3} + 15 \, {\left(4 \, A + 3 \, B\right)} a^{3} f x - 96 \, {\left(A + B\right)} a^{3} \cos\left(f x + e\right) + 3 \, {\left(2 \, B a^{3} \cos\left(f x + e\right)^{3} - {\left(12 \, A + 17 \, B\right)} a^{3} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{24 \, f}"," ",0,"1/24*(8*(A + 3*B)*a^3*cos(f*x + e)^3 + 15*(4*A + 3*B)*a^3*f*x - 96*(A + B)*a^3*cos(f*x + e) + 3*(2*B*a^3*cos(f*x + e)^3 - (12*A + 17*B)*a^3*cos(f*x + e))*sin(f*x + e))/f","A",0
262,1,627,0,1.034370," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{2 \, B a^{3} d^{3} \cos\left(f x + e\right)^{3} - 3 \, {\left(2 \, B a^{3} c^{3} - 2 \, {\left(A + 3 \, B\right)} a^{3} c^{2} d + {\left(6 \, A + 7 \, B\right)} a^{3} c d^{2} - {\left(7 \, A + 5 \, B\right)} a^{3} d^{3}\right)} f x + 3 \, {\left(B a^{3} c d^{2} - {\left(A + 3 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + 3 \, {\left(B a^{3} c^{3} - {\left(A + 2 \, B\right)} a^{3} c^{2} d + {\left(2 \, A + B\right)} a^{3} c d^{2} - A a^{3} d^{3}\right)} \sqrt{-\frac{c - d}{c + d}} \log\left(-\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} - 2 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) - 6 \, {\left(B a^{3} c^{2} d - {\left(A + 3 \, B\right)} a^{3} c d^{2} + {\left(3 \, A + 4 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right)}{6 \, d^{4} f}, \frac{2 \, B a^{3} d^{3} \cos\left(f x + e\right)^{3} - 3 \, {\left(2 \, B a^{3} c^{3} - 2 \, {\left(A + 3 \, B\right)} a^{3} c^{2} d + {\left(6 \, A + 7 \, B\right)} a^{3} c d^{2} - {\left(7 \, A + 5 \, B\right)} a^{3} d^{3}\right)} f x + 3 \, {\left(B a^{3} c d^{2} - {\left(A + 3 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) - 6 \, {\left(B a^{3} c^{3} - {\left(A + 2 \, B\right)} a^{3} c^{2} d + {\left(2 \, A + B\right)} a^{3} c d^{2} - A a^{3} d^{3}\right)} \sqrt{\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(c \sin\left(f x + e\right) + d\right)} \sqrt{\frac{c - d}{c + d}}}{{\left(c - d\right)} \cos\left(f x + e\right)}\right) - 6 \, {\left(B a^{3} c^{2} d - {\left(A + 3 \, B\right)} a^{3} c d^{2} + {\left(3 \, A + 4 \, B\right)} a^{3} d^{3}\right)} \cos\left(f x + e\right)}{6 \, d^{4} f}\right]"," ",0,"[1/6*(2*B*a^3*d^3*cos(f*x + e)^3 - 3*(2*B*a^3*c^3 - 2*(A + 3*B)*a^3*c^2*d + (6*A + 7*B)*a^3*c*d^2 - (7*A + 5*B)*a^3*d^3)*f*x + 3*(B*a^3*c*d^2 - (A + 3*B)*a^3*d^3)*cos(f*x + e)*sin(f*x + e) + 3*(B*a^3*c^3 - (A + 2*B)*a^3*c^2*d + (2*A + B)*a^3*c*d^2 - A*a^3*d^3)*sqrt(-(c - d)/(c + d))*log(-((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 - 2*((c^2 + c*d)*cos(f*x + e)*sin(f*x + e) + (c*d + d^2)*cos(f*x + e))*sqrt(-(c - d)/(c + d)))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) - 6*(B*a^3*c^2*d - (A + 3*B)*a^3*c*d^2 + (3*A + 4*B)*a^3*d^3)*cos(f*x + e))/(d^4*f), 1/6*(2*B*a^3*d^3*cos(f*x + e)^3 - 3*(2*B*a^3*c^3 - 2*(A + 3*B)*a^3*c^2*d + (6*A + 7*B)*a^3*c*d^2 - (7*A + 5*B)*a^3*d^3)*f*x + 3*(B*a^3*c*d^2 - (A + 3*B)*a^3*d^3)*cos(f*x + e)*sin(f*x + e) - 6*(B*a^3*c^3 - (A + 2*B)*a^3*c^2*d + (2*A + B)*a^3*c*d^2 - A*a^3*d^3)*sqrt((c - d)/(c + d))*arctan(-(c*sin(f*x + e) + d)*sqrt((c - d)/(c + d))/((c - d)*cos(f*x + e))) - 6*(B*a^3*c^2*d - (A + 3*B)*a^3*c*d^2 + (3*A + 4*B)*a^3*d^3)*cos(f*x + e))/(d^4*f)]","A",0
263,1,1027,0,1.137700," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(B a^{3} c d^{3} + B a^{3} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(6 \, B a^{3} c^{4} - 2 \, {\left(2 \, A + 3 \, B\right)} a^{3} c^{3} d + {\left(2 \, A - 5 \, B\right)} a^{3} c^{2} d^{2} + {\left(6 \, A + 7 \, B\right)} a^{3} c d^{3}\right)} f x + {\left(3 \, B a^{3} c^{4} - 2 \, A a^{3} c^{3} d - {\left(A + 4 \, B\right)} a^{3} c^{2} d^{2} + {\left(3 \, A + B\right)} a^{3} c d^{3} + {\left(3 \, B a^{3} c^{3} d - 2 \, A a^{3} c^{2} d^{2} - {\left(A + 4 \, B\right)} a^{3} c d^{3} + {\left(3 \, A + B\right)} a^{3} d^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + {\left(6 \, B a^{3} c^{3} d - 2 \, {\left(2 \, A + 3 \, B\right)} a^{3} c^{2} d^{2} + {\left(2 \, A - 5 \, B\right)} a^{3} c d^{3} - {\left(2 \, A + B\right)} a^{3} d^{4}\right)} \cos\left(f x + e\right) + {\left({\left(6 \, B a^{3} c^{3} d - 2 \, {\left(2 \, A + 3 \, B\right)} a^{3} c^{2} d^{2} + {\left(2 \, A - 5 \, B\right)} a^{3} c d^{3} + {\left(6 \, A + 7 \, B\right)} a^{3} d^{4}\right)} f x + {\left(3 \, B a^{3} c^{2} d^{2} - {\left(2 \, A + 3 \, B\right)} a^{3} c d^{3} - 2 \, {\left(A + 3 \, B\right)} a^{3} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c d^{5} + d^{6}\right)} f \sin\left(f x + e\right) + {\left(c^{2} d^{4} + c d^{5}\right)} f\right)}}, \frac{{\left(B a^{3} c d^{3} + B a^{3} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(6 \, B a^{3} c^{4} - 2 \, {\left(2 \, A + 3 \, B\right)} a^{3} c^{3} d + {\left(2 \, A - 5 \, B\right)} a^{3} c^{2} d^{2} + {\left(6 \, A + 7 \, B\right)} a^{3} c d^{3}\right)} f x + 2 \, {\left(3 \, B a^{3} c^{4} - 2 \, A a^{3} c^{3} d - {\left(A + 4 \, B\right)} a^{3} c^{2} d^{2} + {\left(3 \, A + B\right)} a^{3} c d^{3} + {\left(3 \, B a^{3} c^{3} d - 2 \, A a^{3} c^{2} d^{2} - {\left(A + 4 \, B\right)} a^{3} c d^{3} + {\left(3 \, A + B\right)} a^{3} d^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(c \sin\left(f x + e\right) + d\right)} \sqrt{\frac{c - d}{c + d}}}{{\left(c - d\right)} \cos\left(f x + e\right)}\right) + {\left(6 \, B a^{3} c^{3} d - 2 \, {\left(2 \, A + 3 \, B\right)} a^{3} c^{2} d^{2} + {\left(2 \, A - 5 \, B\right)} a^{3} c d^{3} - {\left(2 \, A + B\right)} a^{3} d^{4}\right)} \cos\left(f x + e\right) + {\left({\left(6 \, B a^{3} c^{3} d - 2 \, {\left(2 \, A + 3 \, B\right)} a^{3} c^{2} d^{2} + {\left(2 \, A - 5 \, B\right)} a^{3} c d^{3} + {\left(6 \, A + 7 \, B\right)} a^{3} d^{4}\right)} f x + {\left(3 \, B a^{3} c^{2} d^{2} - {\left(2 \, A + 3 \, B\right)} a^{3} c d^{3} - 2 \, {\left(A + 3 \, B\right)} a^{3} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c d^{5} + d^{6}\right)} f \sin\left(f x + e\right) + {\left(c^{2} d^{4} + c d^{5}\right)} f\right)}}\right]"," ",0,"[1/2*((B*a^3*c*d^3 + B*a^3*d^4)*cos(f*x + e)^3 + (6*B*a^3*c^4 - 2*(2*A + 3*B)*a^3*c^3*d + (2*A - 5*B)*a^3*c^2*d^2 + (6*A + 7*B)*a^3*c*d^3)*f*x + (3*B*a^3*c^4 - 2*A*a^3*c^3*d - (A + 4*B)*a^3*c^2*d^2 + (3*A + B)*a^3*c*d^3 + (3*B*a^3*c^3*d - 2*A*a^3*c^2*d^2 - (A + 4*B)*a^3*c*d^3 + (3*A + B)*a^3*d^4)*sin(f*x + e))*sqrt(-(c - d)/(c + d))*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*((c^2 + c*d)*cos(f*x + e)*sin(f*x + e) + (c*d + d^2)*cos(f*x + e))*sqrt(-(c - d)/(c + d)))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + (6*B*a^3*c^3*d - 2*(2*A + 3*B)*a^3*c^2*d^2 + (2*A - 5*B)*a^3*c*d^3 - (2*A + B)*a^3*d^4)*cos(f*x + e) + ((6*B*a^3*c^3*d - 2*(2*A + 3*B)*a^3*c^2*d^2 + (2*A - 5*B)*a^3*c*d^3 + (6*A + 7*B)*a^3*d^4)*f*x + (3*B*a^3*c^2*d^2 - (2*A + 3*B)*a^3*c*d^3 - 2*(A + 3*B)*a^3*d^4)*cos(f*x + e))*sin(f*x + e))/((c*d^5 + d^6)*f*sin(f*x + e) + (c^2*d^4 + c*d^5)*f), 1/2*((B*a^3*c*d^3 + B*a^3*d^4)*cos(f*x + e)^3 + (6*B*a^3*c^4 - 2*(2*A + 3*B)*a^3*c^3*d + (2*A - 5*B)*a^3*c^2*d^2 + (6*A + 7*B)*a^3*c*d^3)*f*x + 2*(3*B*a^3*c^4 - 2*A*a^3*c^3*d - (A + 4*B)*a^3*c^2*d^2 + (3*A + B)*a^3*c*d^3 + (3*B*a^3*c^3*d - 2*A*a^3*c^2*d^2 - (A + 4*B)*a^3*c*d^3 + (3*A + B)*a^3*d^4)*sin(f*x + e))*sqrt((c - d)/(c + d))*arctan(-(c*sin(f*x + e) + d)*sqrt((c - d)/(c + d))/((c - d)*cos(f*x + e))) + (6*B*a^3*c^3*d - 2*(2*A + 3*B)*a^3*c^2*d^2 + (2*A - 5*B)*a^3*c*d^3 - (2*A + B)*a^3*d^4)*cos(f*x + e) + ((6*B*a^3*c^3*d - 2*(2*A + 3*B)*a^3*c^2*d^2 + (2*A - 5*B)*a^3*c*d^3 + (6*A + 7*B)*a^3*d^4)*f*x + (3*B*a^3*c^2*d^2 - (2*A + 3*B)*a^3*c*d^3 - 2*(A + 3*B)*a^3*d^4)*cos(f*x + e))*sin(f*x + e))/((c*d^5 + d^6)*f*sin(f*x + e) + (c^2*d^4 + c*d^5)*f)]","A",0
264,1,1670,0,1.300531," ","integrate((a+a*sin(f*x+e))^3*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(3 \, B a^{3} c^{3} d^{2} - {\left(A - 3 \, B\right)} a^{3} c^{2} d^{3} - {\left(2 \, A + 3 \, B\right)} a^{3} c d^{4} - {\left(A + 3 \, B\right)} a^{3} d^{5}\right)} f x \cos\left(f x + e\right)^{2} + 4 \, {\left(B a^{3} c^{2} d^{3} + 2 \, B a^{3} c d^{4} + B a^{3} d^{5}\right)} \cos\left(f x + e\right)^{3} - 4 \, {\left(3 \, B a^{3} c^{5} - {\left(A - 3 \, B\right)} a^{3} c^{4} d - 2 \, A a^{3} c^{3} d^{2} - 2 \, A a^{3} c^{2} d^{3} - {\left(2 \, A + 3 \, B\right)} a^{3} c d^{4} - {\left(A + 3 \, B\right)} a^{3} d^{5}\right)} f x - {\left(6 \, B a^{3} c^{5} - 2 \, {\left(A - 6 \, B\right)} a^{3} c^{4} d - 3 \, {\left(2 \, A - 3 \, B\right)} a^{3} c^{3} d^{2} - 3 \, {\left(3 \, A - 2 \, B\right)} a^{3} c^{2} d^{3} - 3 \, {\left(2 \, A - B\right)} a^{3} c d^{4} - {\left(7 \, A + 6 \, B\right)} a^{3} d^{5} - {\left(6 \, B a^{3} c^{3} d^{2} - 2 \, {\left(A - 6 \, B\right)} a^{3} c^{2} d^{3} - 3 \, {\left(2 \, A - B\right)} a^{3} c d^{4} - {\left(7 \, A + 6 \, B\right)} a^{3} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(6 \, B a^{3} c^{4} d - 2 \, {\left(A - 6 \, B\right)} a^{3} c^{3} d^{2} - 3 \, {\left(2 \, A - B\right)} a^{3} c^{2} d^{3} - {\left(7 \, A + 6 \, B\right)} a^{3} c d^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left({\left(c^{2} + c d\right)} \cos\left(f x + e\right) \sin\left(f x + e\right) + {\left(c d + d^{2}\right)} \cos\left(f x + e\right)\right)} \sqrt{-\frac{c - d}{c + d}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) - 2 \, {\left(6 \, B a^{3} c^{4} d - 2 \, {\left(A - 3 \, B\right)} a^{3} c^{3} d^{2} - {\left(4 \, A + 3 \, B\right)} a^{3} c^{2} d^{3} + 5 \, {\left(A + B\right)} a^{3} c d^{4} + {\left(A + 2 \, B\right)} a^{3} d^{5}\right)} \cos\left(f x + e\right) - 2 \, {\left(4 \, {\left(3 \, B a^{3} c^{4} d - {\left(A - 3 \, B\right)} a^{3} c^{3} d^{2} - {\left(2 \, A + 3 \, B\right)} a^{3} c^{2} d^{3} - {\left(A + 3 \, B\right)} a^{3} c d^{4}\right)} f x + {\left(9 \, B a^{3} c^{3} d^{2} - 3 \, {\left(A - 3 \, B\right)} a^{3} c^{2} d^{3} - {\left(3 \, A + 4 \, B\right)} a^{3} c d^{4} + 2 \, {\left(3 \, A + B\right)} a^{3} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(c^{2} d^{6} + 2 \, c d^{7} + d^{8}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{3} d^{5} + 2 \, c^{2} d^{6} + c d^{7}\right)} f \sin\left(f x + e\right) - {\left(c^{4} d^{4} + 2 \, c^{3} d^{5} + 2 \, c^{2} d^{6} + 2 \, c d^{7} + d^{8}\right)} f\right)}}, -\frac{2 \, {\left(3 \, B a^{3} c^{3} d^{2} - {\left(A - 3 \, B\right)} a^{3} c^{2} d^{3} - {\left(2 \, A + 3 \, B\right)} a^{3} c d^{4} - {\left(A + 3 \, B\right)} a^{3} d^{5}\right)} f x \cos\left(f x + e\right)^{2} + 2 \, {\left(B a^{3} c^{2} d^{3} + 2 \, B a^{3} c d^{4} + B a^{3} d^{5}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(3 \, B a^{3} c^{5} - {\left(A - 3 \, B\right)} a^{3} c^{4} d - 2 \, A a^{3} c^{3} d^{2} - 2 \, A a^{3} c^{2} d^{3} - {\left(2 \, A + 3 \, B\right)} a^{3} c d^{4} - {\left(A + 3 \, B\right)} a^{3} d^{5}\right)} f x - {\left(6 \, B a^{3} c^{5} - 2 \, {\left(A - 6 \, B\right)} a^{3} c^{4} d - 3 \, {\left(2 \, A - 3 \, B\right)} a^{3} c^{3} d^{2} - 3 \, {\left(3 \, A - 2 \, B\right)} a^{3} c^{2} d^{3} - 3 \, {\left(2 \, A - B\right)} a^{3} c d^{4} - {\left(7 \, A + 6 \, B\right)} a^{3} d^{5} - {\left(6 \, B a^{3} c^{3} d^{2} - 2 \, {\left(A - 6 \, B\right)} a^{3} c^{2} d^{3} - 3 \, {\left(2 \, A - B\right)} a^{3} c d^{4} - {\left(7 \, A + 6 \, B\right)} a^{3} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(6 \, B a^{3} c^{4} d - 2 \, {\left(A - 6 \, B\right)} a^{3} c^{3} d^{2} - 3 \, {\left(2 \, A - B\right)} a^{3} c^{2} d^{3} - {\left(7 \, A + 6 \, B\right)} a^{3} c d^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{c - d}{c + d}} \arctan\left(-\frac{{\left(c \sin\left(f x + e\right) + d\right)} \sqrt{\frac{c - d}{c + d}}}{{\left(c - d\right)} \cos\left(f x + e\right)}\right) - {\left(6 \, B a^{3} c^{4} d - 2 \, {\left(A - 3 \, B\right)} a^{3} c^{3} d^{2} - {\left(4 \, A + 3 \, B\right)} a^{3} c^{2} d^{3} + 5 \, {\left(A + B\right)} a^{3} c d^{4} + {\left(A + 2 \, B\right)} a^{3} d^{5}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(3 \, B a^{3} c^{4} d - {\left(A - 3 \, B\right)} a^{3} c^{3} d^{2} - {\left(2 \, A + 3 \, B\right)} a^{3} c^{2} d^{3} - {\left(A + 3 \, B\right)} a^{3} c d^{4}\right)} f x + {\left(9 \, B a^{3} c^{3} d^{2} - 3 \, {\left(A - 3 \, B\right)} a^{3} c^{2} d^{3} - {\left(3 \, A + 4 \, B\right)} a^{3} c d^{4} + 2 \, {\left(3 \, A + B\right)} a^{3} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{2} d^{6} + 2 \, c d^{7} + d^{8}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{3} d^{5} + 2 \, c^{2} d^{6} + c d^{7}\right)} f \sin\left(f x + e\right) - {\left(c^{4} d^{4} + 2 \, c^{3} d^{5} + 2 \, c^{2} d^{6} + 2 \, c d^{7} + d^{8}\right)} f\right)}}\right]"," ",0,"[-1/4*(4*(3*B*a^3*c^3*d^2 - (A - 3*B)*a^3*c^2*d^3 - (2*A + 3*B)*a^3*c*d^4 - (A + 3*B)*a^3*d^5)*f*x*cos(f*x + e)^2 + 4*(B*a^3*c^2*d^3 + 2*B*a^3*c*d^4 + B*a^3*d^5)*cos(f*x + e)^3 - 4*(3*B*a^3*c^5 - (A - 3*B)*a^3*c^4*d - 2*A*a^3*c^3*d^2 - 2*A*a^3*c^2*d^3 - (2*A + 3*B)*a^3*c*d^4 - (A + 3*B)*a^3*d^5)*f*x - (6*B*a^3*c^5 - 2*(A - 6*B)*a^3*c^4*d - 3*(2*A - 3*B)*a^3*c^3*d^2 - 3*(3*A - 2*B)*a^3*c^2*d^3 - 3*(2*A - B)*a^3*c*d^4 - (7*A + 6*B)*a^3*d^5 - (6*B*a^3*c^3*d^2 - 2*(A - 6*B)*a^3*c^2*d^3 - 3*(2*A - B)*a^3*c*d^4 - (7*A + 6*B)*a^3*d^5)*cos(f*x + e)^2 + 2*(6*B*a^3*c^4*d - 2*(A - 6*B)*a^3*c^3*d^2 - 3*(2*A - B)*a^3*c^2*d^3 - (7*A + 6*B)*a^3*c*d^4)*sin(f*x + e))*sqrt(-(c - d)/(c + d))*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*((c^2 + c*d)*cos(f*x + e)*sin(f*x + e) + (c*d + d^2)*cos(f*x + e))*sqrt(-(c - d)/(c + d)))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) - 2*(6*B*a^3*c^4*d - 2*(A - 3*B)*a^3*c^3*d^2 - (4*A + 3*B)*a^3*c^2*d^3 + 5*(A + B)*a^3*c*d^4 + (A + 2*B)*a^3*d^5)*cos(f*x + e) - 2*(4*(3*B*a^3*c^4*d - (A - 3*B)*a^3*c^3*d^2 - (2*A + 3*B)*a^3*c^2*d^3 - (A + 3*B)*a^3*c*d^4)*f*x + (9*B*a^3*c^3*d^2 - 3*(A - 3*B)*a^3*c^2*d^3 - (3*A + 4*B)*a^3*c*d^4 + 2*(3*A + B)*a^3*d^5)*cos(f*x + e))*sin(f*x + e))/((c^2*d^6 + 2*c*d^7 + d^8)*f*cos(f*x + e)^2 - 2*(c^3*d^5 + 2*c^2*d^6 + c*d^7)*f*sin(f*x + e) - (c^4*d^4 + 2*c^3*d^5 + 2*c^2*d^6 + 2*c*d^7 + d^8)*f), -1/2*(2*(3*B*a^3*c^3*d^2 - (A - 3*B)*a^3*c^2*d^3 - (2*A + 3*B)*a^3*c*d^4 - (A + 3*B)*a^3*d^5)*f*x*cos(f*x + e)^2 + 2*(B*a^3*c^2*d^3 + 2*B*a^3*c*d^4 + B*a^3*d^5)*cos(f*x + e)^3 - 2*(3*B*a^3*c^5 - (A - 3*B)*a^3*c^4*d - 2*A*a^3*c^3*d^2 - 2*A*a^3*c^2*d^3 - (2*A + 3*B)*a^3*c*d^4 - (A + 3*B)*a^3*d^5)*f*x - (6*B*a^3*c^5 - 2*(A - 6*B)*a^3*c^4*d - 3*(2*A - 3*B)*a^3*c^3*d^2 - 3*(3*A - 2*B)*a^3*c^2*d^3 - 3*(2*A - B)*a^3*c*d^4 - (7*A + 6*B)*a^3*d^5 - (6*B*a^3*c^3*d^2 - 2*(A - 6*B)*a^3*c^2*d^3 - 3*(2*A - B)*a^3*c*d^4 - (7*A + 6*B)*a^3*d^5)*cos(f*x + e)^2 + 2*(6*B*a^3*c^4*d - 2*(A - 6*B)*a^3*c^3*d^2 - 3*(2*A - B)*a^3*c^2*d^3 - (7*A + 6*B)*a^3*c*d^4)*sin(f*x + e))*sqrt((c - d)/(c + d))*arctan(-(c*sin(f*x + e) + d)*sqrt((c - d)/(c + d))/((c - d)*cos(f*x + e))) - (6*B*a^3*c^4*d - 2*(A - 3*B)*a^3*c^3*d^2 - (4*A + 3*B)*a^3*c^2*d^3 + 5*(A + B)*a^3*c*d^4 + (A + 2*B)*a^3*d^5)*cos(f*x + e) - (4*(3*B*a^3*c^4*d - (A - 3*B)*a^3*c^3*d^2 - (2*A + 3*B)*a^3*c^2*d^3 - (A + 3*B)*a^3*c*d^4)*f*x + (9*B*a^3*c^3*d^2 - 3*(A - 3*B)*a^3*c^2*d^3 - (3*A + 4*B)*a^3*c*d^4 + 2*(3*A + B)*a^3*d^5)*cos(f*x + e))*sin(f*x + e))/((c^2*d^6 + 2*c*d^7 + d^8)*f*cos(f*x + e)^2 - 2*(c^3*d^5 + 2*c^2*d^6 + c*d^7)*f*sin(f*x + e) - (c^4*d^4 + 2*c^3*d^5 + 2*c^2*d^6 + 2*c*d^7 + d^8)*f)]","B",0
265,1,470,0,0.992045," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, B d^{3} \cos\left(f x + e\right)^{4} - 6 \, {\left(A - B\right)} c^{3} + 18 \, {\left(A - B\right)} c^{2} d - 18 \, {\left(A - B\right)} c d^{2} + 6 \, {\left(A - B\right)} d^{3} + {\left(9 \, B c d^{2} + {\left(3 \, A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(2 \, B c^{3} + 6 \, {\left(A - B\right)} c^{2} d - 3 \, {\left(2 \, A - 3 \, B\right)} c d^{2} + 3 \, {\left(A - B\right)} d^{3}\right)} f x - 6 \, {\left(3 \, B c^{2} d + 3 \, {\left(A - B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(2 \, {\left(A - B\right)} c^{3} - 6 \, {\left(A - 2 \, B\right)} c^{2} d + 3 \, {\left(4 \, A - 3 \, B\right)} c d^{2} - {\left(3 \, A - 5 \, B\right)} d^{3} - {\left(2 \, B c^{3} + 6 \, {\left(A - B\right)} c^{2} d - 3 \, {\left(2 \, A - 3 \, B\right)} c d^{2} + 3 \, {\left(A - B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right) + {\left(2 \, B d^{3} \cos\left(f x + e\right)^{3} + 6 \, {\left(A - B\right)} c^{3} - 18 \, {\left(A - B\right)} c^{2} d + 18 \, {\left(A - B\right)} c d^{2} - 6 \, {\left(A - B\right)} d^{3} + 3 \, {\left(2 \, B c^{3} + 6 \, {\left(A - B\right)} c^{2} d - 3 \, {\left(2 \, A - 3 \, B\right)} c d^{2} + 3 \, {\left(A - B\right)} d^{3}\right)} f x - 3 \, {\left(3 \, B c d^{2} + {\left(A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(6 \, B c^{2} d + 3 \, {\left(2 \, A - B\right)} c d^{2} - {\left(A - 3 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"1/6*(2*B*d^3*cos(f*x + e)^4 - 6*(A - B)*c^3 + 18*(A - B)*c^2*d - 18*(A - B)*c*d^2 + 6*(A - B)*d^3 + (9*B*c*d^2 + (3*A - B)*d^3)*cos(f*x + e)^3 + 3*(2*B*c^3 + 6*(A - B)*c^2*d - 3*(2*A - 3*B)*c*d^2 + 3*(A - B)*d^3)*f*x - 6*(3*B*c^2*d + 3*(A - B)*c*d^2 - (A - 2*B)*d^3)*cos(f*x + e)^2 - 3*(2*(A - B)*c^3 - 6*(A - 2*B)*c^2*d + 3*(4*A - 3*B)*c*d^2 - (3*A - 5*B)*d^3 - (2*B*c^3 + 6*(A - B)*c^2*d - 3*(2*A - 3*B)*c*d^2 + 3*(A - B)*d^3)*f*x)*cos(f*x + e) + (2*B*d^3*cos(f*x + e)^3 + 6*(A - B)*c^3 - 18*(A - B)*c^2*d + 18*(A - B)*c*d^2 - 6*(A - B)*d^3 + 3*(2*B*c^3 + 6*(A - B)*c^2*d - 3*(2*A - 3*B)*c*d^2 + 3*(A - B)*d^3)*f*x - 3*(3*B*c*d^2 + (A - B)*d^3)*cos(f*x + e)^2 - 3*(6*B*c^2*d + 3*(2*A - B)*c*d^2 - (A - 3*B)*d^3)*cos(f*x + e))*sin(f*x + e))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","B",0
266,1,303,0,0.863122," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{B d^{2} \cos\left(f x + e\right)^{3} - 2 \, {\left(A - B\right)} c^{2} + 4 \, {\left(A - B\right)} c d - 2 \, {\left(A - B\right)} d^{2} + {\left(2 \, B c^{2} + 4 \, {\left(A - B\right)} c d - {\left(2 \, A - 3 \, B\right)} d^{2}\right)} f x - 2 \, {\left(2 \, B c d + {\left(A - B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, {\left(A - B\right)} c^{2} - 4 \, {\left(A - 2 \, B\right)} c d + {\left(4 \, A - 3 \, B\right)} d^{2} - {\left(2 \, B c^{2} + 4 \, {\left(A - B\right)} c d - {\left(2 \, A - 3 \, B\right)} d^{2}\right)} f x\right)} \cos\left(f x + e\right) - {\left(B d^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A - B\right)} c^{2} + 4 \, {\left(A - B\right)} c d - 2 \, {\left(A - B\right)} d^{2} - {\left(2 \, B c^{2} + 4 \, {\left(A - B\right)} c d - {\left(2 \, A - 3 \, B\right)} d^{2}\right)} f x + {\left(4 \, B c d + {\left(2 \, A - B\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"1/2*(B*d^2*cos(f*x + e)^3 - 2*(A - B)*c^2 + 4*(A - B)*c*d - 2*(A - B)*d^2 + (2*B*c^2 + 4*(A - B)*c*d - (2*A - 3*B)*d^2)*f*x - 2*(2*B*c*d + (A - B)*d^2)*cos(f*x + e)^2 - (2*(A - B)*c^2 - 4*(A - 2*B)*c*d + (4*A - 3*B)*d^2 - (2*B*c^2 + 4*(A - B)*c*d - (2*A - 3*B)*d^2)*f*x)*cos(f*x + e) - (B*d^2*cos(f*x + e)^2 - 2*(A - B)*c^2 + 4*(A - B)*c*d - 2*(A - B)*d^2 - (2*B*c^2 + 4*(A - B)*c*d - (2*A - 3*B)*d^2)*f*x + (4*B*c*d + (2*A - B)*d^2)*cos(f*x + e))*sin(f*x + e))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","B",0
267,1,154,0,1.096297," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{B d \cos\left(f x + e\right)^{2} - {\left(B c + {\left(A - B\right)} d\right)} f x + {\left(A - B\right)} c - {\left(A - B\right)} d - {\left({\left(B c + {\left(A - B\right)} d\right)} f x - {\left(A - B\right)} c + {\left(A - 2 \, B\right)} d\right)} \cos\left(f x + e\right) - {\left({\left(B c + {\left(A - B\right)} d\right)} f x - B d \cos\left(f x + e\right) + {\left(A - B\right)} c - {\left(A - B\right)} d\right)} \sin\left(f x + e\right)}{a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f}"," ",0,"-(B*d*cos(f*x + e)^2 - (B*c + (A - B)*d)*f*x + (A - B)*c - (A - B)*d - ((B*c + (A - B)*d)*f*x - (A - B)*c + (A - 2*B)*d)*cos(f*x + e) - ((B*c + (A - B)*d)*f*x - B*d*cos(f*x + e) + (A - B)*c - (A - B)*d)*sin(f*x + e))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","B",0
268,1,66,0,0.881288," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","\frac{B f x + {\left(B f x - A + B\right)} \cos\left(f x + e\right) + {\left(B f x + A - B\right)} \sin\left(f x + e\right) - A + B}{a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f}"," ",0,"(B*f*x + (B*f*x - A + B)*cos(f*x + e) + (B*f*x + A - B)*sin(f*x + e) - A + B)/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","A",0
269,1,595,0,0.571814," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(A - B\right)} c^{2} - 2 \, {\left(A - B\right)} d^{2} + {\left(B c - A d + {\left(B c - A d\right)} \cos\left(f x + e\right) + {\left(B c - A d\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left({\left(A - B\right)} c^{2} - {\left(A - B\right)} d^{2}\right)} \cos\left(f x + e\right) - 2 \, {\left({\left(A - B\right)} c^{2} - {\left(A - B\right)} d^{2}\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f \cos\left(f x + e\right) + {\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f \sin\left(f x + e\right) + {\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f\right)}}, -\frac{{\left(A - B\right)} c^{2} - {\left(A - B\right)} d^{2} + {\left(B c - A d + {\left(B c - A d\right)} \cos\left(f x + e\right) + {\left(B c - A d\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + {\left({\left(A - B\right)} c^{2} - {\left(A - B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left({\left(A - B\right)} c^{2} - {\left(A - B\right)} d^{2}\right)} \sin\left(f x + e\right)}{{\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f \cos\left(f x + e\right) + {\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f \sin\left(f x + e\right) + {\left(a c^{3} - a c^{2} d - a c d^{2} + a d^{3}\right)} f}\right]"," ",0,"[-1/2*(2*(A - B)*c^2 - 2*(A - B)*d^2 + (B*c - A*d + (B*c - A*d)*cos(f*x + e) + (B*c - A*d)*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*((A - B)*c^2 - (A - B)*d^2)*cos(f*x + e) - 2*((A - B)*c^2 - (A - B)*d^2)*sin(f*x + e))/((a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f*cos(f*x + e) + (a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f*sin(f*x + e) + (a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f), -((A - B)*c^2 - (A - B)*d^2 + (B*c - A*d + (B*c - A*d)*cos(f*x + e) + (B*c - A*d)*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + ((A - B)*c^2 - (A - B)*d^2)*cos(f*x + e) - ((A - B)*c^2 - (A - B)*d^2)*sin(f*x + e))/((a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f*cos(f*x + e) + (a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f*sin(f*x + e) + (a*c^3 - a*c^2*d - a*c*d^2 + a*d^3)*f)]","B",0
270,1,1538,0,0.624061," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(A - B\right)} c^{4} - 4 \, {\left(A - B\right)} c^{2} d^{2} + 2 \, {\left(A - B\right)} d^{4} + 2 \, {\left({\left(A - 2 \, B\right)} c^{3} d + {\left(2 \, A - B\right)} c^{2} d^{2} - {\left(A - 2 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{3} - 2 \, {\left(A - B\right)} c^{2} d - {\left(3 \, A - 2 \, B\right)} c d^{2} - {\left(A - B\right)} d^{3} - {\left(B c^{2} d - {\left(2 \, A - B\right)} c d^{2} - {\left(A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{3} - {\left(2 \, A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(B c^{3} - 2 \, {\left(A - B\right)} c^{2} d - {\left(3 \, A - 2 \, B\right)} c d^{2} - {\left(A - B\right)} d^{3} + {\left(B c^{2} d - {\left(2 \, A - B\right)} c d^{2} - {\left(A - B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left({\left(A - B\right)} c^{4} + {\left(A - 2 \, B\right)} c^{3} d + B c^{2} d^{2} - {\left(A - 2 \, B\right)} c d^{3} - A d^{4}\right)} \cos\left(f x + e\right) - 2 \, {\left({\left(A - B\right)} c^{4} - 2 \, {\left(A - B\right)} c^{2} d^{2} + {\left(A - B\right)} d^{4} - {\left({\left(A - 2 \, B\right)} c^{3} d + {\left(2 \, A - B\right)} c^{2} d^{2} - {\left(A - 2 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a c^{5} d - a c^{4} d^{2} - 2 \, a c^{3} d^{3} + 2 \, a c^{2} d^{4} + a c d^{5} - a d^{6}\right)} f \cos\left(f x + e\right)^{2} - {\left(a c^{6} - a c^{5} d - 2 \, a c^{4} d^{2} + 2 \, a c^{3} d^{3} + a c^{2} d^{4} - a c d^{5}\right)} f \cos\left(f x + e\right) - {\left(a c^{6} - 3 \, a c^{4} d^{2} + 3 \, a c^{2} d^{4} - a d^{6}\right)} f - {\left({\left(a c^{5} d - a c^{4} d^{2} - 2 \, a c^{3} d^{3} + 2 \, a c^{2} d^{4} + a c d^{5} - a d^{6}\right)} f \cos\left(f x + e\right) + {\left(a c^{6} - 3 \, a c^{4} d^{2} + 3 \, a c^{2} d^{4} - a d^{6}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{{\left(A - B\right)} c^{4} - 2 \, {\left(A - B\right)} c^{2} d^{2} + {\left(A - B\right)} d^{4} + {\left({\left(A - 2 \, B\right)} c^{3} d + {\left(2 \, A - B\right)} c^{2} d^{2} - {\left(A - 2 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{3} - 2 \, {\left(A - B\right)} c^{2} d - {\left(3 \, A - 2 \, B\right)} c d^{2} - {\left(A - B\right)} d^{3} - {\left(B c^{2} d - {\left(2 \, A - B\right)} c d^{2} - {\left(A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{3} - {\left(2 \, A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(B c^{3} - 2 \, {\left(A - B\right)} c^{2} d - {\left(3 \, A - 2 \, B\right)} c d^{2} - {\left(A - B\right)} d^{3} + {\left(B c^{2} d - {\left(2 \, A - B\right)} c d^{2} - {\left(A - B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + {\left({\left(A - B\right)} c^{4} + {\left(A - 2 \, B\right)} c^{3} d + B c^{2} d^{2} - {\left(A - 2 \, B\right)} c d^{3} - A d^{4}\right)} \cos\left(f x + e\right) - {\left({\left(A - B\right)} c^{4} - 2 \, {\left(A - B\right)} c^{2} d^{2} + {\left(A - B\right)} d^{4} - {\left({\left(A - 2 \, B\right)} c^{3} d + {\left(2 \, A - B\right)} c^{2} d^{2} - {\left(A - 2 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{{\left(a c^{5} d - a c^{4} d^{2} - 2 \, a c^{3} d^{3} + 2 \, a c^{2} d^{4} + a c d^{5} - a d^{6}\right)} f \cos\left(f x + e\right)^{2} - {\left(a c^{6} - a c^{5} d - 2 \, a c^{4} d^{2} + 2 \, a c^{3} d^{3} + a c^{2} d^{4} - a c d^{5}\right)} f \cos\left(f x + e\right) - {\left(a c^{6} - 3 \, a c^{4} d^{2} + 3 \, a c^{2} d^{4} - a d^{6}\right)} f - {\left({\left(a c^{5} d - a c^{4} d^{2} - 2 \, a c^{3} d^{3} + 2 \, a c^{2} d^{4} + a c d^{5} - a d^{6}\right)} f \cos\left(f x + e\right) + {\left(a c^{6} - 3 \, a c^{4} d^{2} + 3 \, a c^{2} d^{4} - a d^{6}\right)} f\right)} \sin\left(f x + e\right)}\right]"," ",0,"[1/2*(2*(A - B)*c^4 - 4*(A - B)*c^2*d^2 + 2*(A - B)*d^4 + 2*((A - 2*B)*c^3*d + (2*A - B)*c^2*d^2 - (A - 2*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e)^2 + (B*c^3 - 2*(A - B)*c^2*d - (3*A - 2*B)*c*d^2 - (A - B)*d^3 - (B*c^2*d - (2*A - B)*c*d^2 - (A - B)*d^3)*cos(f*x + e)^2 + (B*c^3 - (2*A - B)*c^2*d - (A - B)*c*d^2)*cos(f*x + e) + (B*c^3 - 2*(A - B)*c^2*d - (3*A - 2*B)*c*d^2 - (A - B)*d^3 + (B*c^2*d - (2*A - B)*c*d^2 - (A - B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*((A - B)*c^4 + (A - 2*B)*c^3*d + B*c^2*d^2 - (A - 2*B)*c*d^3 - A*d^4)*cos(f*x + e) - 2*((A - B)*c^4 - 2*(A - B)*c^2*d^2 + (A - B)*d^4 - ((A - 2*B)*c^3*d + (2*A - B)*c^2*d^2 - (A - 2*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e))*sin(f*x + e))/((a*c^5*d - a*c^4*d^2 - 2*a*c^3*d^3 + 2*a*c^2*d^4 + a*c*d^5 - a*d^6)*f*cos(f*x + e)^2 - (a*c^6 - a*c^5*d - 2*a*c^4*d^2 + 2*a*c^3*d^3 + a*c^2*d^4 - a*c*d^5)*f*cos(f*x + e) - (a*c^6 - 3*a*c^4*d^2 + 3*a*c^2*d^4 - a*d^6)*f - ((a*c^5*d - a*c^4*d^2 - 2*a*c^3*d^3 + 2*a*c^2*d^4 + a*c*d^5 - a*d^6)*f*cos(f*x + e) + (a*c^6 - 3*a*c^4*d^2 + 3*a*c^2*d^4 - a*d^6)*f)*sin(f*x + e)), ((A - B)*c^4 - 2*(A - B)*c^2*d^2 + (A - B)*d^4 + ((A - 2*B)*c^3*d + (2*A - B)*c^2*d^2 - (A - 2*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e)^2 + (B*c^3 - 2*(A - B)*c^2*d - (3*A - 2*B)*c*d^2 - (A - B)*d^3 - (B*c^2*d - (2*A - B)*c*d^2 - (A - B)*d^3)*cos(f*x + e)^2 + (B*c^3 - (2*A - B)*c^2*d - (A - B)*c*d^2)*cos(f*x + e) + (B*c^3 - 2*(A - B)*c^2*d - (3*A - 2*B)*c*d^2 - (A - B)*d^3 + (B*c^2*d - (2*A - B)*c*d^2 - (A - B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + ((A - B)*c^4 + (A - 2*B)*c^3*d + B*c^2*d^2 - (A - 2*B)*c*d^3 - A*d^4)*cos(f*x + e) - ((A - B)*c^4 - 2*(A - B)*c^2*d^2 + (A - B)*d^4 - ((A - 2*B)*c^3*d + (2*A - B)*c^2*d^2 - (A - 2*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e))*sin(f*x + e))/((a*c^5*d - a*c^4*d^2 - 2*a*c^3*d^3 + 2*a*c^2*d^4 + a*c*d^5 - a*d^6)*f*cos(f*x + e)^2 - (a*c^6 - a*c^5*d - 2*a*c^4*d^2 + 2*a*c^3*d^3 + a*c^2*d^4 - a*c*d^5)*f*cos(f*x + e) - (a*c^6 - 3*a*c^4*d^2 + 3*a*c^2*d^4 - a*d^6)*f - ((a*c^5*d - a*c^4*d^2 - 2*a*c^3*d^3 + 2*a*c^2*d^4 + a*c*d^5 - a*d^6)*f*cos(f*x + e) + (a*c^6 - 3*a*c^4*d^2 + 3*a*c^2*d^4 - a*d^6)*f)*sin(f*x + e))]","B",0
271,1,3303,0,1.089489," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(A - B\right)} c^{6} - 12 \, {\left(A - B\right)} c^{4} d^{2} + 12 \, {\left(A - B\right)} c^{2} d^{4} - 4 \, {\left(A - B\right)} d^{6} - 2 \, {\left({\left(2 \, A - 5 \, B\right)} c^{4} d^{2} + 3 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{3} + {\left(2 \, A + B\right)} c^{2} d^{4} - 3 \, {\left(3 \, A - 2 \, B\right)} c d^{5} - 4 \, {\left(A - B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(4 \, {\left(A - 2 \, B\right)} c^{5} d + 4 \, {\left(3 \, A - 2 \, B\right)} c^{4} d^{2} - {\left(2 \, A - 7 \, B\right)} c^{3} d^{3} - 5 \, {\left(3 \, A - 2 \, B\right)} c^{2} d^{4} - {\left(2 \, A - B\right)} c d^{5} + {\left(3 \, A - 2 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, B c^{5} - 2 \, {\left(3 \, A - 4 \, B\right)} c^{4} d - {\left(18 \, A - 17 \, B\right)} c^{3} d^{2} - {\left(21 \, A - 20 \, B\right)} c^{2} d^{3} - {\left(12 \, A - 11 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5} - {\left(2 \, B c^{3} d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(6 \, A - 7 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(4 \, B c^{4} d - 2 \, {\left(6 \, A - 5 \, B\right)} c^{3} d^{2} - 18 \, {\left(A - B\right)} c^{2} d^{3} - {\left(12 \, A - 11 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, B c^{5} - 2 \, {\left(3 \, A - 2 \, B\right)} c^{4} d - 3 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{2} - 3 \, {\left(3 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(6 \, A - 7 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) + {\left(2 \, B c^{5} - 2 \, {\left(3 \, A - 4 \, B\right)} c^{4} d - {\left(18 \, A - 17 \, B\right)} c^{3} d^{2} - {\left(21 \, A - 20 \, B\right)} c^{2} d^{3} - {\left(12 \, A - 11 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5} - {\left(2 \, B c^{3} d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(6 \, A - 7 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, B c^{4} d - 2 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{2} - {\left(6 \, A - 7 \, B\right)} c^{2} d^{3} - {\left(3 \, A - 2 \, B\right)} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(-\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} - 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left(2 \, {\left(A - B\right)} c^{6} + 4 \, {\left(A - 2 \, B\right)} c^{5} d + {\left(8 \, A - 7 \, B\right)} c^{4} d^{2} + {\left(7 \, A + B\right)} c^{3} d^{3} - {\left(7 \, A - 5 \, B\right)} c^{2} d^{4} - {\left(11 \, A - 7 \, B\right)} c d^{5} - {\left(3 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) - 2 \, {\left(2 \, {\left(A - B\right)} c^{6} - 6 \, {\left(A - B\right)} c^{4} d^{2} + 6 \, {\left(A - B\right)} c^{2} d^{4} - 2 \, {\left(A - B\right)} d^{6} - {\left({\left(2 \, A - 5 \, B\right)} c^{4} d^{2} + 3 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{3} + {\left(2 \, A + B\right)} c^{2} d^{4} - 3 \, {\left(3 \, A - 2 \, B\right)} c d^{5} - 4 \, {\left(A - B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} - {\left(4 \, {\left(A - 2 \, B\right)} c^{5} d + {\left(14 \, A - 13 \, B\right)} c^{4} d^{2} + {\left(7 \, A + B\right)} c^{3} d^{3} - {\left(13 \, A - 11 \, B\right)} c^{2} d^{4} - {\left(11 \, A - 7 \, B\right)} c d^{5} - {\left(A - 2 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{4 \, {\left({\left(a c^{7} d^{2} - a c^{6} d^{3} - 3 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} + 3 \, a c^{3} d^{6} - 3 \, a c^{2} d^{7} - a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, a c^{8} d - a c^{7} d^{2} - 7 \, a c^{6} d^{3} + 3 \, a c^{5} d^{4} + 9 \, a c^{4} d^{5} - 3 \, a c^{3} d^{6} - 5 \, a c^{2} d^{7} + a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right)^{2} - {\left(a c^{9} - a c^{8} d - 2 \, a c^{7} d^{2} + 2 \, a c^{6} d^{3} + 2 \, a c^{3} d^{6} - 2 \, a c^{2} d^{7} - a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right) - {\left(a c^{9} + a c^{8} d - 4 \, a c^{7} d^{2} - 4 \, a c^{6} d^{3} + 6 \, a c^{5} d^{4} + 6 \, a c^{4} d^{5} - 4 \, a c^{3} d^{6} - 4 \, a c^{2} d^{7} + a c d^{8} + a d^{9}\right)} f + {\left({\left(a c^{7} d^{2} - a c^{6} d^{3} - 3 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} + 3 \, a c^{3} d^{6} - 3 \, a c^{2} d^{7} - a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a c^{8} d - a c^{7} d^{2} - 3 \, a c^{6} d^{3} + 3 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} - 3 \, a c^{3} d^{6} - a c^{2} d^{7} + a c d^{8}\right)} f \cos\left(f x + e\right) - {\left(a c^{9} + a c^{8} d - 4 \, a c^{7} d^{2} - 4 \, a c^{6} d^{3} + 6 \, a c^{5} d^{4} + 6 \, a c^{4} d^{5} - 4 \, a c^{3} d^{6} - 4 \, a c^{2} d^{7} + a c d^{8} + a d^{9}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{2 \, {\left(A - B\right)} c^{6} - 6 \, {\left(A - B\right)} c^{4} d^{2} + 6 \, {\left(A - B\right)} c^{2} d^{4} - 2 \, {\left(A - B\right)} d^{6} - {\left({\left(2 \, A - 5 \, B\right)} c^{4} d^{2} + 3 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{3} + {\left(2 \, A + B\right)} c^{2} d^{4} - 3 \, {\left(3 \, A - 2 \, B\right)} c d^{5} - 4 \, {\left(A - B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} + {\left(4 \, {\left(A - 2 \, B\right)} c^{5} d + 4 \, {\left(3 \, A - 2 \, B\right)} c^{4} d^{2} - {\left(2 \, A - 7 \, B\right)} c^{3} d^{3} - 5 \, {\left(3 \, A - 2 \, B\right)} c^{2} d^{4} - {\left(2 \, A - B\right)} c d^{5} + {\left(3 \, A - 2 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, B c^{5} - 2 \, {\left(3 \, A - 4 \, B\right)} c^{4} d - {\left(18 \, A - 17 \, B\right)} c^{3} d^{2} - {\left(21 \, A - 20 \, B\right)} c^{2} d^{3} - {\left(12 \, A - 11 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5} - {\left(2 \, B c^{3} d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(6 \, A - 7 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(4 \, B c^{4} d - 2 \, {\left(6 \, A - 5 \, B\right)} c^{3} d^{2} - 18 \, {\left(A - B\right)} c^{2} d^{3} - {\left(12 \, A - 11 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, B c^{5} - 2 \, {\left(3 \, A - 2 \, B\right)} c^{4} d - 3 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{2} - 3 \, {\left(3 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(6 \, A - 7 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) + {\left(2 \, B c^{5} - 2 \, {\left(3 \, A - 4 \, B\right)} c^{4} d - {\left(18 \, A - 17 \, B\right)} c^{3} d^{2} - {\left(21 \, A - 20 \, B\right)} c^{2} d^{3} - {\left(12 \, A - 11 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5} - {\left(2 \, B c^{3} d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(6 \, A - 7 \, B\right)} c d^{4} - {\left(3 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(2 \, B c^{4} d - 2 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{2} - {\left(6 \, A - 7 \, B\right)} c^{2} d^{3} - {\left(3 \, A - 2 \, B\right)} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + {\left(2 \, {\left(A - B\right)} c^{6} + 4 \, {\left(A - 2 \, B\right)} c^{5} d + {\left(8 \, A - 7 \, B\right)} c^{4} d^{2} + {\left(7 \, A + B\right)} c^{3} d^{3} - {\left(7 \, A - 5 \, B\right)} c^{2} d^{4} - {\left(11 \, A - 7 \, B\right)} c d^{5} - {\left(3 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(A - B\right)} c^{6} - 6 \, {\left(A - B\right)} c^{4} d^{2} + 6 \, {\left(A - B\right)} c^{2} d^{4} - 2 \, {\left(A - B\right)} d^{6} - {\left({\left(2 \, A - 5 \, B\right)} c^{4} d^{2} + 3 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{3} + {\left(2 \, A + B\right)} c^{2} d^{4} - 3 \, {\left(3 \, A - 2 \, B\right)} c d^{5} - 4 \, {\left(A - B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} - {\left(4 \, {\left(A - 2 \, B\right)} c^{5} d + {\left(14 \, A - 13 \, B\right)} c^{4} d^{2} + {\left(7 \, A + B\right)} c^{3} d^{3} - {\left(13 \, A - 11 \, B\right)} c^{2} d^{4} - {\left(11 \, A - 7 \, B\right)} c d^{5} - {\left(A - 2 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(a c^{7} d^{2} - a c^{6} d^{3} - 3 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} + 3 \, a c^{3} d^{6} - 3 \, a c^{2} d^{7} - a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, a c^{8} d - a c^{7} d^{2} - 7 \, a c^{6} d^{3} + 3 \, a c^{5} d^{4} + 9 \, a c^{4} d^{5} - 3 \, a c^{3} d^{6} - 5 \, a c^{2} d^{7} + a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right)^{2} - {\left(a c^{9} - a c^{8} d - 2 \, a c^{7} d^{2} + 2 \, a c^{6} d^{3} + 2 \, a c^{3} d^{6} - 2 \, a c^{2} d^{7} - a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right) - {\left(a c^{9} + a c^{8} d - 4 \, a c^{7} d^{2} - 4 \, a c^{6} d^{3} + 6 \, a c^{5} d^{4} + 6 \, a c^{4} d^{5} - 4 \, a c^{3} d^{6} - 4 \, a c^{2} d^{7} + a c d^{8} + a d^{9}\right)} f + {\left({\left(a c^{7} d^{2} - a c^{6} d^{3} - 3 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} + 3 \, a c^{3} d^{6} - 3 \, a c^{2} d^{7} - a c d^{8} + a d^{9}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a c^{8} d - a c^{7} d^{2} - 3 \, a c^{6} d^{3} + 3 \, a c^{5} d^{4} + 3 \, a c^{4} d^{5} - 3 \, a c^{3} d^{6} - a c^{2} d^{7} + a c d^{8}\right)} f \cos\left(f x + e\right) - {\left(a c^{9} + a c^{8} d - 4 \, a c^{7} d^{2} - 4 \, a c^{6} d^{3} + 6 \, a c^{5} d^{4} + 6 \, a c^{4} d^{5} - 4 \, a c^{3} d^{6} - 4 \, a c^{2} d^{7} + a c d^{8} + a d^{9}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(4*(A - B)*c^6 - 12*(A - B)*c^4*d^2 + 12*(A - B)*c^2*d^4 - 4*(A - B)*d^6 - 2*((2*A - 5*B)*c^4*d^2 + 3*(3*A - 2*B)*c^3*d^3 + (2*A + B)*c^2*d^4 - 3*(3*A - 2*B)*c*d^5 - 4*(A - B)*d^6)*cos(f*x + e)^3 + 2*(4*(A - 2*B)*c^5*d + 4*(3*A - 2*B)*c^4*d^2 - (2*A - 7*B)*c^3*d^3 - 5*(3*A - 2*B)*c^2*d^4 - (2*A - B)*c*d^5 + (3*A - 2*B)*d^6)*cos(f*x + e)^2 - (2*B*c^5 - 2*(3*A - 4*B)*c^4*d - (18*A - 17*B)*c^3*d^2 - (21*A - 20*B)*c^2*d^3 - (12*A - 11*B)*c*d^4 - (3*A - 2*B)*d^5 - (2*B*c^3*d^2 - 2*(3*A - 2*B)*c^2*d^3 - (6*A - 7*B)*c*d^4 - (3*A - 2*B)*d^5)*cos(f*x + e)^3 - (4*B*c^4*d - 2*(6*A - 5*B)*c^3*d^2 - 18*(A - B)*c^2*d^3 - (12*A - 11*B)*c*d^4 - (3*A - 2*B)*d^5)*cos(f*x + e)^2 + (2*B*c^5 - 2*(3*A - 2*B)*c^4*d - 3*(2*A - 3*B)*c^3*d^2 - 3*(3*A - 2*B)*c^2*d^3 - (6*A - 7*B)*c*d^4 - (3*A - 2*B)*d^5)*cos(f*x + e) + (2*B*c^5 - 2*(3*A - 4*B)*c^4*d - (18*A - 17*B)*c^3*d^2 - (21*A - 20*B)*c^2*d^3 - (12*A - 11*B)*c*d^4 - (3*A - 2*B)*d^5 - (2*B*c^3*d^2 - 2*(3*A - 2*B)*c^2*d^3 - (6*A - 7*B)*c*d^4 - (3*A - 2*B)*d^5)*cos(f*x + e)^2 + 2*(2*B*c^4*d - 2*(3*A - 2*B)*c^3*d^2 - (6*A - 7*B)*c^2*d^3 - (3*A - 2*B)*c*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(-c^2 + d^2)*log(-((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 - 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*(2*(A - B)*c^6 + 4*(A - 2*B)*c^5*d + (8*A - 7*B)*c^4*d^2 + (7*A + B)*c^3*d^3 - (7*A - 5*B)*c^2*d^4 - (11*A - 7*B)*c*d^5 - (3*A - 4*B)*d^6)*cos(f*x + e) - 2*(2*(A - B)*c^6 - 6*(A - B)*c^4*d^2 + 6*(A - B)*c^2*d^4 - 2*(A - B)*d^6 - ((2*A - 5*B)*c^4*d^2 + 3*(3*A - 2*B)*c^3*d^3 + (2*A + B)*c^2*d^4 - 3*(3*A - 2*B)*c*d^5 - 4*(A - B)*d^6)*cos(f*x + e)^2 - (4*(A - 2*B)*c^5*d + (14*A - 13*B)*c^4*d^2 + (7*A + B)*c^3*d^3 - (13*A - 11*B)*c^2*d^4 - (11*A - 7*B)*c*d^5 - (A - 2*B)*d^6)*cos(f*x + e))*sin(f*x + e))/((a*c^7*d^2 - a*c^6*d^3 - 3*a*c^5*d^4 + 3*a*c^4*d^5 + 3*a*c^3*d^6 - 3*a*c^2*d^7 - a*c*d^8 + a*d^9)*f*cos(f*x + e)^3 + (2*a*c^8*d - a*c^7*d^2 - 7*a*c^6*d^3 + 3*a*c^5*d^4 + 9*a*c^4*d^5 - 3*a*c^3*d^6 - 5*a*c^2*d^7 + a*c*d^8 + a*d^9)*f*cos(f*x + e)^2 - (a*c^9 - a*c^8*d - 2*a*c^7*d^2 + 2*a*c^6*d^3 + 2*a*c^3*d^6 - 2*a*c^2*d^7 - a*c*d^8 + a*d^9)*f*cos(f*x + e) - (a*c^9 + a*c^8*d - 4*a*c^7*d^2 - 4*a*c^6*d^3 + 6*a*c^5*d^4 + 6*a*c^4*d^5 - 4*a*c^3*d^6 - 4*a*c^2*d^7 + a*c*d^8 + a*d^9)*f + ((a*c^7*d^2 - a*c^6*d^3 - 3*a*c^5*d^4 + 3*a*c^4*d^5 + 3*a*c^3*d^6 - 3*a*c^2*d^7 - a*c*d^8 + a*d^9)*f*cos(f*x + e)^2 - 2*(a*c^8*d - a*c^7*d^2 - 3*a*c^6*d^3 + 3*a*c^5*d^4 + 3*a*c^4*d^5 - 3*a*c^3*d^6 - a*c^2*d^7 + a*c*d^8)*f*cos(f*x + e) - (a*c^9 + a*c^8*d - 4*a*c^7*d^2 - 4*a*c^6*d^3 + 6*a*c^5*d^4 + 6*a*c^4*d^5 - 4*a*c^3*d^6 - 4*a*c^2*d^7 + a*c*d^8 + a*d^9)*f)*sin(f*x + e)), 1/2*(2*(A - B)*c^6 - 6*(A - B)*c^4*d^2 + 6*(A - B)*c^2*d^4 - 2*(A - B)*d^6 - ((2*A - 5*B)*c^4*d^2 + 3*(3*A - 2*B)*c^3*d^3 + (2*A + B)*c^2*d^4 - 3*(3*A - 2*B)*c*d^5 - 4*(A - B)*d^6)*cos(f*x + e)^3 + (4*(A - 2*B)*c^5*d + 4*(3*A - 2*B)*c^4*d^2 - (2*A - 7*B)*c^3*d^3 - 5*(3*A - 2*B)*c^2*d^4 - (2*A - B)*c*d^5 + (3*A - 2*B)*d^6)*cos(f*x + e)^2 + (2*B*c^5 - 2*(3*A - 4*B)*c^4*d - (18*A - 17*B)*c^3*d^2 - (21*A - 20*B)*c^2*d^3 - (12*A - 11*B)*c*d^4 - (3*A - 2*B)*d^5 - (2*B*c^3*d^2 - 2*(3*A - 2*B)*c^2*d^3 - (6*A - 7*B)*c*d^4 - (3*A - 2*B)*d^5)*cos(f*x + e)^3 - (4*B*c^4*d - 2*(6*A - 5*B)*c^3*d^2 - 18*(A - B)*c^2*d^3 - (12*A - 11*B)*c*d^4 - (3*A - 2*B)*d^5)*cos(f*x + e)^2 + (2*B*c^5 - 2*(3*A - 2*B)*c^4*d - 3*(2*A - 3*B)*c^3*d^2 - 3*(3*A - 2*B)*c^2*d^3 - (6*A - 7*B)*c*d^4 - (3*A - 2*B)*d^5)*cos(f*x + e) + (2*B*c^5 - 2*(3*A - 4*B)*c^4*d - (18*A - 17*B)*c^3*d^2 - (21*A - 20*B)*c^2*d^3 - (12*A - 11*B)*c*d^4 - (3*A - 2*B)*d^5 - (2*B*c^3*d^2 - 2*(3*A - 2*B)*c^2*d^3 - (6*A - 7*B)*c*d^4 - (3*A - 2*B)*d^5)*cos(f*x + e)^2 + 2*(2*B*c^4*d - 2*(3*A - 2*B)*c^3*d^2 - (6*A - 7*B)*c^2*d^3 - (3*A - 2*B)*c*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + (2*(A - B)*c^6 + 4*(A - 2*B)*c^5*d + (8*A - 7*B)*c^4*d^2 + (7*A + B)*c^3*d^3 - (7*A - 5*B)*c^2*d^4 - (11*A - 7*B)*c*d^5 - (3*A - 4*B)*d^6)*cos(f*x + e) - (2*(A - B)*c^6 - 6*(A - B)*c^4*d^2 + 6*(A - B)*c^2*d^4 - 2*(A - B)*d^6 - ((2*A - 5*B)*c^4*d^2 + 3*(3*A - 2*B)*c^3*d^3 + (2*A + B)*c^2*d^4 - 3*(3*A - 2*B)*c*d^5 - 4*(A - B)*d^6)*cos(f*x + e)^2 - (4*(A - 2*B)*c^5*d + (14*A - 13*B)*c^4*d^2 + (7*A + B)*c^3*d^3 - (13*A - 11*B)*c^2*d^4 - (11*A - 7*B)*c*d^5 - (A - 2*B)*d^6)*cos(f*x + e))*sin(f*x + e))/((a*c^7*d^2 - a*c^6*d^3 - 3*a*c^5*d^4 + 3*a*c^4*d^5 + 3*a*c^3*d^6 - 3*a*c^2*d^7 - a*c*d^8 + a*d^9)*f*cos(f*x + e)^3 + (2*a*c^8*d - a*c^7*d^2 - 7*a*c^6*d^3 + 3*a*c^5*d^4 + 9*a*c^4*d^5 - 3*a*c^3*d^6 - 5*a*c^2*d^7 + a*c*d^8 + a*d^9)*f*cos(f*x + e)^2 - (a*c^9 - a*c^8*d - 2*a*c^7*d^2 + 2*a*c^6*d^3 + 2*a*c^3*d^6 - 2*a*c^2*d^7 - a*c*d^8 + a*d^9)*f*cos(f*x + e) - (a*c^9 + a*c^8*d - 4*a*c^7*d^2 - 4*a*c^6*d^3 + 6*a*c^5*d^4 + 6*a*c^4*d^5 - 4*a*c^3*d^6 - 4*a*c^2*d^7 + a*c*d^8 + a*d^9)*f + ((a*c^7*d^2 - a*c^6*d^3 - 3*a*c^5*d^4 + 3*a*c^4*d^5 + 3*a*c^3*d^6 - 3*a*c^2*d^7 - a*c*d^8 + a*d^9)*f*cos(f*x + e)^2 - 2*(a*c^8*d - a*c^7*d^2 - 3*a*c^6*d^3 + 3*a*c^5*d^4 + 3*a*c^4*d^5 - 3*a*c^3*d^6 - a*c^2*d^7 + a*c*d^8)*f*cos(f*x + e) - (a*c^9 + a*c^8*d - 4*a*c^7*d^2 - 4*a*c^6*d^3 + 6*a*c^5*d^4 + 6*a*c^4*d^5 - 4*a*c^3*d^6 - 4*a*c^2*d^7 + a*c*d^8 + a*d^9)*f)*sin(f*x + e))]","B",0
272,1,584,0,0.671708," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{3 \, B d^{3} \cos\left(f x + e\right)^{4} - 2 \, {\left(A - B\right)} c^{3} + 6 \, {\left(A - B\right)} c^{2} d - 6 \, {\left(A - B\right)} c d^{2} + 2 \, {\left(A - B\right)} d^{3} + 6 \, {\left(3 \, B c d^{2} + {\left(A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} + 6 \, {\left(6 \, B c^{2} d + 6 \, {\left(A - 2 \, B\right)} c d^{2} - {\left(4 \, A - 7 \, B\right)} d^{3}\right)} f x - {\left(2 \, {\left(A + 2 \, B\right)} c^{3} + 6 \, {\left(2 \, A - 5 \, B\right)} c^{2} d - 6 \, {\left(5 \, A - 11 \, B\right)} c d^{2} + {\left(22 \, A - 31 \, B\right)} d^{3} + 3 \, {\left(6 \, B c^{2} d + 6 \, {\left(A - 2 \, B\right)} c d^{2} - {\left(4 \, A - 7 \, B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, {\left(2 \, A + B\right)} c^{3} + 6 \, {\left(A - 4 \, B\right)} c^{2} d - 6 \, {\left(4 \, A - 13 \, B\right)} c d^{2} + 2 \, {\left(13 \, A - 19 \, B\right)} d^{3} - 3 \, {\left(6 \, B c^{2} d + 6 \, {\left(A - 2 \, B\right)} c d^{2} - {\left(4 \, A - 7 \, B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right) + {\left(3 \, B d^{3} \cos\left(f x + e\right)^{3} + 2 \, {\left(A - B\right)} c^{3} - 6 \, {\left(A - B\right)} c^{2} d + 6 \, {\left(A - B\right)} c d^{2} - 2 \, {\left(A - B\right)} d^{3} + 6 \, {\left(6 \, B c^{2} d + 6 \, {\left(A - 2 \, B\right)} c d^{2} - {\left(4 \, A - 7 \, B\right)} d^{3}\right)} f x - 3 \, {\left(6 \, B c d^{2} + {\left(2 \, A - 3 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(2 \, {\left(A + 2 \, B\right)} c^{3} + 6 \, {\left(2 \, A - 5 \, B\right)} c^{2} d - 6 \, {\left(5 \, A - 14 \, B\right)} c d^{2} + 4 \, {\left(7 \, A - 10 \, B\right)} d^{3} - 3 \, {\left(6 \, B c^{2} d + 6 \, {\left(A - 2 \, B\right)} c d^{2} - {\left(4 \, A - 7 \, B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/6*(3*B*d^3*cos(f*x + e)^4 - 2*(A - B)*c^3 + 6*(A - B)*c^2*d - 6*(A - B)*c*d^2 + 2*(A - B)*d^3 + 6*(3*B*c*d^2 + (A - B)*d^3)*cos(f*x + e)^3 + 6*(6*B*c^2*d + 6*(A - 2*B)*c*d^2 - (4*A - 7*B)*d^3)*f*x - (2*(A + 2*B)*c^3 + 6*(2*A - 5*B)*c^2*d - 6*(5*A - 11*B)*c*d^2 + (22*A - 31*B)*d^3 + 3*(6*B*c^2*d + 6*(A - 2*B)*c*d^2 - (4*A - 7*B)*d^3)*f*x)*cos(f*x + e)^2 - (2*(2*A + B)*c^3 + 6*(A - 4*B)*c^2*d - 6*(4*A - 13*B)*c*d^2 + 2*(13*A - 19*B)*d^3 - 3*(6*B*c^2*d + 6*(A - 2*B)*c*d^2 - (4*A - 7*B)*d^3)*f*x)*cos(f*x + e) + (3*B*d^3*cos(f*x + e)^3 + 2*(A - B)*c^3 - 6*(A - B)*c^2*d + 6*(A - B)*c*d^2 - 2*(A - B)*d^3 + 6*(6*B*c^2*d + 6*(A - 2*B)*c*d^2 - (4*A - 7*B)*d^3)*f*x - 3*(6*B*c*d^2 + (2*A - 3*B)*d^3)*cos(f*x + e)^2 - (2*(A + 2*B)*c^3 + 6*(2*A - 5*B)*c^2*d - 6*(5*A - 14*B)*c*d^2 + 4*(7*A - 10*B)*d^3 - 3*(6*B*c^2*d + 6*(A - 2*B)*c*d^2 - (4*A - 7*B)*d^3)*f*x)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
273,1,375,0,0.588605," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{3 \, B d^{2} \cos\left(f x + e\right)^{3} - {\left(A - B\right)} c^{2} + 2 \, {\left(A - B\right)} c d - {\left(A - B\right)} d^{2} + 6 \, {\left(2 \, B c d + {\left(A - 2 \, B\right)} d^{2}\right)} f x - {\left({\left(A + 2 \, B\right)} c^{2} + 2 \, {\left(2 \, A - 5 \, B\right)} c d - {\left(5 \, A - 11 \, B\right)} d^{2} + 3 \, {\left(2 \, B c d + {\left(A - 2 \, B\right)} d^{2}\right)} f x\right)} \cos\left(f x + e\right)^{2} - {\left({\left(2 \, A + B\right)} c^{2} + 2 \, {\left(A - 4 \, B\right)} c d - {\left(4 \, A - 13 \, B\right)} d^{2} - 3 \, {\left(2 \, B c d + {\left(A - 2 \, B\right)} d^{2}\right)} f x\right)} \cos\left(f x + e\right) - {\left(3 \, B d^{2} \cos\left(f x + e\right)^{2} - {\left(A - B\right)} c^{2} + 2 \, {\left(A - B\right)} c d - {\left(A - B\right)} d^{2} - 6 \, {\left(2 \, B c d + {\left(A - 2 \, B\right)} d^{2}\right)} f x + {\left({\left(A + 2 \, B\right)} c^{2} + 2 \, {\left(2 \, A - 5 \, B\right)} c d - {\left(5 \, A - 14 \, B\right)} d^{2} - 3 \, {\left(2 \, B c d + {\left(A - 2 \, B\right)} d^{2}\right)} f x\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/3*(3*B*d^2*cos(f*x + e)^3 - (A - B)*c^2 + 2*(A - B)*c*d - (A - B)*d^2 + 6*(2*B*c*d + (A - 2*B)*d^2)*f*x - ((A + 2*B)*c^2 + 2*(2*A - 5*B)*c*d - (5*A - 11*B)*d^2 + 3*(2*B*c*d + (A - 2*B)*d^2)*f*x)*cos(f*x + e)^2 - ((2*A + B)*c^2 + 2*(A - 4*B)*c*d - (4*A - 13*B)*d^2 - 3*(2*B*c*d + (A - 2*B)*d^2)*f*x)*cos(f*x + e) - (3*B*d^2*cos(f*x + e)^2 - (A - B)*c^2 + 2*(A - B)*c*d - (A - B)*d^2 - 6*(2*B*c*d + (A - 2*B)*d^2)*f*x + ((A + 2*B)*c^2 + 2*(2*A - 5*B)*c*d - (5*A - 14*B)*d^2 - 3*(2*B*c*d + (A - 2*B)*d^2)*f*x)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
274,1,208,0,0.770200," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{6 \, B d f x - {\left(3 \, B d f x + {\left(A + 2 \, B\right)} c + {\left(2 \, A - 5 \, B\right)} d\right)} \cos\left(f x + e\right)^{2} - {\left(A - B\right)} c + {\left(A - B\right)} d + {\left(3 \, B d f x - {\left(2 \, A + B\right)} c - {\left(A - 4 \, B\right)} d\right)} \cos\left(f x + e\right) + {\left(6 \, B d f x + {\left(A - B\right)} c - {\left(A - B\right)} d + {\left(3 \, B d f x - {\left(A + 2 \, B\right)} c - {\left(2 \, A - 5 \, B\right)} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/3*(6*B*d*f*x - (3*B*d*f*x + (A + 2*B)*c + (2*A - 5*B)*d)*cos(f*x + e)^2 - (A - B)*c + (A - B)*d + (3*B*d*f*x - (2*A + B)*c - (A - 4*B)*d)*cos(f*x + e) + (6*B*d*f*x + (A - B)*c - (A - B)*d + (3*B*d*f*x - (A + 2*B)*c - (2*A - 5*B)*d)*cos(f*x + e))*sin(f*x + e))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
275,1,117,0,0.622659," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","\frac{{\left(A + 2 \, B\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, A + B\right)} \cos\left(f x + e\right) + {\left({\left(A + 2 \, B\right)} \cos\left(f x + e\right) - A + B\right)} \sin\left(f x + e\right) + A - B}{3 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/3*((A + 2*B)*cos(f*x + e)^2 + (2*A + B)*cos(f*x + e) + ((A + 2*B)*cos(f*x + e) - A + B)*sin(f*x + e) + A - B)/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","A",0
276,1,1285,0,0.753048," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(A - B\right)} c^{3} - 2 \, {\left(A - B\right)} c^{2} d - 2 \, {\left(A - B\right)} c d^{2} + 2 \, {\left(A - B\right)} d^{3} + 2 \, {\left({\left(A + 2 \, B\right)} c^{3} - {\left(4 \, A - B\right)} c^{2} d - {\left(A + 2 \, B\right)} c d^{2} + {\left(4 \, A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(2 \, B c d - 2 \, A d^{2} - {\left(B c d - A d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B c d - A d^{2}\right)} \cos\left(f x + e\right) + {\left(2 \, B c d - 2 \, A d^{2} + {\left(B c d - A d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left({\left(2 \, A + B\right)} c^{3} - {\left(5 \, A - 2 \, B\right)} c^{2} d - {\left(2 \, A + B\right)} c d^{2} + {\left(5 \, A - 2 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) - 2 \, {\left({\left(A - B\right)} c^{3} - {\left(A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2} + {\left(A - B\right)} d^{3} - {\left({\left(A + 2 \, B\right)} c^{3} - {\left(4 \, A - B\right)} c^{2} d - {\left(A + 2 \, B\right)} c d^{2} + {\left(4 \, A - B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f - {\left({\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{{\left(A - B\right)} c^{3} - {\left(A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2} + {\left(A - B\right)} d^{3} + {\left({\left(A + 2 \, B\right)} c^{3} - {\left(4 \, A - B\right)} c^{2} d - {\left(A + 2 \, B\right)} c d^{2} + {\left(4 \, A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(2 \, B c d - 2 \, A d^{2} - {\left(B c d - A d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B c d - A d^{2}\right)} \cos\left(f x + e\right) + {\left(2 \, B c d - 2 \, A d^{2} + {\left(B c d - A d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + {\left({\left(2 \, A + B\right)} c^{3} - {\left(5 \, A - 2 \, B\right)} c^{2} d - {\left(2 \, A + B\right)} c d^{2} + {\left(5 \, A - 2 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) - {\left({\left(A - B\right)} c^{3} - {\left(A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2} + {\left(A - B\right)} d^{3} - {\left({\left(A + 2 \, B\right)} c^{3} - {\left(4 \, A - B\right)} c^{2} d - {\left(A + 2 \, B\right)} c d^{2} + {\left(4 \, A - B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left({\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f - {\left({\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{4} - 2 \, a^{2} c^{3} d + 2 \, a^{2} c d^{3} - a^{2} d^{4}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/6*(2*(A - B)*c^3 - 2*(A - B)*c^2*d - 2*(A - B)*c*d^2 + 2*(A - B)*d^3 + 2*((A + 2*B)*c^3 - (4*A - B)*c^2*d - (A + 2*B)*c*d^2 + (4*A - B)*d^3)*cos(f*x + e)^2 - 3*(2*B*c*d - 2*A*d^2 - (B*c*d - A*d^2)*cos(f*x + e)^2 + (B*c*d - A*d^2)*cos(f*x + e) + (2*B*c*d - 2*A*d^2 + (B*c*d - A*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*((2*A + B)*c^3 - (5*A - 2*B)*c^2*d - (2*A + B)*c*d^2 + (5*A - 2*B)*d^3)*cos(f*x + e) - 2*((A - B)*c^3 - (A - B)*c^2*d - (A - B)*c*d^2 + (A - B)*d^3 - ((A + 2*B)*c^3 - (4*A - B)*c^2*d - (A + 2*B)*c*d^2 + (4*A - B)*d^3)*cos(f*x + e))*sin(f*x + e))/((a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e)^2 - (a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e) - 2*(a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f - ((a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e) + 2*(a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f)*sin(f*x + e)), 1/3*((A - B)*c^3 - (A - B)*c^2*d - (A - B)*c*d^2 + (A - B)*d^3 + ((A + 2*B)*c^3 - (4*A - B)*c^2*d - (A + 2*B)*c*d^2 + (4*A - B)*d^3)*cos(f*x + e)^2 - 3*(2*B*c*d - 2*A*d^2 - (B*c*d - A*d^2)*cos(f*x + e)^2 + (B*c*d - A*d^2)*cos(f*x + e) + (2*B*c*d - 2*A*d^2 + (B*c*d - A*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + ((2*A + B)*c^3 - (5*A - 2*B)*c^2*d - (2*A + B)*c*d^2 + (5*A - 2*B)*d^3)*cos(f*x + e) - ((A - B)*c^3 - (A - B)*c^2*d - (A - B)*c*d^2 + (A - B)*d^3 - ((A + 2*B)*c^3 - (4*A - B)*c^2*d - (A + 2*B)*c*d^2 + (4*A - B)*d^3)*cos(f*x + e))*sin(f*x + e))/((a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e)^2 - (a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e) - 2*(a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f - ((a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f*cos(f*x + e) + 2*(a^2*c^4 - 2*a^2*c^3*d + 2*a^2*c*d^3 - a^2*d^4)*f)*sin(f*x + e))]","B",0
277,1,3123,0,1.025810," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(A - B\right)} c^{5} - 2 \, {\left(A - B\right)} c^{4} d - 4 \, {\left(A - B\right)} c^{3} d^{2} + 4 \, {\left(A - B\right)} c^{2} d^{3} + 2 \, {\left(A - B\right)} c d^{4} - 2 \, {\left(A - B\right)} d^{5} - 2 \, {\left({\left(A + 2 \, B\right)} c^{4} d - 3 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{2} - {\left(11 \, A - 2 \, B\right)} c^{2} d^{3} + 3 \, {\left(2 \, A - 3 \, B\right)} c d^{4} + 2 \, {\left(5 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left({\left(A + 2 \, B\right)} c^{5} - 5 \, {\left(A - B\right)} c^{4} d - {\left(8 \, A - 5 \, B\right)} c^{3} d^{2} + {\left(A - 4 \, B\right)} c^{2} d^{3} + 7 \, {\left(A - B\right)} c d^{4} + {\left(4 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(4 \, B c^{3} d - 2 \, {\left(3 \, A - 4 \, B\right)} c^{2} d^{2} - 2 \, {\left(5 \, A - 3 \, B\right)} c d^{3} - 2 \, {\left(2 \, A - B\right)} d^{4} - {\left(2 \, B c^{2} d^{2} - {\left(3 \, A - 2 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(2 \, B c^{3} d - 3 \, {\left(A - 2 \, B\right)} c^{2} d^{2} - {\left(8 \, A - 5 \, B\right)} c d^{3} - 2 \, {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, B c^{3} d - {\left(3 \, A - 4 \, B\right)} c^{2} d^{2} - {\left(5 \, A - 3 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right) + {\left(4 \, B c^{3} d - 2 \, {\left(3 \, A - 4 \, B\right)} c^{2} d^{2} - 2 \, {\left(5 \, A - 3 \, B\right)} c d^{3} - 2 \, {\left(2 \, A - B\right)} d^{4} - {\left(2 \, B c^{2} d^{2} - {\left(3 \, A - 2 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, B c^{3} d - {\left(3 \, A - 4 \, B\right)} c^{2} d^{2} - {\left(5 \, A - 3 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left({\left(2 \, A + B\right)} c^{5} - {\left(5 \, A - 8 \, B\right)} c^{4} d - 16 \, {\left(A - B\right)} c^{3} d^{2} - 4 \, {\left(2 \, A + B\right)} c^{2} d^{3} + {\left(14 \, A - 17 \, B\right)} c d^{4} + {\left(13 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) - 2 \, {\left({\left(A - B\right)} c^{5} - {\left(A - B\right)} c^{4} d - 2 \, {\left(A - B\right)} c^{3} d^{2} + 2 \, {\left(A - B\right)} c^{2} d^{3} + {\left(A - B\right)} c d^{4} - {\left(A - B\right)} d^{5} - {\left({\left(A + 2 \, B\right)} c^{4} d - 3 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{2} - {\left(11 \, A - 2 \, B\right)} c^{2} d^{3} + 3 \, {\left(2 \, A - 3 \, B\right)} c d^{4} + 2 \, {\left(5 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(A + 2 \, B\right)} c^{5} - {\left(4 \, A - 7 \, B\right)} c^{4} d - 14 \, {\left(A - B\right)} c^{3} d^{2} - 2 \, {\left(5 \, A + B\right)} c^{2} d^{3} + {\left(13 \, A - 16 \, B\right)} c d^{4} + {\left(14 \, A - 5 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(a^{2} c^{6} d - 2 \, a^{2} c^{5} d^{2} - a^{2} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} - a^{2} c^{2} d^{5} - 2 \, a^{2} c d^{6} + a^{2} d^{7}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{7} - 5 \, a^{2} c^{5} d^{2} + 2 \, a^{2} c^{4} d^{3} + 7 \, a^{2} c^{3} d^{4} - 4 \, a^{2} c^{2} d^{5} - 3 \, a^{2} c d^{6} + 2 \, a^{2} d^{7}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{7} - a^{2} c^{6} d - 3 \, a^{2} c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3} + 3 \, a^{2} c^{3} d^{4} - 3 \, a^{2} c^{2} d^{5} - a^{2} c d^{6} + a^{2} d^{7}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{7} - a^{2} c^{6} d - 3 \, a^{2} c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3} + 3 \, a^{2} c^{3} d^{4} - 3 \, a^{2} c^{2} d^{5} - a^{2} c d^{6} + a^{2} d^{7}\right)} f + {\left({\left(a^{2} c^{6} d - 2 \, a^{2} c^{5} d^{2} - a^{2} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} - a^{2} c^{2} d^{5} - 2 \, a^{2} c d^{6} + a^{2} d^{7}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{7} - a^{2} c^{6} d - 3 \, a^{2} c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3} + 3 \, a^{2} c^{3} d^{4} - 3 \, a^{2} c^{2} d^{5} - a^{2} c d^{6} + a^{2} d^{7}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{7} - a^{2} c^{6} d - 3 \, a^{2} c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3} + 3 \, a^{2} c^{3} d^{4} - 3 \, a^{2} c^{2} d^{5} - a^{2} c d^{6} + a^{2} d^{7}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{{\left(A - B\right)} c^{5} - {\left(A - B\right)} c^{4} d - 2 \, {\left(A - B\right)} c^{3} d^{2} + 2 \, {\left(A - B\right)} c^{2} d^{3} + {\left(A - B\right)} c d^{4} - {\left(A - B\right)} d^{5} - {\left({\left(A + 2 \, B\right)} c^{4} d - 3 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{2} - {\left(11 \, A - 2 \, B\right)} c^{2} d^{3} + 3 \, {\left(2 \, A - 3 \, B\right)} c d^{4} + 2 \, {\left(5 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} + {\left({\left(A + 2 \, B\right)} c^{5} - 5 \, {\left(A - B\right)} c^{4} d - {\left(8 \, A - 5 \, B\right)} c^{3} d^{2} + {\left(A - 4 \, B\right)} c^{2} d^{3} + 7 \, {\left(A - B\right)} c d^{4} + {\left(4 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(4 \, B c^{3} d - 2 \, {\left(3 \, A - 4 \, B\right)} c^{2} d^{2} - 2 \, {\left(5 \, A - 3 \, B\right)} c d^{3} - 2 \, {\left(2 \, A - B\right)} d^{4} - {\left(2 \, B c^{2} d^{2} - {\left(3 \, A - 2 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(2 \, B c^{3} d - 3 \, {\left(A - 2 \, B\right)} c^{2} d^{2} - {\left(8 \, A - 5 \, B\right)} c d^{3} - 2 \, {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, B c^{3} d - {\left(3 \, A - 4 \, B\right)} c^{2} d^{2} - {\left(5 \, A - 3 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right) + {\left(4 \, B c^{3} d - 2 \, {\left(3 \, A - 4 \, B\right)} c^{2} d^{2} - 2 \, {\left(5 \, A - 3 \, B\right)} c d^{3} - 2 \, {\left(2 \, A - B\right)} d^{4} - {\left(2 \, B c^{2} d^{2} - {\left(3 \, A - 2 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, B c^{3} d - {\left(3 \, A - 4 \, B\right)} c^{2} d^{2} - {\left(5 \, A - 3 \, B\right)} c d^{3} - {\left(2 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + {\left({\left(2 \, A + B\right)} c^{5} - {\left(5 \, A - 8 \, B\right)} c^{4} d - 16 \, {\left(A - B\right)} c^{3} d^{2} - 4 \, {\left(2 \, A + B\right)} c^{2} d^{3} + {\left(14 \, A - 17 \, B\right)} c d^{4} + {\left(13 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) - {\left({\left(A - B\right)} c^{5} - {\left(A - B\right)} c^{4} d - 2 \, {\left(A - B\right)} c^{3} d^{2} + 2 \, {\left(A - B\right)} c^{2} d^{3} + {\left(A - B\right)} c d^{4} - {\left(A - B\right)} d^{5} - {\left({\left(A + 2 \, B\right)} c^{4} d - 3 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{2} - {\left(11 \, A - 2 \, B\right)} c^{2} d^{3} + 3 \, {\left(2 \, A - 3 \, B\right)} c d^{4} + 2 \, {\left(5 \, A - 2 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(A + 2 \, B\right)} c^{5} - {\left(4 \, A - 7 \, B\right)} c^{4} d - 14 \, {\left(A - B\right)} c^{3} d^{2} - 2 \, {\left(5 \, A + B\right)} c^{2} d^{3} + {\left(13 \, A - 16 \, B\right)} c d^{4} + {\left(14 \, A - 5 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{3 \, {\left({\left(a^{2} c^{6} d - 2 \, a^{2} c^{5} d^{2} - a^{2} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} - a^{2} c^{2} d^{5} - 2 \, a^{2} c d^{6} + a^{2} d^{7}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{7} - 5 \, a^{2} c^{5} d^{2} + 2 \, a^{2} c^{4} d^{3} + 7 \, a^{2} c^{3} d^{4} - 4 \, a^{2} c^{2} d^{5} - 3 \, a^{2} c d^{6} + 2 \, a^{2} d^{7}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{7} - a^{2} c^{6} d - 3 \, a^{2} c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3} + 3 \, a^{2} c^{3} d^{4} - 3 \, a^{2} c^{2} d^{5} - a^{2} c d^{6} + a^{2} d^{7}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{7} - a^{2} c^{6} d - 3 \, a^{2} c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3} + 3 \, a^{2} c^{3} d^{4} - 3 \, a^{2} c^{2} d^{5} - a^{2} c d^{6} + a^{2} d^{7}\right)} f + {\left({\left(a^{2} c^{6} d - 2 \, a^{2} c^{5} d^{2} - a^{2} c^{4} d^{3} + 4 \, a^{2} c^{3} d^{4} - a^{2} c^{2} d^{5} - 2 \, a^{2} c d^{6} + a^{2} d^{7}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{7} - a^{2} c^{6} d - 3 \, a^{2} c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3} + 3 \, a^{2} c^{3} d^{4} - 3 \, a^{2} c^{2} d^{5} - a^{2} c d^{6} + a^{2} d^{7}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{7} - a^{2} c^{6} d - 3 \, a^{2} c^{5} d^{2} + 3 \, a^{2} c^{4} d^{3} + 3 \, a^{2} c^{3} d^{4} - 3 \, a^{2} c^{2} d^{5} - a^{2} c d^{6} + a^{2} d^{7}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/6*(2*(A - B)*c^5 - 2*(A - B)*c^4*d - 4*(A - B)*c^3*d^2 + 4*(A - B)*c^2*d^3 + 2*(A - B)*c*d^4 - 2*(A - B)*d^5 - 2*((A + 2*B)*c^4*d - 3*(2*A - 3*B)*c^3*d^2 - (11*A - 2*B)*c^2*d^3 + 3*(2*A - 3*B)*c*d^4 + 2*(5*A - 2*B)*d^5)*cos(f*x + e)^3 + 2*((A + 2*B)*c^5 - 5*(A - B)*c^4*d - (8*A - 5*B)*c^3*d^2 + (A - 4*B)*c^2*d^3 + 7*(A - B)*c*d^4 + (4*A - B)*d^5)*cos(f*x + e)^2 - 3*(4*B*c^3*d - 2*(3*A - 4*B)*c^2*d^2 - 2*(5*A - 3*B)*c*d^3 - 2*(2*A - B)*d^4 - (2*B*c^2*d^2 - (3*A - 2*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e)^3 - (2*B*c^3*d - 3*(A - 2*B)*c^2*d^2 - (8*A - 5*B)*c*d^3 - 2*(2*A - B)*d^4)*cos(f*x + e)^2 + (2*B*c^3*d - (3*A - 4*B)*c^2*d^2 - (5*A - 3*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e) + (4*B*c^3*d - 2*(3*A - 4*B)*c^2*d^2 - 2*(5*A - 3*B)*c*d^3 - 2*(2*A - B)*d^4 - (2*B*c^2*d^2 - (3*A - 2*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e)^2 + (2*B*c^3*d - (3*A - 4*B)*c^2*d^2 - (5*A - 3*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*((2*A + B)*c^5 - (5*A - 8*B)*c^4*d - 16*(A - B)*c^3*d^2 - 4*(2*A + B)*c^2*d^3 + (14*A - 17*B)*c*d^4 + (13*A - 4*B)*d^5)*cos(f*x + e) - 2*((A - B)*c^5 - (A - B)*c^4*d - 2*(A - B)*c^3*d^2 + 2*(A - B)*c^2*d^3 + (A - B)*c*d^4 - (A - B)*d^5 - ((A + 2*B)*c^4*d - 3*(2*A - 3*B)*c^3*d^2 - (11*A - 2*B)*c^2*d^3 + 3*(2*A - 3*B)*c*d^4 + 2*(5*A - 2*B)*d^5)*cos(f*x + e)^2 - ((A + 2*B)*c^5 - (4*A - 7*B)*c^4*d - 14*(A - B)*c^3*d^2 - 2*(5*A + B)*c^2*d^3 + (13*A - 16*B)*c*d^4 + (14*A - 5*B)*d^5)*cos(f*x + e))*sin(f*x + e))/((a^2*c^6*d - 2*a^2*c^5*d^2 - a^2*c^4*d^3 + 4*a^2*c^3*d^4 - a^2*c^2*d^5 - 2*a^2*c*d^6 + a^2*d^7)*f*cos(f*x + e)^3 + (a^2*c^7 - 5*a^2*c^5*d^2 + 2*a^2*c^4*d^3 + 7*a^2*c^3*d^4 - 4*a^2*c^2*d^5 - 3*a^2*c*d^6 + 2*a^2*d^7)*f*cos(f*x + e)^2 - (a^2*c^7 - a^2*c^6*d - 3*a^2*c^5*d^2 + 3*a^2*c^4*d^3 + 3*a^2*c^3*d^4 - 3*a^2*c^2*d^5 - a^2*c*d^6 + a^2*d^7)*f*cos(f*x + e) - 2*(a^2*c^7 - a^2*c^6*d - 3*a^2*c^5*d^2 + 3*a^2*c^4*d^3 + 3*a^2*c^3*d^4 - 3*a^2*c^2*d^5 - a^2*c*d^6 + a^2*d^7)*f + ((a^2*c^6*d - 2*a^2*c^5*d^2 - a^2*c^4*d^3 + 4*a^2*c^3*d^4 - a^2*c^2*d^5 - 2*a^2*c*d^6 + a^2*d^7)*f*cos(f*x + e)^2 - (a^2*c^7 - a^2*c^6*d - 3*a^2*c^5*d^2 + 3*a^2*c^4*d^3 + 3*a^2*c^3*d^4 - 3*a^2*c^2*d^5 - a^2*c*d^6 + a^2*d^7)*f*cos(f*x + e) - 2*(a^2*c^7 - a^2*c^6*d - 3*a^2*c^5*d^2 + 3*a^2*c^4*d^3 + 3*a^2*c^3*d^4 - 3*a^2*c^2*d^5 - a^2*c*d^6 + a^2*d^7)*f)*sin(f*x + e)), 1/3*((A - B)*c^5 - (A - B)*c^4*d - 2*(A - B)*c^3*d^2 + 2*(A - B)*c^2*d^3 + (A - B)*c*d^4 - (A - B)*d^5 - ((A + 2*B)*c^4*d - 3*(2*A - 3*B)*c^3*d^2 - (11*A - 2*B)*c^2*d^3 + 3*(2*A - 3*B)*c*d^4 + 2*(5*A - 2*B)*d^5)*cos(f*x + e)^3 + ((A + 2*B)*c^5 - 5*(A - B)*c^4*d - (8*A - 5*B)*c^3*d^2 + (A - 4*B)*c^2*d^3 + 7*(A - B)*c*d^4 + (4*A - B)*d^5)*cos(f*x + e)^2 - 3*(4*B*c^3*d - 2*(3*A - 4*B)*c^2*d^2 - 2*(5*A - 3*B)*c*d^3 - 2*(2*A - B)*d^4 - (2*B*c^2*d^2 - (3*A - 2*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e)^3 - (2*B*c^3*d - 3*(A - 2*B)*c^2*d^2 - (8*A - 5*B)*c*d^3 - 2*(2*A - B)*d^4)*cos(f*x + e)^2 + (2*B*c^3*d - (3*A - 4*B)*c^2*d^2 - (5*A - 3*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e) + (4*B*c^3*d - 2*(3*A - 4*B)*c^2*d^2 - 2*(5*A - 3*B)*c*d^3 - 2*(2*A - B)*d^4 - (2*B*c^2*d^2 - (3*A - 2*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e)^2 + (2*B*c^3*d - (3*A - 4*B)*c^2*d^2 - (5*A - 3*B)*c*d^3 - (2*A - B)*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + ((2*A + B)*c^5 - (5*A - 8*B)*c^4*d - 16*(A - B)*c^3*d^2 - 4*(2*A + B)*c^2*d^3 + (14*A - 17*B)*c*d^4 + (13*A - 4*B)*d^5)*cos(f*x + e) - ((A - B)*c^5 - (A - B)*c^4*d - 2*(A - B)*c^3*d^2 + 2*(A - B)*c^2*d^3 + (A - B)*c*d^4 - (A - B)*d^5 - ((A + 2*B)*c^4*d - 3*(2*A - 3*B)*c^3*d^2 - (11*A - 2*B)*c^2*d^3 + 3*(2*A - 3*B)*c*d^4 + 2*(5*A - 2*B)*d^5)*cos(f*x + e)^2 - ((A + 2*B)*c^5 - (4*A - 7*B)*c^4*d - 14*(A - B)*c^3*d^2 - 2*(5*A + B)*c^2*d^3 + (13*A - 16*B)*c*d^4 + (14*A - 5*B)*d^5)*cos(f*x + e))*sin(f*x + e))/((a^2*c^6*d - 2*a^2*c^5*d^2 - a^2*c^4*d^3 + 4*a^2*c^3*d^4 - a^2*c^2*d^5 - 2*a^2*c*d^6 + a^2*d^7)*f*cos(f*x + e)^3 + (a^2*c^7 - 5*a^2*c^5*d^2 + 2*a^2*c^4*d^3 + 7*a^2*c^3*d^4 - 4*a^2*c^2*d^5 - 3*a^2*c*d^6 + 2*a^2*d^7)*f*cos(f*x + e)^2 - (a^2*c^7 - a^2*c^6*d - 3*a^2*c^5*d^2 + 3*a^2*c^4*d^3 + 3*a^2*c^3*d^4 - 3*a^2*c^2*d^5 - a^2*c*d^6 + a^2*d^7)*f*cos(f*x + e) - 2*(a^2*c^7 - a^2*c^6*d - 3*a^2*c^5*d^2 + 3*a^2*c^4*d^3 + 3*a^2*c^3*d^4 - 3*a^2*c^2*d^5 - a^2*c*d^6 + a^2*d^7)*f + ((a^2*c^6*d - 2*a^2*c^5*d^2 - a^2*c^4*d^3 + 4*a^2*c^3*d^4 - a^2*c^2*d^5 - 2*a^2*c*d^6 + a^2*d^7)*f*cos(f*x + e)^2 - (a^2*c^7 - a^2*c^6*d - 3*a^2*c^5*d^2 + 3*a^2*c^4*d^3 + 3*a^2*c^3*d^4 - 3*a^2*c^2*d^5 - a^2*c*d^6 + a^2*d^7)*f*cos(f*x + e) - 2*(a^2*c^7 - a^2*c^6*d - 3*a^2*c^5*d^2 + 3*a^2*c^4*d^3 + 3*a^2*c^3*d^4 - 3*a^2*c^2*d^5 - a^2*c*d^6 + a^2*d^7)*f)*sin(f*x + e))]","B",0
278,1,4997,0,0.759372," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^2/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(A - B\right)} c^{7} - 4 \, {\left(A - B\right)} c^{6} d - 12 \, {\left(A - B\right)} c^{5} d^{2} + 12 \, {\left(A - B\right)} c^{4} d^{3} + 12 \, {\left(A - B\right)} c^{3} d^{4} - 12 \, {\left(A - B\right)} c^{2} d^{5} - 4 \, {\left(A - B\right)} c d^{6} + 4 \, {\left(A - B\right)} d^{7} - 2 \, {\left(2 \, {\left(A + 2 \, B\right)} c^{5} d^{2} - {\left(16 \, A - 37 \, B\right)} c^{4} d^{3} - {\left(61 \, A - 40 \, B\right)} c^{3} d^{4} - {\left(16 \, A + 17 \, B\right)} c^{2} d^{5} + {\left(59 \, A - 44 \, B\right)} c d^{6} + 4 \, {\left(8 \, A - 5 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(4 \, {\left(A + 2 \, B\right)} c^{6} d - 4 \, {\left(7 \, A - 16 \, B\right)} c^{5} d^{2} - 118 \, {\left(A - B\right)} c^{4} d^{3} - {\left(106 \, A - 25 \, B\right)} c^{3} d^{4} + {\left(71 \, A - 98 \, B\right)} c^{2} d^{5} + {\left(134 \, A - 89 \, B\right)} c d^{6} + {\left(43 \, A - 28 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(2 \, {\left(A + 2 \, B\right)} c^{7} - 6 \, {\left(2 \, A - 3 \, B\right)} c^{6} d - 12 \, {\left(3 \, A - 4 \, B\right)} c^{5} d^{2} - 3 \, {\left(18 \, A - 17 \, B\right)} c^{4} d^{3} - 3 \, {\left(13 \, A + B\right)} c^{3} d^{4} + 3 \, {\left(13 \, A - 17 \, B\right)} c^{2} d^{5} + {\left(73 \, A - 49 \, B\right)} c d^{6} + 9 \, {\left(3 \, A - 2 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(12 \, B c^{5} d - 24 \, {\left(A - 2 \, B\right)} c^{4} d^{2} - 2 \, {\left(40 \, A - 43 \, B\right)} c^{3} d^{3} - 6 \, {\left(17 \, A - 14 \, B\right)} c^{2} d^{4} - 6 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - 2 \, {\left(7 \, A - 4 \, B\right)} d^{6} + {\left(6 \, B c^{3} d^{3} - 12 \, {\left(A - B\right)} c^{2} d^{4} - {\left(16 \, A - 13 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left(12 \, B c^{4} d^{2} - 6 \, {\left(4 \, A - 5 \, B\right)} c^{3} d^{3} - 2 \, {\left(22 \, A - 19 \, B\right)} c^{2} d^{4} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(6 \, B c^{5} d - 12 \, {\left(A - 3 \, B\right)} c^{4} d^{2} - {\left(64 \, A - 79 \, B\right)} c^{3} d^{3} - {\left(107 \, A - 92 \, B\right)} c^{2} d^{4} - {\left(76 \, A - 55 \, B\right)} c d^{5} - 3 \, {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, B c^{5} d - 12 \, {\left(A - 2 \, B\right)} c^{4} d^{2} - {\left(40 \, A - 43 \, B\right)} c^{3} d^{3} - 3 \, {\left(17 \, A - 14 \, B\right)} c^{2} d^{4} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) + {\left(12 \, B c^{5} d - 24 \, {\left(A - 2 \, B\right)} c^{4} d^{2} - 2 \, {\left(40 \, A - 43 \, B\right)} c^{3} d^{3} - 6 \, {\left(17 \, A - 14 \, B\right)} c^{2} d^{4} - 6 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - 2 \, {\left(7 \, A - 4 \, B\right)} d^{6} - {\left(6 \, B c^{3} d^{3} - 12 \, {\left(A - B\right)} c^{2} d^{4} - {\left(16 \, A - 13 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(6 \, B c^{4} d^{2} - 6 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{3} - {\left(28 \, A - 25 \, B\right)} c^{2} d^{4} - {\left(23 \, A - 17 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, B c^{5} d - 12 \, {\left(A - 2 \, B\right)} c^{4} d^{2} - {\left(40 \, A - 43 \, B\right)} c^{3} d^{3} - 3 \, {\left(17 \, A - 14 \, B\right)} c^{2} d^{4} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(-\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} - 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 4 \, {\left({\left(2 \, A + B\right)} c^{7} - {\left(5 \, A - 14 \, B\right)} c^{6} d - 3 \, {\left(12 \, A - 19 \, B\right)} c^{5} d^{2} - 3 \, {\left(25 \, A - 21 \, B\right)} c^{4} d^{3} - 3 \, {\left(13 \, A + 4 \, B\right)} c^{3} d^{4} + 3 \, {\left(20 \, A - 21 \, B\right)} c^{2} d^{5} + {\left(73 \, A - 46 \, B\right)} c d^{6} + 2 \, {\left(10 \, A - 7 \, B\right)} d^{7}\right)} \cos\left(f x + e\right) - 2 \, {\left(2 \, {\left(A - B\right)} c^{7} - 2 \, {\left(A - B\right)} c^{6} d - 6 \, {\left(A - B\right)} c^{5} d^{2} + 6 \, {\left(A - B\right)} c^{4} d^{3} + 6 \, {\left(A - B\right)} c^{3} d^{4} - 6 \, {\left(A - B\right)} c^{2} d^{5} - 2 \, {\left(A - B\right)} c d^{6} + 2 \, {\left(A - B\right)} d^{7} + {\left(2 \, {\left(A + 2 \, B\right)} c^{5} d^{2} - {\left(16 \, A - 37 \, B\right)} c^{4} d^{3} - {\left(61 \, A - 40 \, B\right)} c^{3} d^{4} - {\left(16 \, A + 17 \, B\right)} c^{2} d^{5} + {\left(59 \, A - 44 \, B\right)} c d^{6} + 4 \, {\left(8 \, A - 5 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{3} - {\left(4 \, {\left(A + 2 \, B\right)} c^{6} d - 30 \, {\left(A - 2 \, B\right)} c^{5} d^{2} - 3 \, {\left(34 \, A - 27 \, B\right)} c^{4} d^{3} - 15 \, {\left(3 \, A + B\right)} c^{3} d^{4} + 3 \, {\left(29 \, A - 27 \, B\right)} c^{2} d^{5} + 15 \, {\left(5 \, A - 3 \, B\right)} c d^{6} + {\left(11 \, A - 8 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left({\left(A + 2 \, B\right)} c^{7} - {\left(4 \, A - 13 \, B\right)} c^{6} d - 3 \, {\left(11 \, A - 18 \, B\right)} c^{5} d^{2} - 6 \, {\left(13 \, A - 11 \, B\right)} c^{4} d^{3} - 3 \, {\left(14 \, A + 3 \, B\right)} c^{3} d^{4} + 3 \, {\left(21 \, A - 22 \, B\right)} c^{2} d^{5} + {\left(74 \, A - 47 \, B\right)} c d^{6} + {\left(19 \, A - 13 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{12 \, {\left({\left(a^{2} c^{8} d^{2} - 2 \, a^{2} c^{7} d^{3} - 2 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{3} d^{7} + 2 \, a^{2} c^{2} d^{8} + 2 \, a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{4} - {\left(2 \, a^{2} c^{9} d - 3 \, a^{2} c^{8} d^{2} - 6 \, a^{2} c^{7} d^{3} + 10 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 12 \, a^{2} c^{4} d^{6} - 2 \, a^{2} c^{3} d^{7} + 6 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{3} - {\left(a^{2} c^{10} + 2 \, a^{2} c^{9} d - 7 \, a^{2} c^{8} d^{2} - 8 \, a^{2} c^{7} d^{3} + 18 \, a^{2} c^{6} d^{4} + 12 \, a^{2} c^{5} d^{5} - 22 \, a^{2} c^{4} d^{6} - 8 \, a^{2} c^{3} d^{7} + 13 \, a^{2} c^{2} d^{8} + 2 \, a^{2} c d^{9} - 3 \, a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{10} - 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} - 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{10} - 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} - 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f - {\left({\left(a^{2} c^{8} d^{2} - 2 \, a^{2} c^{7} d^{3} - 2 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{3} d^{7} + 2 \, a^{2} c^{2} d^{8} + 2 \, a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{3} + 2 \, {\left(a^{2} c^{9} d - a^{2} c^{8} d^{2} - 4 \, a^{2} c^{7} d^{3} + 4 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{4} d^{6} - 4 \, a^{2} c^{3} d^{7} + 4 \, a^{2} c^{2} d^{8} + a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{10} - 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} - 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{10} - 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} - 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f\right)} \sin\left(f x + e\right)\right)}}, -\frac{2 \, {\left(A - B\right)} c^{7} - 2 \, {\left(A - B\right)} c^{6} d - 6 \, {\left(A - B\right)} c^{5} d^{2} + 6 \, {\left(A - B\right)} c^{4} d^{3} + 6 \, {\left(A - B\right)} c^{3} d^{4} - 6 \, {\left(A - B\right)} c^{2} d^{5} - 2 \, {\left(A - B\right)} c d^{6} + 2 \, {\left(A - B\right)} d^{7} - {\left(2 \, {\left(A + 2 \, B\right)} c^{5} d^{2} - {\left(16 \, A - 37 \, B\right)} c^{4} d^{3} - {\left(61 \, A - 40 \, B\right)} c^{3} d^{4} - {\left(16 \, A + 17 \, B\right)} c^{2} d^{5} + {\left(59 \, A - 44 \, B\right)} c d^{6} + 4 \, {\left(8 \, A - 5 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{4} - {\left(4 \, {\left(A + 2 \, B\right)} c^{6} d - 4 \, {\left(7 \, A - 16 \, B\right)} c^{5} d^{2} - 118 \, {\left(A - B\right)} c^{4} d^{3} - {\left(106 \, A - 25 \, B\right)} c^{3} d^{4} + {\left(71 \, A - 98 \, B\right)} c^{2} d^{5} + {\left(134 \, A - 89 \, B\right)} c d^{6} + {\left(43 \, A - 28 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, {\left(A + 2 \, B\right)} c^{7} - 6 \, {\left(2 \, A - 3 \, B\right)} c^{6} d - 12 \, {\left(3 \, A - 4 \, B\right)} c^{5} d^{2} - 3 \, {\left(18 \, A - 17 \, B\right)} c^{4} d^{3} - 3 \, {\left(13 \, A + B\right)} c^{3} d^{4} + 3 \, {\left(13 \, A - 17 \, B\right)} c^{2} d^{5} + {\left(73 \, A - 49 \, B\right)} c d^{6} + 9 \, {\left(3 \, A - 2 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(12 \, B c^{5} d - 24 \, {\left(A - 2 \, B\right)} c^{4} d^{2} - 2 \, {\left(40 \, A - 43 \, B\right)} c^{3} d^{3} - 6 \, {\left(17 \, A - 14 \, B\right)} c^{2} d^{4} - 6 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - 2 \, {\left(7 \, A - 4 \, B\right)} d^{6} + {\left(6 \, B c^{3} d^{3} - 12 \, {\left(A - B\right)} c^{2} d^{4} - {\left(16 \, A - 13 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left(12 \, B c^{4} d^{2} - 6 \, {\left(4 \, A - 5 \, B\right)} c^{3} d^{3} - 2 \, {\left(22 \, A - 19 \, B\right)} c^{2} d^{4} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(6 \, B c^{5} d - 12 \, {\left(A - 3 \, B\right)} c^{4} d^{2} - {\left(64 \, A - 79 \, B\right)} c^{3} d^{3} - {\left(107 \, A - 92 \, B\right)} c^{2} d^{4} - {\left(76 \, A - 55 \, B\right)} c d^{5} - 3 \, {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, B c^{5} d - 12 \, {\left(A - 2 \, B\right)} c^{4} d^{2} - {\left(40 \, A - 43 \, B\right)} c^{3} d^{3} - 3 \, {\left(17 \, A - 14 \, B\right)} c^{2} d^{4} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) + {\left(12 \, B c^{5} d - 24 \, {\left(A - 2 \, B\right)} c^{4} d^{2} - 2 \, {\left(40 \, A - 43 \, B\right)} c^{3} d^{3} - 6 \, {\left(17 \, A - 14 \, B\right)} c^{2} d^{4} - 6 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - 2 \, {\left(7 \, A - 4 \, B\right)} d^{6} - {\left(6 \, B c^{3} d^{3} - 12 \, {\left(A - B\right)} c^{2} d^{4} - {\left(16 \, A - 13 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(6 \, B c^{4} d^{2} - 6 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{3} - {\left(28 \, A - 25 \, B\right)} c^{2} d^{4} - {\left(23 \, A - 17 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(6 \, B c^{5} d - 12 \, {\left(A - 2 \, B\right)} c^{4} d^{2} - {\left(40 \, A - 43 \, B\right)} c^{3} d^{3} - 3 \, {\left(17 \, A - 14 \, B\right)} c^{2} d^{4} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{5} - {\left(7 \, A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + 2 \, {\left({\left(2 \, A + B\right)} c^{7} - {\left(5 \, A - 14 \, B\right)} c^{6} d - 3 \, {\left(12 \, A - 19 \, B\right)} c^{5} d^{2} - 3 \, {\left(25 \, A - 21 \, B\right)} c^{4} d^{3} - 3 \, {\left(13 \, A + 4 \, B\right)} c^{3} d^{4} + 3 \, {\left(20 \, A - 21 \, B\right)} c^{2} d^{5} + {\left(73 \, A - 46 \, B\right)} c d^{6} + 2 \, {\left(10 \, A - 7 \, B\right)} d^{7}\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(A - B\right)} c^{7} - 2 \, {\left(A - B\right)} c^{6} d - 6 \, {\left(A - B\right)} c^{5} d^{2} + 6 \, {\left(A - B\right)} c^{4} d^{3} + 6 \, {\left(A - B\right)} c^{3} d^{4} - 6 \, {\left(A - B\right)} c^{2} d^{5} - 2 \, {\left(A - B\right)} c d^{6} + 2 \, {\left(A - B\right)} d^{7} + {\left(2 \, {\left(A + 2 \, B\right)} c^{5} d^{2} - {\left(16 \, A - 37 \, B\right)} c^{4} d^{3} - {\left(61 \, A - 40 \, B\right)} c^{3} d^{4} - {\left(16 \, A + 17 \, B\right)} c^{2} d^{5} + {\left(59 \, A - 44 \, B\right)} c d^{6} + 4 \, {\left(8 \, A - 5 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{3} - {\left(4 \, {\left(A + 2 \, B\right)} c^{6} d - 30 \, {\left(A - 2 \, B\right)} c^{5} d^{2} - 3 \, {\left(34 \, A - 27 \, B\right)} c^{4} d^{3} - 15 \, {\left(3 \, A + B\right)} c^{3} d^{4} + 3 \, {\left(29 \, A - 27 \, B\right)} c^{2} d^{5} + 15 \, {\left(5 \, A - 3 \, B\right)} c d^{6} + {\left(11 \, A - 8 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left({\left(A + 2 \, B\right)} c^{7} - {\left(4 \, A - 13 \, B\right)} c^{6} d - 3 \, {\left(11 \, A - 18 \, B\right)} c^{5} d^{2} - 6 \, {\left(13 \, A - 11 \, B\right)} c^{4} d^{3} - 3 \, {\left(14 \, A + 3 \, B\right)} c^{3} d^{4} + 3 \, {\left(21 \, A - 22 \, B\right)} c^{2} d^{5} + {\left(74 \, A - 47 \, B\right)} c d^{6} + {\left(19 \, A - 13 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{6 \, {\left({\left(a^{2} c^{8} d^{2} - 2 \, a^{2} c^{7} d^{3} - 2 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{3} d^{7} + 2 \, a^{2} c^{2} d^{8} + 2 \, a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{4} - {\left(2 \, a^{2} c^{9} d - 3 \, a^{2} c^{8} d^{2} - 6 \, a^{2} c^{7} d^{3} + 10 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 12 \, a^{2} c^{4} d^{6} - 2 \, a^{2} c^{3} d^{7} + 6 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{3} - {\left(a^{2} c^{10} + 2 \, a^{2} c^{9} d - 7 \, a^{2} c^{8} d^{2} - 8 \, a^{2} c^{7} d^{3} + 18 \, a^{2} c^{6} d^{4} + 12 \, a^{2} c^{5} d^{5} - 22 \, a^{2} c^{4} d^{6} - 8 \, a^{2} c^{3} d^{7} + 13 \, a^{2} c^{2} d^{8} + 2 \, a^{2} c d^{9} - 3 \, a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{10} - 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} - 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{10} - 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} - 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f - {\left({\left(a^{2} c^{8} d^{2} - 2 \, a^{2} c^{7} d^{3} - 2 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{3} d^{7} + 2 \, a^{2} c^{2} d^{8} + 2 \, a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{3} + 2 \, {\left(a^{2} c^{9} d - a^{2} c^{8} d^{2} - 4 \, a^{2} c^{7} d^{3} + 4 \, a^{2} c^{6} d^{4} + 6 \, a^{2} c^{5} d^{5} - 6 \, a^{2} c^{4} d^{6} - 4 \, a^{2} c^{3} d^{7} + 4 \, a^{2} c^{2} d^{8} + a^{2} c d^{9} - a^{2} d^{10}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{10} - 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} - 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{10} - 5 \, a^{2} c^{8} d^{2} + 10 \, a^{2} c^{6} d^{4} - 10 \, a^{2} c^{4} d^{6} + 5 \, a^{2} c^{2} d^{8} - a^{2} d^{10}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/12*(4*(A - B)*c^7 - 4*(A - B)*c^6*d - 12*(A - B)*c^5*d^2 + 12*(A - B)*c^4*d^3 + 12*(A - B)*c^3*d^4 - 12*(A - B)*c^2*d^5 - 4*(A - B)*c*d^6 + 4*(A - B)*d^7 - 2*(2*(A + 2*B)*c^5*d^2 - (16*A - 37*B)*c^4*d^3 - (61*A - 40*B)*c^3*d^4 - (16*A + 17*B)*c^2*d^5 + (59*A - 44*B)*c*d^6 + 4*(8*A - 5*B)*d^7)*cos(f*x + e)^4 - 2*(4*(A + 2*B)*c^6*d - 4*(7*A - 16*B)*c^5*d^2 - 118*(A - B)*c^4*d^3 - (106*A - 25*B)*c^3*d^4 + (71*A - 98*B)*c^2*d^5 + (134*A - 89*B)*c*d^6 + (43*A - 28*B)*d^7)*cos(f*x + e)^3 + 2*(2*(A + 2*B)*c^7 - 6*(2*A - 3*B)*c^6*d - 12*(3*A - 4*B)*c^5*d^2 - 3*(18*A - 17*B)*c^4*d^3 - 3*(13*A + B)*c^3*d^4 + 3*(13*A - 17*B)*c^2*d^5 + (73*A - 49*B)*c*d^6 + 9*(3*A - 2*B)*d^7)*cos(f*x + e)^2 + 3*(12*B*c^5*d - 24*(A - 2*B)*c^4*d^2 - 2*(40*A - 43*B)*c^3*d^3 - 6*(17*A - 14*B)*c^2*d^4 - 6*(10*A - 7*B)*c*d^5 - 2*(7*A - 4*B)*d^6 + (6*B*c^3*d^3 - 12*(A - B)*c^2*d^4 - (16*A - 13*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e)^4 - (12*B*c^4*d^2 - 6*(4*A - 5*B)*c^3*d^3 - 2*(22*A - 19*B)*c^2*d^4 - 3*(10*A - 7*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e)^3 - (6*B*c^5*d - 12*(A - 3*B)*c^4*d^2 - (64*A - 79*B)*c^3*d^3 - (107*A - 92*B)*c^2*d^4 - (76*A - 55*B)*c*d^5 - 3*(7*A - 4*B)*d^6)*cos(f*x + e)^2 + (6*B*c^5*d - 12*(A - 2*B)*c^4*d^2 - (40*A - 43*B)*c^3*d^3 - 3*(17*A - 14*B)*c^2*d^4 - 3*(10*A - 7*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e) + (12*B*c^5*d - 24*(A - 2*B)*c^4*d^2 - 2*(40*A - 43*B)*c^3*d^3 - 6*(17*A - 14*B)*c^2*d^4 - 6*(10*A - 7*B)*c*d^5 - 2*(7*A - 4*B)*d^6 - (6*B*c^3*d^3 - 12*(A - B)*c^2*d^4 - (16*A - 13*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e)^3 - 2*(6*B*c^4*d^2 - 6*(2*A - 3*B)*c^3*d^3 - (28*A - 25*B)*c^2*d^4 - (23*A - 17*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e)^2 + (6*B*c^5*d - 12*(A - 2*B)*c^4*d^2 - (40*A - 43*B)*c^3*d^3 - 3*(17*A - 14*B)*c^2*d^4 - 3*(10*A - 7*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e))*sin(f*x + e))*sqrt(-c^2 + d^2)*log(-((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 - 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 4*((2*A + B)*c^7 - (5*A - 14*B)*c^6*d - 3*(12*A - 19*B)*c^5*d^2 - 3*(25*A - 21*B)*c^4*d^3 - 3*(13*A + 4*B)*c^3*d^4 + 3*(20*A - 21*B)*c^2*d^5 + (73*A - 46*B)*c*d^6 + 2*(10*A - 7*B)*d^7)*cos(f*x + e) - 2*(2*(A - B)*c^7 - 2*(A - B)*c^6*d - 6*(A - B)*c^5*d^2 + 6*(A - B)*c^4*d^3 + 6*(A - B)*c^3*d^4 - 6*(A - B)*c^2*d^5 - 2*(A - B)*c*d^6 + 2*(A - B)*d^7 + (2*(A + 2*B)*c^5*d^2 - (16*A - 37*B)*c^4*d^3 - (61*A - 40*B)*c^3*d^4 - (16*A + 17*B)*c^2*d^5 + (59*A - 44*B)*c*d^6 + 4*(8*A - 5*B)*d^7)*cos(f*x + e)^3 - (4*(A + 2*B)*c^6*d - 30*(A - 2*B)*c^5*d^2 - 3*(34*A - 27*B)*c^4*d^3 - 15*(3*A + B)*c^3*d^4 + 3*(29*A - 27*B)*c^2*d^5 + 15*(5*A - 3*B)*c*d^6 + (11*A - 8*B)*d^7)*cos(f*x + e)^2 - 2*((A + 2*B)*c^7 - (4*A - 13*B)*c^6*d - 3*(11*A - 18*B)*c^5*d^2 - 6*(13*A - 11*B)*c^4*d^3 - 3*(14*A + 3*B)*c^3*d^4 + 3*(21*A - 22*B)*c^2*d^5 + (74*A - 47*B)*c*d^6 + (19*A - 13*B)*d^7)*cos(f*x + e))*sin(f*x + e))/((a^2*c^8*d^2 - 2*a^2*c^7*d^3 - 2*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^3*d^7 + 2*a^2*c^2*d^8 + 2*a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e)^4 - (2*a^2*c^9*d - 3*a^2*c^8*d^2 - 6*a^2*c^7*d^3 + 10*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 12*a^2*c^4*d^6 - 2*a^2*c^3*d^7 + 6*a^2*c^2*d^8 - a^2*d^10)*f*cos(f*x + e)^3 - (a^2*c^10 + 2*a^2*c^9*d - 7*a^2*c^8*d^2 - 8*a^2*c^7*d^3 + 18*a^2*c^6*d^4 + 12*a^2*c^5*d^5 - 22*a^2*c^4*d^6 - 8*a^2*c^3*d^7 + 13*a^2*c^2*d^8 + 2*a^2*c*d^9 - 3*a^2*d^10)*f*cos(f*x + e)^2 + (a^2*c^10 - 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 - 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 - a^2*d^10)*f*cos(f*x + e) + 2*(a^2*c^10 - 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 - 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 - a^2*d^10)*f - ((a^2*c^8*d^2 - 2*a^2*c^7*d^3 - 2*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^3*d^7 + 2*a^2*c^2*d^8 + 2*a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e)^3 + 2*(a^2*c^9*d - a^2*c^8*d^2 - 4*a^2*c^7*d^3 + 4*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^4*d^6 - 4*a^2*c^3*d^7 + 4*a^2*c^2*d^8 + a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e)^2 - (a^2*c^10 - 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 - 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 - a^2*d^10)*f*cos(f*x + e) - 2*(a^2*c^10 - 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 - 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 - a^2*d^10)*f)*sin(f*x + e)), -1/6*(2*(A - B)*c^7 - 2*(A - B)*c^6*d - 6*(A - B)*c^5*d^2 + 6*(A - B)*c^4*d^3 + 6*(A - B)*c^3*d^4 - 6*(A - B)*c^2*d^5 - 2*(A - B)*c*d^6 + 2*(A - B)*d^7 - (2*(A + 2*B)*c^5*d^2 - (16*A - 37*B)*c^4*d^3 - (61*A - 40*B)*c^3*d^4 - (16*A + 17*B)*c^2*d^5 + (59*A - 44*B)*c*d^6 + 4*(8*A - 5*B)*d^7)*cos(f*x + e)^4 - (4*(A + 2*B)*c^6*d - 4*(7*A - 16*B)*c^5*d^2 - 118*(A - B)*c^4*d^3 - (106*A - 25*B)*c^3*d^4 + (71*A - 98*B)*c^2*d^5 + (134*A - 89*B)*c*d^6 + (43*A - 28*B)*d^7)*cos(f*x + e)^3 + (2*(A + 2*B)*c^7 - 6*(2*A - 3*B)*c^6*d - 12*(3*A - 4*B)*c^5*d^2 - 3*(18*A - 17*B)*c^4*d^3 - 3*(13*A + B)*c^3*d^4 + 3*(13*A - 17*B)*c^2*d^5 + (73*A - 49*B)*c*d^6 + 9*(3*A - 2*B)*d^7)*cos(f*x + e)^2 - 3*(12*B*c^5*d - 24*(A - 2*B)*c^4*d^2 - 2*(40*A - 43*B)*c^3*d^3 - 6*(17*A - 14*B)*c^2*d^4 - 6*(10*A - 7*B)*c*d^5 - 2*(7*A - 4*B)*d^6 + (6*B*c^3*d^3 - 12*(A - B)*c^2*d^4 - (16*A - 13*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e)^4 - (12*B*c^4*d^2 - 6*(4*A - 5*B)*c^3*d^3 - 2*(22*A - 19*B)*c^2*d^4 - 3*(10*A - 7*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e)^3 - (6*B*c^5*d - 12*(A - 3*B)*c^4*d^2 - (64*A - 79*B)*c^3*d^3 - (107*A - 92*B)*c^2*d^4 - (76*A - 55*B)*c*d^5 - 3*(7*A - 4*B)*d^6)*cos(f*x + e)^2 + (6*B*c^5*d - 12*(A - 2*B)*c^4*d^2 - (40*A - 43*B)*c^3*d^3 - 3*(17*A - 14*B)*c^2*d^4 - 3*(10*A - 7*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e) + (12*B*c^5*d - 24*(A - 2*B)*c^4*d^2 - 2*(40*A - 43*B)*c^3*d^3 - 6*(17*A - 14*B)*c^2*d^4 - 6*(10*A - 7*B)*c*d^5 - 2*(7*A - 4*B)*d^6 - (6*B*c^3*d^3 - 12*(A - B)*c^2*d^4 - (16*A - 13*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e)^3 - 2*(6*B*c^4*d^2 - 6*(2*A - 3*B)*c^3*d^3 - (28*A - 25*B)*c^2*d^4 - (23*A - 17*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e)^2 + (6*B*c^5*d - 12*(A - 2*B)*c^4*d^2 - (40*A - 43*B)*c^3*d^3 - 3*(17*A - 14*B)*c^2*d^4 - 3*(10*A - 7*B)*c*d^5 - (7*A - 4*B)*d^6)*cos(f*x + e))*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + 2*((2*A + B)*c^7 - (5*A - 14*B)*c^6*d - 3*(12*A - 19*B)*c^5*d^2 - 3*(25*A - 21*B)*c^4*d^3 - 3*(13*A + 4*B)*c^3*d^4 + 3*(20*A - 21*B)*c^2*d^5 + (73*A - 46*B)*c*d^6 + 2*(10*A - 7*B)*d^7)*cos(f*x + e) - (2*(A - B)*c^7 - 2*(A - B)*c^6*d - 6*(A - B)*c^5*d^2 + 6*(A - B)*c^4*d^3 + 6*(A - B)*c^3*d^4 - 6*(A - B)*c^2*d^5 - 2*(A - B)*c*d^6 + 2*(A - B)*d^7 + (2*(A + 2*B)*c^5*d^2 - (16*A - 37*B)*c^4*d^3 - (61*A - 40*B)*c^3*d^4 - (16*A + 17*B)*c^2*d^5 + (59*A - 44*B)*c*d^6 + 4*(8*A - 5*B)*d^7)*cos(f*x + e)^3 - (4*(A + 2*B)*c^6*d - 30*(A - 2*B)*c^5*d^2 - 3*(34*A - 27*B)*c^4*d^3 - 15*(3*A + B)*c^3*d^4 + 3*(29*A - 27*B)*c^2*d^5 + 15*(5*A - 3*B)*c*d^6 + (11*A - 8*B)*d^7)*cos(f*x + e)^2 - 2*((A + 2*B)*c^7 - (4*A - 13*B)*c^6*d - 3*(11*A - 18*B)*c^5*d^2 - 6*(13*A - 11*B)*c^4*d^3 - 3*(14*A + 3*B)*c^3*d^4 + 3*(21*A - 22*B)*c^2*d^5 + (74*A - 47*B)*c*d^6 + (19*A - 13*B)*d^7)*cos(f*x + e))*sin(f*x + e))/((a^2*c^8*d^2 - 2*a^2*c^7*d^3 - 2*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^3*d^7 + 2*a^2*c^2*d^8 + 2*a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e)^4 - (2*a^2*c^9*d - 3*a^2*c^8*d^2 - 6*a^2*c^7*d^3 + 10*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 12*a^2*c^4*d^6 - 2*a^2*c^3*d^7 + 6*a^2*c^2*d^8 - a^2*d^10)*f*cos(f*x + e)^3 - (a^2*c^10 + 2*a^2*c^9*d - 7*a^2*c^8*d^2 - 8*a^2*c^7*d^3 + 18*a^2*c^6*d^4 + 12*a^2*c^5*d^5 - 22*a^2*c^4*d^6 - 8*a^2*c^3*d^7 + 13*a^2*c^2*d^8 + 2*a^2*c*d^9 - 3*a^2*d^10)*f*cos(f*x + e)^2 + (a^2*c^10 - 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 - 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 - a^2*d^10)*f*cos(f*x + e) + 2*(a^2*c^10 - 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 - 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 - a^2*d^10)*f - ((a^2*c^8*d^2 - 2*a^2*c^7*d^3 - 2*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^3*d^7 + 2*a^2*c^2*d^8 + 2*a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e)^3 + 2*(a^2*c^9*d - a^2*c^8*d^2 - 4*a^2*c^7*d^3 + 4*a^2*c^6*d^4 + 6*a^2*c^5*d^5 - 6*a^2*c^4*d^6 - 4*a^2*c^3*d^7 + 4*a^2*c^2*d^8 + a^2*c*d^9 - a^2*d^10)*f*cos(f*x + e)^2 - (a^2*c^10 - 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 - 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 - a^2*d^10)*f*cos(f*x + e) - 2*(a^2*c^10 - 5*a^2*c^8*d^2 + 10*a^2*c^6*d^4 - 10*a^2*c^4*d^6 + 5*a^2*c^2*d^8 - a^2*d^10)*f)*sin(f*x + e))]","B",0
279,1,649,0,0.693138," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{15 \, B d^{3} \cos\left(f x + e\right)^{4} - 3 \, {\left(A - B\right)} c^{3} + 9 \, {\left(A - B\right)} c^{2} d - 9 \, {\left(A - B\right)} c d^{2} + 3 \, {\left(A - B\right)} d^{3} + {\left({\left(2 \, A + 3 \, B\right)} c^{3} + 3 \, {\left(3 \, A + 7 \, B\right)} c^{2} d + 3 \, {\left(7 \, A - 32 \, B\right)} c d^{2} - {\left(32 \, A - 117 \, B\right)} d^{3} - 15 \, {\left(3 \, B c d^{2} + {\left(A - 3 \, B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right)^{3} + 60 \, {\left(3 \, B c d^{2} + {\left(A - 3 \, B\right)} d^{3}\right)} f x - {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{3} + 3 \, {\left(6 \, A - B\right)} c^{2} d - 3 \, {\left(A + 19 \, B\right)} c d^{2} - {\left(19 \, A - 84 \, B\right)} d^{3} + 45 \, {\left(3 \, B c d^{2} + {\left(A - 3 \, B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(3 \, A + 2 \, B\right)} c^{3} + 3 \, {\left(2 \, A + 3 \, B\right)} c^{2} d + 9 \, {\left(A - 6 \, B\right)} c d^{2} - 9 \, {\left(2 \, A - 7 \, B\right)} d^{3} - 10 \, {\left(3 \, B c d^{2} + {\left(A - 3 \, B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right) + {\left(15 \, B d^{3} \cos\left(f x + e\right)^{3} + 3 \, {\left(A - B\right)} c^{3} - 9 \, {\left(A - B\right)} c^{2} d + 9 \, {\left(A - B\right)} c d^{2} - 3 \, {\left(A - B\right)} d^{3} + 60 \, {\left(3 \, B c d^{2} + {\left(A - 3 \, B\right)} d^{3}\right)} f x - {\left({\left(2 \, A + 3 \, B\right)} c^{3} + 3 \, {\left(3 \, A + 7 \, B\right)} c^{2} d + 3 \, {\left(7 \, A - 32 \, B\right)} c d^{2} - 2 \, {\left(16 \, A - 51 \, B\right)} d^{3} + 15 \, {\left(3 \, B c d^{2} + {\left(A - 3 \, B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(2 \, A + 3 \, B\right)} c^{3} + 3 \, {\left(3 \, A + 2 \, B\right)} c^{2} d + 3 \, {\left(2 \, A - 17 \, B\right)} c d^{2} - {\left(17 \, A - 62 \, B\right)} d^{3} - 10 \, {\left(3 \, B c d^{2} + {\left(A - 3 \, B\right)} d^{3}\right)} f x\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/15*(15*B*d^3*cos(f*x + e)^4 - 3*(A - B)*c^3 + 9*(A - B)*c^2*d - 9*(A - B)*c*d^2 + 3*(A - B)*d^3 + ((2*A + 3*B)*c^3 + 3*(3*A + 7*B)*c^2*d + 3*(7*A - 32*B)*c*d^2 - (32*A - 117*B)*d^3 - 15*(3*B*c*d^2 + (A - 3*B)*d^3)*f*x)*cos(f*x + e)^3 + 60*(3*B*c*d^2 + (A - 3*B)*d^3)*f*x - (2*(2*A + 3*B)*c^3 + 3*(6*A - B)*c^2*d - 3*(A + 19*B)*c*d^2 - (19*A - 84*B)*d^3 + 45*(3*B*c*d^2 + (A - 3*B)*d^3)*f*x)*cos(f*x + e)^2 - 3*((3*A + 2*B)*c^3 + 3*(2*A + 3*B)*c^2*d + 9*(A - 6*B)*c*d^2 - 9*(2*A - 7*B)*d^3 - 10*(3*B*c*d^2 + (A - 3*B)*d^3)*f*x)*cos(f*x + e) + (15*B*d^3*cos(f*x + e)^3 + 3*(A - B)*c^3 - 9*(A - B)*c^2*d + 9*(A - B)*c*d^2 - 3*(A - B)*d^3 + 60*(3*B*c*d^2 + (A - 3*B)*d^3)*f*x - ((2*A + 3*B)*c^3 + 3*(3*A + 7*B)*c^2*d + 3*(7*A - 32*B)*c*d^2 - 2*(16*A - 51*B)*d^3 + 15*(3*B*c*d^2 + (A - 3*B)*d^3)*f*x)*cos(f*x + e)^2 - 3*((2*A + 3*B)*c^3 + 3*(3*A + 2*B)*c^2*d + 3*(2*A - 17*B)*c*d^2 - (17*A - 62*B)*d^3 - 10*(3*B*c*d^2 + (A - 3*B)*d^3)*f*x)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
280,1,432,0,0.519871," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{60 \, B d^{2} f x - {\left(15 \, B d^{2} f x - {\left(2 \, A + 3 \, B\right)} c^{2} - 2 \, {\left(3 \, A + 7 \, B\right)} c d - {\left(7 \, A - 32 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(A - B\right)} c^{2} + 6 \, {\left(A - B\right)} c d - 3 \, {\left(A - B\right)} d^{2} - {\left(45 \, B d^{2} f x + 2 \, {\left(2 \, A + 3 \, B\right)} c^{2} + 2 \, {\left(6 \, A - B\right)} c d - {\left(A + 19 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(10 \, B d^{2} f x - {\left(3 \, A + 2 \, B\right)} c^{2} - 2 \, {\left(2 \, A + 3 \, B\right)} c d - 3 \, {\left(A - 6 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) + {\left(60 \, B d^{2} f x + 3 \, {\left(A - B\right)} c^{2} - 6 \, {\left(A - B\right)} c d + 3 \, {\left(A - B\right)} d^{2} - {\left(15 \, B d^{2} f x + {\left(2 \, A + 3 \, B\right)} c^{2} + 2 \, {\left(3 \, A + 7 \, B\right)} c d + {\left(7 \, A - 32 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(10 \, B d^{2} f x - {\left(2 \, A + 3 \, B\right)} c^{2} - 2 \, {\left(3 \, A + 2 \, B\right)} c d - {\left(2 \, A - 17 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/15*(60*B*d^2*f*x - (15*B*d^2*f*x - (2*A + 3*B)*c^2 - 2*(3*A + 7*B)*c*d - (7*A - 32*B)*d^2)*cos(f*x + e)^3 - 3*(A - B)*c^2 + 6*(A - B)*c*d - 3*(A - B)*d^2 - (45*B*d^2*f*x + 2*(2*A + 3*B)*c^2 + 2*(6*A - B)*c*d - (A + 19*B)*d^2)*cos(f*x + e)^2 + 3*(10*B*d^2*f*x - (3*A + 2*B)*c^2 - 2*(2*A + 3*B)*c*d - 3*(A - 6*B)*d^2)*cos(f*x + e) + (60*B*d^2*f*x + 3*(A - B)*c^2 - 6*(A - B)*c*d + 3*(A - B)*d^2 - (15*B*d^2*f*x + (2*A + 3*B)*c^2 + 2*(3*A + 7*B)*c*d + (7*A - 32*B)*d^2)*cos(f*x + e)^2 + 3*(10*B*d^2*f*x - (2*A + 3*B)*c^2 - 2*(3*A + 2*B)*c*d - (2*A - 17*B)*d^2)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
281,1,271,0,0.607435," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left({\left(2 \, A + 3 \, B\right)} c + {\left(3 \, A + 7 \, B\right)} d\right)} \cos\left(f x + e\right)^{3} - {\left(2 \, {\left(2 \, A + 3 \, B\right)} c + {\left(6 \, A - B\right)} d\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(A - B\right)} c + 3 \, {\left(A - B\right)} d - 3 \, {\left({\left(3 \, A + 2 \, B\right)} c + {\left(2 \, A + 3 \, B\right)} d\right)} \cos\left(f x + e\right) - {\left({\left({\left(2 \, A + 3 \, B\right)} c + {\left(3 \, A + 7 \, B\right)} d\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(A - B\right)} c + 3 \, {\left(A - B\right)} d + 3 \, {\left({\left(2 \, A + 3 \, B\right)} c + {\left(3 \, A + 2 \, B\right)} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/15*(((2*A + 3*B)*c + (3*A + 7*B)*d)*cos(f*x + e)^3 - (2*(2*A + 3*B)*c + (6*A - B)*d)*cos(f*x + e)^2 - 3*(A - B)*c + 3*(A - B)*d - 3*((3*A + 2*B)*c + (2*A + 3*B)*d)*cos(f*x + e) - (((2*A + 3*B)*c + (3*A + 7*B)*d)*cos(f*x + e)^2 - 3*(A - B)*c + 3*(A - B)*d + 3*((2*A + 3*B)*c + (3*A + 2*B)*d)*cos(f*x + e))*sin(f*x + e))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
282,1,190,0,0.676362," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{{\left(2 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(2 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left(3 \, A + 2 \, B\right)} \cos\left(f x + e\right) - {\left({\left(2 \, A + 3 \, B\right)} \cos\left(f x + e\right)^{2} + 3 \, {\left(2 \, A + 3 \, B\right)} \cos\left(f x + e\right) - 3 \, A + 3 \, B\right)} \sin\left(f x + e\right) - 3 \, A + 3 \, B}{15 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/15*((2*A + 3*B)*cos(f*x + e)^3 - 2*(2*A + 3*B)*cos(f*x + e)^2 - 3*(3*A + 2*B)*cos(f*x + e) - ((2*A + 3*B)*cos(f*x + e)^2 + 3*(2*A + 3*B)*cos(f*x + e) - 3*A + 3*B)*sin(f*x + e) - 3*A + 3*B)/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","A",0
283,1,2292,0,0.777097," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(A - B\right)} c^{4} - 12 \, {\left(A - B\right)} c^{3} d + 12 \, {\left(A - B\right)} c d^{3} - 6 \, {\left(A - B\right)} d^{4} - 2 \, {\left({\left(2 \, A + 3 \, B\right)} c^{4} - {\left(9 \, A + 16 \, B\right)} c^{3} d + 5 \, {\left(4 \, A - B\right)} c^{2} d^{2} + {\left(9 \, A + 16 \, B\right)} c d^{3} - 2 \, {\left(11 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{4} - {\left(18 \, A + 17 \, B\right)} c^{3} d + 5 \, {\left(5 \, A - 2 \, B\right)} c^{2} d^{2} + {\left(18 \, A + 17 \, B\right)} c d^{3} - {\left(29 \, A - 4 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + 15 \, {\left(4 \, B c d^{2} - 4 \, A d^{3} - {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right) + {\left(4 \, B c d^{2} - 4 \, A d^{3} - {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 6 \, {\left({\left(3 \, A + 2 \, B\right)} c^{4} - {\left(11 \, A + 9 \, B\right)} c^{3} d + 5 \, {\left(3 \, A - B\right)} c^{2} d^{2} + {\left(11 \, A + 9 \, B\right)} c d^{3} - 3 \, {\left(6 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right) - 2 \, {\left(3 \, {\left(A - B\right)} c^{4} - 6 \, {\left(A - B\right)} c^{3} d + 6 \, {\left(A - B\right)} c d^{3} - 3 \, {\left(A - B\right)} d^{4} - {\left({\left(2 \, A + 3 \, B\right)} c^{4} - {\left(9 \, A + 16 \, B\right)} c^{3} d + 5 \, {\left(4 \, A - B\right)} c^{2} d^{2} + {\left(9 \, A + 16 \, B\right)} c d^{3} - 2 \, {\left(11 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(2 \, A + 3 \, B\right)} c^{4} - {\left(9 \, A + 11 \, B\right)} c^{3} d + 5 \, {\left(3 \, A - B\right)} c^{2} d^{2} + {\left(9 \, A + 11 \, B\right)} c d^{3} - {\left(17 \, A - 2 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left({\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f + {\left({\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{3 \, {\left(A - B\right)} c^{4} - 6 \, {\left(A - B\right)} c^{3} d + 6 \, {\left(A - B\right)} c d^{3} - 3 \, {\left(A - B\right)} d^{4} - {\left({\left(2 \, A + 3 \, B\right)} c^{4} - {\left(9 \, A + 16 \, B\right)} c^{3} d + 5 \, {\left(4 \, A - B\right)} c^{2} d^{2} + {\left(9 \, A + 16 \, B\right)} c d^{3} - 2 \, {\left(11 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{4} - {\left(18 \, A + 17 \, B\right)} c^{3} d + 5 \, {\left(5 \, A - 2 \, B\right)} c^{2} d^{2} + {\left(18 \, A + 17 \, B\right)} c d^{3} - {\left(29 \, A - 4 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + 15 \, {\left(4 \, B c d^{2} - 4 \, A d^{3} - {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right) + {\left(4 \, B c d^{2} - 4 \, A d^{3} - {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B c d^{2} - A d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + 3 \, {\left({\left(3 \, A + 2 \, B\right)} c^{4} - {\left(11 \, A + 9 \, B\right)} c^{3} d + 5 \, {\left(3 \, A - B\right)} c^{2} d^{2} + {\left(11 \, A + 9 \, B\right)} c d^{3} - 3 \, {\left(6 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right) - {\left(3 \, {\left(A - B\right)} c^{4} - 6 \, {\left(A - B\right)} c^{3} d + 6 \, {\left(A - B\right)} c d^{3} - 3 \, {\left(A - B\right)} d^{4} - {\left({\left(2 \, A + 3 \, B\right)} c^{4} - {\left(9 \, A + 16 \, B\right)} c^{3} d + 5 \, {\left(4 \, A - B\right)} c^{2} d^{2} + {\left(9 \, A + 16 \, B\right)} c d^{3} - 2 \, {\left(11 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(2 \, A + 3 \, B\right)} c^{4} - {\left(9 \, A + 11 \, B\right)} c^{3} d + 5 \, {\left(3 \, A - B\right)} c^{2} d^{2} + {\left(9 \, A + 11 \, B\right)} c d^{3} - {\left(17 \, A - 2 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left({\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f + {\left({\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{5} - 3 \, a^{3} c^{4} d + 2 \, a^{3} c^{3} d^{2} + 2 \, a^{3} c^{2} d^{3} - 3 \, a^{3} c d^{4} + a^{3} d^{5}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/30*(6*(A - B)*c^4 - 12*(A - B)*c^3*d + 12*(A - B)*c*d^3 - 6*(A - B)*d^4 - 2*((2*A + 3*B)*c^4 - (9*A + 16*B)*c^3*d + 5*(4*A - B)*c^2*d^2 + (9*A + 16*B)*c*d^3 - 2*(11*A - B)*d^4)*cos(f*x + e)^3 + 2*(2*(2*A + 3*B)*c^4 - (18*A + 17*B)*c^3*d + 5*(5*A - 2*B)*c^2*d^2 + (18*A + 17*B)*c*d^3 - (29*A - 4*B)*d^4)*cos(f*x + e)^2 + 15*(4*B*c*d^2 - 4*A*d^3 - (B*c*d^2 - A*d^3)*cos(f*x + e)^3 - 3*(B*c*d^2 - A*d^3)*cos(f*x + e)^2 + 2*(B*c*d^2 - A*d^3)*cos(f*x + e) + (4*B*c*d^2 - 4*A*d^3 - (B*c*d^2 - A*d^3)*cos(f*x + e)^2 + 2*(B*c*d^2 - A*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 6*((3*A + 2*B)*c^4 - (11*A + 9*B)*c^3*d + 5*(3*A - B)*c^2*d^2 + (11*A + 9*B)*c*d^3 - 3*(6*A - B)*d^4)*cos(f*x + e) - 2*(3*(A - B)*c^4 - 6*(A - B)*c^3*d + 6*(A - B)*c*d^3 - 3*(A - B)*d^4 - ((2*A + 3*B)*c^4 - (9*A + 16*B)*c^3*d + 5*(4*A - B)*c^2*d^2 + (9*A + 16*B)*c*d^3 - 2*(11*A - B)*d^4)*cos(f*x + e)^2 - 3*((2*A + 3*B)*c^4 - (9*A + 11*B)*c^3*d + 5*(3*A - B)*c^2*d^2 + (9*A + 11*B)*c*d^3 - (17*A - 2*B)*d^4)*cos(f*x + e))*sin(f*x + e))/((a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^3 + 3*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^2 - 2*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e) - 4*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f + ((a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^2 - 2*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e) - 4*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f)*sin(f*x + e)), 1/15*(3*(A - B)*c^4 - 6*(A - B)*c^3*d + 6*(A - B)*c*d^3 - 3*(A - B)*d^4 - ((2*A + 3*B)*c^4 - (9*A + 16*B)*c^3*d + 5*(4*A - B)*c^2*d^2 + (9*A + 16*B)*c*d^3 - 2*(11*A - B)*d^4)*cos(f*x + e)^3 + (2*(2*A + 3*B)*c^4 - (18*A + 17*B)*c^3*d + 5*(5*A - 2*B)*c^2*d^2 + (18*A + 17*B)*c*d^3 - (29*A - 4*B)*d^4)*cos(f*x + e)^2 + 15*(4*B*c*d^2 - 4*A*d^3 - (B*c*d^2 - A*d^3)*cos(f*x + e)^3 - 3*(B*c*d^2 - A*d^3)*cos(f*x + e)^2 + 2*(B*c*d^2 - A*d^3)*cos(f*x + e) + (4*B*c*d^2 - 4*A*d^3 - (B*c*d^2 - A*d^3)*cos(f*x + e)^2 + 2*(B*c*d^2 - A*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + 3*((3*A + 2*B)*c^4 - (11*A + 9*B)*c^3*d + 5*(3*A - B)*c^2*d^2 + (11*A + 9*B)*c*d^3 - 3*(6*A - B)*d^4)*cos(f*x + e) - (3*(A - B)*c^4 - 6*(A - B)*c^3*d + 6*(A - B)*c*d^3 - 3*(A - B)*d^4 - ((2*A + 3*B)*c^4 - (9*A + 16*B)*c^3*d + 5*(4*A - B)*c^2*d^2 + (9*A + 16*B)*c*d^3 - 2*(11*A - B)*d^4)*cos(f*x + e)^2 - 3*((2*A + 3*B)*c^4 - (9*A + 11*B)*c^3*d + 5*(3*A - B)*c^2*d^2 + (9*A + 11*B)*c*d^3 - (17*A - 2*B)*d^4)*cos(f*x + e))*sin(f*x + e))/((a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^3 + 3*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^2 - 2*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e) - 4*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f + ((a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e)^2 - 2*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f*cos(f*x + e) - 4*(a^3*c^5 - 3*a^3*c^4*d + 2*a^3*c^3*d^2 + 2*a^3*c^2*d^3 - 3*a^3*c*d^4 + a^3*d^5)*f)*sin(f*x + e))]","B",0
284,1,4486,0,0.852662," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(A - B\right)} c^{6} - 12 \, {\left(A - B\right)} c^{5} d - 6 \, {\left(A - B\right)} c^{4} d^{2} + 24 \, {\left(A - B\right)} c^{3} d^{3} - 6 \, {\left(A - B\right)} c^{2} d^{4} - 12 \, {\left(A - B\right)} c d^{5} + 6 \, {\left(A - B\right)} d^{6} - 2 \, {\left({\left(2 \, A + 3 \, B\right)} c^{5} d - {\left(12 \, A + 23 \, B\right)} c^{4} d^{2} + {\left(41 \, A - 66 \, B\right)} c^{3} d^{3} + {\left(84 \, A + B\right)} c^{2} d^{4} - {\left(43 \, A - 63 \, B\right)} c d^{5} - 2 \, {\left(36 \, A - 11 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left({\left(2 \, A + 3 \, B\right)} c^{6} - 2 \, {\left(3 \, A + 7 \, B\right)} c^{5} d + 5 \, {\left(A - 18 \, B\right)} c^{4} d^{2} + {\left(147 \, A - 152 \, B\right)} c^{3} d^{3} + 4 \, {\left(41 \, A + 9 \, B\right)} c^{2} d^{4} - {\left(141 \, A - 166 \, B\right)} c d^{5} - 3 \, {\left(57 \, A - 17 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{6} - {\left(19 \, A + 16 \, B\right)} c^{5} d + 11 \, {\left(2 \, A - 7 \, B\right)} c^{4} d^{2} + 8 \, {\left(16 \, A - 11 \, B\right)} c^{3} d^{3} + 2 \, {\left(32 \, A + 23 \, B\right)} c^{2} d^{4} - {\left(109 \, A - 104 \, B\right)} c d^{5} - 5 \, {\left(18 \, A - 5 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + 15 \, {\left(12 \, B c^{3} d^{2} - 8 \, {\left(2 \, A - 3 \, B\right)} c^{2} d^{3} - 4 \, {\left(7 \, A - 4 \, B\right)} c d^{4} - 4 \, {\left(3 \, A - B\right)} d^{5} + {\left(3 \, B c^{2} d^{3} - {\left(4 \, A - 3 \, B\right)} c d^{4} - {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{4} - {\left(3 \, B c^{3} d^{2} - {\left(4 \, A - 9 \, B\right)} c^{2} d^{3} - {\left(11 \, A - 7 \, B\right)} c d^{4} - 2 \, {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(9 \, B c^{3} d^{2} - 12 \, {\left(A - 2 \, B\right)} c^{2} d^{3} - {\left(29 \, A - 18 \, B\right)} c d^{4} - 5 \, {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, B c^{3} d^{2} - 2 \, {\left(2 \, A - 3 \, B\right)} c^{2} d^{3} - {\left(7 \, A - 4 \, B\right)} c d^{4} - {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right) + {\left(12 \, B c^{3} d^{2} - 8 \, {\left(2 \, A - 3 \, B\right)} c^{2} d^{3} - 4 \, {\left(7 \, A - 4 \, B\right)} c d^{4} - 4 \, {\left(3 \, A - B\right)} d^{5} - {\left(3 \, B c^{2} d^{3} - {\left(4 \, A - 3 \, B\right)} c d^{4} - {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(3 \, B c^{3} d^{2} - 4 \, {\left(A - 3 \, B\right)} c^{2} d^{3} - 5 \, {\left(3 \, A - 2 \, B\right)} c d^{4} - 3 \, {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, B c^{3} d^{2} - 2 \, {\left(2 \, A - 3 \, B\right)} c^{2} d^{3} - {\left(7 \, A - 4 \, B\right)} c d^{4} - {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 6 \, {\left({\left(3 \, A + 2 \, B\right)} c^{6} - {\left(11 \, A + 9 \, B\right)} c^{5} d + {\left(12 \, A - 47 \, B\right)} c^{4} d^{2} + 2 \, {\left(41 \, A - 31 \, B\right)} c^{3} d^{3} + {\left(47 \, A + 28 \, B\right)} c^{2} d^{4} - 71 \, {\left(A - B\right)} c d^{5} - {\left(62 \, A - 17 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) - 2 \, {\left(3 \, {\left(A - B\right)} c^{6} - 6 \, {\left(A - B\right)} c^{5} d - 3 \, {\left(A - B\right)} c^{4} d^{2} + 12 \, {\left(A - B\right)} c^{3} d^{3} - 3 \, {\left(A - B\right)} c^{2} d^{4} - 6 \, {\left(A - B\right)} c d^{5} + 3 \, {\left(A - B\right)} d^{6} + {\left({\left(2 \, A + 3 \, B\right)} c^{5} d - {\left(12 \, A + 23 \, B\right)} c^{4} d^{2} + {\left(41 \, A - 66 \, B\right)} c^{3} d^{3} + {\left(84 \, A + B\right)} c^{2} d^{4} - {\left(43 \, A - 63 \, B\right)} c d^{5} - 2 \, {\left(36 \, A - 11 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(2 \, A + 3 \, B\right)} c^{6} - {\left(8 \, A + 17 \, B\right)} c^{5} d + {\left(17 \, A - 67 \, B\right)} c^{4} d^{2} + 2 \, {\left(53 \, A - 43 \, B\right)} c^{3} d^{3} + 5 \, {\left(16 \, A + 7 \, B\right)} c^{2} d^{4} - {\left(98 \, A - 103 \, B\right)} c d^{5} - {\left(99 \, A - 29 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(2 \, A + 3 \, B\right)} c^{6} - {\left(9 \, A + 11 \, B\right)} c^{5} d + {\left(13 \, A - 48 \, B\right)} c^{4} d^{2} + 2 \, {\left(39 \, A - 29 \, B\right)} c^{3} d^{3} + 3 \, {\left(16 \, A + 9 \, B\right)} c^{2} d^{4} - 69 \, {\left(A - B\right)} c d^{5} - 9 \, {\left(7 \, A - 2 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left({\left(a^{3} c^{7} d - 3 \, a^{3} c^{6} d^{2} + a^{3} c^{5} d^{3} + 5 \, a^{3} c^{4} d^{4} - 5 \, a^{3} c^{3} d^{5} - a^{3} c^{2} d^{6} + 3 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{4} - {\left(a^{3} c^{8} - a^{3} c^{7} d - 5 \, a^{3} c^{6} d^{2} + 7 \, a^{3} c^{5} d^{3} + 5 \, a^{3} c^{4} d^{4} - 11 \, a^{3} c^{3} d^{5} + a^{3} c^{2} d^{6} + 5 \, a^{3} c d^{7} - 2 \, a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} - {\left(3 \, a^{3} c^{8} - 4 \, a^{3} c^{7} d - 12 \, a^{3} c^{6} d^{2} + 20 \, a^{3} c^{5} d^{3} + 10 \, a^{3} c^{4} d^{4} - 28 \, a^{3} c^{3} d^{5} + 4 \, a^{3} c^{2} d^{6} + 12 \, a^{3} c d^{7} - 5 \, a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f - {\left({\left(a^{3} c^{7} d - 3 \, a^{3} c^{6} d^{2} + a^{3} c^{5} d^{3} + 5 \, a^{3} c^{4} d^{4} - 5 \, a^{3} c^{3} d^{5} - a^{3} c^{2} d^{6} + 3 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{3} c^{8} - 8 \, a^{3} c^{6} d^{2} + 8 \, a^{3} c^{5} d^{3} + 10 \, a^{3} c^{4} d^{4} - 16 \, a^{3} c^{3} d^{5} + 8 \, a^{3} c d^{7} - 3 \, a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f\right)} \sin\left(f x + e\right)\right)}}, -\frac{3 \, {\left(A - B\right)} c^{6} - 6 \, {\left(A - B\right)} c^{5} d - 3 \, {\left(A - B\right)} c^{4} d^{2} + 12 \, {\left(A - B\right)} c^{3} d^{3} - 3 \, {\left(A - B\right)} c^{2} d^{4} - 6 \, {\left(A - B\right)} c d^{5} + 3 \, {\left(A - B\right)} d^{6} - {\left({\left(2 \, A + 3 \, B\right)} c^{5} d - {\left(12 \, A + 23 \, B\right)} c^{4} d^{2} + {\left(41 \, A - 66 \, B\right)} c^{3} d^{3} + {\left(84 \, A + B\right)} c^{2} d^{4} - {\left(43 \, A - 63 \, B\right)} c d^{5} - 2 \, {\left(36 \, A - 11 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left({\left(2 \, A + 3 \, B\right)} c^{6} - 2 \, {\left(3 \, A + 7 \, B\right)} c^{5} d + 5 \, {\left(A - 18 \, B\right)} c^{4} d^{2} + {\left(147 \, A - 152 \, B\right)} c^{3} d^{3} + 4 \, {\left(41 \, A + 9 \, B\right)} c^{2} d^{4} - {\left(141 \, A - 166 \, B\right)} c d^{5} - 3 \, {\left(57 \, A - 17 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} + {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{6} - {\left(19 \, A + 16 \, B\right)} c^{5} d + 11 \, {\left(2 \, A - 7 \, B\right)} c^{4} d^{2} + 8 \, {\left(16 \, A - 11 \, B\right)} c^{3} d^{3} + 2 \, {\left(32 \, A + 23 \, B\right)} c^{2} d^{4} - {\left(109 \, A - 104 \, B\right)} c d^{5} - 5 \, {\left(18 \, A - 5 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + 15 \, {\left(12 \, B c^{3} d^{2} - 8 \, {\left(2 \, A - 3 \, B\right)} c^{2} d^{3} - 4 \, {\left(7 \, A - 4 \, B\right)} c d^{4} - 4 \, {\left(3 \, A - B\right)} d^{5} + {\left(3 \, B c^{2} d^{3} - {\left(4 \, A - 3 \, B\right)} c d^{4} - {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{4} - {\left(3 \, B c^{3} d^{2} - {\left(4 \, A - 9 \, B\right)} c^{2} d^{3} - {\left(11 \, A - 7 \, B\right)} c d^{4} - 2 \, {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(9 \, B c^{3} d^{2} - 12 \, {\left(A - 2 \, B\right)} c^{2} d^{3} - {\left(29 \, A - 18 \, B\right)} c d^{4} - 5 \, {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, B c^{3} d^{2} - 2 \, {\left(2 \, A - 3 \, B\right)} c^{2} d^{3} - {\left(7 \, A - 4 \, B\right)} c d^{4} - {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right) + {\left(12 \, B c^{3} d^{2} - 8 \, {\left(2 \, A - 3 \, B\right)} c^{2} d^{3} - 4 \, {\left(7 \, A - 4 \, B\right)} c d^{4} - 4 \, {\left(3 \, A - B\right)} d^{5} - {\left(3 \, B c^{2} d^{3} - {\left(4 \, A - 3 \, B\right)} c d^{4} - {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(3 \, B c^{3} d^{2} - 4 \, {\left(A - 3 \, B\right)} c^{2} d^{3} - 5 \, {\left(3 \, A - 2 \, B\right)} c d^{4} - 3 \, {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, B c^{3} d^{2} - 2 \, {\left(2 \, A - 3 \, B\right)} c^{2} d^{3} - {\left(7 \, A - 4 \, B\right)} c d^{4} - {\left(3 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + 3 \, {\left({\left(3 \, A + 2 \, B\right)} c^{6} - {\left(11 \, A + 9 \, B\right)} c^{5} d + {\left(12 \, A - 47 \, B\right)} c^{4} d^{2} + 2 \, {\left(41 \, A - 31 \, B\right)} c^{3} d^{3} + {\left(47 \, A + 28 \, B\right)} c^{2} d^{4} - 71 \, {\left(A - B\right)} c d^{5} - {\left(62 \, A - 17 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) - {\left(3 \, {\left(A - B\right)} c^{6} - 6 \, {\left(A - B\right)} c^{5} d - 3 \, {\left(A - B\right)} c^{4} d^{2} + 12 \, {\left(A - B\right)} c^{3} d^{3} - 3 \, {\left(A - B\right)} c^{2} d^{4} - 6 \, {\left(A - B\right)} c d^{5} + 3 \, {\left(A - B\right)} d^{6} + {\left({\left(2 \, A + 3 \, B\right)} c^{5} d - {\left(12 \, A + 23 \, B\right)} c^{4} d^{2} + {\left(41 \, A - 66 \, B\right)} c^{3} d^{3} + {\left(84 \, A + B\right)} c^{2} d^{4} - {\left(43 \, A - 63 \, B\right)} c d^{5} - 2 \, {\left(36 \, A - 11 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(2 \, A + 3 \, B\right)} c^{6} - {\left(8 \, A + 17 \, B\right)} c^{5} d + {\left(17 \, A - 67 \, B\right)} c^{4} d^{2} + 2 \, {\left(53 \, A - 43 \, B\right)} c^{3} d^{3} + 5 \, {\left(16 \, A + 7 \, B\right)} c^{2} d^{4} - {\left(98 \, A - 103 \, B\right)} c d^{5} - {\left(99 \, A - 29 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(2 \, A + 3 \, B\right)} c^{6} - {\left(9 \, A + 11 \, B\right)} c^{5} d + {\left(13 \, A - 48 \, B\right)} c^{4} d^{2} + 2 \, {\left(39 \, A - 29 \, B\right)} c^{3} d^{3} + 3 \, {\left(16 \, A + 9 \, B\right)} c^{2} d^{4} - 69 \, {\left(A - B\right)} c d^{5} - 9 \, {\left(7 \, A - 2 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{15 \, {\left({\left(a^{3} c^{7} d - 3 \, a^{3} c^{6} d^{2} + a^{3} c^{5} d^{3} + 5 \, a^{3} c^{4} d^{4} - 5 \, a^{3} c^{3} d^{5} - a^{3} c^{2} d^{6} + 3 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{4} - {\left(a^{3} c^{8} - a^{3} c^{7} d - 5 \, a^{3} c^{6} d^{2} + 7 \, a^{3} c^{5} d^{3} + 5 \, a^{3} c^{4} d^{4} - 11 \, a^{3} c^{3} d^{5} + a^{3} c^{2} d^{6} + 5 \, a^{3} c d^{7} - 2 \, a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} - {\left(3 \, a^{3} c^{8} - 4 \, a^{3} c^{7} d - 12 \, a^{3} c^{6} d^{2} + 20 \, a^{3} c^{5} d^{3} + 10 \, a^{3} c^{4} d^{4} - 28 \, a^{3} c^{3} d^{5} + 4 \, a^{3} c^{2} d^{6} + 12 \, a^{3} c d^{7} - 5 \, a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f - {\left({\left(a^{3} c^{7} d - 3 \, a^{3} c^{6} d^{2} + a^{3} c^{5} d^{3} + 5 \, a^{3} c^{4} d^{4} - 5 \, a^{3} c^{3} d^{5} - a^{3} c^{2} d^{6} + 3 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{3} c^{8} - 8 \, a^{3} c^{6} d^{2} + 8 \, a^{3} c^{5} d^{3} + 10 \, a^{3} c^{4} d^{4} - 16 \, a^{3} c^{3} d^{5} + 8 \, a^{3} c d^{7} - 3 \, a^{3} d^{8}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{8} - 2 \, a^{3} c^{7} d - 2 \, a^{3} c^{6} d^{2} + 6 \, a^{3} c^{5} d^{3} - 6 \, a^{3} c^{3} d^{5} + 2 \, a^{3} c^{2} d^{6} + 2 \, a^{3} c d^{7} - a^{3} d^{8}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/30*(6*(A - B)*c^6 - 12*(A - B)*c^5*d - 6*(A - B)*c^4*d^2 + 24*(A - B)*c^3*d^3 - 6*(A - B)*c^2*d^4 - 12*(A - B)*c*d^5 + 6*(A - B)*d^6 - 2*((2*A + 3*B)*c^5*d - (12*A + 23*B)*c^4*d^2 + (41*A - 66*B)*c^3*d^3 + (84*A + B)*c^2*d^4 - (43*A - 63*B)*c*d^5 - 2*(36*A - 11*B)*d^6)*cos(f*x + e)^4 - 2*((2*A + 3*B)*c^6 - 2*(3*A + 7*B)*c^5*d + 5*(A - 18*B)*c^4*d^2 + (147*A - 152*B)*c^3*d^3 + 4*(41*A + 9*B)*c^2*d^4 - (141*A - 166*B)*c*d^5 - 3*(57*A - 17*B)*d^6)*cos(f*x + e)^3 + 2*(2*(2*A + 3*B)*c^6 - (19*A + 16*B)*c^5*d + 11*(2*A - 7*B)*c^4*d^2 + 8*(16*A - 11*B)*c^3*d^3 + 2*(32*A + 23*B)*c^2*d^4 - (109*A - 104*B)*c*d^5 - 5*(18*A - 5*B)*d^6)*cos(f*x + e)^2 + 15*(12*B*c^3*d^2 - 8*(2*A - 3*B)*c^2*d^3 - 4*(7*A - 4*B)*c*d^4 - 4*(3*A - B)*d^5 + (3*B*c^2*d^3 - (4*A - 3*B)*c*d^4 - (3*A - B)*d^5)*cos(f*x + e)^4 - (3*B*c^3*d^2 - (4*A - 9*B)*c^2*d^3 - (11*A - 7*B)*c*d^4 - 2*(3*A - B)*d^5)*cos(f*x + e)^3 - (9*B*c^3*d^2 - 12*(A - 2*B)*c^2*d^3 - (29*A - 18*B)*c*d^4 - 5*(3*A - B)*d^5)*cos(f*x + e)^2 + 2*(3*B*c^3*d^2 - 2*(2*A - 3*B)*c^2*d^3 - (7*A - 4*B)*c*d^4 - (3*A - B)*d^5)*cos(f*x + e) + (12*B*c^3*d^2 - 8*(2*A - 3*B)*c^2*d^3 - 4*(7*A - 4*B)*c*d^4 - 4*(3*A - B)*d^5 - (3*B*c^2*d^3 - (4*A - 3*B)*c*d^4 - (3*A - B)*d^5)*cos(f*x + e)^3 - (3*B*c^3*d^2 - 4*(A - 3*B)*c^2*d^3 - 5*(3*A - 2*B)*c*d^4 - 3*(3*A - B)*d^5)*cos(f*x + e)^2 + 2*(3*B*c^3*d^2 - 2*(2*A - 3*B)*c^2*d^3 - (7*A - 4*B)*c*d^4 - (3*A - B)*d^5)*cos(f*x + e))*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 6*((3*A + 2*B)*c^6 - (11*A + 9*B)*c^5*d + (12*A - 47*B)*c^4*d^2 + 2*(41*A - 31*B)*c^3*d^3 + (47*A + 28*B)*c^2*d^4 - 71*(A - B)*c*d^5 - (62*A - 17*B)*d^6)*cos(f*x + e) - 2*(3*(A - B)*c^6 - 6*(A - B)*c^5*d - 3*(A - B)*c^4*d^2 + 12*(A - B)*c^3*d^3 - 3*(A - B)*c^2*d^4 - 6*(A - B)*c*d^5 + 3*(A - B)*d^6 + ((2*A + 3*B)*c^5*d - (12*A + 23*B)*c^4*d^2 + (41*A - 66*B)*c^3*d^3 + (84*A + B)*c^2*d^4 - (43*A - 63*B)*c*d^5 - 2*(36*A - 11*B)*d^6)*cos(f*x + e)^3 - ((2*A + 3*B)*c^6 - (8*A + 17*B)*c^5*d + (17*A - 67*B)*c^4*d^2 + 2*(53*A - 43*B)*c^3*d^3 + 5*(16*A + 7*B)*c^2*d^4 - (98*A - 103*B)*c*d^5 - (99*A - 29*B)*d^6)*cos(f*x + e)^2 - 3*((2*A + 3*B)*c^6 - (9*A + 11*B)*c^5*d + (13*A - 48*B)*c^4*d^2 + 2*(39*A - 29*B)*c^3*d^3 + 3*(16*A + 9*B)*c^2*d^4 - 69*(A - B)*c*d^5 - 9*(7*A - 2*B)*d^6)*cos(f*x + e))*sin(f*x + e))/((a^3*c^7*d - 3*a^3*c^6*d^2 + a^3*c^5*d^3 + 5*a^3*c^4*d^4 - 5*a^3*c^3*d^5 - a^3*c^2*d^6 + 3*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e)^4 - (a^3*c^8 - a^3*c^7*d - 5*a^3*c^6*d^2 + 7*a^3*c^5*d^3 + 5*a^3*c^4*d^4 - 11*a^3*c^3*d^5 + a^3*c^2*d^6 + 5*a^3*c*d^7 - 2*a^3*d^8)*f*cos(f*x + e)^3 - (3*a^3*c^8 - 4*a^3*c^7*d - 12*a^3*c^6*d^2 + 20*a^3*c^5*d^3 + 10*a^3*c^4*d^4 - 28*a^3*c^3*d^5 + 4*a^3*c^2*d^6 + 12*a^3*c*d^7 - 5*a^3*d^8)*f*cos(f*x + e)^2 + 2*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e) + 4*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f - ((a^3*c^7*d - 3*a^3*c^6*d^2 + a^3*c^5*d^3 + 5*a^3*c^4*d^4 - 5*a^3*c^3*d^5 - a^3*c^2*d^6 + 3*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e)^3 + (a^3*c^8 - 8*a^3*c^6*d^2 + 8*a^3*c^5*d^3 + 10*a^3*c^4*d^4 - 16*a^3*c^3*d^5 + 8*a^3*c*d^7 - 3*a^3*d^8)*f*cos(f*x + e)^2 - 2*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e) - 4*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f)*sin(f*x + e)), -1/15*(3*(A - B)*c^6 - 6*(A - B)*c^5*d - 3*(A - B)*c^4*d^2 + 12*(A - B)*c^3*d^3 - 3*(A - B)*c^2*d^4 - 6*(A - B)*c*d^5 + 3*(A - B)*d^6 - ((2*A + 3*B)*c^5*d - (12*A + 23*B)*c^4*d^2 + (41*A - 66*B)*c^3*d^3 + (84*A + B)*c^2*d^4 - (43*A - 63*B)*c*d^5 - 2*(36*A - 11*B)*d^6)*cos(f*x + e)^4 - ((2*A + 3*B)*c^6 - 2*(3*A + 7*B)*c^5*d + 5*(A - 18*B)*c^4*d^2 + (147*A - 152*B)*c^3*d^3 + 4*(41*A + 9*B)*c^2*d^4 - (141*A - 166*B)*c*d^5 - 3*(57*A - 17*B)*d^6)*cos(f*x + e)^3 + (2*(2*A + 3*B)*c^6 - (19*A + 16*B)*c^5*d + 11*(2*A - 7*B)*c^4*d^2 + 8*(16*A - 11*B)*c^3*d^3 + 2*(32*A + 23*B)*c^2*d^4 - (109*A - 104*B)*c*d^5 - 5*(18*A - 5*B)*d^6)*cos(f*x + e)^2 + 15*(12*B*c^3*d^2 - 8*(2*A - 3*B)*c^2*d^3 - 4*(7*A - 4*B)*c*d^4 - 4*(3*A - B)*d^5 + (3*B*c^2*d^3 - (4*A - 3*B)*c*d^4 - (3*A - B)*d^5)*cos(f*x + e)^4 - (3*B*c^3*d^2 - (4*A - 9*B)*c^2*d^3 - (11*A - 7*B)*c*d^4 - 2*(3*A - B)*d^5)*cos(f*x + e)^3 - (9*B*c^3*d^2 - 12*(A - 2*B)*c^2*d^3 - (29*A - 18*B)*c*d^4 - 5*(3*A - B)*d^5)*cos(f*x + e)^2 + 2*(3*B*c^3*d^2 - 2*(2*A - 3*B)*c^2*d^3 - (7*A - 4*B)*c*d^4 - (3*A - B)*d^5)*cos(f*x + e) + (12*B*c^3*d^2 - 8*(2*A - 3*B)*c^2*d^3 - 4*(7*A - 4*B)*c*d^4 - 4*(3*A - B)*d^5 - (3*B*c^2*d^3 - (4*A - 3*B)*c*d^4 - (3*A - B)*d^5)*cos(f*x + e)^3 - (3*B*c^3*d^2 - 4*(A - 3*B)*c^2*d^3 - 5*(3*A - 2*B)*c*d^4 - 3*(3*A - B)*d^5)*cos(f*x + e)^2 + 2*(3*B*c^3*d^2 - 2*(2*A - 3*B)*c^2*d^3 - (7*A - 4*B)*c*d^4 - (3*A - B)*d^5)*cos(f*x + e))*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + 3*((3*A + 2*B)*c^6 - (11*A + 9*B)*c^5*d + (12*A - 47*B)*c^4*d^2 + 2*(41*A - 31*B)*c^3*d^3 + (47*A + 28*B)*c^2*d^4 - 71*(A - B)*c*d^5 - (62*A - 17*B)*d^6)*cos(f*x + e) - (3*(A - B)*c^6 - 6*(A - B)*c^5*d - 3*(A - B)*c^4*d^2 + 12*(A - B)*c^3*d^3 - 3*(A - B)*c^2*d^4 - 6*(A - B)*c*d^5 + 3*(A - B)*d^6 + ((2*A + 3*B)*c^5*d - (12*A + 23*B)*c^4*d^2 + (41*A - 66*B)*c^3*d^3 + (84*A + B)*c^2*d^4 - (43*A - 63*B)*c*d^5 - 2*(36*A - 11*B)*d^6)*cos(f*x + e)^3 - ((2*A + 3*B)*c^6 - (8*A + 17*B)*c^5*d + (17*A - 67*B)*c^4*d^2 + 2*(53*A - 43*B)*c^3*d^3 + 5*(16*A + 7*B)*c^2*d^4 - (98*A - 103*B)*c*d^5 - (99*A - 29*B)*d^6)*cos(f*x + e)^2 - 3*((2*A + 3*B)*c^6 - (9*A + 11*B)*c^5*d + (13*A - 48*B)*c^4*d^2 + 2*(39*A - 29*B)*c^3*d^3 + 3*(16*A + 9*B)*c^2*d^4 - 69*(A - B)*c*d^5 - 9*(7*A - 2*B)*d^6)*cos(f*x + e))*sin(f*x + e))/((a^3*c^7*d - 3*a^3*c^6*d^2 + a^3*c^5*d^3 + 5*a^3*c^4*d^4 - 5*a^3*c^3*d^5 - a^3*c^2*d^6 + 3*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e)^4 - (a^3*c^8 - a^3*c^7*d - 5*a^3*c^6*d^2 + 7*a^3*c^5*d^3 + 5*a^3*c^4*d^4 - 11*a^3*c^3*d^5 + a^3*c^2*d^6 + 5*a^3*c*d^7 - 2*a^3*d^8)*f*cos(f*x + e)^3 - (3*a^3*c^8 - 4*a^3*c^7*d - 12*a^3*c^6*d^2 + 20*a^3*c^5*d^3 + 10*a^3*c^4*d^4 - 28*a^3*c^3*d^5 + 4*a^3*c^2*d^6 + 12*a^3*c*d^7 - 5*a^3*d^8)*f*cos(f*x + e)^2 + 2*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e) + 4*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f - ((a^3*c^7*d - 3*a^3*c^6*d^2 + a^3*c^5*d^3 + 5*a^3*c^4*d^4 - 5*a^3*c^3*d^5 - a^3*c^2*d^6 + 3*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e)^3 + (a^3*c^8 - 8*a^3*c^6*d^2 + 8*a^3*c^5*d^3 + 10*a^3*c^4*d^4 - 16*a^3*c^3*d^5 + 8*a^3*c*d^7 - 3*a^3*d^8)*f*cos(f*x + e)^2 - 2*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f*cos(f*x + e) - 4*(a^3*c^8 - 2*a^3*c^7*d - 2*a^3*c^6*d^2 + 6*a^3*c^5*d^3 - 6*a^3*c^3*d^5 + 2*a^3*c^2*d^6 + 2*a^3*c*d^7 - a^3*d^8)*f)*sin(f*x + e))]","B",0
285,1,7283,0,1.147354," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^3/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(A - B\right)} c^{8} - 24 \, {\left(A - B\right)} c^{7} d - 24 \, {\left(A - B\right)} c^{6} d^{2} + 72 \, {\left(A - B\right)} c^{5} d^{3} - 72 \, {\left(A - B\right)} c^{3} d^{5} + 24 \, {\left(A - B\right)} c^{2} d^{6} + 24 \, {\left(A - B\right)} c d^{7} - 12 \, {\left(A - B\right)} d^{8} + 2 \, {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{6} d^{2} - 30 \, {\left(A + 2 \, B\right)} c^{5} d^{3} + 3 \, {\left(46 \, A - 121 \, B\right)} c^{4} d^{4} + 15 \, {\left(37 \, A - 22 \, B\right)} c^{3} d^{5} + 3 \, {\left(54 \, A + 71 \, B\right)} c^{2} d^{6} - 15 \, {\left(35 \, A - 26 \, B\right)} c d^{7} - 16 \, {\left(19 \, A - 9 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{5} - 2 \, {\left(4 \, {\left(2 \, A + 3 \, B\right)} c^{7} d - 4 \, {\left(13 \, A + 27 \, B\right)} c^{6} d^{2} + 18 \, {\left(12 \, A - 37 \, B\right)} c^{5} d^{3} + 6 \, {\left(181 \, A - 171 \, B\right)} c^{4} d^{4} + 3 \, {\left(328 \, A - 33 \, B\right)} c^{3} d^{5} - 9 \, {\left(69 \, A - 104 \, B\right)} c^{2} d^{6} - {\left(1208 \, A - 753 \, B\right)} c d^{7} - {\left(413 \, A - 198 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{8} - 6 \, {\left(A + 4 \, B\right)} c^{7} d - 20 \, {\left(A + 21 \, B\right)} c^{6} d^{2} + 6 \, {\left(128 \, A - 293 \, B\right)} c^{5} d^{3} + 3 \, {\left(892 \, A - 827 \, B\right)} c^{4} d^{4} + 3 \, {\left(769 \, A - 49 \, B\right)} c^{3} d^{5} - {\left(1573 \, A - 2373 \, B\right)} c^{2} d^{6} - 3 \, {\left(1023 \, A - 643 \, B\right)} c d^{7} - {\left(1087 \, A - 522 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{3} + 4 \, {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{8} - 5 \, {\left(4 \, A + 3 \, B\right)} c^{7} d + {\left(19 \, A - 174 \, B\right)} c^{6} d^{2} + 15 \, {\left(22 \, A - 35 \, B\right)} c^{5} d^{3} + 3 \, {\left(233 \, A - 173 \, B\right)} c^{4} d^{4} + 15 \, {\left(23 \, A + 10 \, B\right)} c^{3} d^{5} - {\left(526 \, A - 591 \, B\right)} c^{2} d^{6} - 5 \, {\left(131 \, A - 78 \, B\right)} c d^{7} - 4 \, {\left(49 \, A - 24 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{2} - 15 \, {\left(48 \, B c^{5} d^{2} - 16 \, {\left(5 \, A - 12 \, B\right)} c^{4} d^{3} - 4 \, {\left(70 \, A - 81 \, B\right)} c^{3} d^{4} - 12 \, {\left(31 \, A - 24 \, B\right)} c^{2} d^{5} - 4 \, {\left(56 \, A - 33 \, B\right)} c d^{6} - 4 \, {\left(13 \, A - 6 \, B\right)} d^{7} + {\left(12 \, B c^{3} d^{4} - 4 \, {\left(5 \, A - 6 \, B\right)} c^{2} d^{5} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{5} + {\left(24 \, B c^{4} d^{3} - 4 \, {\left(10 \, A - 21 \, B\right)} c^{3} d^{4} - 6 \, {\left(20 \, A - 19 \, B\right)} c^{2} d^{5} - {\left(116 \, A - 75 \, B\right)} c d^{6} - 3 \, {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{4} - {\left(12 \, B c^{5} d^{2} - 4 \, {\left(5 \, A - 18 \, B\right)} c^{4} d^{3} - {\left(110 \, A - 153 \, B\right)} c^{3} d^{4} - {\left(193 \, A - 162 \, B\right)} c^{2} d^{5} - {\left(142 \, A - 87 \, B\right)} c d^{6} - 3 \, {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{3} - {\left(36 \, B c^{5} d^{2} - 12 \, {\left(5 \, A - 16 \, B\right)} c^{4} d^{3} - {\left(290 \, A - 387 \, B\right)} c^{3} d^{4} - {\left(479 \, A - 396 \, B\right)} c^{2} d^{5} - {\left(340 \, A - 207 \, B\right)} c d^{6} - 7 \, {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(12 \, B c^{5} d^{2} - 4 \, {\left(5 \, A - 12 \, B\right)} c^{4} d^{3} - {\left(70 \, A - 81 \, B\right)} c^{3} d^{4} - 3 \, {\left(31 \, A - 24 \, B\right)} c^{2} d^{5} - {\left(56 \, A - 33 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right) + {\left(48 \, B c^{5} d^{2} - 16 \, {\left(5 \, A - 12 \, B\right)} c^{4} d^{3} - 4 \, {\left(70 \, A - 81 \, B\right)} c^{3} d^{4} - 12 \, {\left(31 \, A - 24 \, B\right)} c^{2} d^{5} - 4 \, {\left(56 \, A - 33 \, B\right)} c d^{6} - 4 \, {\left(13 \, A - 6 \, B\right)} d^{7} + {\left(12 \, B c^{3} d^{4} - 4 \, {\left(5 \, A - 6 \, B\right)} c^{2} d^{5} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(12 \, B c^{4} d^{3} - 4 \, {\left(5 \, A - 9 \, B\right)} c^{3} d^{4} - 5 \, {\left(10 \, A - 9 \, B\right)} c^{2} d^{5} - {\left(43 \, A - 27 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{3} - {\left(12 \, B c^{5} d^{2} - 4 \, {\left(5 \, A - 24 \, B\right)} c^{4} d^{3} - 75 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{4} - {\left(293 \, A - 252 \, B\right)} c^{2} d^{5} - 3 \, {\left(76 \, A - 47 \, B\right)} c d^{6} - 5 \, {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(12 \, B c^{5} d^{2} - 4 \, {\left(5 \, A - 12 \, B\right)} c^{4} d^{3} - {\left(70 \, A - 81 \, B\right)} c^{3} d^{4} - 3 \, {\left(31 \, A - 24 \, B\right)} c^{2} d^{5} - {\left(56 \, A - 33 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(-\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} - 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 12 \, {\left({\left(3 \, A + 2 \, B\right)} c^{8} - {\left(11 \, A + 9 \, B\right)} c^{7} d + {\left(9 \, A - 109 \, B\right)} c^{6} d^{2} + {\left(213 \, A - 353 \, B\right)} c^{5} d^{3} + 5 \, {\left(95 \, A - 71 \, B\right)} c^{4} d^{4} + {\left(237 \, A + 103 \, B\right)} c^{3} d^{5} - {\left(359 \, A - 399 \, B\right)} c^{2} d^{6} - {\left(439 \, A - 259 \, B\right)} c d^{7} - {\left(128 \, A - 63 \, B\right)} d^{8}\right)} \cos\left(f x + e\right) - 2 \, {\left(6 \, {\left(A - B\right)} c^{8} - 12 \, {\left(A - B\right)} c^{7} d - 12 \, {\left(A - B\right)} c^{6} d^{2} + 36 \, {\left(A - B\right)} c^{5} d^{3} - 36 \, {\left(A - B\right)} c^{3} d^{5} + 12 \, {\left(A - B\right)} c^{2} d^{6} + 12 \, {\left(A - B\right)} c d^{7} - 6 \, {\left(A - B\right)} d^{8} + {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{6} d^{2} - 30 \, {\left(A + 2 \, B\right)} c^{5} d^{3} + 3 \, {\left(46 \, A - 121 \, B\right)} c^{4} d^{4} + 15 \, {\left(37 \, A - 22 \, B\right)} c^{3} d^{5} + 3 \, {\left(54 \, A + 71 \, B\right)} c^{2} d^{6} - 15 \, {\left(35 \, A - 26 \, B\right)} c d^{7} - 16 \, {\left(19 \, A - 9 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{4} + {\left(4 \, {\left(2 \, A + 3 \, B\right)} c^{7} d - 6 \, {\left(8 \, A + 17 \, B\right)} c^{6} d^{2} + 6 \, {\left(31 \, A - 121 \, B\right)} c^{5} d^{3} + 3 \, {\left(408 \, A - 463 \, B\right)} c^{4} d^{4} + 3 \, {\left(513 \, A - 143 \, B\right)} c^{3} d^{5} - 3 \, {\left(153 \, A - 383 \, B\right)} c^{2} d^{6} - {\left(1733 \, A - 1143 \, B\right)} c d^{7} - 3 \, {\left(239 \, A - 114 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left({\left(2 \, A + 3 \, B\right)} c^{8} - {\left(7 \, A + 18 \, B\right)} c^{7} d + {\left(14 \, A - 159 \, B\right)} c^{6} d^{2} + 3 \, {\left(97 \, A - 172 \, B\right)} c^{5} d^{3} + 6 \, {\left(121 \, A - 91 \, B\right)} c^{4} d^{4} + 3 \, {\left(128 \, A + 47 \, B\right)} c^{3} d^{5} - {\left(557 \, A - 612 \, B\right)} c^{2} d^{6} - {\left(668 \, A - 393 \, B\right)} c d^{7} - 5 \, {\left(37 \, A - 18 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{2} - 6 \, {\left({\left(2 \, A + 3 \, B\right)} c^{8} - {\left(9 \, A + 11 \, B\right)} c^{7} d + {\left(11 \, A - 111 \, B\right)} c^{6} d^{2} + {\left(207 \, A - 347 \, B\right)} c^{5} d^{3} + 5 \, {\left(95 \, A - 71 \, B\right)} c^{4} d^{4} + {\left(243 \, A + 97 \, B\right)} c^{3} d^{5} - {\left(361 \, A - 401 \, B\right)} c^{2} d^{6} - 9 \, {\left(49 \, A - 29 \, B\right)} c d^{7} - {\left(127 \, A - 62 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{60 \, {\left({\left(a^{3} c^{9} d^{2} - 3 \, a^{3} c^{8} d^{3} + 8 \, a^{3} c^{6} d^{5} - 6 \, a^{3} c^{5} d^{6} - 6 \, a^{3} c^{4} d^{7} + 8 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{5} + {\left(2 \, a^{3} c^{10} d - 3 \, a^{3} c^{9} d^{2} - 9 \, a^{3} c^{8} d^{3} + 16 \, a^{3} c^{7} d^{4} + 12 \, a^{3} c^{6} d^{5} - 30 \, a^{3} c^{5} d^{6} - 2 \, a^{3} c^{4} d^{7} + 24 \, a^{3} c^{3} d^{8} - 6 \, a^{3} c^{2} d^{9} - 7 \, a^{3} c d^{10} + 3 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{4} - {\left(a^{3} c^{11} + a^{3} c^{10} d - 9 \, a^{3} c^{9} d^{2} - a^{3} c^{8} d^{3} + 26 \, a^{3} c^{7} d^{4} - 6 \, a^{3} c^{6} d^{5} - 34 \, a^{3} c^{5} d^{6} + 14 \, a^{3} c^{4} d^{7} + 21 \, a^{3} c^{3} d^{8} - 11 \, a^{3} c^{2} d^{9} - 5 \, a^{3} c d^{10} + 3 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{3} - {\left(3 \, a^{3} c^{11} + a^{3} c^{10} d - 23 \, a^{3} c^{9} d^{2} + 3 \, a^{3} c^{8} d^{3} + 62 \, a^{3} c^{7} d^{4} - 22 \, a^{3} c^{6} d^{5} - 78 \, a^{3} c^{5} d^{6} + 38 \, a^{3} c^{4} d^{7} + 47 \, a^{3} c^{3} d^{8} - 27 \, a^{3} c^{2} d^{9} - 11 \, a^{3} c d^{10} + 7 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{11} - a^{3} c^{10} d - 5 \, a^{3} c^{9} d^{2} + 5 \, a^{3} c^{8} d^{3} + 10 \, a^{3} c^{7} d^{4} - 10 \, a^{3} c^{6} d^{5} - 10 \, a^{3} c^{5} d^{6} + 10 \, a^{3} c^{4} d^{7} + 5 \, a^{3} c^{3} d^{8} - 5 \, a^{3} c^{2} d^{9} - a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{11} - a^{3} c^{10} d - 5 \, a^{3} c^{9} d^{2} + 5 \, a^{3} c^{8} d^{3} + 10 \, a^{3} c^{7} d^{4} - 10 \, a^{3} c^{6} d^{5} - 10 \, a^{3} c^{5} d^{6} + 10 \, a^{3} c^{4} d^{7} + 5 \, a^{3} c^{3} d^{8} - 5 \, a^{3} c^{2} d^{9} - a^{3} c d^{10} + a^{3} d^{11}\right)} f + {\left({\left(a^{3} c^{9} d^{2} - 3 \, a^{3} c^{8} d^{3} + 8 \, a^{3} c^{6} d^{5} - 6 \, a^{3} c^{5} d^{6} - 6 \, a^{3} c^{4} d^{7} + 8 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{4} - 2 \, {\left(a^{3} c^{10} d - 2 \, a^{3} c^{9} d^{2} - 3 \, a^{3} c^{8} d^{3} + 8 \, a^{3} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{5} - 12 \, a^{3} c^{5} d^{6} + 2 \, a^{3} c^{4} d^{7} + 8 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{9} - 2 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{3} - {\left(a^{3} c^{11} + 3 \, a^{3} c^{10} d - 13 \, a^{3} c^{9} d^{2} - 7 \, a^{3} c^{8} d^{3} + 42 \, a^{3} c^{7} d^{4} - 2 \, a^{3} c^{6} d^{5} - 58 \, a^{3} c^{5} d^{6} + 18 \, a^{3} c^{4} d^{7} + 37 \, a^{3} c^{3} d^{8} - 17 \, a^{3} c^{2} d^{9} - 9 \, a^{3} c d^{10} + 5 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{11} - a^{3} c^{10} d - 5 \, a^{3} c^{9} d^{2} + 5 \, a^{3} c^{8} d^{3} + 10 \, a^{3} c^{7} d^{4} - 10 \, a^{3} c^{6} d^{5} - 10 \, a^{3} c^{5} d^{6} + 10 \, a^{3} c^{4} d^{7} + 5 \, a^{3} c^{3} d^{8} - 5 \, a^{3} c^{2} d^{9} - a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{11} - a^{3} c^{10} d - 5 \, a^{3} c^{9} d^{2} + 5 \, a^{3} c^{8} d^{3} + 10 \, a^{3} c^{7} d^{4} - 10 \, a^{3} c^{6} d^{5} - 10 \, a^{3} c^{5} d^{6} + 10 \, a^{3} c^{4} d^{7} + 5 \, a^{3} c^{3} d^{8} - 5 \, a^{3} c^{2} d^{9} - a^{3} c d^{10} + a^{3} d^{11}\right)} f\right)} \sin\left(f x + e\right)\right)}}, -\frac{6 \, {\left(A - B\right)} c^{8} - 12 \, {\left(A - B\right)} c^{7} d - 12 \, {\left(A - B\right)} c^{6} d^{2} + 36 \, {\left(A - B\right)} c^{5} d^{3} - 36 \, {\left(A - B\right)} c^{3} d^{5} + 12 \, {\left(A - B\right)} c^{2} d^{6} + 12 \, {\left(A - B\right)} c d^{7} - 6 \, {\left(A - B\right)} d^{8} + {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{6} d^{2} - 30 \, {\left(A + 2 \, B\right)} c^{5} d^{3} + 3 \, {\left(46 \, A - 121 \, B\right)} c^{4} d^{4} + 15 \, {\left(37 \, A - 22 \, B\right)} c^{3} d^{5} + 3 \, {\left(54 \, A + 71 \, B\right)} c^{2} d^{6} - 15 \, {\left(35 \, A - 26 \, B\right)} c d^{7} - 16 \, {\left(19 \, A - 9 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{5} - {\left(4 \, {\left(2 \, A + 3 \, B\right)} c^{7} d - 4 \, {\left(13 \, A + 27 \, B\right)} c^{6} d^{2} + 18 \, {\left(12 \, A - 37 \, B\right)} c^{5} d^{3} + 6 \, {\left(181 \, A - 171 \, B\right)} c^{4} d^{4} + 3 \, {\left(328 \, A - 33 \, B\right)} c^{3} d^{5} - 9 \, {\left(69 \, A - 104 \, B\right)} c^{2} d^{6} - {\left(1208 \, A - 753 \, B\right)} c d^{7} - {\left(413 \, A - 198 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{4} - {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{8} - 6 \, {\left(A + 4 \, B\right)} c^{7} d - 20 \, {\left(A + 21 \, B\right)} c^{6} d^{2} + 6 \, {\left(128 \, A - 293 \, B\right)} c^{5} d^{3} + 3 \, {\left(892 \, A - 827 \, B\right)} c^{4} d^{4} + 3 \, {\left(769 \, A - 49 \, B\right)} c^{3} d^{5} - {\left(1573 \, A - 2373 \, B\right)} c^{2} d^{6} - 3 \, {\left(1023 \, A - 643 \, B\right)} c d^{7} - {\left(1087 \, A - 522 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{8} - 5 \, {\left(4 \, A + 3 \, B\right)} c^{7} d + {\left(19 \, A - 174 \, B\right)} c^{6} d^{2} + 15 \, {\left(22 \, A - 35 \, B\right)} c^{5} d^{3} + 3 \, {\left(233 \, A - 173 \, B\right)} c^{4} d^{4} + 15 \, {\left(23 \, A + 10 \, B\right)} c^{3} d^{5} - {\left(526 \, A - 591 \, B\right)} c^{2} d^{6} - 5 \, {\left(131 \, A - 78 \, B\right)} c d^{7} - 4 \, {\left(49 \, A - 24 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{2} + 15 \, {\left(48 \, B c^{5} d^{2} - 16 \, {\left(5 \, A - 12 \, B\right)} c^{4} d^{3} - 4 \, {\left(70 \, A - 81 \, B\right)} c^{3} d^{4} - 12 \, {\left(31 \, A - 24 \, B\right)} c^{2} d^{5} - 4 \, {\left(56 \, A - 33 \, B\right)} c d^{6} - 4 \, {\left(13 \, A - 6 \, B\right)} d^{7} + {\left(12 \, B c^{3} d^{4} - 4 \, {\left(5 \, A - 6 \, B\right)} c^{2} d^{5} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{5} + {\left(24 \, B c^{4} d^{3} - 4 \, {\left(10 \, A - 21 \, B\right)} c^{3} d^{4} - 6 \, {\left(20 \, A - 19 \, B\right)} c^{2} d^{5} - {\left(116 \, A - 75 \, B\right)} c d^{6} - 3 \, {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{4} - {\left(12 \, B c^{5} d^{2} - 4 \, {\left(5 \, A - 18 \, B\right)} c^{4} d^{3} - {\left(110 \, A - 153 \, B\right)} c^{3} d^{4} - {\left(193 \, A - 162 \, B\right)} c^{2} d^{5} - {\left(142 \, A - 87 \, B\right)} c d^{6} - 3 \, {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{3} - {\left(36 \, B c^{5} d^{2} - 12 \, {\left(5 \, A - 16 \, B\right)} c^{4} d^{3} - {\left(290 \, A - 387 \, B\right)} c^{3} d^{4} - {\left(479 \, A - 396 \, B\right)} c^{2} d^{5} - {\left(340 \, A - 207 \, B\right)} c d^{6} - 7 \, {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(12 \, B c^{5} d^{2} - 4 \, {\left(5 \, A - 12 \, B\right)} c^{4} d^{3} - {\left(70 \, A - 81 \, B\right)} c^{3} d^{4} - 3 \, {\left(31 \, A - 24 \, B\right)} c^{2} d^{5} - {\left(56 \, A - 33 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right) + {\left(48 \, B c^{5} d^{2} - 16 \, {\left(5 \, A - 12 \, B\right)} c^{4} d^{3} - 4 \, {\left(70 \, A - 81 \, B\right)} c^{3} d^{4} - 12 \, {\left(31 \, A - 24 \, B\right)} c^{2} d^{5} - 4 \, {\left(56 \, A - 33 \, B\right)} c d^{6} - 4 \, {\left(13 \, A - 6 \, B\right)} d^{7} + {\left(12 \, B c^{3} d^{4} - 4 \, {\left(5 \, A - 6 \, B\right)} c^{2} d^{5} - 3 \, {\left(10 \, A - 7 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(12 \, B c^{4} d^{3} - 4 \, {\left(5 \, A - 9 \, B\right)} c^{3} d^{4} - 5 \, {\left(10 \, A - 9 \, B\right)} c^{2} d^{5} - {\left(43 \, A - 27 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{3} - {\left(12 \, B c^{5} d^{2} - 4 \, {\left(5 \, A - 24 \, B\right)} c^{4} d^{3} - 75 \, {\left(2 \, A - 3 \, B\right)} c^{3} d^{4} - {\left(293 \, A - 252 \, B\right)} c^{2} d^{5} - 3 \, {\left(76 \, A - 47 \, B\right)} c d^{6} - 5 \, {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(12 \, B c^{5} d^{2} - 4 \, {\left(5 \, A - 12 \, B\right)} c^{4} d^{3} - {\left(70 \, A - 81 \, B\right)} c^{3} d^{4} - 3 \, {\left(31 \, A - 24 \, B\right)} c^{2} d^{5} - {\left(56 \, A - 33 \, B\right)} c d^{6} - {\left(13 \, A - 6 \, B\right)} d^{7}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + 6 \, {\left({\left(3 \, A + 2 \, B\right)} c^{8} - {\left(11 \, A + 9 \, B\right)} c^{7} d + {\left(9 \, A - 109 \, B\right)} c^{6} d^{2} + {\left(213 \, A - 353 \, B\right)} c^{5} d^{3} + 5 \, {\left(95 \, A - 71 \, B\right)} c^{4} d^{4} + {\left(237 \, A + 103 \, B\right)} c^{3} d^{5} - {\left(359 \, A - 399 \, B\right)} c^{2} d^{6} - {\left(439 \, A - 259 \, B\right)} c d^{7} - {\left(128 \, A - 63 \, B\right)} d^{8}\right)} \cos\left(f x + e\right) - {\left(6 \, {\left(A - B\right)} c^{8} - 12 \, {\left(A - B\right)} c^{7} d - 12 \, {\left(A - B\right)} c^{6} d^{2} + 36 \, {\left(A - B\right)} c^{5} d^{3} - 36 \, {\left(A - B\right)} c^{3} d^{5} + 12 \, {\left(A - B\right)} c^{2} d^{6} + 12 \, {\left(A - B\right)} c d^{7} - 6 \, {\left(A - B\right)} d^{8} + {\left(2 \, {\left(2 \, A + 3 \, B\right)} c^{6} d^{2} - 30 \, {\left(A + 2 \, B\right)} c^{5} d^{3} + 3 \, {\left(46 \, A - 121 \, B\right)} c^{4} d^{4} + 15 \, {\left(37 \, A - 22 \, B\right)} c^{3} d^{5} + 3 \, {\left(54 \, A + 71 \, B\right)} c^{2} d^{6} - 15 \, {\left(35 \, A - 26 \, B\right)} c d^{7} - 16 \, {\left(19 \, A - 9 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{4} + {\left(4 \, {\left(2 \, A + 3 \, B\right)} c^{7} d - 6 \, {\left(8 \, A + 17 \, B\right)} c^{6} d^{2} + 6 \, {\left(31 \, A - 121 \, B\right)} c^{5} d^{3} + 3 \, {\left(408 \, A - 463 \, B\right)} c^{4} d^{4} + 3 \, {\left(513 \, A - 143 \, B\right)} c^{3} d^{5} - 3 \, {\left(153 \, A - 383 \, B\right)} c^{2} d^{6} - {\left(1733 \, A - 1143 \, B\right)} c d^{7} - 3 \, {\left(239 \, A - 114 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left({\left(2 \, A + 3 \, B\right)} c^{8} - {\left(7 \, A + 18 \, B\right)} c^{7} d + {\left(14 \, A - 159 \, B\right)} c^{6} d^{2} + 3 \, {\left(97 \, A - 172 \, B\right)} c^{5} d^{3} + 6 \, {\left(121 \, A - 91 \, B\right)} c^{4} d^{4} + 3 \, {\left(128 \, A + 47 \, B\right)} c^{3} d^{5} - {\left(557 \, A - 612 \, B\right)} c^{2} d^{6} - {\left(668 \, A - 393 \, B\right)} c d^{7} - 5 \, {\left(37 \, A - 18 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)^{2} - 6 \, {\left({\left(2 \, A + 3 \, B\right)} c^{8} - {\left(9 \, A + 11 \, B\right)} c^{7} d + {\left(11 \, A - 111 \, B\right)} c^{6} d^{2} + {\left(207 \, A - 347 \, B\right)} c^{5} d^{3} + 5 \, {\left(95 \, A - 71 \, B\right)} c^{4} d^{4} + {\left(243 \, A + 97 \, B\right)} c^{3} d^{5} - {\left(361 \, A - 401 \, B\right)} c^{2} d^{6} - 9 \, {\left(49 \, A - 29 \, B\right)} c d^{7} - {\left(127 \, A - 62 \, B\right)} d^{8}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{30 \, {\left({\left(a^{3} c^{9} d^{2} - 3 \, a^{3} c^{8} d^{3} + 8 \, a^{3} c^{6} d^{5} - 6 \, a^{3} c^{5} d^{6} - 6 \, a^{3} c^{4} d^{7} + 8 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{5} + {\left(2 \, a^{3} c^{10} d - 3 \, a^{3} c^{9} d^{2} - 9 \, a^{3} c^{8} d^{3} + 16 \, a^{3} c^{7} d^{4} + 12 \, a^{3} c^{6} d^{5} - 30 \, a^{3} c^{5} d^{6} - 2 \, a^{3} c^{4} d^{7} + 24 \, a^{3} c^{3} d^{8} - 6 \, a^{3} c^{2} d^{9} - 7 \, a^{3} c d^{10} + 3 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{4} - {\left(a^{3} c^{11} + a^{3} c^{10} d - 9 \, a^{3} c^{9} d^{2} - a^{3} c^{8} d^{3} + 26 \, a^{3} c^{7} d^{4} - 6 \, a^{3} c^{6} d^{5} - 34 \, a^{3} c^{5} d^{6} + 14 \, a^{3} c^{4} d^{7} + 21 \, a^{3} c^{3} d^{8} - 11 \, a^{3} c^{2} d^{9} - 5 \, a^{3} c d^{10} + 3 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{3} - {\left(3 \, a^{3} c^{11} + a^{3} c^{10} d - 23 \, a^{3} c^{9} d^{2} + 3 \, a^{3} c^{8} d^{3} + 62 \, a^{3} c^{7} d^{4} - 22 \, a^{3} c^{6} d^{5} - 78 \, a^{3} c^{5} d^{6} + 38 \, a^{3} c^{4} d^{7} + 47 \, a^{3} c^{3} d^{8} - 27 \, a^{3} c^{2} d^{9} - 11 \, a^{3} c d^{10} + 7 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{11} - a^{3} c^{10} d - 5 \, a^{3} c^{9} d^{2} + 5 \, a^{3} c^{8} d^{3} + 10 \, a^{3} c^{7} d^{4} - 10 \, a^{3} c^{6} d^{5} - 10 \, a^{3} c^{5} d^{6} + 10 \, a^{3} c^{4} d^{7} + 5 \, a^{3} c^{3} d^{8} - 5 \, a^{3} c^{2} d^{9} - a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{11} - a^{3} c^{10} d - 5 \, a^{3} c^{9} d^{2} + 5 \, a^{3} c^{8} d^{3} + 10 \, a^{3} c^{7} d^{4} - 10 \, a^{3} c^{6} d^{5} - 10 \, a^{3} c^{5} d^{6} + 10 \, a^{3} c^{4} d^{7} + 5 \, a^{3} c^{3} d^{8} - 5 \, a^{3} c^{2} d^{9} - a^{3} c d^{10} + a^{3} d^{11}\right)} f + {\left({\left(a^{3} c^{9} d^{2} - 3 \, a^{3} c^{8} d^{3} + 8 \, a^{3} c^{6} d^{5} - 6 \, a^{3} c^{5} d^{6} - 6 \, a^{3} c^{4} d^{7} + 8 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{4} - 2 \, {\left(a^{3} c^{10} d - 2 \, a^{3} c^{9} d^{2} - 3 \, a^{3} c^{8} d^{3} + 8 \, a^{3} c^{7} d^{4} + 2 \, a^{3} c^{6} d^{5} - 12 \, a^{3} c^{5} d^{6} + 2 \, a^{3} c^{4} d^{7} + 8 \, a^{3} c^{3} d^{8} - 3 \, a^{3} c^{2} d^{9} - 2 \, a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{3} - {\left(a^{3} c^{11} + 3 \, a^{3} c^{10} d - 13 \, a^{3} c^{9} d^{2} - 7 \, a^{3} c^{8} d^{3} + 42 \, a^{3} c^{7} d^{4} - 2 \, a^{3} c^{6} d^{5} - 58 \, a^{3} c^{5} d^{6} + 18 \, a^{3} c^{4} d^{7} + 37 \, a^{3} c^{3} d^{8} - 17 \, a^{3} c^{2} d^{9} - 9 \, a^{3} c d^{10} + 5 \, a^{3} d^{11}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{11} - a^{3} c^{10} d - 5 \, a^{3} c^{9} d^{2} + 5 \, a^{3} c^{8} d^{3} + 10 \, a^{3} c^{7} d^{4} - 10 \, a^{3} c^{6} d^{5} - 10 \, a^{3} c^{5} d^{6} + 10 \, a^{3} c^{4} d^{7} + 5 \, a^{3} c^{3} d^{8} - 5 \, a^{3} c^{2} d^{9} - a^{3} c d^{10} + a^{3} d^{11}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{11} - a^{3} c^{10} d - 5 \, a^{3} c^{9} d^{2} + 5 \, a^{3} c^{8} d^{3} + 10 \, a^{3} c^{7} d^{4} - 10 \, a^{3} c^{6} d^{5} - 10 \, a^{3} c^{5} d^{6} + 10 \, a^{3} c^{4} d^{7} + 5 \, a^{3} c^{3} d^{8} - 5 \, a^{3} c^{2} d^{9} - a^{3} c d^{10} + a^{3} d^{11}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/60*(12*(A - B)*c^8 - 24*(A - B)*c^7*d - 24*(A - B)*c^6*d^2 + 72*(A - B)*c^5*d^3 - 72*(A - B)*c^3*d^5 + 24*(A - B)*c^2*d^6 + 24*(A - B)*c*d^7 - 12*(A - B)*d^8 + 2*(2*(2*A + 3*B)*c^6*d^2 - 30*(A + 2*B)*c^5*d^3 + 3*(46*A - 121*B)*c^4*d^4 + 15*(37*A - 22*B)*c^3*d^5 + 3*(54*A + 71*B)*c^2*d^6 - 15*(35*A - 26*B)*c*d^7 - 16*(19*A - 9*B)*d^8)*cos(f*x + e)^5 - 2*(4*(2*A + 3*B)*c^7*d - 4*(13*A + 27*B)*c^6*d^2 + 18*(12*A - 37*B)*c^5*d^3 + 6*(181*A - 171*B)*c^4*d^4 + 3*(328*A - 33*B)*c^3*d^5 - 9*(69*A - 104*B)*c^2*d^6 - (1208*A - 753*B)*c*d^7 - (413*A - 198*B)*d^8)*cos(f*x + e)^4 - 2*(2*(2*A + 3*B)*c^8 - 6*(A + 4*B)*c^7*d - 20*(A + 21*B)*c^6*d^2 + 6*(128*A - 293*B)*c^5*d^3 + 3*(892*A - 827*B)*c^4*d^4 + 3*(769*A - 49*B)*c^3*d^5 - (1573*A - 2373*B)*c^2*d^6 - 3*(1023*A - 643*B)*c*d^7 - (1087*A - 522*B)*d^8)*cos(f*x + e)^3 + 4*(2*(2*A + 3*B)*c^8 - 5*(4*A + 3*B)*c^7*d + (19*A - 174*B)*c^6*d^2 + 15*(22*A - 35*B)*c^5*d^3 + 3*(233*A - 173*B)*c^4*d^4 + 15*(23*A + 10*B)*c^3*d^5 - (526*A - 591*B)*c^2*d^6 - 5*(131*A - 78*B)*c*d^7 - 4*(49*A - 24*B)*d^8)*cos(f*x + e)^2 - 15*(48*B*c^5*d^2 - 16*(5*A - 12*B)*c^4*d^3 - 4*(70*A - 81*B)*c^3*d^4 - 12*(31*A - 24*B)*c^2*d^5 - 4*(56*A - 33*B)*c*d^6 - 4*(13*A - 6*B)*d^7 + (12*B*c^3*d^4 - 4*(5*A - 6*B)*c^2*d^5 - 3*(10*A - 7*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e)^5 + (24*B*c^4*d^3 - 4*(10*A - 21*B)*c^3*d^4 - 6*(20*A - 19*B)*c^2*d^5 - (116*A - 75*B)*c*d^6 - 3*(13*A - 6*B)*d^7)*cos(f*x + e)^4 - (12*B*c^5*d^2 - 4*(5*A - 18*B)*c^4*d^3 - (110*A - 153*B)*c^3*d^4 - (193*A - 162*B)*c^2*d^5 - (142*A - 87*B)*c*d^6 - 3*(13*A - 6*B)*d^7)*cos(f*x + e)^3 - (36*B*c^5*d^2 - 12*(5*A - 16*B)*c^4*d^3 - (290*A - 387*B)*c^3*d^4 - (479*A - 396*B)*c^2*d^5 - (340*A - 207*B)*c*d^6 - 7*(13*A - 6*B)*d^7)*cos(f*x + e)^2 + 2*(12*B*c^5*d^2 - 4*(5*A - 12*B)*c^4*d^3 - (70*A - 81*B)*c^3*d^4 - 3*(31*A - 24*B)*c^2*d^5 - (56*A - 33*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e) + (48*B*c^5*d^2 - 16*(5*A - 12*B)*c^4*d^3 - 4*(70*A - 81*B)*c^3*d^4 - 12*(31*A - 24*B)*c^2*d^5 - 4*(56*A - 33*B)*c*d^6 - 4*(13*A - 6*B)*d^7 + (12*B*c^3*d^4 - 4*(5*A - 6*B)*c^2*d^5 - 3*(10*A - 7*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e)^4 - 2*(12*B*c^4*d^3 - 4*(5*A - 9*B)*c^3*d^4 - 5*(10*A - 9*B)*c^2*d^5 - (43*A - 27*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e)^3 - (12*B*c^5*d^2 - 4*(5*A - 24*B)*c^4*d^3 - 75*(2*A - 3*B)*c^3*d^4 - (293*A - 252*B)*c^2*d^5 - 3*(76*A - 47*B)*c*d^6 - 5*(13*A - 6*B)*d^7)*cos(f*x + e)^2 + 2*(12*B*c^5*d^2 - 4*(5*A - 12*B)*c^4*d^3 - (70*A - 81*B)*c^3*d^4 - 3*(31*A - 24*B)*c^2*d^5 - (56*A - 33*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e))*sin(f*x + e))*sqrt(-c^2 + d^2)*log(-((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 - 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 12*((3*A + 2*B)*c^8 - (11*A + 9*B)*c^7*d + (9*A - 109*B)*c^6*d^2 + (213*A - 353*B)*c^5*d^3 + 5*(95*A - 71*B)*c^4*d^4 + (237*A + 103*B)*c^3*d^5 - (359*A - 399*B)*c^2*d^6 - (439*A - 259*B)*c*d^7 - (128*A - 63*B)*d^8)*cos(f*x + e) - 2*(6*(A - B)*c^8 - 12*(A - B)*c^7*d - 12*(A - B)*c^6*d^2 + 36*(A - B)*c^5*d^3 - 36*(A - B)*c^3*d^5 + 12*(A - B)*c^2*d^6 + 12*(A - B)*c*d^7 - 6*(A - B)*d^8 + (2*(2*A + 3*B)*c^6*d^2 - 30*(A + 2*B)*c^5*d^3 + 3*(46*A - 121*B)*c^4*d^4 + 15*(37*A - 22*B)*c^3*d^5 + 3*(54*A + 71*B)*c^2*d^6 - 15*(35*A - 26*B)*c*d^7 - 16*(19*A - 9*B)*d^8)*cos(f*x + e)^4 + (4*(2*A + 3*B)*c^7*d - 6*(8*A + 17*B)*c^6*d^2 + 6*(31*A - 121*B)*c^5*d^3 + 3*(408*A - 463*B)*c^4*d^4 + 3*(513*A - 143*B)*c^3*d^5 - 3*(153*A - 383*B)*c^2*d^6 - (1733*A - 1143*B)*c*d^7 - 3*(239*A - 114*B)*d^8)*cos(f*x + e)^3 - 2*((2*A + 3*B)*c^8 - (7*A + 18*B)*c^7*d + (14*A - 159*B)*c^6*d^2 + 3*(97*A - 172*B)*c^5*d^3 + 6*(121*A - 91*B)*c^4*d^4 + 3*(128*A + 47*B)*c^3*d^5 - (557*A - 612*B)*c^2*d^6 - (668*A - 393*B)*c*d^7 - 5*(37*A - 18*B)*d^8)*cos(f*x + e)^2 - 6*((2*A + 3*B)*c^8 - (9*A + 11*B)*c^7*d + (11*A - 111*B)*c^6*d^2 + (207*A - 347*B)*c^5*d^3 + 5*(95*A - 71*B)*c^4*d^4 + (243*A + 97*B)*c^3*d^5 - (361*A - 401*B)*c^2*d^6 - 9*(49*A - 29*B)*c*d^7 - (127*A - 62*B)*d^8)*cos(f*x + e))*sin(f*x + e))/((a^3*c^9*d^2 - 3*a^3*c^8*d^3 + 8*a^3*c^6*d^5 - 6*a^3*c^5*d^6 - 6*a^3*c^4*d^7 + 8*a^3*c^3*d^8 - 3*a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e)^5 + (2*a^3*c^10*d - 3*a^3*c^9*d^2 - 9*a^3*c^8*d^3 + 16*a^3*c^7*d^4 + 12*a^3*c^6*d^5 - 30*a^3*c^5*d^6 - 2*a^3*c^4*d^7 + 24*a^3*c^3*d^8 - 6*a^3*c^2*d^9 - 7*a^3*c*d^10 + 3*a^3*d^11)*f*cos(f*x + e)^4 - (a^3*c^11 + a^3*c^10*d - 9*a^3*c^9*d^2 - a^3*c^8*d^3 + 26*a^3*c^7*d^4 - 6*a^3*c^6*d^5 - 34*a^3*c^5*d^6 + 14*a^3*c^4*d^7 + 21*a^3*c^3*d^8 - 11*a^3*c^2*d^9 - 5*a^3*c*d^10 + 3*a^3*d^11)*f*cos(f*x + e)^3 - (3*a^3*c^11 + a^3*c^10*d - 23*a^3*c^9*d^2 + 3*a^3*c^8*d^3 + 62*a^3*c^7*d^4 - 22*a^3*c^6*d^5 - 78*a^3*c^5*d^6 + 38*a^3*c^4*d^7 + 47*a^3*c^3*d^8 - 27*a^3*c^2*d^9 - 11*a^3*c*d^10 + 7*a^3*d^11)*f*cos(f*x + e)^2 + 2*(a^3*c^11 - a^3*c^10*d - 5*a^3*c^9*d^2 + 5*a^3*c^8*d^3 + 10*a^3*c^7*d^4 - 10*a^3*c^6*d^5 - 10*a^3*c^5*d^6 + 10*a^3*c^4*d^7 + 5*a^3*c^3*d^8 - 5*a^3*c^2*d^9 - a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e) + 4*(a^3*c^11 - a^3*c^10*d - 5*a^3*c^9*d^2 + 5*a^3*c^8*d^3 + 10*a^3*c^7*d^4 - 10*a^3*c^6*d^5 - 10*a^3*c^5*d^6 + 10*a^3*c^4*d^7 + 5*a^3*c^3*d^8 - 5*a^3*c^2*d^9 - a^3*c*d^10 + a^3*d^11)*f + ((a^3*c^9*d^2 - 3*a^3*c^8*d^3 + 8*a^3*c^6*d^5 - 6*a^3*c^5*d^6 - 6*a^3*c^4*d^7 + 8*a^3*c^3*d^8 - 3*a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e)^4 - 2*(a^3*c^10*d - 2*a^3*c^9*d^2 - 3*a^3*c^8*d^3 + 8*a^3*c^7*d^4 + 2*a^3*c^6*d^5 - 12*a^3*c^5*d^6 + 2*a^3*c^4*d^7 + 8*a^3*c^3*d^8 - 3*a^3*c^2*d^9 - 2*a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e)^3 - (a^3*c^11 + 3*a^3*c^10*d - 13*a^3*c^9*d^2 - 7*a^3*c^8*d^3 + 42*a^3*c^7*d^4 - 2*a^3*c^6*d^5 - 58*a^3*c^5*d^6 + 18*a^3*c^4*d^7 + 37*a^3*c^3*d^8 - 17*a^3*c^2*d^9 - 9*a^3*c*d^10 + 5*a^3*d^11)*f*cos(f*x + e)^2 + 2*(a^3*c^11 - a^3*c^10*d - 5*a^3*c^9*d^2 + 5*a^3*c^8*d^3 + 10*a^3*c^7*d^4 - 10*a^3*c^6*d^5 - 10*a^3*c^5*d^6 + 10*a^3*c^4*d^7 + 5*a^3*c^3*d^8 - 5*a^3*c^2*d^9 - a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e) + 4*(a^3*c^11 - a^3*c^10*d - 5*a^3*c^9*d^2 + 5*a^3*c^8*d^3 + 10*a^3*c^7*d^4 - 10*a^3*c^6*d^5 - 10*a^3*c^5*d^6 + 10*a^3*c^4*d^7 + 5*a^3*c^3*d^8 - 5*a^3*c^2*d^9 - a^3*c*d^10 + a^3*d^11)*f)*sin(f*x + e)), -1/30*(6*(A - B)*c^8 - 12*(A - B)*c^7*d - 12*(A - B)*c^6*d^2 + 36*(A - B)*c^5*d^3 - 36*(A - B)*c^3*d^5 + 12*(A - B)*c^2*d^6 + 12*(A - B)*c*d^7 - 6*(A - B)*d^8 + (2*(2*A + 3*B)*c^6*d^2 - 30*(A + 2*B)*c^5*d^3 + 3*(46*A - 121*B)*c^4*d^4 + 15*(37*A - 22*B)*c^3*d^5 + 3*(54*A + 71*B)*c^2*d^6 - 15*(35*A - 26*B)*c*d^7 - 16*(19*A - 9*B)*d^8)*cos(f*x + e)^5 - (4*(2*A + 3*B)*c^7*d - 4*(13*A + 27*B)*c^6*d^2 + 18*(12*A - 37*B)*c^5*d^3 + 6*(181*A - 171*B)*c^4*d^4 + 3*(328*A - 33*B)*c^3*d^5 - 9*(69*A - 104*B)*c^2*d^6 - (1208*A - 753*B)*c*d^7 - (413*A - 198*B)*d^8)*cos(f*x + e)^4 - (2*(2*A + 3*B)*c^8 - 6*(A + 4*B)*c^7*d - 20*(A + 21*B)*c^6*d^2 + 6*(128*A - 293*B)*c^5*d^3 + 3*(892*A - 827*B)*c^4*d^4 + 3*(769*A - 49*B)*c^3*d^5 - (1573*A - 2373*B)*c^2*d^6 - 3*(1023*A - 643*B)*c*d^7 - (1087*A - 522*B)*d^8)*cos(f*x + e)^3 + 2*(2*(2*A + 3*B)*c^8 - 5*(4*A + 3*B)*c^7*d + (19*A - 174*B)*c^6*d^2 + 15*(22*A - 35*B)*c^5*d^3 + 3*(233*A - 173*B)*c^4*d^4 + 15*(23*A + 10*B)*c^3*d^5 - (526*A - 591*B)*c^2*d^6 - 5*(131*A - 78*B)*c*d^7 - 4*(49*A - 24*B)*d^8)*cos(f*x + e)^2 + 15*(48*B*c^5*d^2 - 16*(5*A - 12*B)*c^4*d^3 - 4*(70*A - 81*B)*c^3*d^4 - 12*(31*A - 24*B)*c^2*d^5 - 4*(56*A - 33*B)*c*d^6 - 4*(13*A - 6*B)*d^7 + (12*B*c^3*d^4 - 4*(5*A - 6*B)*c^2*d^5 - 3*(10*A - 7*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e)^5 + (24*B*c^4*d^3 - 4*(10*A - 21*B)*c^3*d^4 - 6*(20*A - 19*B)*c^2*d^5 - (116*A - 75*B)*c*d^6 - 3*(13*A - 6*B)*d^7)*cos(f*x + e)^4 - (12*B*c^5*d^2 - 4*(5*A - 18*B)*c^4*d^3 - (110*A - 153*B)*c^3*d^4 - (193*A - 162*B)*c^2*d^5 - (142*A - 87*B)*c*d^6 - 3*(13*A - 6*B)*d^7)*cos(f*x + e)^3 - (36*B*c^5*d^2 - 12*(5*A - 16*B)*c^4*d^3 - (290*A - 387*B)*c^3*d^4 - (479*A - 396*B)*c^2*d^5 - (340*A - 207*B)*c*d^6 - 7*(13*A - 6*B)*d^7)*cos(f*x + e)^2 + 2*(12*B*c^5*d^2 - 4*(5*A - 12*B)*c^4*d^3 - (70*A - 81*B)*c^3*d^4 - 3*(31*A - 24*B)*c^2*d^5 - (56*A - 33*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e) + (48*B*c^5*d^2 - 16*(5*A - 12*B)*c^4*d^3 - 4*(70*A - 81*B)*c^3*d^4 - 12*(31*A - 24*B)*c^2*d^5 - 4*(56*A - 33*B)*c*d^6 - 4*(13*A - 6*B)*d^7 + (12*B*c^3*d^4 - 4*(5*A - 6*B)*c^2*d^5 - 3*(10*A - 7*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e)^4 - 2*(12*B*c^4*d^3 - 4*(5*A - 9*B)*c^3*d^4 - 5*(10*A - 9*B)*c^2*d^5 - (43*A - 27*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e)^3 - (12*B*c^5*d^2 - 4*(5*A - 24*B)*c^4*d^3 - 75*(2*A - 3*B)*c^3*d^4 - (293*A - 252*B)*c^2*d^5 - 3*(76*A - 47*B)*c*d^6 - 5*(13*A - 6*B)*d^7)*cos(f*x + e)^2 + 2*(12*B*c^5*d^2 - 4*(5*A - 12*B)*c^4*d^3 - (70*A - 81*B)*c^3*d^4 - 3*(31*A - 24*B)*c^2*d^5 - (56*A - 33*B)*c*d^6 - (13*A - 6*B)*d^7)*cos(f*x + e))*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + 6*((3*A + 2*B)*c^8 - (11*A + 9*B)*c^7*d + (9*A - 109*B)*c^6*d^2 + (213*A - 353*B)*c^5*d^3 + 5*(95*A - 71*B)*c^4*d^4 + (237*A + 103*B)*c^3*d^5 - (359*A - 399*B)*c^2*d^6 - (439*A - 259*B)*c*d^7 - (128*A - 63*B)*d^8)*cos(f*x + e) - (6*(A - B)*c^8 - 12*(A - B)*c^7*d - 12*(A - B)*c^6*d^2 + 36*(A - B)*c^5*d^3 - 36*(A - B)*c^3*d^5 + 12*(A - B)*c^2*d^6 + 12*(A - B)*c*d^7 - 6*(A - B)*d^8 + (2*(2*A + 3*B)*c^6*d^2 - 30*(A + 2*B)*c^5*d^3 + 3*(46*A - 121*B)*c^4*d^4 + 15*(37*A - 22*B)*c^3*d^5 + 3*(54*A + 71*B)*c^2*d^6 - 15*(35*A - 26*B)*c*d^7 - 16*(19*A - 9*B)*d^8)*cos(f*x + e)^4 + (4*(2*A + 3*B)*c^7*d - 6*(8*A + 17*B)*c^6*d^2 + 6*(31*A - 121*B)*c^5*d^3 + 3*(408*A - 463*B)*c^4*d^4 + 3*(513*A - 143*B)*c^3*d^5 - 3*(153*A - 383*B)*c^2*d^6 - (1733*A - 1143*B)*c*d^7 - 3*(239*A - 114*B)*d^8)*cos(f*x + e)^3 - 2*((2*A + 3*B)*c^8 - (7*A + 18*B)*c^7*d + (14*A - 159*B)*c^6*d^2 + 3*(97*A - 172*B)*c^5*d^3 + 6*(121*A - 91*B)*c^4*d^4 + 3*(128*A + 47*B)*c^3*d^5 - (557*A - 612*B)*c^2*d^6 - (668*A - 393*B)*c*d^7 - 5*(37*A - 18*B)*d^8)*cos(f*x + e)^2 - 6*((2*A + 3*B)*c^8 - (9*A + 11*B)*c^7*d + (11*A - 111*B)*c^6*d^2 + (207*A - 347*B)*c^5*d^3 + 5*(95*A - 71*B)*c^4*d^4 + (243*A + 97*B)*c^3*d^5 - (361*A - 401*B)*c^2*d^6 - 9*(49*A - 29*B)*c*d^7 - (127*A - 62*B)*d^8)*cos(f*x + e))*sin(f*x + e))/((a^3*c^9*d^2 - 3*a^3*c^8*d^3 + 8*a^3*c^6*d^5 - 6*a^3*c^5*d^6 - 6*a^3*c^4*d^7 + 8*a^3*c^3*d^8 - 3*a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e)^5 + (2*a^3*c^10*d - 3*a^3*c^9*d^2 - 9*a^3*c^8*d^3 + 16*a^3*c^7*d^4 + 12*a^3*c^6*d^5 - 30*a^3*c^5*d^6 - 2*a^3*c^4*d^7 + 24*a^3*c^3*d^8 - 6*a^3*c^2*d^9 - 7*a^3*c*d^10 + 3*a^3*d^11)*f*cos(f*x + e)^4 - (a^3*c^11 + a^3*c^10*d - 9*a^3*c^9*d^2 - a^3*c^8*d^3 + 26*a^3*c^7*d^4 - 6*a^3*c^6*d^5 - 34*a^3*c^5*d^6 + 14*a^3*c^4*d^7 + 21*a^3*c^3*d^8 - 11*a^3*c^2*d^9 - 5*a^3*c*d^10 + 3*a^3*d^11)*f*cos(f*x + e)^3 - (3*a^3*c^11 + a^3*c^10*d - 23*a^3*c^9*d^2 + 3*a^3*c^8*d^3 + 62*a^3*c^7*d^4 - 22*a^3*c^6*d^5 - 78*a^3*c^5*d^6 + 38*a^3*c^4*d^7 + 47*a^3*c^3*d^8 - 27*a^3*c^2*d^9 - 11*a^3*c*d^10 + 7*a^3*d^11)*f*cos(f*x + e)^2 + 2*(a^3*c^11 - a^3*c^10*d - 5*a^3*c^9*d^2 + 5*a^3*c^8*d^3 + 10*a^3*c^7*d^4 - 10*a^3*c^6*d^5 - 10*a^3*c^5*d^6 + 10*a^3*c^4*d^7 + 5*a^3*c^3*d^8 - 5*a^3*c^2*d^9 - a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e) + 4*(a^3*c^11 - a^3*c^10*d - 5*a^3*c^9*d^2 + 5*a^3*c^8*d^3 + 10*a^3*c^7*d^4 - 10*a^3*c^6*d^5 - 10*a^3*c^5*d^6 + 10*a^3*c^4*d^7 + 5*a^3*c^3*d^8 - 5*a^3*c^2*d^9 - a^3*c*d^10 + a^3*d^11)*f + ((a^3*c^9*d^2 - 3*a^3*c^8*d^3 + 8*a^3*c^6*d^5 - 6*a^3*c^5*d^6 - 6*a^3*c^4*d^7 + 8*a^3*c^3*d^8 - 3*a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e)^4 - 2*(a^3*c^10*d - 2*a^3*c^9*d^2 - 3*a^3*c^8*d^3 + 8*a^3*c^7*d^4 + 2*a^3*c^6*d^5 - 12*a^3*c^5*d^6 + 2*a^3*c^4*d^7 + 8*a^3*c^3*d^8 - 3*a^3*c^2*d^9 - 2*a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e)^3 - (a^3*c^11 + 3*a^3*c^10*d - 13*a^3*c^9*d^2 - 7*a^3*c^8*d^3 + 42*a^3*c^7*d^4 - 2*a^3*c^6*d^5 - 58*a^3*c^5*d^6 + 18*a^3*c^4*d^7 + 37*a^3*c^3*d^8 - 17*a^3*c^2*d^9 - 9*a^3*c*d^10 + 5*a^3*d^11)*f*cos(f*x + e)^2 + 2*(a^3*c^11 - a^3*c^10*d - 5*a^3*c^9*d^2 + 5*a^3*c^8*d^3 + 10*a^3*c^7*d^4 - 10*a^3*c^6*d^5 - 10*a^3*c^5*d^6 + 10*a^3*c^4*d^7 + 5*a^3*c^3*d^8 - 5*a^3*c^2*d^9 - a^3*c*d^10 + a^3*d^11)*f*cos(f*x + e) + 4*(a^3*c^11 - a^3*c^10*d - 5*a^3*c^9*d^2 + 5*a^3*c^8*d^3 + 10*a^3*c^7*d^4 - 10*a^3*c^6*d^5 - 10*a^3*c^5*d^6 + 10*a^3*c^4*d^7 + 5*a^3*c^3*d^8 - 5*a^3*c^2*d^9 - a^3*c*d^10 + a^3*d^11)*f)*sin(f*x + e))]","B",0
286,1,467,0,0.691930," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, B d^{3} \cos\left(f x + e\right)^{5} - 5 \, {\left(27 \, B c d^{2} + {\left(9 \, A + B\right)} d^{3}\right)} \cos\left(f x + e\right)^{4} + 105 \, {\left(3 \, A + B\right)} c^{3} + 63 \, {\left(5 \, A + 7 \, B\right)} c^{2} d + 9 \, {\left(49 \, A + 27 \, B\right)} c d^{2} + {\left(81 \, A + 107 \, B\right)} d^{3} - {\left(189 \, B c^{2} d + 27 \, {\left(7 \, A + 6 \, B\right)} c d^{2} + 2 \, {\left(27 \, A + 59 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(105 \, B c^{3} + 63 \, {\left(5 \, A + B\right)} c^{2} d + 9 \, {\left(7 \, A + 36 \, B\right)} c d^{2} + 2 \, {\left(54 \, A + 13 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(105 \, {\left(3 \, A + 2 \, B\right)} c^{3} + 63 \, {\left(10 \, A + 11 \, B\right)} c^{2} d + 99 \, {\left(7 \, A + 6 \, B\right)} c d^{2} + {\left(198 \, A + 211 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) - {\left(35 \, B d^{3} \cos\left(f x + e\right)^{4} + 105 \, {\left(3 \, A + B\right)} c^{3} + 63 \, {\left(5 \, A + 7 \, B\right)} c^{2} d + 9 \, {\left(49 \, A + 27 \, B\right)} c d^{2} + {\left(81 \, A + 107 \, B\right)} d^{3} + 5 \, {\left(27 \, B c d^{2} + {\left(9 \, A + 8 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(63 \, B c^{2} d + 9 \, {\left(7 \, A + B\right)} c d^{2} + {\left(3 \, A + 26 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(105 \, B c^{3} + 63 \, {\left(5 \, A + 4 \, B\right)} c^{2} d + 9 \, {\left(28 \, A + 39 \, B\right)} c d^{2} + 13 \, {\left(9 \, A + 8 \, B\right)} 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}}{315 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/315*(35*B*d^3*cos(f*x + e)^5 - 5*(27*B*c*d^2 + (9*A + B)*d^3)*cos(f*x + e)^4 + 105*(3*A + B)*c^3 + 63*(5*A + 7*B)*c^2*d + 9*(49*A + 27*B)*c*d^2 + (81*A + 107*B)*d^3 - (189*B*c^2*d + 27*(7*A + 6*B)*c*d^2 + 2*(27*A + 59*B)*d^3)*cos(f*x + e)^3 + (105*B*c^3 + 63*(5*A + B)*c^2*d + 9*(7*A + 36*B)*c*d^2 + 2*(54*A + 13*B)*d^3)*cos(f*x + e)^2 + (105*(3*A + 2*B)*c^3 + 63*(10*A + 11*B)*c^2*d + 99*(7*A + 6*B)*c*d^2 + (198*A + 211*B)*d^3)*cos(f*x + e) - (35*B*d^3*cos(f*x + e)^4 + 105*(3*A + B)*c^3 + 63*(5*A + 7*B)*c^2*d + 9*(49*A + 27*B)*c*d^2 + (81*A + 107*B)*d^3 + 5*(27*B*c*d^2 + (9*A + 8*B)*d^3)*cos(f*x + e)^3 - 3*(63*B*c^2*d + 9*(7*A + B)*c*d^2 + (3*A + 26*B)*d^3)*cos(f*x + e)^2 - (105*B*c^3 + 63*(5*A + 4*B)*c^2*d + 9*(28*A + 39*B)*c*d^2 + 13*(9*A + 8*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
287,1,306,0,0.584604," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B d^{2} \cos\left(f x + e\right)^{4} + 3 \, {\left(14 \, B c d + {\left(7 \, A + 6 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{3} - 35 \, {\left(3 \, A + B\right)} c^{2} - 14 \, {\left(5 \, A + 7 \, B\right)} c d - {\left(49 \, A + 27 \, B\right)} d^{2} - {\left(35 \, B c^{2} + 14 \, {\left(5 \, A + B\right)} c d + {\left(7 \, A + 36 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(35 \, {\left(3 \, A + 2 \, B\right)} c^{2} + 14 \, {\left(10 \, A + 11 \, B\right)} c d + 11 \, {\left(7 \, A + 6 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) + {\left(15 \, B d^{2} \cos\left(f x + e\right)^{3} + 35 \, {\left(3 \, A + B\right)} c^{2} + 14 \, {\left(5 \, A + 7 \, B\right)} c d + {\left(49 \, A + 27 \, B\right)} d^{2} - 3 \, {\left(14 \, B c d + {\left(7 \, A + B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(35 \, B c^{2} + 14 \, {\left(5 \, A + 4 \, B\right)} c d + {\left(28 \, A + 39 \, B\right)} 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}}{105 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/105*(15*B*d^2*cos(f*x + e)^4 + 3*(14*B*c*d + (7*A + 6*B)*d^2)*cos(f*x + e)^3 - 35*(3*A + B)*c^2 - 14*(5*A + 7*B)*c*d - (49*A + 27*B)*d^2 - (35*B*c^2 + 14*(5*A + B)*c*d + (7*A + 36*B)*d^2)*cos(f*x + e)^2 - (35*(3*A + 2*B)*c^2 + 14*(10*A + 11*B)*c*d + 11*(7*A + 6*B)*d^2)*cos(f*x + e) + (15*B*d^2*cos(f*x + e)^3 + 35*(3*A + B)*c^2 + 14*(5*A + 7*B)*c*d + (49*A + 27*B)*d^2 - 3*(14*B*c*d + (7*A + B)*d^2)*cos(f*x + e)^2 - (35*B*c^2 + 14*(5*A + 4*B)*c*d + (28*A + 39*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
288,1,175,0,0.687894," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B d \cos\left(f x + e\right)^{3} - {\left(5 \, B c + {\left(5 \, A + B\right)} d\right)} \cos\left(f x + e\right)^{2} - 5 \, {\left(3 \, A + B\right)} c - {\left(5 \, A + 7 \, B\right)} d - {\left(5 \, {\left(3 \, A + 2 \, B\right)} c + {\left(10 \, A + 11 \, B\right)} d\right)} \cos\left(f x + e\right) - {\left(3 \, B d \cos\left(f x + e\right)^{2} - 5 \, {\left(3 \, A + B\right)} c - {\left(5 \, A + 7 \, B\right)} d + {\left(5 \, B c + {\left(5 \, A + 4 \, B\right)} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{15 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/15*(3*B*d*cos(f*x + e)^3 - (5*B*c + (5*A + B)*d)*cos(f*x + e)^2 - 5*(3*A + B)*c - (5*A + 7*B)*d - (5*(3*A + 2*B)*c + (10*A + 11*B)*d)*cos(f*x + e) - (3*B*d*cos(f*x + e)^2 - 5*(3*A + B)*c - (5*A + 7*B)*d + (5*B*c + (5*A + 4*B)*d)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
289,1,85,0,0.782614," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(B \cos\left(f x + e\right)^{2} + {\left(3 \, A + 2 \, B\right)} \cos\left(f x + e\right) + {\left(B \cos\left(f x + e\right) - 3 \, A - B\right)} \sin\left(f x + e\right) + 3 \, A + B\right)} \sqrt{a \sin\left(f x + e\right) + a}}{3 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/3*(B*cos(f*x + e)^2 + (3*A + 2*B)*cos(f*x + e) + (B*cos(f*x + e) - 3*A - B)*sin(f*x + e) + 3*A + B)*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
290,1,651,0,2.405172," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{{\left(B c - A d + {\left(B c - A d\right)} \cos\left(f x + e\right) + {\left(B c - A d\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(B \cos\left(f x + e\right) - B \sin\left(f x + e\right) + B\right)} \sqrt{a \sin\left(f x + e\right) + a}}{2 \, {\left(d f \cos\left(f x + e\right) + d f \sin\left(f x + e\right) + d f\right)}}, \frac{{\left(B c - A d + {\left(B c - A d\right)} \cos\left(f x + e\right) + {\left(B c - A d\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) - 2 \, {\left(B \cos\left(f x + e\right) - B \sin\left(f x + e\right) + B\right)} \sqrt{a \sin\left(f x + e\right) + a}}{d f \cos\left(f x + e\right) + d f \sin\left(f x + e\right) + d f}\right]"," ",0,"[-1/2*((B*c - A*d + (B*c - A*d)*cos(f*x + e) + (B*c - A*d)*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(B*cos(f*x + e) - B*sin(f*x + e) + B)*sqrt(a*sin(f*x + e) + a))/(d*f*cos(f*x + e) + d*f*sin(f*x + e) + d*f), ((B*c - A*d + (B*c - A*d)*cos(f*x + e) + (B*c - A*d)*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) - 2*(B*cos(f*x + e) - B*sin(f*x + e) + B)*sqrt(a*sin(f*x + e) + a))/(d*f*cos(f*x + e) + d*f*sin(f*x + e) + d*f)]","A",0
291,1,1012,0,1.989752," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{{\left(B c^{2} + {\left(A + 3 \, B\right)} c d + {\left(A + 2 \, B\right)} d^{2} - {\left(B c d + {\left(A + 2 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{2} + {\left(A + 2 \, B\right)} c d\right)} \cos\left(f x + e\right) + {\left(B c^{2} + {\left(A + 3 \, B\right)} c d + {\left(A + 2 \, B\right)} d^{2} + {\left(B c d + {\left(A + 2 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(B c - A d + {\left(B c - A d\right)} \cos\left(f x + e\right) - {\left(B c - A d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{4 \, {\left({\left(c d^{2} + d^{3}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{2} d + c d^{2}\right)} f \cos\left(f x + e\right) - {\left(c^{2} d + 2 \, c d^{2} + d^{3}\right)} f - {\left({\left(c d^{2} + d^{3}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d + 2 \, c d^{2} + d^{3}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{{\left(B c^{2} + {\left(A + 3 \, B\right)} c d + {\left(A + 2 \, B\right)} d^{2} - {\left(B c d + {\left(A + 2 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{2} + {\left(A + 2 \, B\right)} c d\right)} \cos\left(f x + e\right) + {\left(B c^{2} + {\left(A + 3 \, B\right)} c d + {\left(A + 2 \, B\right)} d^{2} + {\left(B c d + {\left(A + 2 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) - 2 \, {\left(B c - A d + {\left(B c - A d\right)} \cos\left(f x + e\right) - {\left(B c - A d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{2 \, {\left({\left(c d^{2} + d^{3}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{2} d + c d^{2}\right)} f \cos\left(f x + e\right) - {\left(c^{2} d + 2 \, c d^{2} + d^{3}\right)} f - {\left({\left(c d^{2} + d^{3}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d + 2 \, c d^{2} + d^{3}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*((B*c^2 + (A + 3*B)*c*d + (A + 2*B)*d^2 - (B*c*d + (A + 2*B)*d^2)*cos(f*x + e)^2 + (B*c^2 + (A + 2*B)*c*d)*cos(f*x + e) + (B*c^2 + (A + 3*B)*c*d + (A + 2*B)*d^2 + (B*c*d + (A + 2*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(B*c - A*d + (B*c - A*d)*cos(f*x + e) - (B*c - A*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c*d^2 + d^3)*f*cos(f*x + e)^2 - (c^2*d + c*d^2)*f*cos(f*x + e) - (c^2*d + 2*c*d^2 + d^3)*f - ((c*d^2 + d^3)*f*cos(f*x + e) + (c^2*d + 2*c*d^2 + d^3)*f)*sin(f*x + e)), 1/2*((B*c^2 + (A + 3*B)*c*d + (A + 2*B)*d^2 - (B*c*d + (A + 2*B)*d^2)*cos(f*x + e)^2 + (B*c^2 + (A + 2*B)*c*d)*cos(f*x + e) + (B*c^2 + (A + 3*B)*c*d + (A + 2*B)*d^2 + (B*c*d + (A + 2*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) - 2*(B*c - A*d + (B*c - A*d)*cos(f*x + e) - (B*c - A*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c*d^2 + d^3)*f*cos(f*x + e)^2 - (c^2*d + c*d^2)*f*cos(f*x + e) - (c^2*d + 2*c*d^2 + d^3)*f - ((c*d^2 + d^3)*f*cos(f*x + e) + (c^2*d + 2*c*d^2 + d^3)*f)*sin(f*x + e))]","B",0
292,1,1750,0,3.875824," ","integrate((A+B*sin(f*x+e))*(a+a*sin(f*x+e))^(1/2)/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(B c^{3} + 3 \, {\left(A + 2 \, B\right)} c^{2} d + 3 \, {\left(2 \, A + 3 \, B\right)} c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3} - {\left(B c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(2 \, B c^{2} d + 3 \, {\left(2 \, A + 3 \, B\right)} c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{3} + {\left(3 \, A + 4 \, B\right)} c^{2} d + B c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(B c^{3} + 3 \, {\left(A + 2 \, B\right)} c^{2} d + 3 \, {\left(2 \, A + 3 \, B\right)} c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3} - {\left(B c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B c^{2} d + {\left(3 \, A + 4 \, B\right)} c d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(B c^{2} - {\left(5 \, A + B\right)} c d + {\left(A + 4 \, B\right)} d^{2} - {\left(B c d + {\left(3 \, A + 4 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{2} - {\left(5 \, A + 2 \, B\right)} c d - 2 \, A d^{2}\right)} \cos\left(f x + e\right) - {\left(B c^{2} - {\left(5 \, A + B\right)} c d + {\left(A + 4 \, B\right)} d^{2} + {\left(B c d + {\left(3 \, A + 4 \, B\right)} 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}}{16 \, {\left({\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, c^{3} d^{2} + 5 \, c^{2} d^{3} + 4 \, c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{4} d + 2 \, c^{3} d^{2} + 2 \, c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d + 4 \, c^{3} d^{2} + 6 \, c^{2} d^{3} + 4 \, c d^{4} + d^{5}\right)} f + {\left({\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{3} d^{2} + 2 \, c^{2} d^{3} + c d^{4}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d + 4 \, c^{3} d^{2} + 6 \, c^{2} d^{3} + 4 \, c d^{4} + d^{5}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{{\left(B c^{3} + 3 \, {\left(A + 2 \, B\right)} c^{2} d + 3 \, {\left(2 \, A + 3 \, B\right)} c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3} - {\left(B c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(2 \, B c^{2} d + 3 \, {\left(2 \, A + 3 \, B\right)} c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{3} + {\left(3 \, A + 4 \, B\right)} c^{2} d + B c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(B c^{3} + 3 \, {\left(A + 2 \, B\right)} c^{2} d + 3 \, {\left(2 \, A + 3 \, B\right)} c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3} - {\left(B c d^{2} + {\left(3 \, A + 4 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B c^{2} d + {\left(3 \, A + 4 \, B\right)} c d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) - 2 \, {\left(B c^{2} - {\left(5 \, A + B\right)} c d + {\left(A + 4 \, B\right)} d^{2} - {\left(B c d + {\left(3 \, A + 4 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{2} - {\left(5 \, A + 2 \, B\right)} c d - 2 \, A d^{2}\right)} \cos\left(f x + e\right) - {\left(B c^{2} - {\left(5 \, A + B\right)} c d + {\left(A + 4 \, B\right)} d^{2} + {\left(B c d + {\left(3 \, A + 4 \, B\right)} 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}}{8 \, {\left({\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, c^{3} d^{2} + 5 \, c^{2} d^{3} + 4 \, c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{4} d + 2 \, c^{3} d^{2} + 2 \, c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d + 4 \, c^{3} d^{2} + 6 \, c^{2} d^{3} + 4 \, c d^{4} + d^{5}\right)} f + {\left({\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{3} d^{2} + 2 \, c^{2} d^{3} + c d^{4}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d + 4 \, c^{3} d^{2} + 6 \, c^{2} d^{3} + 4 \, c d^{4} + d^{5}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/16*((B*c^3 + 3*(A + 2*B)*c^2*d + 3*(2*A + 3*B)*c*d^2 + (3*A + 4*B)*d^3 - (B*c*d^2 + (3*A + 4*B)*d^3)*cos(f*x + e)^3 - (2*B*c^2*d + 3*(2*A + 3*B)*c*d^2 + (3*A + 4*B)*d^3)*cos(f*x + e)^2 + (B*c^3 + (3*A + 4*B)*c^2*d + B*c*d^2 + (3*A + 4*B)*d^3)*cos(f*x + e) + (B*c^3 + 3*(A + 2*B)*c^2*d + 3*(2*A + 3*B)*c*d^2 + (3*A + 4*B)*d^3 - (B*c*d^2 + (3*A + 4*B)*d^3)*cos(f*x + e)^2 + 2*(B*c^2*d + (3*A + 4*B)*c*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(B*c^2 - (5*A + B)*c*d + (A + 4*B)*d^2 - (B*c*d + (3*A + 4*B)*d^2)*cos(f*x + e)^2 + (B*c^2 - (5*A + 2*B)*c*d - 2*A*d^2)*cos(f*x + e) - (B*c^2 - (5*A + B)*c*d + (A + 4*B)*d^2 + (B*c*d + (3*A + 4*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c^2*d^3 + 2*c*d^4 + d^5)*f*cos(f*x + e)^3 + (2*c^3*d^2 + 5*c^2*d^3 + 4*c*d^4 + d^5)*f*cos(f*x + e)^2 - (c^4*d + 2*c^3*d^2 + 2*c^2*d^3 + 2*c*d^4 + d^5)*f*cos(f*x + e) - (c^4*d + 4*c^3*d^2 + 6*c^2*d^3 + 4*c*d^4 + d^5)*f + ((c^2*d^3 + 2*c*d^4 + d^5)*f*cos(f*x + e)^2 - 2*(c^3*d^2 + 2*c^2*d^3 + c*d^4)*f*cos(f*x + e) - (c^4*d + 4*c^3*d^2 + 6*c^2*d^3 + 4*c*d^4 + d^5)*f)*sin(f*x + e)), 1/8*((B*c^3 + 3*(A + 2*B)*c^2*d + 3*(2*A + 3*B)*c*d^2 + (3*A + 4*B)*d^3 - (B*c*d^2 + (3*A + 4*B)*d^3)*cos(f*x + e)^3 - (2*B*c^2*d + 3*(2*A + 3*B)*c*d^2 + (3*A + 4*B)*d^3)*cos(f*x + e)^2 + (B*c^3 + (3*A + 4*B)*c^2*d + B*c*d^2 + (3*A + 4*B)*d^3)*cos(f*x + e) + (B*c^3 + 3*(A + 2*B)*c^2*d + 3*(2*A + 3*B)*c*d^2 + (3*A + 4*B)*d^3 - (B*c*d^2 + (3*A + 4*B)*d^3)*cos(f*x + e)^2 + 2*(B*c^2*d + (3*A + 4*B)*c*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) - 2*(B*c^2 - (5*A + B)*c*d + (A + 4*B)*d^2 - (B*c*d + (3*A + 4*B)*d^2)*cos(f*x + e)^2 + (B*c^2 - (5*A + 2*B)*c*d - 2*A*d^2)*cos(f*x + e) - (B*c^2 - (5*A + B)*c*d + (A + 4*B)*d^2 + (B*c*d + (3*A + 4*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c^2*d^3 + 2*c*d^4 + d^5)*f*cos(f*x + e)^3 + (2*c^3*d^2 + 5*c^2*d^3 + 4*c*d^4 + d^5)*f*cos(f*x + e)^2 - (c^4*d + 2*c^3*d^2 + 2*c^2*d^3 + 2*c*d^4 + d^5)*f*cos(f*x + e) - (c^4*d + 4*c^3*d^2 + 6*c^2*d^3 + 4*c*d^4 + d^5)*f + ((c^2*d^3 + 2*c*d^4 + d^5)*f*cos(f*x + e)^2 - 2*(c^3*d^2 + 2*c^2*d^3 + c*d^4)*f*cos(f*x + e) - (c^4*d + 4*c^3*d^2 + 6*c^2*d^3 + 4*c*d^4 + d^5)*f)*sin(f*x + e))]","B",0
293,1,637,0,0.732408," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, B a d^{3} \cos\left(f x + e\right)^{6} + 35 \, {\left(33 \, B a c d^{2} + {\left(11 \, A + 21 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{5} + 924 \, {\left(5 \, A + 3 \, B\right)} a c^{3} + 396 \, {\left(21 \, A + 19 \, B\right)} a c^{2} d + 132 \, {\left(57 \, A + 47 \, B\right)} a c d^{2} + 4 \, {\left(517 \, A + 483 \, B\right)} a d^{3} - 5 \, {\left(297 \, B a c^{2} d + 33 \, {\left(9 \, A + 10 \, B\right)} a c d^{2} + 10 \, {\left(11 \, A + 21 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{4} - {\left(693 \, B a c^{3} + 297 \, {\left(7 \, A + 13 \, B\right)} a c^{2} d + 33 \, {\left(117 \, A + 172 \, B\right)} a c d^{2} + 2 \, {\left(946 \, A + 1239 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{3} + {\left(231 \, {\left(5 \, A + 6 \, B\right)} a c^{3} + 99 \, {\left(42 \, A + 43 \, B\right)} a c^{2} d + 33 \, {\left(129 \, A + 134 \, B\right)} a c d^{2} + {\left(1474 \, A + 1491 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(231 \, {\left(25 \, A + 21 \, B\right)} a c^{3} + 99 \, {\left(147 \, A + 143 \, B\right)} a c^{2} d + 33 \, {\left(429 \, A + 409 \, B\right)} a c d^{2} + {\left(4499 \, A + 4431 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right) + {\left(315 \, B a d^{3} \cos\left(f x + e\right)^{5} - 924 \, {\left(5 \, A + 3 \, B\right)} a c^{3} - 396 \, {\left(21 \, A + 19 \, B\right)} a c^{2} d - 132 \, {\left(57 \, A + 47 \, B\right)} a c d^{2} - 4 \, {\left(517 \, A + 483 \, B\right)} a d^{3} - 35 \, {\left(33 \, B a c d^{2} + {\left(11 \, A + 12 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{4} - 5 \, {\left(297 \, B a c^{2} d + 33 \, {\left(9 \, A + 17 \, B\right)} a c d^{2} + {\left(187 \, A + 294 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(231 \, B a c^{3} + 99 \, {\left(7 \, A + 8 \, B\right)} a c^{2} d + 33 \, {\left(24 \, A + 29 \, B\right)} a c d^{2} + {\left(319 \, A + 336 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(231 \, {\left(5 \, A + 9 \, B\right)} a c^{3} + 99 \, {\left(63 \, A + 67 \, B\right)} a c^{2} d + 33 \, {\left(201 \, A + 221 \, B\right)} a c d^{2} + 17 \, {\left(143 \, A + 147 \, B\right)} a 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}}{3465 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/3465*(315*B*a*d^3*cos(f*x + e)^6 + 35*(33*B*a*c*d^2 + (11*A + 21*B)*a*d^3)*cos(f*x + e)^5 + 924*(5*A + 3*B)*a*c^3 + 396*(21*A + 19*B)*a*c^2*d + 132*(57*A + 47*B)*a*c*d^2 + 4*(517*A + 483*B)*a*d^3 - 5*(297*B*a*c^2*d + 33*(9*A + 10*B)*a*c*d^2 + 10*(11*A + 21*B)*a*d^3)*cos(f*x + e)^4 - (693*B*a*c^3 + 297*(7*A + 13*B)*a*c^2*d + 33*(117*A + 172*B)*a*c*d^2 + 2*(946*A + 1239*B)*a*d^3)*cos(f*x + e)^3 + (231*(5*A + 6*B)*a*c^3 + 99*(42*A + 43*B)*a*c^2*d + 33*(129*A + 134*B)*a*c*d^2 + (1474*A + 1491*B)*a*d^3)*cos(f*x + e)^2 + (231*(25*A + 21*B)*a*c^3 + 99*(147*A + 143*B)*a*c^2*d + 33*(429*A + 409*B)*a*c*d^2 + (4499*A + 4431*B)*a*d^3)*cos(f*x + e) + (315*B*a*d^3*cos(f*x + e)^5 - 924*(5*A + 3*B)*a*c^3 - 396*(21*A + 19*B)*a*c^2*d - 132*(57*A + 47*B)*a*c*d^2 - 4*(517*A + 483*B)*a*d^3 - 35*(33*B*a*c*d^2 + (11*A + 12*B)*a*d^3)*cos(f*x + e)^4 - 5*(297*B*a*c^2*d + 33*(9*A + 17*B)*a*c*d^2 + (187*A + 294*B)*a*d^3)*cos(f*x + e)^3 + 3*(231*B*a*c^3 + 99*(7*A + 8*B)*a*c^2*d + 33*(24*A + 29*B)*a*c*d^2 + (319*A + 336*B)*a*d^3)*cos(f*x + e)^2 + (231*(5*A + 9*B)*a*c^3 + 99*(63*A + 67*B)*a*c^2*d + 33*(201*A + 221*B)*a*c*d^2 + 17*(143*A + 147*B)*a*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
294,1,430,0,0.617381," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, B a d^{2} \cos\left(f x + e\right)^{5} - 5 \, {\left(18 \, B a c d + {\left(9 \, A + 10 \, B\right)} a d^{2}\right)} \cos\left(f x + e\right)^{4} + 84 \, {\left(5 \, A + 3 \, B\right)} a c^{2} + 24 \, {\left(21 \, A + 19 \, B\right)} a c d + 4 \, {\left(57 \, A + 47 \, B\right)} a d^{2} - {\left(63 \, B a c^{2} + 18 \, {\left(7 \, A + 13 \, B\right)} a c d + {\left(117 \, A + 172 \, B\right)} a d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(21 \, {\left(5 \, A + 6 \, B\right)} a c^{2} + 6 \, {\left(42 \, A + 43 \, B\right)} a c d + {\left(129 \, A + 134 \, B\right)} a d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(21 \, {\left(25 \, A + 21 \, B\right)} a c^{2} + 6 \, {\left(147 \, A + 143 \, B\right)} a c d + {\left(429 \, A + 409 \, B\right)} a d^{2}\right)} \cos\left(f x + e\right) - {\left(35 \, B a d^{2} \cos\left(f x + e\right)^{4} + 84 \, {\left(5 \, A + 3 \, B\right)} a c^{2} + 24 \, {\left(21 \, A + 19 \, B\right)} a c d + 4 \, {\left(57 \, A + 47 \, B\right)} a d^{2} + 5 \, {\left(18 \, B a c d + {\left(9 \, A + 17 \, B\right)} a d^{2}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(21 \, B a c^{2} + 6 \, {\left(7 \, A + 8 \, B\right)} a c d + {\left(24 \, A + 29 \, B\right)} a d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(21 \, {\left(5 \, A + 9 \, B\right)} a c^{2} + 6 \, {\left(63 \, A + 67 \, B\right)} a c d + {\left(201 \, A + 221 \, B\right)} a 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}}{315 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/315*(35*B*a*d^2*cos(f*x + e)^5 - 5*(18*B*a*c*d + (9*A + 10*B)*a*d^2)*cos(f*x + e)^4 + 84*(5*A + 3*B)*a*c^2 + 24*(21*A + 19*B)*a*c*d + 4*(57*A + 47*B)*a*d^2 - (63*B*a*c^2 + 18*(7*A + 13*B)*a*c*d + (117*A + 172*B)*a*d^2)*cos(f*x + e)^3 + (21*(5*A + 6*B)*a*c^2 + 6*(42*A + 43*B)*a*c*d + (129*A + 134*B)*a*d^2)*cos(f*x + e)^2 + (21*(25*A + 21*B)*a*c^2 + 6*(147*A + 143*B)*a*c*d + (429*A + 409*B)*a*d^2)*cos(f*x + e) - (35*B*a*d^2*cos(f*x + e)^4 + 84*(5*A + 3*B)*a*c^2 + 24*(21*A + 19*B)*a*c*d + 4*(57*A + 47*B)*a*d^2 + 5*(18*B*a*c*d + (9*A + 17*B)*a*d^2)*cos(f*x + e)^3 - 3*(21*B*a*c^2 + 6*(7*A + 8*B)*a*c*d + (24*A + 29*B)*a*d^2)*cos(f*x + e)^2 - (21*(5*A + 9*B)*a*c^2 + 6*(63*A + 67*B)*a*c*d + (201*A + 221*B)*a*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
295,1,257,0,0.785793," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B a d \cos\left(f x + e\right)^{4} + 3 \, {\left(7 \, B a c + {\left(7 \, A + 13 \, B\right)} a d\right)} \cos\left(f x + e\right)^{3} - 28 \, {\left(5 \, A + 3 \, B\right)} a c - 4 \, {\left(21 \, A + 19 \, B\right)} a d - {\left(7 \, {\left(5 \, A + 6 \, B\right)} a c + {\left(42 \, A + 43 \, B\right)} a d\right)} \cos\left(f x + e\right)^{2} - {\left(7 \, {\left(25 \, A + 21 \, B\right)} a c + {\left(147 \, A + 143 \, B\right)} a d\right)} \cos\left(f x + e\right) + {\left(15 \, B a d \cos\left(f x + e\right)^{3} + 28 \, {\left(5 \, A + 3 \, B\right)} a c + 4 \, {\left(21 \, A + 19 \, B\right)} a d - 3 \, {\left(7 \, B a c + {\left(7 \, A + 8 \, B\right)} a d\right)} \cos\left(f x + e\right)^{2} - {\left(7 \, {\left(5 \, A + 9 \, B\right)} a c + {\left(63 \, A + 67 \, B\right)} a d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{105 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/105*(15*B*a*d*cos(f*x + e)^4 + 3*(7*B*a*c + (7*A + 13*B)*a*d)*cos(f*x + e)^3 - 28*(5*A + 3*B)*a*c - 4*(21*A + 19*B)*a*d - (7*(5*A + 6*B)*a*c + (42*A + 43*B)*a*d)*cos(f*x + e)^2 - (7*(25*A + 21*B)*a*c + (147*A + 143*B)*a*d)*cos(f*x + e) + (15*B*a*d*cos(f*x + e)^3 + 28*(5*A + 3*B)*a*c + 4*(21*A + 19*B)*a*d - 3*(7*B*a*c + (7*A + 8*B)*a*d)*cos(f*x + e)^2 - (7*(5*A + 9*B)*a*c + (63*A + 67*B)*a*d)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
296,1,137,0,0.646669," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(3 \, B a \cos\left(f x + e\right)^{3} - {\left(5 \, A + 6 \, B\right)} a \cos\left(f x + e\right)^{2} - {\left(25 \, A + 21 \, B\right)} a \cos\left(f x + e\right) - 4 \, {\left(5 \, A + 3 \, B\right)} a - {\left(3 \, B a \cos\left(f x + e\right)^{2} + {\left(5 \, A + 9 \, B\right)} a \cos\left(f x + e\right) - 4 \, {\left(5 \, A + 3 \, B\right)} a\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{15 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/15*(3*B*a*cos(f*x + e)^3 - (5*A + 6*B)*a*cos(f*x + e)^2 - (25*A + 21*B)*a*cos(f*x + e) - 4*(5*A + 3*B)*a - (3*B*a*cos(f*x + e)^2 + (5*A + 9*B)*a*cos(f*x + e) - 4*(5*A + 3*B)*a)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
297,1,880,0,2.259037," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(B a c^{2} - {\left(A + B\right)} a c d + A a d^{2} + {\left(B a c^{2} - {\left(A + B\right)} a c d + A a d^{2}\right)} \cos\left(f x + e\right) + {\left(B a c^{2} - {\left(A + B\right)} a c d + A a d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(B a d \cos\left(f x + e\right)^{2} - 3 \, B a c + {\left(3 \, A + 4 \, B\right)} a d - {\left(3 \, B a c - {\left(3 \, A + 5 \, B\right)} a d\right)} \cos\left(f x + e\right) + {\left(B a d \cos\left(f x + e\right) + 3 \, B a c - {\left(3 \, A + 4 \, B\right)} a d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{6 \, {\left(d^{2} f \cos\left(f x + e\right) + d^{2} f \sin\left(f x + e\right) + d^{2} f\right)}}, -\frac{3 \, {\left(B a c^{2} - {\left(A + B\right)} a c d + A a d^{2} + {\left(B a c^{2} - {\left(A + B\right)} a c d + A a d^{2}\right)} \cos\left(f x + e\right) + {\left(B a c^{2} - {\left(A + B\right)} a c d + A a d^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) + 2 \, {\left(B a d \cos\left(f x + e\right)^{2} - 3 \, B a c + {\left(3 \, A + 4 \, B\right)} a d - {\left(3 \, B a c - {\left(3 \, A + 5 \, B\right)} a d\right)} \cos\left(f x + e\right) + {\left(B a d \cos\left(f x + e\right) + 3 \, B a c - {\left(3 \, A + 4 \, B\right)} a d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{3 \, {\left(d^{2} f \cos\left(f x + e\right) + d^{2} f \sin\left(f x + e\right) + d^{2} f\right)}}\right]"," ",0,"[-1/6*(3*(B*a*c^2 - (A + B)*a*c*d + A*a*d^2 + (B*a*c^2 - (A + B)*a*c*d + A*a*d^2)*cos(f*x + e) + (B*a*c^2 - (A + B)*a*c*d + A*a*d^2)*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(B*a*d*cos(f*x + e)^2 - 3*B*a*c + (3*A + 4*B)*a*d - (3*B*a*c - (3*A + 5*B)*a*d)*cos(f*x + e) + (B*a*d*cos(f*x + e) + 3*B*a*c - (3*A + 4*B)*a*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(d^2*f*cos(f*x + e) + d^2*f*sin(f*x + e) + d^2*f), -1/3*(3*(B*a*c^2 - (A + B)*a*c*d + A*a*d^2 + (B*a*c^2 - (A + B)*a*c*d + A*a*d^2)*cos(f*x + e) + (B*a*c^2 - (A + B)*a*c*d + A*a*d^2)*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) + 2*(B*a*d*cos(f*x + e)^2 - 3*B*a*c + (3*A + 4*B)*a*d - (3*B*a*c - (3*A + 5*B)*a*d)*cos(f*x + e) + (B*a*d*cos(f*x + e) + 3*B*a*c - (3*A + 4*B)*a*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(d^2*f*cos(f*x + e) + d^2*f*sin(f*x + e) + d^2*f)]","B",0
298,1,1428,0,2.447080," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{{\left(3 \, B a c^{3} - {\left(A - 6 \, B\right)} a c^{2} d - {\left(4 \, A - B\right)} a c d^{2} - {\left(3 \, A + 2 \, B\right)} a d^{3} - {\left(3 \, B a c^{2} d - {\left(A - 3 \, B\right)} a c d^{2} - {\left(3 \, A + 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{3} - {\left(A - 3 \, B\right)} a c^{2} d - {\left(3 \, A + 2 \, B\right)} a c d^{2}\right)} \cos\left(f x + e\right) + {\left(3 \, B a c^{3} - {\left(A - 6 \, B\right)} a c^{2} d - {\left(4 \, A - B\right)} a c d^{2} - {\left(3 \, A + 2 \, B\right)} a d^{3} + {\left(3 \, B a c^{2} d - {\left(A - 3 \, B\right)} a c d^{2} - {\left(3 \, A + 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(3 \, B a c^{2} - {\left(A + B\right)} a c d + {\left(A - 2 \, B\right)} a d^{2} + 2 \, {\left(B a c d + B a d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{2} - {\left(A - B\right)} a c d + A a d^{2}\right)} \cos\left(f x + e\right) - {\left(3 \, B a c^{2} - {\left(A + B\right)} a c d + {\left(A - 2 \, B\right)} a d^{2} - 2 \, {\left(B a c d + B a 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}}{4 \, {\left({\left(c d^{3} + d^{4}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{2} d^{2} + c d^{3}\right)} f \cos\left(f x + e\right) - {\left(c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} f - {\left({\left(c d^{3} + d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} f\right)} \sin\left(f x + e\right)\right)}}, -\frac{{\left(3 \, B a c^{3} - {\left(A - 6 \, B\right)} a c^{2} d - {\left(4 \, A - B\right)} a c d^{2} - {\left(3 \, A + 2 \, B\right)} a d^{3} - {\left(3 \, B a c^{2} d - {\left(A - 3 \, B\right)} a c d^{2} - {\left(3 \, A + 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{3} - {\left(A - 3 \, B\right)} a c^{2} d - {\left(3 \, A + 2 \, B\right)} a c d^{2}\right)} \cos\left(f x + e\right) + {\left(3 \, B a c^{3} - {\left(A - 6 \, B\right)} a c^{2} d - {\left(4 \, A - B\right)} a c d^{2} - {\left(3 \, A + 2 \, B\right)} a d^{3} + {\left(3 \, B a c^{2} d - {\left(A - 3 \, B\right)} a c d^{2} - {\left(3 \, A + 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) - 2 \, {\left(3 \, B a c^{2} - {\left(A + B\right)} a c d + {\left(A - 2 \, B\right)} a d^{2} + 2 \, {\left(B a c d + B a d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{2} - {\left(A - B\right)} a c d + A a d^{2}\right)} \cos\left(f x + e\right) - {\left(3 \, B a c^{2} - {\left(A + B\right)} a c d + {\left(A - 2 \, B\right)} a d^{2} - 2 \, {\left(B a c d + B a 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}}{2 \, {\left({\left(c d^{3} + d^{4}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{2} d^{2} + c d^{3}\right)} f \cos\left(f x + e\right) - {\left(c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} f - {\left({\left(c d^{3} + d^{4}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d^{2} + 2 \, c d^{3} + d^{4}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*((3*B*a*c^3 - (A - 6*B)*a*c^2*d - (4*A - B)*a*c*d^2 - (3*A + 2*B)*a*d^3 - (3*B*a*c^2*d - (A - 3*B)*a*c*d^2 - (3*A + 2*B)*a*d^3)*cos(f*x + e)^2 + (3*B*a*c^3 - (A - 3*B)*a*c^2*d - (3*A + 2*B)*a*c*d^2)*cos(f*x + e) + (3*B*a*c^3 - (A - 6*B)*a*c^2*d - (4*A - B)*a*c*d^2 - (3*A + 2*B)*a*d^3 + (3*B*a*c^2*d - (A - 3*B)*a*c*d^2 - (3*A + 2*B)*a*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(3*B*a*c^2 - (A + B)*a*c*d + (A - 2*B)*a*d^2 + 2*(B*a*c*d + B*a*d^2)*cos(f*x + e)^2 + (3*B*a*c^2 - (A - B)*a*c*d + A*a*d^2)*cos(f*x + e) - (3*B*a*c^2 - (A + B)*a*c*d + (A - 2*B)*a*d^2 - 2*(B*a*c*d + B*a*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c*d^3 + d^4)*f*cos(f*x + e)^2 - (c^2*d^2 + c*d^3)*f*cos(f*x + e) - (c^2*d^2 + 2*c*d^3 + d^4)*f - ((c*d^3 + d^4)*f*cos(f*x + e) + (c^2*d^2 + 2*c*d^3 + d^4)*f)*sin(f*x + e)), -1/2*((3*B*a*c^3 - (A - 6*B)*a*c^2*d - (4*A - B)*a*c*d^2 - (3*A + 2*B)*a*d^3 - (3*B*a*c^2*d - (A - 3*B)*a*c*d^2 - (3*A + 2*B)*a*d^3)*cos(f*x + e)^2 + (3*B*a*c^3 - (A - 3*B)*a*c^2*d - (3*A + 2*B)*a*c*d^2)*cos(f*x + e) + (3*B*a*c^3 - (A - 6*B)*a*c^2*d - (4*A - B)*a*c*d^2 - (3*A + 2*B)*a*d^3 + (3*B*a*c^2*d - (A - 3*B)*a*c*d^2 - (3*A + 2*B)*a*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) - 2*(3*B*a*c^2 - (A + B)*a*c*d + (A - 2*B)*a*d^2 + 2*(B*a*c*d + B*a*d^2)*cos(f*x + e)^2 + (3*B*a*c^2 - (A - B)*a*c*d + A*a*d^2)*cos(f*x + e) - (3*B*a*c^2 - (A + B)*a*c*d + (A - 2*B)*a*d^2 - 2*(B*a*c*d + B*a*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c*d^3 + d^4)*f*cos(f*x + e)^2 - (c^2*d^2 + c*d^3)*f*cos(f*x + e) - (c^2*d^2 + 2*c*d^3 + d^4)*f - ((c*d^3 + d^4)*f*cos(f*x + e) + (c^2*d^2 + 2*c*d^3 + d^4)*f)*sin(f*x + e))]","B",0
299,1,2208,0,4.069773," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, B a c^{4} + {\left(A + 15 \, B\right)} a c^{3} d + 3 \, {\left(3 \, A + 11 \, B\right)} a c^{2} d^{2} + 3 \, {\left(5 \, A + 11 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4} - {\left(3 \, B a c^{2} d^{2} + {\left(A + 9 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(6 \, B a c^{3} d + {\left(2 \, A + 21 \, B\right)} a c^{2} d^{2} + 3 \, {\left(5 \, A + 11 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{4} + {\left(A + 9 \, B\right)} a c^{3} d + {\left(7 \, A + 15 \, B\right)} a c^{2} d^{2} + {\left(A + 9 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right) + {\left(3 \, B a c^{4} + {\left(A + 15 \, B\right)} a c^{3} d + 3 \, {\left(3 \, A + 11 \, B\right)} a c^{2} d^{2} + 3 \, {\left(5 \, A + 11 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4} - {\left(3 \, B a c^{2} d^{2} + {\left(A + 9 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, B a c^{3} d + {\left(A + 9 \, B\right)} a c^{2} d^{2} + {\left(7 \, A + 12 \, B\right)} a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(3 \, B a c^{3} + {\left(A + 2 \, B\right)} a c^{2} d - 3 \, {\left(2 \, A + 3 \, B\right)} a c d^{2} + {\left(5 \, A + 4 \, B\right)} a d^{3} + {\left(5 \, B a c^{2} d - {\left(A - 7 \, B\right)} a c d^{2} - {\left(7 \, A + 4 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{3} + {\left(A + 7 \, B\right)} a c^{2} d - {\left(7 \, A + 2 \, B\right)} a c d^{2} - 2 \, A a d^{3}\right)} \cos\left(f x + e\right) - {\left(3 \, B a c^{3} + {\left(A + 2 \, B\right)} a c^{2} d - 3 \, {\left(2 \, A + 3 \, B\right)} a c d^{2} + {\left(5 \, A + 4 \, B\right)} a d^{3} - {\left(5 \, B a c^{2} d - {\left(A - 7 \, B\right)} a c d^{2} - {\left(7 \, A + 4 \, B\right)} a 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}}{16 \, {\left({\left(c^{2} d^{4} + 2 \, c d^{5} + d^{6}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, c^{3} d^{3} + 5 \, c^{2} d^{4} + 4 \, c d^{5} + d^{6}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{4} d^{2} + 2 \, c^{3} d^{3} + 2 \, c^{2} d^{4} + 2 \, c d^{5} + d^{6}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d^{2} + 4 \, c^{3} d^{3} + 6 \, c^{2} d^{4} + 4 \, c d^{5} + d^{6}\right)} f + {\left({\left(c^{2} d^{4} + 2 \, c d^{5} + d^{6}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{3} d^{3} + 2 \, c^{2} d^{4} + c d^{5}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d^{2} + 4 \, c^{3} d^{3} + 6 \, c^{2} d^{4} + 4 \, c d^{5} + d^{6}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{{\left(3 \, B a c^{4} + {\left(A + 15 \, B\right)} a c^{3} d + 3 \, {\left(3 \, A + 11 \, B\right)} a c^{2} d^{2} + 3 \, {\left(5 \, A + 11 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4} - {\left(3 \, B a c^{2} d^{2} + {\left(A + 9 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(6 \, B a c^{3} d + {\left(2 \, A + 21 \, B\right)} a c^{2} d^{2} + 3 \, {\left(5 \, A + 11 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{4} + {\left(A + 9 \, B\right)} a c^{3} d + {\left(7 \, A + 15 \, B\right)} a c^{2} d^{2} + {\left(A + 9 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right) + {\left(3 \, B a c^{4} + {\left(A + 15 \, B\right)} a c^{3} d + 3 \, {\left(3 \, A + 11 \, B\right)} a c^{2} d^{2} + 3 \, {\left(5 \, A + 11 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4} - {\left(3 \, B a c^{2} d^{2} + {\left(A + 9 \, B\right)} a c d^{3} + {\left(7 \, A + 12 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, B a c^{3} d + {\left(A + 9 \, B\right)} a c^{2} d^{2} + {\left(7 \, A + 12 \, B\right)} a c d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) - 2 \, {\left(3 \, B a c^{3} + {\left(A + 2 \, B\right)} a c^{2} d - 3 \, {\left(2 \, A + 3 \, B\right)} a c d^{2} + {\left(5 \, A + 4 \, B\right)} a d^{3} + {\left(5 \, B a c^{2} d - {\left(A - 7 \, B\right)} a c d^{2} - {\left(7 \, A + 4 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{3} + {\left(A + 7 \, B\right)} a c^{2} d - {\left(7 \, A + 2 \, B\right)} a c d^{2} - 2 \, A a d^{3}\right)} \cos\left(f x + e\right) - {\left(3 \, B a c^{3} + {\left(A + 2 \, B\right)} a c^{2} d - 3 \, {\left(2 \, A + 3 \, B\right)} a c d^{2} + {\left(5 \, A + 4 \, B\right)} a d^{3} - {\left(5 \, B a c^{2} d - {\left(A - 7 \, B\right)} a c d^{2} - {\left(7 \, A + 4 \, B\right)} a 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}}{8 \, {\left({\left(c^{2} d^{4} + 2 \, c d^{5} + d^{6}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, c^{3} d^{3} + 5 \, c^{2} d^{4} + 4 \, c d^{5} + d^{6}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{4} d^{2} + 2 \, c^{3} d^{3} + 2 \, c^{2} d^{4} + 2 \, c d^{5} + d^{6}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d^{2} + 4 \, c^{3} d^{3} + 6 \, c^{2} d^{4} + 4 \, c d^{5} + d^{6}\right)} f + {\left({\left(c^{2} d^{4} + 2 \, c d^{5} + d^{6}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{3} d^{3} + 2 \, c^{2} d^{4} + c d^{5}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d^{2} + 4 \, c^{3} d^{3} + 6 \, c^{2} d^{4} + 4 \, c d^{5} + d^{6}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/16*((3*B*a*c^4 + (A + 15*B)*a*c^3*d + 3*(3*A + 11*B)*a*c^2*d^2 + 3*(5*A + 11*B)*a*c*d^3 + (7*A + 12*B)*a*d^4 - (3*B*a*c^2*d^2 + (A + 9*B)*a*c*d^3 + (7*A + 12*B)*a*d^4)*cos(f*x + e)^3 - (6*B*a*c^3*d + (2*A + 21*B)*a*c^2*d^2 + 3*(5*A + 11*B)*a*c*d^3 + (7*A + 12*B)*a*d^4)*cos(f*x + e)^2 + (3*B*a*c^4 + (A + 9*B)*a*c^3*d + (7*A + 15*B)*a*c^2*d^2 + (A + 9*B)*a*c*d^3 + (7*A + 12*B)*a*d^4)*cos(f*x + e) + (3*B*a*c^4 + (A + 15*B)*a*c^3*d + 3*(3*A + 11*B)*a*c^2*d^2 + 3*(5*A + 11*B)*a*c*d^3 + (7*A + 12*B)*a*d^4 - (3*B*a*c^2*d^2 + (A + 9*B)*a*c*d^3 + (7*A + 12*B)*a*d^4)*cos(f*x + e)^2 + 2*(3*B*a*c^3*d + (A + 9*B)*a*c^2*d^2 + (7*A + 12*B)*a*c*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(3*B*a*c^3 + (A + 2*B)*a*c^2*d - 3*(2*A + 3*B)*a*c*d^2 + (5*A + 4*B)*a*d^3 + (5*B*a*c^2*d - (A - 7*B)*a*c*d^2 - (7*A + 4*B)*a*d^3)*cos(f*x + e)^2 + (3*B*a*c^3 + (A + 7*B)*a*c^2*d - (7*A + 2*B)*a*c*d^2 - 2*A*a*d^3)*cos(f*x + e) - (3*B*a*c^3 + (A + 2*B)*a*c^2*d - 3*(2*A + 3*B)*a*c*d^2 + (5*A + 4*B)*a*d^3 - (5*B*a*c^2*d - (A - 7*B)*a*c*d^2 - (7*A + 4*B)*a*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c^2*d^4 + 2*c*d^5 + d^6)*f*cos(f*x + e)^3 + (2*c^3*d^3 + 5*c^2*d^4 + 4*c*d^5 + d^6)*f*cos(f*x + e)^2 - (c^4*d^2 + 2*c^3*d^3 + 2*c^2*d^4 + 2*c*d^5 + d^6)*f*cos(f*x + e) - (c^4*d^2 + 4*c^3*d^3 + 6*c^2*d^4 + 4*c*d^5 + d^6)*f + ((c^2*d^4 + 2*c*d^5 + d^6)*f*cos(f*x + e)^2 - 2*(c^3*d^3 + 2*c^2*d^4 + c*d^5)*f*cos(f*x + e) - (c^4*d^2 + 4*c^3*d^3 + 6*c^2*d^4 + 4*c*d^5 + d^6)*f)*sin(f*x + e)), 1/8*((3*B*a*c^4 + (A + 15*B)*a*c^3*d + 3*(3*A + 11*B)*a*c^2*d^2 + 3*(5*A + 11*B)*a*c*d^3 + (7*A + 12*B)*a*d^4 - (3*B*a*c^2*d^2 + (A + 9*B)*a*c*d^3 + (7*A + 12*B)*a*d^4)*cos(f*x + e)^3 - (6*B*a*c^3*d + (2*A + 21*B)*a*c^2*d^2 + 3*(5*A + 11*B)*a*c*d^3 + (7*A + 12*B)*a*d^4)*cos(f*x + e)^2 + (3*B*a*c^4 + (A + 9*B)*a*c^3*d + (7*A + 15*B)*a*c^2*d^2 + (A + 9*B)*a*c*d^3 + (7*A + 12*B)*a*d^4)*cos(f*x + e) + (3*B*a*c^4 + (A + 15*B)*a*c^3*d + 3*(3*A + 11*B)*a*c^2*d^2 + 3*(5*A + 11*B)*a*c*d^3 + (7*A + 12*B)*a*d^4 - (3*B*a*c^2*d^2 + (A + 9*B)*a*c*d^3 + (7*A + 12*B)*a*d^4)*cos(f*x + e)^2 + 2*(3*B*a*c^3*d + (A + 9*B)*a*c^2*d^2 + (7*A + 12*B)*a*c*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) - 2*(3*B*a*c^3 + (A + 2*B)*a*c^2*d - 3*(2*A + 3*B)*a*c*d^2 + (5*A + 4*B)*a*d^3 + (5*B*a*c^2*d - (A - 7*B)*a*c*d^2 - (7*A + 4*B)*a*d^3)*cos(f*x + e)^2 + (3*B*a*c^3 + (A + 7*B)*a*c^2*d - (7*A + 2*B)*a*c*d^2 - 2*A*a*d^3)*cos(f*x + e) - (3*B*a*c^3 + (A + 2*B)*a*c^2*d - 3*(2*A + 3*B)*a*c*d^2 + (5*A + 4*B)*a*d^3 - (5*B*a*c^2*d - (A - 7*B)*a*c*d^2 - (7*A + 4*B)*a*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c^2*d^4 + 2*c*d^5 + d^6)*f*cos(f*x + e)^3 + (2*c^3*d^3 + 5*c^2*d^4 + 4*c*d^5 + d^6)*f*cos(f*x + e)^2 - (c^4*d^2 + 2*c^3*d^3 + 2*c^2*d^4 + 2*c*d^5 + d^6)*f*cos(f*x + e) - (c^4*d^2 + 4*c^3*d^3 + 6*c^2*d^4 + 4*c*d^5 + d^6)*f + ((c^2*d^4 + 2*c*d^5 + d^6)*f*cos(f*x + e)^2 - 2*(c^3*d^3 + 2*c^2*d^4 + c*d^5)*f*cos(f*x + e) - (c^4*d^2 + 4*c^3*d^3 + 6*c^2*d^4 + 4*c*d^5 + d^6)*f)*sin(f*x + e))]","B",0
300,1,863,0,0.823398," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\frac{2 \, {\left(3465 \, B a^{2} d^{3} \cos\left(f x + e\right)^{7} - 315 \, {\left(39 \, B a^{2} c d^{2} + {\left(13 \, A + 27 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{6} - 13728 \, {\left(7 \, A + 5 \, B\right)} a^{2} c^{3} - 13728 \, {\left(15 \, A + 13 \, B\right)} a^{2} c^{2} d - 1248 \, {\left(143 \, A + 125 \, B\right)} a^{2} c d^{2} - 32 \, {\left(1625 \, A + 1483 \, B\right)} a^{2} d^{3} - 35 \, {\left(429 \, B a^{2} c^{2} d + 39 \, {\left(11 \, A + 32 \, B\right)} a^{2} c d^{2} + 4 \, {\left(104 \, A + 205 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{5} + 5 \, {\left(1287 \, B a^{2} c^{3} + 429 \, {\left(9 \, A + 19 \, B\right)} a^{2} c^{2} d + 39 \, {\left(209 \, A + 320 \, B\right)} a^{2} c d^{2} + 2 \, {\left(2080 \, A + 2813 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{4} + {\left(1287 \, {\left(7 \, A + 20 \, B\right)} a^{2} c^{3} + 429 \, {\left(180 \, A + 289 \, B\right)} a^{2} c^{2} d + 39 \, {\left(3179 \, A + 4370 \, B\right)} a^{2} c d^{2} + {\left(56810 \, A + 72109 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(429 \, {\left(77 \, A + 85 \, B\right)} a^{2} c^{3} + 429 \, {\left(255 \, A + 263 \, B\right)} a^{2} c^{2} d + 39 \, {\left(2893 \, A + 2965 \, B\right)} a^{2} c d^{2} + {\left(38545 \, A + 39113 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(429 \, {\left(161 \, A + 145 \, B\right)} a^{2} c^{3} + 429 \, {\left(435 \, A + 419 \, B\right)} a^{2} c^{2} d + 39 \, {\left(4609 \, A + 4465 \, B\right)} a^{2} c d^{2} + {\left(58045 \, A + 56909 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right) - {\left(3465 \, B a^{2} d^{3} \cos\left(f x + e\right)^{6} - 13728 \, {\left(7 \, A + 5 \, B\right)} a^{2} c^{3} - 13728 \, {\left(15 \, A + 13 \, B\right)} a^{2} c^{2} d - 1248 \, {\left(143 \, A + 125 \, B\right)} a^{2} c d^{2} - 32 \, {\left(1625 \, A + 1483 \, B\right)} a^{2} d^{3} + 315 \, {\left(39 \, B a^{2} c d^{2} + {\left(13 \, A + 38 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{5} - 35 \, {\left(429 \, B a^{2} c^{2} d + 39 \, {\left(11 \, A + 23 \, B\right)} a^{2} c d^{2} + {\left(299 \, A + 478 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{4} - 5 \, {\left(1287 \, B a^{2} c^{3} + 429 \, {\left(9 \, A + 26 \, B\right)} a^{2} c^{2} d + 507 \, {\left(22 \, A + 37 \, B\right)} a^{2} c d^{2} + {\left(6253 \, A + 8972 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(429 \, {\left(7 \, A + 15 \, B\right)} a^{2} c^{3} + 429 \, {\left(45 \, A + 53 \, B\right)} a^{2} c^{2} d + 39 \, {\left(583 \, A + 655 \, B\right)} a^{2} c d^{2} + {\left(8515 \, A + 9083 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(429 \, {\left(49 \, A + 65 \, B\right)} a^{2} c^{3} + 429 \, {\left(195 \, A + 211 \, B\right)} a^{2} c^{2} d + 39 \, {\left(2321 \, A + 2465 \, B\right)} a^{2} c d^{2} + {\left(32045 \, A + 33181 \, B\right)} a^{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}}{45045 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/45045*(3465*B*a^2*d^3*cos(f*x + e)^7 - 315*(39*B*a^2*c*d^2 + (13*A + 27*B)*a^2*d^3)*cos(f*x + e)^6 - 13728*(7*A + 5*B)*a^2*c^3 - 13728*(15*A + 13*B)*a^2*c^2*d - 1248*(143*A + 125*B)*a^2*c*d^2 - 32*(1625*A + 1483*B)*a^2*d^3 - 35*(429*B*a^2*c^2*d + 39*(11*A + 32*B)*a^2*c*d^2 + 4*(104*A + 205*B)*a^2*d^3)*cos(f*x + e)^5 + 5*(1287*B*a^2*c^3 + 429*(9*A + 19*B)*a^2*c^2*d + 39*(209*A + 320*B)*a^2*c*d^2 + 2*(2080*A + 2813*B)*a^2*d^3)*cos(f*x + e)^4 + (1287*(7*A + 20*B)*a^2*c^3 + 429*(180*A + 289*B)*a^2*c^2*d + 39*(3179*A + 4370*B)*a^2*c*d^2 + (56810*A + 72109*B)*a^2*d^3)*cos(f*x + e)^3 - (429*(77*A + 85*B)*a^2*c^3 + 429*(255*A + 263*B)*a^2*c^2*d + 39*(2893*A + 2965*B)*a^2*c*d^2 + (38545*A + 39113*B)*a^2*d^3)*cos(f*x + e)^2 - 2*(429*(161*A + 145*B)*a^2*c^3 + 429*(435*A + 419*B)*a^2*c^2*d + 39*(4609*A + 4465*B)*a^2*c*d^2 + (58045*A + 56909*B)*a^2*d^3)*cos(f*x + e) - (3465*B*a^2*d^3*cos(f*x + e)^6 - 13728*(7*A + 5*B)*a^2*c^3 - 13728*(15*A + 13*B)*a^2*c^2*d - 1248*(143*A + 125*B)*a^2*c*d^2 - 32*(1625*A + 1483*B)*a^2*d^3 + 315*(39*B*a^2*c*d^2 + (13*A + 38*B)*a^2*d^3)*cos(f*x + e)^5 - 35*(429*B*a^2*c^2*d + 39*(11*A + 23*B)*a^2*c*d^2 + (299*A + 478*B)*a^2*d^3)*cos(f*x + e)^4 - 5*(1287*B*a^2*c^3 + 429*(9*A + 26*B)*a^2*c^2*d + 507*(22*A + 37*B)*a^2*c*d^2 + (6253*A + 8972*B)*a^2*d^3)*cos(f*x + e)^3 + 3*(429*(7*A + 15*B)*a^2*c^3 + 429*(45*A + 53*B)*a^2*c^2*d + 39*(583*A + 655*B)*a^2*c*d^2 + (8515*A + 9083*B)*a^2*d^3)*cos(f*x + e)^2 + 2*(429*(49*A + 65*B)*a^2*c^3 + 429*(195*A + 211*B)*a^2*c^2*d + 39*(2321*A + 2465*B)*a^2*c*d^2 + (32045*A + 33181*B)*a^2*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
301,1,593,0,0.855594," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(315 \, B a^{2} d^{2} \cos\left(f x + e\right)^{6} + 35 \, {\left(22 \, B a^{2} c d + {\left(11 \, A + 32 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{5} + 1056 \, {\left(7 \, A + 5 \, B\right)} a^{2} c^{2} + 704 \, {\left(15 \, A + 13 \, B\right)} a^{2} c d + 32 \, {\left(143 \, A + 125 \, B\right)} a^{2} d^{2} - 5 \, {\left(99 \, B a^{2} c^{2} + 22 \, {\left(9 \, A + 19 \, B\right)} a^{2} c d + {\left(209 \, A + 320 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{4} - {\left(99 \, {\left(7 \, A + 20 \, B\right)} a^{2} c^{2} + 22 \, {\left(180 \, A + 289 \, B\right)} a^{2} c d + {\left(3179 \, A + 4370 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + {\left(33 \, {\left(77 \, A + 85 \, B\right)} a^{2} c^{2} + 22 \, {\left(255 \, A + 263 \, B\right)} a^{2} c d + {\left(2893 \, A + 2965 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(161 \, A + 145 \, B\right)} a^{2} c^{2} + 22 \, {\left(435 \, A + 419 \, B\right)} a^{2} c d + {\left(4609 \, A + 4465 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right) + {\left(315 \, B a^{2} d^{2} \cos\left(f x + e\right)^{5} - 1056 \, {\left(7 \, A + 5 \, B\right)} a^{2} c^{2} - 704 \, {\left(15 \, A + 13 \, B\right)} a^{2} c d - 32 \, {\left(143 \, A + 125 \, B\right)} a^{2} d^{2} - 35 \, {\left(22 \, B a^{2} c d + {\left(11 \, A + 23 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{4} - 5 \, {\left(99 \, B a^{2} c^{2} + 22 \, {\left(9 \, A + 26 \, B\right)} a^{2} c d + 13 \, {\left(22 \, A + 37 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(33 \, {\left(7 \, A + 15 \, B\right)} a^{2} c^{2} + 22 \, {\left(45 \, A + 53 \, B\right)} a^{2} c d + {\left(583 \, A + 655 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(49 \, A + 65 \, B\right)} a^{2} c^{2} + 22 \, {\left(195 \, A + 211 \, B\right)} a^{2} c d + {\left(2321 \, A + 2465 \, B\right)} a^{2} 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}}{3465 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/3465*(315*B*a^2*d^2*cos(f*x + e)^6 + 35*(22*B*a^2*c*d + (11*A + 32*B)*a^2*d^2)*cos(f*x + e)^5 + 1056*(7*A + 5*B)*a^2*c^2 + 704*(15*A + 13*B)*a^2*c*d + 32*(143*A + 125*B)*a^2*d^2 - 5*(99*B*a^2*c^2 + 22*(9*A + 19*B)*a^2*c*d + (209*A + 320*B)*a^2*d^2)*cos(f*x + e)^4 - (99*(7*A + 20*B)*a^2*c^2 + 22*(180*A + 289*B)*a^2*c*d + (3179*A + 4370*B)*a^2*d^2)*cos(f*x + e)^3 + (33*(77*A + 85*B)*a^2*c^2 + 22*(255*A + 263*B)*a^2*c*d + (2893*A + 2965*B)*a^2*d^2)*cos(f*x + e)^2 + 2*(33*(161*A + 145*B)*a^2*c^2 + 22*(435*A + 419*B)*a^2*c*d + (4609*A + 4465*B)*a^2*d^2)*cos(f*x + e) + (315*B*a^2*d^2*cos(f*x + e)^5 - 1056*(7*A + 5*B)*a^2*c^2 - 704*(15*A + 13*B)*a^2*c*d - 32*(143*A + 125*B)*a^2*d^2 - 35*(22*B*a^2*c*d + (11*A + 23*B)*a^2*d^2)*cos(f*x + e)^4 - 5*(99*B*a^2*c^2 + 22*(9*A + 26*B)*a^2*c*d + 13*(22*A + 37*B)*a^2*d^2)*cos(f*x + e)^3 + 3*(33*(7*A + 15*B)*a^2*c^2 + 22*(45*A + 53*B)*a^2*c*d + (583*A + 655*B)*a^2*d^2)*cos(f*x + e)^2 + 2*(33*(49*A + 65*B)*a^2*c^2 + 22*(195*A + 211*B)*a^2*c*d + (2321*A + 2465*B)*a^2*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
302,1,361,0,0.915970," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{2 \, {\left(35 \, B a^{2} d \cos\left(f x + e\right)^{5} - 5 \, {\left(9 \, B a^{2} c + {\left(9 \, A + 19 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right)^{4} + 96 \, {\left(7 \, A + 5 \, B\right)} a^{2} c + 32 \, {\left(15 \, A + 13 \, B\right)} a^{2} d - {\left(9 \, {\left(7 \, A + 20 \, B\right)} a^{2} c + {\left(180 \, A + 289 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right)^{3} + {\left(3 \, {\left(77 \, A + 85 \, B\right)} a^{2} c + {\left(255 \, A + 263 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(161 \, A + 145 \, B\right)} a^{2} c + {\left(435 \, A + 419 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right) - {\left(35 \, B a^{2} d \cos\left(f x + e\right)^{4} + 96 \, {\left(7 \, A + 5 \, B\right)} a^{2} c + 32 \, {\left(15 \, A + 13 \, B\right)} a^{2} d + 5 \, {\left(9 \, B a^{2} c + {\left(9 \, A + 26 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(3 \, {\left(7 \, A + 15 \, B\right)} a^{2} c + {\left(45 \, A + 53 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, {\left(49 \, A + 65 \, B\right)} a^{2} c + {\left(195 \, A + 211 \, B\right)} a^{2} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{315 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"-2/315*(35*B*a^2*d*cos(f*x + e)^5 - 5*(9*B*a^2*c + (9*A + 19*B)*a^2*d)*cos(f*x + e)^4 + 96*(7*A + 5*B)*a^2*c + 32*(15*A + 13*B)*a^2*d - (9*(7*A + 20*B)*a^2*c + (180*A + 289*B)*a^2*d)*cos(f*x + e)^3 + (3*(77*A + 85*B)*a^2*c + (255*A + 263*B)*a^2*d)*cos(f*x + e)^2 + 2*(3*(161*A + 145*B)*a^2*c + (435*A + 419*B)*a^2*d)*cos(f*x + e) - (35*B*a^2*d*cos(f*x + e)^4 + 96*(7*A + 5*B)*a^2*c + 32*(15*A + 13*B)*a^2*d + 5*(9*B*a^2*c + (9*A + 26*B)*a^2*d)*cos(f*x + e)^3 - 3*(3*(7*A + 15*B)*a^2*c + (45*A + 53*B)*a^2*d)*cos(f*x + e)^2 - 2*(3*(49*A + 65*B)*a^2*c + (195*A + 211*B)*a^2*d)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
303,1,191,0,0.891793," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","\frac{2 \, {\left(15 \, B a^{2} \cos\left(f x + e\right)^{4} + 3 \, {\left(7 \, A + 20 \, B\right)} a^{2} \cos\left(f x + e\right)^{3} - {\left(77 \, A + 85 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(161 \, A + 145 \, B\right)} a^{2} \cos\left(f x + e\right) - 32 \, {\left(7 \, A + 5 \, B\right)} a^{2} + {\left(15 \, B a^{2} \cos\left(f x + e\right)^{3} - 3 \, {\left(7 \, A + 15 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(49 \, A + 65 \, B\right)} a^{2} \cos\left(f x + e\right) + 32 \, {\left(7 \, A + 5 \, B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{105 \, {\left(f \cos\left(f x + e\right) + f \sin\left(f x + e\right) + f\right)}}"," ",0,"2/105*(15*B*a^2*cos(f*x + e)^4 + 3*(7*A + 20*B)*a^2*cos(f*x + e)^3 - (77*A + 85*B)*a^2*cos(f*x + e)^2 - 2*(161*A + 145*B)*a^2*cos(f*x + e) - 32*(7*A + 5*B)*a^2 + (15*B*a^2*cos(f*x + e)^3 - 3*(7*A + 15*B)*a^2*cos(f*x + e)^2 - 2*(49*A + 65*B)*a^2*cos(f*x + e) + 32*(7*A + 5*B)*a^2)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)/(f*cos(f*x + e) + f*sin(f*x + e) + f)","A",0
304,1,1314,0,3.433908," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(B a^{2} c^{3} - {\left(A + 2 \, B\right)} a^{2} c^{2} d + {\left(2 \, A + B\right)} a^{2} c d^{2} - A a^{2} d^{3} + {\left(B a^{2} c^{3} - {\left(A + 2 \, B\right)} a^{2} c^{2} d + {\left(2 \, A + B\right)} a^{2} c d^{2} - A a^{2} d^{3}\right)} \cos\left(f x + e\right) + {\left(B a^{2} c^{3} - {\left(A + 2 \, B\right)} a^{2} c^{2} d + {\left(2 \, A + B\right)} a^{2} c d^{2} - A a^{2} d^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(3 \, B a^{2} d^{2} \cos\left(f x + e\right)^{3} - 15 \, B a^{2} c^{2} + 5 \, {\left(3 \, A + 7 \, B\right)} a^{2} c d - {\left(35 \, A + 32 \, B\right)} a^{2} d^{2} + {\left(5 \, B a^{2} c d - {\left(5 \, A + 11 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(15 \, B a^{2} c^{2} - 5 \, {\left(3 \, A + 8 \, B\right)} a^{2} c d + 2 \, {\left(20 \, A + 23 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right) - {\left(3 \, B a^{2} d^{2} \cos\left(f x + e\right)^{2} - 15 \, B a^{2} c^{2} + 5 \, {\left(3 \, A + 7 \, B\right)} a^{2} c d - {\left(35 \, A + 32 \, B\right)} a^{2} d^{2} - {\left(5 \, B a^{2} c d - {\left(5 \, A + 14 \, B\right)} a^{2} 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}}{30 \, {\left(d^{3} f \cos\left(f x + e\right) + d^{3} f \sin\left(f x + e\right) + d^{3} f\right)}}, \frac{15 \, {\left(B a^{2} c^{3} - {\left(A + 2 \, B\right)} a^{2} c^{2} d + {\left(2 \, A + B\right)} a^{2} c d^{2} - A a^{2} d^{3} + {\left(B a^{2} c^{3} - {\left(A + 2 \, B\right)} a^{2} c^{2} d + {\left(2 \, A + B\right)} a^{2} c d^{2} - A a^{2} d^{3}\right)} \cos\left(f x + e\right) + {\left(B a^{2} c^{3} - {\left(A + 2 \, B\right)} a^{2} c^{2} d + {\left(2 \, A + B\right)} a^{2} c d^{2} - A a^{2} d^{3}\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) + 2 \, {\left(3 \, B a^{2} d^{2} \cos\left(f x + e\right)^{3} - 15 \, B a^{2} c^{2} + 5 \, {\left(3 \, A + 7 \, B\right)} a^{2} c d - {\left(35 \, A + 32 \, B\right)} a^{2} d^{2} + {\left(5 \, B a^{2} c d - {\left(5 \, A + 11 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(15 \, B a^{2} c^{2} - 5 \, {\left(3 \, A + 8 \, B\right)} a^{2} c d + 2 \, {\left(20 \, A + 23 \, B\right)} a^{2} d^{2}\right)} \cos\left(f x + e\right) - {\left(3 \, B a^{2} d^{2} \cos\left(f x + e\right)^{2} - 15 \, B a^{2} c^{2} + 5 \, {\left(3 \, A + 7 \, B\right)} a^{2} c d - {\left(35 \, A + 32 \, B\right)} a^{2} d^{2} - {\left(5 \, B a^{2} c d - {\left(5 \, A + 14 \, B\right)} a^{2} 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}}{15 \, {\left(d^{3} f \cos\left(f x + e\right) + d^{3} f \sin\left(f x + e\right) + d^{3} f\right)}}\right]"," ",0,"[1/30*(15*(B*a^2*c^3 - (A + 2*B)*a^2*c^2*d + (2*A + B)*a^2*c*d^2 - A*a^2*d^3 + (B*a^2*c^3 - (A + 2*B)*a^2*c^2*d + (2*A + B)*a^2*c*d^2 - A*a^2*d^3)*cos(f*x + e) + (B*a^2*c^3 - (A + 2*B)*a^2*c^2*d + (2*A + B)*a^2*c*d^2 - A*a^2*d^3)*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(3*B*a^2*d^2*cos(f*x + e)^3 - 15*B*a^2*c^2 + 5*(3*A + 7*B)*a^2*c*d - (35*A + 32*B)*a^2*d^2 + (5*B*a^2*c*d - (5*A + 11*B)*a^2*d^2)*cos(f*x + e)^2 - (15*B*a^2*c^2 - 5*(3*A + 8*B)*a^2*c*d + 2*(20*A + 23*B)*a^2*d^2)*cos(f*x + e) - (3*B*a^2*d^2*cos(f*x + e)^2 - 15*B*a^2*c^2 + 5*(3*A + 7*B)*a^2*c*d - (35*A + 32*B)*a^2*d^2 - (5*B*a^2*c*d - (5*A + 14*B)*a^2*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(d^3*f*cos(f*x + e) + d^3*f*sin(f*x + e) + d^3*f), 1/15*(15*(B*a^2*c^3 - (A + 2*B)*a^2*c^2*d + (2*A + B)*a^2*c*d^2 - A*a^2*d^3 + (B*a^2*c^3 - (A + 2*B)*a^2*c^2*d + (2*A + B)*a^2*c*d^2 - A*a^2*d^3)*cos(f*x + e) + (B*a^2*c^3 - (A + 2*B)*a^2*c^2*d + (2*A + B)*a^2*c*d^2 - A*a^2*d^3)*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) + 2*(3*B*a^2*d^2*cos(f*x + e)^3 - 15*B*a^2*c^2 + 5*(3*A + 7*B)*a^2*c*d - (35*A + 32*B)*a^2*d^2 + (5*B*a^2*c*d - (5*A + 11*B)*a^2*d^2)*cos(f*x + e)^2 - (15*B*a^2*c^2 - 5*(3*A + 8*B)*a^2*c*d + 2*(20*A + 23*B)*a^2*d^2)*cos(f*x + e) - (3*B*a^2*d^2*cos(f*x + e)^2 - 15*B*a^2*c^2 + 5*(3*A + 7*B)*a^2*c*d - (35*A + 32*B)*a^2*d^2 - (5*B*a^2*c*d - (5*A + 14*B)*a^2*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(d^3*f*cos(f*x + e) + d^3*f*sin(f*x + e) + d^3*f)]","B",0
305,1,2046,0,3.770683," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(5 \, B a^{2} c^{4} - {\left(3 \, A - 5 \, B\right)} a^{2} c^{3} d - {\left(5 \, A + 7 \, B\right)} a^{2} c^{2} d^{2} + {\left(3 \, A - 5 \, B\right)} a^{2} c d^{3} + {\left(5 \, A + 2 \, B\right)} a^{2} d^{4} - {\left(5 \, B a^{2} c^{3} d - 3 \, A a^{2} c^{2} d^{2} - {\left(2 \, A + 7 \, B\right)} a^{2} c d^{3} + {\left(5 \, A + 2 \, B\right)} a^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(5 \, B a^{2} c^{4} - 3 \, A a^{2} c^{3} d - {\left(2 \, A + 7 \, B\right)} a^{2} c^{2} d^{2} + {\left(5 \, A + 2 \, B\right)} a^{2} c d^{3}\right)} \cos\left(f x + e\right) + {\left(5 \, B a^{2} c^{4} - {\left(3 \, A - 5 \, B\right)} a^{2} c^{3} d - {\left(5 \, A + 7 \, B\right)} a^{2} c^{2} d^{2} + {\left(3 \, A - 5 \, B\right)} a^{2} c d^{3} + {\left(5 \, A + 2 \, B\right)} a^{2} d^{4} + {\left(5 \, B a^{2} c^{3} d - 3 \, A a^{2} c^{2} d^{2} - {\left(2 \, A + 7 \, B\right)} a^{2} c d^{3} + {\left(5 \, A + 2 \, B\right)} a^{2} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(15 \, B a^{2} c^{3} - {\left(9 \, A + 20 \, B\right)} a^{2} c^{2} d + 3 \, {\left(2 \, A - 3 \, B\right)} a^{2} c d^{2} + {\left(3 \, A + 14 \, B\right)} a^{2} d^{3} + 2 \, {\left(B a^{2} c d^{2} + B a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(5 \, B a^{2} c^{2} d - {\left(3 \, A + 2 \, B\right)} a^{2} c d^{2} - {\left(3 \, A + 7 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a^{2} c^{3} - {\left(9 \, A + 10 \, B\right)} a^{2} c^{2} d - 15 \, B a^{2} c d^{2} - {\left(3 \, A + 2 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right) - {\left(15 \, B a^{2} c^{3} - {\left(9 \, A + 20 \, B\right)} a^{2} c^{2} d + 3 \, {\left(2 \, A - 3 \, B\right)} a^{2} c d^{2} + {\left(3 \, A + 14 \, B\right)} a^{2} d^{3} + 2 \, {\left(B a^{2} c d^{2} + B a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, B a^{2} c^{2} d - 3 \, {\left(A + B\right)} a^{2} c d^{2} - {\left(3 \, A + 8 \, B\right)} a^{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}}{12 \, {\left({\left(c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{2} d^{3} + c d^{4}\right)} f \cos\left(f x + e\right) - {\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f - {\left({\left(c d^{4} + d^{5}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{3 \, {\left(5 \, B a^{2} c^{4} - {\left(3 \, A - 5 \, B\right)} a^{2} c^{3} d - {\left(5 \, A + 7 \, B\right)} a^{2} c^{2} d^{2} + {\left(3 \, A - 5 \, B\right)} a^{2} c d^{3} + {\left(5 \, A + 2 \, B\right)} a^{2} d^{4} - {\left(5 \, B a^{2} c^{3} d - 3 \, A a^{2} c^{2} d^{2} - {\left(2 \, A + 7 \, B\right)} a^{2} c d^{3} + {\left(5 \, A + 2 \, B\right)} a^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(5 \, B a^{2} c^{4} - 3 \, A a^{2} c^{3} d - {\left(2 \, A + 7 \, B\right)} a^{2} c^{2} d^{2} + {\left(5 \, A + 2 \, B\right)} a^{2} c d^{3}\right)} \cos\left(f x + e\right) + {\left(5 \, B a^{2} c^{4} - {\left(3 \, A - 5 \, B\right)} a^{2} c^{3} d - {\left(5 \, A + 7 \, B\right)} a^{2} c^{2} d^{2} + {\left(3 \, A - 5 \, B\right)} a^{2} c d^{3} + {\left(5 \, A + 2 \, B\right)} a^{2} d^{4} + {\left(5 \, B a^{2} c^{3} d - 3 \, A a^{2} c^{2} d^{2} - {\left(2 \, A + 7 \, B\right)} a^{2} c d^{3} + {\left(5 \, A + 2 \, B\right)} a^{2} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) - 2 \, {\left(15 \, B a^{2} c^{3} - {\left(9 \, A + 20 \, B\right)} a^{2} c^{2} d + 3 \, {\left(2 \, A - 3 \, B\right)} a^{2} c d^{2} + {\left(3 \, A + 14 \, B\right)} a^{2} d^{3} + 2 \, {\left(B a^{2} c d^{2} + B a^{2} d^{3}\right)} \cos\left(f x + e\right)^{3} + 2 \, {\left(5 \, B a^{2} c^{2} d - {\left(3 \, A + 2 \, B\right)} a^{2} c d^{2} - {\left(3 \, A + 7 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a^{2} c^{3} - {\left(9 \, A + 10 \, B\right)} a^{2} c^{2} d - 15 \, B a^{2} c d^{2} - {\left(3 \, A + 2 \, B\right)} a^{2} d^{3}\right)} \cos\left(f x + e\right) - {\left(15 \, B a^{2} c^{3} - {\left(9 \, A + 20 \, B\right)} a^{2} c^{2} d + 3 \, {\left(2 \, A - 3 \, B\right)} a^{2} c d^{2} + {\left(3 \, A + 14 \, B\right)} a^{2} d^{3} + 2 \, {\left(B a^{2} c d^{2} + B a^{2} d^{3}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(5 \, B a^{2} c^{2} d - 3 \, {\left(A + B\right)} a^{2} c d^{2} - {\left(3 \, A + 8 \, B\right)} a^{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}}{6 \, {\left({\left(c d^{4} + d^{5}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{2} d^{3} + c d^{4}\right)} f \cos\left(f x + e\right) - {\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f - {\left({\left(c d^{4} + d^{5}\right)} f \cos\left(f x + e\right) + {\left(c^{2} d^{3} + 2 \, c d^{4} + d^{5}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/12*(3*(5*B*a^2*c^4 - (3*A - 5*B)*a^2*c^3*d - (5*A + 7*B)*a^2*c^2*d^2 + (3*A - 5*B)*a^2*c*d^3 + (5*A + 2*B)*a^2*d^4 - (5*B*a^2*c^3*d - 3*A*a^2*c^2*d^2 - (2*A + 7*B)*a^2*c*d^3 + (5*A + 2*B)*a^2*d^4)*cos(f*x + e)^2 + (5*B*a^2*c^4 - 3*A*a^2*c^3*d - (2*A + 7*B)*a^2*c^2*d^2 + (5*A + 2*B)*a^2*c*d^3)*cos(f*x + e) + (5*B*a^2*c^4 - (3*A - 5*B)*a^2*c^3*d - (5*A + 7*B)*a^2*c^2*d^2 + (3*A - 5*B)*a^2*c*d^3 + (5*A + 2*B)*a^2*d^4 + (5*B*a^2*c^3*d - 3*A*a^2*c^2*d^2 - (2*A + 7*B)*a^2*c*d^3 + (5*A + 2*B)*a^2*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(15*B*a^2*c^3 - (9*A + 20*B)*a^2*c^2*d + 3*(2*A - 3*B)*a^2*c*d^2 + (3*A + 14*B)*a^2*d^3 + 2*(B*a^2*c*d^2 + B*a^2*d^3)*cos(f*x + e)^3 + 2*(5*B*a^2*c^2*d - (3*A + 2*B)*a^2*c*d^2 - (3*A + 7*B)*a^2*d^3)*cos(f*x + e)^2 + (15*B*a^2*c^3 - (9*A + 10*B)*a^2*c^2*d - 15*B*a^2*c*d^2 - (3*A + 2*B)*a^2*d^3)*cos(f*x + e) - (15*B*a^2*c^3 - (9*A + 20*B)*a^2*c^2*d + 3*(2*A - 3*B)*a^2*c*d^2 + (3*A + 14*B)*a^2*d^3 + 2*(B*a^2*c*d^2 + B*a^2*d^3)*cos(f*x + e)^2 - 2*(5*B*a^2*c^2*d - 3*(A + B)*a^2*c*d^2 - (3*A + 8*B)*a^2*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c*d^4 + d^5)*f*cos(f*x + e)^2 - (c^2*d^3 + c*d^4)*f*cos(f*x + e) - (c^2*d^3 + 2*c*d^4 + d^5)*f - ((c*d^4 + d^5)*f*cos(f*x + e) + (c^2*d^3 + 2*c*d^4 + d^5)*f)*sin(f*x + e)), 1/6*(3*(5*B*a^2*c^4 - (3*A - 5*B)*a^2*c^3*d - (5*A + 7*B)*a^2*c^2*d^2 + (3*A - 5*B)*a^2*c*d^3 + (5*A + 2*B)*a^2*d^4 - (5*B*a^2*c^3*d - 3*A*a^2*c^2*d^2 - (2*A + 7*B)*a^2*c*d^3 + (5*A + 2*B)*a^2*d^4)*cos(f*x + e)^2 + (5*B*a^2*c^4 - 3*A*a^2*c^3*d - (2*A + 7*B)*a^2*c^2*d^2 + (5*A + 2*B)*a^2*c*d^3)*cos(f*x + e) + (5*B*a^2*c^4 - (3*A - 5*B)*a^2*c^3*d - (5*A + 7*B)*a^2*c^2*d^2 + (3*A - 5*B)*a^2*c*d^3 + (5*A + 2*B)*a^2*d^4 + (5*B*a^2*c^3*d - 3*A*a^2*c^2*d^2 - (2*A + 7*B)*a^2*c*d^3 + (5*A + 2*B)*a^2*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) - 2*(15*B*a^2*c^3 - (9*A + 20*B)*a^2*c^2*d + 3*(2*A - 3*B)*a^2*c*d^2 + (3*A + 14*B)*a^2*d^3 + 2*(B*a^2*c*d^2 + B*a^2*d^3)*cos(f*x + e)^3 + 2*(5*B*a^2*c^2*d - (3*A + 2*B)*a^2*c*d^2 - (3*A + 7*B)*a^2*d^3)*cos(f*x + e)^2 + (15*B*a^2*c^3 - (9*A + 10*B)*a^2*c^2*d - 15*B*a^2*c*d^2 - (3*A + 2*B)*a^2*d^3)*cos(f*x + e) - (15*B*a^2*c^3 - (9*A + 20*B)*a^2*c^2*d + 3*(2*A - 3*B)*a^2*c*d^2 + (3*A + 14*B)*a^2*d^3 + 2*(B*a^2*c*d^2 + B*a^2*d^3)*cos(f*x + e)^2 - 2*(5*B*a^2*c^2*d - 3*(A + B)*a^2*c*d^2 - (3*A + 8*B)*a^2*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c*d^4 + d^5)*f*cos(f*x + e)^2 - (c^2*d^3 + c*d^4)*f*cos(f*x + e) - (c^2*d^3 + 2*c*d^4 + d^5)*f - ((c*d^4 + d^5)*f*cos(f*x + e) + (c^2*d^3 + 2*c*d^4 + d^5)*f)*sin(f*x + e))]","B",0
306,1,3046,0,4.709499," ","integrate((a+a*sin(f*x+e))^(5/2)*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{{\left(15 \, B a^{2} c^{5} - 3 \, {\left(A - 20 \, B\right)} a^{2} c^{4} d - 2 \, {\left(8 \, A - 41 \, B\right)} a^{2} c^{3} d^{2} - 6 \, {\left(7 \, A - 4 \, B\right)} a^{2} c^{2} d^{3} - 3 \, {\left(16 \, A + 11 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5} - {\left(15 \, B a^{2} c^{3} d^{2} - 3 \, {\left(A - 10 \, B\right)} a^{2} c^{2} d^{3} - {\left(10 \, A - 7 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(30 \, B a^{2} c^{4} d - 3 \, {\left(2 \, A - 25 \, B\right)} a^{2} c^{3} d^{2} - {\left(23 \, A - 44 \, B\right)} a^{2} c^{2} d^{3} - 3 \, {\left(16 \, A + 11 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a^{2} c^{5} - 3 \, {\left(A - 10 \, B\right)} a^{2} c^{4} d - 2 \, {\left(5 \, A - 11 \, B\right)} a^{2} c^{3} d^{2} - 2 \, {\left(11 \, A - 5 \, B\right)} a^{2} c^{2} d^{3} - {\left(10 \, A - 7 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right) + {\left(15 \, B a^{2} c^{5} - 3 \, {\left(A - 20 \, B\right)} a^{2} c^{4} d - 2 \, {\left(8 \, A - 41 \, B\right)} a^{2} c^{3} d^{2} - 6 \, {\left(7 \, A - 4 \, B\right)} a^{2} c^{2} d^{3} - 3 \, {\left(16 \, A + 11 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5} - {\left(15 \, B a^{2} c^{3} d^{2} - 3 \, {\left(A - 10 \, B\right)} a^{2} c^{2} d^{3} - {\left(10 \, A - 7 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(15 \, B a^{2} c^{4} d - 3 \, {\left(A - 10 \, B\right)} a^{2} c^{3} d^{2} - {\left(10 \, A - 7 \, B\right)} a^{2} c^{2} d^{3} - {\left(19 \, A + 20 \, B\right)} a^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{\frac{a}{c d + d^{2}}} \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(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} - {\left(c d^{2} + d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(c^{2} d + 3 \, c d^{2} + 2 \, d^{3}\right)} \cos\left(f x + e\right) - {\left(c^{2} d + 4 \, c d^{2} + 3 \, d^{3} + {\left(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{\frac{a}{c d + d^{2}}} - {\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) + 4 \, {\left(15 \, B a^{2} c^{4} - {\left(3 \, A + 5 \, B\right)} a^{2} c^{3} d - {\left(3 \, A + 31 \, B\right)} a^{2} c^{2} d^{2} + {\left(15 \, A + 17 \, B\right)} a^{2} c d^{3} - {\left(9 \, A - 4 \, B\right)} a^{2} d^{4} - 8 \, {\left(B a^{2} c^{2} d^{2} + 2 \, B a^{2} c d^{3} + B a^{2} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(25 \, B a^{2} c^{3} d - {\left(5 \, A - 26 \, B\right)} a^{2} c^{2} d^{2} - 3 \, {\left(2 \, A + 5 \, B\right)} a^{2} c d^{3} + {\left(11 \, A - 4 \, B\right)} a^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a^{2} c^{4} - {\left(3 \, A - 20 \, B\right)} a^{2} c^{3} d - {\left(8 \, A - 3 \, B\right)} a^{2} c^{2} d^{2} + 9 \, {\left(A + 2 \, B\right)} a^{2} c d^{3} + 2 \, {\left(A + 4 \, B\right)} a^{2} d^{4}\right)} \cos\left(f x + e\right) - {\left(15 \, B a^{2} c^{4} - {\left(3 \, A + 5 \, B\right)} a^{2} c^{3} d - {\left(3 \, A + 31 \, B\right)} a^{2} c^{2} d^{2} + {\left(15 \, A + 17 \, B\right)} a^{2} c d^{3} - {\left(9 \, A - 4 \, B\right)} a^{2} d^{4} - 8 \, {\left(B a^{2} c^{2} d^{2} + 2 \, B a^{2} c d^{3} + B a^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} - {\left(25 \, B a^{2} c^{3} d - {\left(5 \, A - 34 \, B\right)} a^{2} c^{2} d^{2} - {\left(6 \, A - B\right)} a^{2} c d^{3} + {\left(11 \, A + 4 \, B\right)} a^{2} 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}}{16 \, {\left({\left(c^{2} d^{5} + 2 \, c d^{6} + d^{7}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, c^{3} d^{4} + 5 \, c^{2} d^{5} + 4 \, c d^{6} + d^{7}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{4} d^{3} + 2 \, c^{3} d^{4} + 2 \, c^{2} d^{5} + 2 \, c d^{6} + d^{7}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d^{3} + 4 \, c^{3} d^{4} + 6 \, c^{2} d^{5} + 4 \, c d^{6} + d^{7}\right)} f + {\left({\left(c^{2} d^{5} + 2 \, c d^{6} + d^{7}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{3} d^{4} + 2 \, c^{2} d^{5} + c d^{6}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d^{3} + 4 \, c^{3} d^{4} + 6 \, c^{2} d^{5} + 4 \, c d^{6} + d^{7}\right)} f\right)} \sin\left(f x + e\right)\right)}}, -\frac{{\left(15 \, B a^{2} c^{5} - 3 \, {\left(A - 20 \, B\right)} a^{2} c^{4} d - 2 \, {\left(8 \, A - 41 \, B\right)} a^{2} c^{3} d^{2} - 6 \, {\left(7 \, A - 4 \, B\right)} a^{2} c^{2} d^{3} - 3 \, {\left(16 \, A + 11 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5} - {\left(15 \, B a^{2} c^{3} d^{2} - 3 \, {\left(A - 10 \, B\right)} a^{2} c^{2} d^{3} - {\left(10 \, A - 7 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(30 \, B a^{2} c^{4} d - 3 \, {\left(2 \, A - 25 \, B\right)} a^{2} c^{3} d^{2} - {\left(23 \, A - 44 \, B\right)} a^{2} c^{2} d^{3} - 3 \, {\left(16 \, A + 11 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a^{2} c^{5} - 3 \, {\left(A - 10 \, B\right)} a^{2} c^{4} d - 2 \, {\left(5 \, A - 11 \, B\right)} a^{2} c^{3} d^{2} - 2 \, {\left(11 \, A - 5 \, B\right)} a^{2} c^{2} d^{3} - {\left(10 \, A - 7 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right) + {\left(15 \, B a^{2} c^{5} - 3 \, {\left(A - 20 \, B\right)} a^{2} c^{4} d - 2 \, {\left(8 \, A - 41 \, B\right)} a^{2} c^{3} d^{2} - 6 \, {\left(7 \, A - 4 \, B\right)} a^{2} c^{2} d^{3} - 3 \, {\left(16 \, A + 11 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5} - {\left(15 \, B a^{2} c^{3} d^{2} - 3 \, {\left(A - 10 \, B\right)} a^{2} c^{2} d^{3} - {\left(10 \, A - 7 \, B\right)} a^{2} c d^{4} - {\left(19 \, A + 20 \, B\right)} a^{2} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(15 \, B a^{2} c^{4} d - 3 \, {\left(A - 10 \, B\right)} a^{2} c^{3} d^{2} - {\left(10 \, A - 7 \, B\right)} a^{2} c^{2} d^{3} - {\left(19 \, A + 20 \, B\right)} a^{2} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-\frac{a}{c d + d^{2}}} \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}{c d + d^{2}}}}{2 \, a \cos\left(f x + e\right)}\right) - 2 \, {\left(15 \, B a^{2} c^{4} - {\left(3 \, A + 5 \, B\right)} a^{2} c^{3} d - {\left(3 \, A + 31 \, B\right)} a^{2} c^{2} d^{2} + {\left(15 \, A + 17 \, B\right)} a^{2} c d^{3} - {\left(9 \, A - 4 \, B\right)} a^{2} d^{4} - 8 \, {\left(B a^{2} c^{2} d^{2} + 2 \, B a^{2} c d^{3} + B a^{2} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left(25 \, B a^{2} c^{3} d - {\left(5 \, A - 26 \, B\right)} a^{2} c^{2} d^{2} - 3 \, {\left(2 \, A + 5 \, B\right)} a^{2} c d^{3} + {\left(11 \, A - 4 \, B\right)} a^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a^{2} c^{4} - {\left(3 \, A - 20 \, B\right)} a^{2} c^{3} d - {\left(8 \, A - 3 \, B\right)} a^{2} c^{2} d^{2} + 9 \, {\left(A + 2 \, B\right)} a^{2} c d^{3} + 2 \, {\left(A + 4 \, B\right)} a^{2} d^{4}\right)} \cos\left(f x + e\right) - {\left(15 \, B a^{2} c^{4} - {\left(3 \, A + 5 \, B\right)} a^{2} c^{3} d - {\left(3 \, A + 31 \, B\right)} a^{2} c^{2} d^{2} + {\left(15 \, A + 17 \, B\right)} a^{2} c d^{3} - {\left(9 \, A - 4 \, B\right)} a^{2} d^{4} - 8 \, {\left(B a^{2} c^{2} d^{2} + 2 \, B a^{2} c d^{3} + B a^{2} d^{4}\right)} \cos\left(f x + e\right)^{2} - {\left(25 \, B a^{2} c^{3} d - {\left(5 \, A - 34 \, B\right)} a^{2} c^{2} d^{2} - {\left(6 \, A - B\right)} a^{2} c d^{3} + {\left(11 \, A + 4 \, B\right)} a^{2} 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}}{8 \, {\left({\left(c^{2} d^{5} + 2 \, c d^{6} + d^{7}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, c^{3} d^{4} + 5 \, c^{2} d^{5} + 4 \, c d^{6} + d^{7}\right)} f \cos\left(f x + e\right)^{2} - {\left(c^{4} d^{3} + 2 \, c^{3} d^{4} + 2 \, c^{2} d^{5} + 2 \, c d^{6} + d^{7}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d^{3} + 4 \, c^{3} d^{4} + 6 \, c^{2} d^{5} + 4 \, c d^{6} + d^{7}\right)} f + {\left({\left(c^{2} d^{5} + 2 \, c d^{6} + d^{7}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(c^{3} d^{4} + 2 \, c^{2} d^{5} + c d^{6}\right)} f \cos\left(f x + e\right) - {\left(c^{4} d^{3} + 4 \, c^{3} d^{4} + 6 \, c^{2} d^{5} + 4 \, c d^{6} + d^{7}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*((15*B*a^2*c^5 - 3*(A - 20*B)*a^2*c^4*d - 2*(8*A - 41*B)*a^2*c^3*d^2 - 6*(7*A - 4*B)*a^2*c^2*d^3 - 3*(16*A + 11*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5 - (15*B*a^2*c^3*d^2 - 3*(A - 10*B)*a^2*c^2*d^3 - (10*A - 7*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5)*cos(f*x + e)^3 - (30*B*a^2*c^4*d - 3*(2*A - 25*B)*a^2*c^3*d^2 - (23*A - 44*B)*a^2*c^2*d^3 - 3*(16*A + 11*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5)*cos(f*x + e)^2 + (15*B*a^2*c^5 - 3*(A - 10*B)*a^2*c^4*d - 2*(5*A - 11*B)*a^2*c^3*d^2 - 2*(11*A - 5*B)*a^2*c^2*d^3 - (10*A - 7*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5)*cos(f*x + e) + (15*B*a^2*c^5 - 3*(A - 20*B)*a^2*c^4*d - 2*(8*A - 41*B)*a^2*c^3*d^2 - 6*(7*A - 4*B)*a^2*c^2*d^3 - 3*(16*A + 11*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5 - (15*B*a^2*c^3*d^2 - 3*(A - 10*B)*a^2*c^2*d^3 - (10*A - 7*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5)*cos(f*x + e)^2 + 2*(15*B*a^2*c^4*d - 3*(A - 10*B)*a^2*c^3*d^2 - (10*A - 7*B)*a^2*c^2*d^3 - (19*A + 20*B)*a^2*c*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a/(c*d + d^2))*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^2*d + 4*c*d^2 + 3*d^3 - (c*d^2 + d^3)*cos(f*x + e)^2 + (c^2*d + 3*c*d^2 + 2*d^3)*cos(f*x + e) - (c^2*d + 4*c*d^2 + 3*d^3 + (c*d^2 + d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a)*sqrt(a/(c*d + d^2)) - (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))) + 4*(15*B*a^2*c^4 - (3*A + 5*B)*a^2*c^3*d - (3*A + 31*B)*a^2*c^2*d^2 + (15*A + 17*B)*a^2*c*d^3 - (9*A - 4*B)*a^2*d^4 - 8*(B*a^2*c^2*d^2 + 2*B*a^2*c*d^3 + B*a^2*d^4)*cos(f*x + e)^3 + (25*B*a^2*c^3*d - (5*A - 26*B)*a^2*c^2*d^2 - 3*(2*A + 5*B)*a^2*c*d^3 + (11*A - 4*B)*a^2*d^4)*cos(f*x + e)^2 + (15*B*a^2*c^4 - (3*A - 20*B)*a^2*c^3*d - (8*A - 3*B)*a^2*c^2*d^2 + 9*(A + 2*B)*a^2*c*d^3 + 2*(A + 4*B)*a^2*d^4)*cos(f*x + e) - (15*B*a^2*c^4 - (3*A + 5*B)*a^2*c^3*d - (3*A + 31*B)*a^2*c^2*d^2 + (15*A + 17*B)*a^2*c*d^3 - (9*A - 4*B)*a^2*d^4 - 8*(B*a^2*c^2*d^2 + 2*B*a^2*c*d^3 + B*a^2*d^4)*cos(f*x + e)^2 - (25*B*a^2*c^3*d - (5*A - 34*B)*a^2*c^2*d^2 - (6*A - B)*a^2*c*d^3 + (11*A + 4*B)*a^2*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c^2*d^5 + 2*c*d^6 + d^7)*f*cos(f*x + e)^3 + (2*c^3*d^4 + 5*c^2*d^5 + 4*c*d^6 + d^7)*f*cos(f*x + e)^2 - (c^4*d^3 + 2*c^3*d^4 + 2*c^2*d^5 + 2*c*d^6 + d^7)*f*cos(f*x + e) - (c^4*d^3 + 4*c^3*d^4 + 6*c^2*d^5 + 4*c*d^6 + d^7)*f + ((c^2*d^5 + 2*c*d^6 + d^7)*f*cos(f*x + e)^2 - 2*(c^3*d^4 + 2*c^2*d^5 + c*d^6)*f*cos(f*x + e) - (c^4*d^3 + 4*c^3*d^4 + 6*c^2*d^5 + 4*c*d^6 + d^7)*f)*sin(f*x + e)), -1/8*((15*B*a^2*c^5 - 3*(A - 20*B)*a^2*c^4*d - 2*(8*A - 41*B)*a^2*c^3*d^2 - 6*(7*A - 4*B)*a^2*c^2*d^3 - 3*(16*A + 11*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5 - (15*B*a^2*c^3*d^2 - 3*(A - 10*B)*a^2*c^2*d^3 - (10*A - 7*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5)*cos(f*x + e)^3 - (30*B*a^2*c^4*d - 3*(2*A - 25*B)*a^2*c^3*d^2 - (23*A - 44*B)*a^2*c^2*d^3 - 3*(16*A + 11*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5)*cos(f*x + e)^2 + (15*B*a^2*c^5 - 3*(A - 10*B)*a^2*c^4*d - 2*(5*A - 11*B)*a^2*c^3*d^2 - 2*(11*A - 5*B)*a^2*c^2*d^3 - (10*A - 7*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5)*cos(f*x + e) + (15*B*a^2*c^5 - 3*(A - 20*B)*a^2*c^4*d - 2*(8*A - 41*B)*a^2*c^3*d^2 - 6*(7*A - 4*B)*a^2*c^2*d^3 - 3*(16*A + 11*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5 - (15*B*a^2*c^3*d^2 - 3*(A - 10*B)*a^2*c^2*d^3 - (10*A - 7*B)*a^2*c*d^4 - (19*A + 20*B)*a^2*d^5)*cos(f*x + e)^2 + 2*(15*B*a^2*c^4*d - 3*(A - 10*B)*a^2*c^3*d^2 - (10*A - 7*B)*a^2*c^2*d^3 - (19*A + 20*B)*a^2*c*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(-a/(c*d + d^2))*arctan(1/2*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)*sqrt(-a/(c*d + d^2))/(a*cos(f*x + e))) - 2*(15*B*a^2*c^4 - (3*A + 5*B)*a^2*c^3*d - (3*A + 31*B)*a^2*c^2*d^2 + (15*A + 17*B)*a^2*c*d^3 - (9*A - 4*B)*a^2*d^4 - 8*(B*a^2*c^2*d^2 + 2*B*a^2*c*d^3 + B*a^2*d^4)*cos(f*x + e)^3 + (25*B*a^2*c^3*d - (5*A - 26*B)*a^2*c^2*d^2 - 3*(2*A + 5*B)*a^2*c*d^3 + (11*A - 4*B)*a^2*d^4)*cos(f*x + e)^2 + (15*B*a^2*c^4 - (3*A - 20*B)*a^2*c^3*d - (8*A - 3*B)*a^2*c^2*d^2 + 9*(A + 2*B)*a^2*c*d^3 + 2*(A + 4*B)*a^2*d^4)*cos(f*x + e) - (15*B*a^2*c^4 - (3*A + 5*B)*a^2*c^3*d - (3*A + 31*B)*a^2*c^2*d^2 + (15*A + 17*B)*a^2*c*d^3 - (9*A - 4*B)*a^2*d^4 - 8*(B*a^2*c^2*d^2 + 2*B*a^2*c*d^3 + B*a^2*d^4)*cos(f*x + e)^2 - (25*B*a^2*c^3*d - (5*A - 34*B)*a^2*c^2*d^2 - (6*A - B)*a^2*c*d^3 + (11*A + 4*B)*a^2*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((c^2*d^5 + 2*c*d^6 + d^7)*f*cos(f*x + e)^3 + (2*c^3*d^4 + 5*c^2*d^5 + 4*c*d^6 + d^7)*f*cos(f*x + e)^2 - (c^4*d^3 + 2*c^3*d^4 + 2*c^2*d^5 + 2*c*d^6 + d^7)*f*cos(f*x + e) - (c^4*d^3 + 4*c^3*d^4 + 6*c^2*d^5 + 4*c*d^6 + d^7)*f + ((c^2*d^5 + 2*c*d^6 + d^7)*f*cos(f*x + e)^2 - 2*(c^3*d^4 + 2*c^2*d^5 + c*d^6)*f*cos(f*x + e) - (c^4*d^3 + 4*c^3*d^4 + 6*c^2*d^5 + 4*c*d^6 + d^7)*f)*sin(f*x + e))]","B",0
307,1,629,0,0.731594," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\frac{105 \, \sqrt{2} {\left({\left(A - B\right)} a c^{3} - 3 \, {\left(A - B\right)} a c^{2} d + 3 \, {\left(A - B\right)} a c d^{2} - {\left(A - B\right)} a d^{3} + {\left({\left(A - B\right)} a c^{3} - 3 \, {\left(A - B\right)} a c^{2} d + 3 \, {\left(A - B\right)} a c d^{2} - {\left(A - B\right)} a d^{3}\right)} \cos\left(f x + e\right) + {\left({\left(A - B\right)} a c^{3} - 3 \, {\left(A - B\right)} a c^{2} d + 3 \, {\left(A - B\right)} a c d^{2} - {\left(A - B\right)} a d^{3}\right)} \sin\left(f x + e\right)\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)}{\sqrt{a}} + 4 \, {\left(15 \, B d^{3} \cos\left(f x + e\right)^{4} - 105 \, B c^{3} - 105 \, {\left(3 \, A - 2 \, B\right)} c^{2} d + 21 \, {\left(10 \, A - 17 \, B\right)} c d^{2} - {\left(119 \, A - 92 \, B\right)} d^{3} + 3 \, {\left(21 \, B c d^{2} + {\left(7 \, A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(105 \, B c^{2} d + 21 \, {\left(5 \, A - 4 \, B\right)} c d^{2} - 4 \, {\left(7 \, A - 16 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(105 \, B c^{3} + 105 \, {\left(3 \, A - B\right)} c^{2} d - 21 \, {\left(5 \, A - 16 \, B\right)} c d^{2} + 2 \, {\left(56 \, A - 23 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(15 \, B d^{3} \cos\left(f x + e\right)^{3} + 105 \, B c^{3} + 105 \, {\left(3 \, A - 2 \, B\right)} c^{2} d - 21 \, {\left(10 \, A - 17 \, B\right)} c d^{2} + {\left(119 \, A - 92 \, B\right)} d^{3} - 3 \, {\left(21 \, B c d^{2} + {\left(7 \, A - 6 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - {\left(105 \, B c^{2} d + 21 \, {\left(5 \, A - B\right)} c d^{2} - {\left(7 \, A - 46 \, B\right)} 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}}{210 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"1/210*(105*sqrt(2)*((A - B)*a*c^3 - 3*(A - B)*a*c^2*d + 3*(A - B)*a*c*d^2 - (A - B)*a*d^3 + ((A - B)*a*c^3 - 3*(A - B)*a*c^2*d + 3*(A - B)*a*c*d^2 - (A - B)*a*d^3)*cos(f*x + e) + ((A - B)*a*c^3 - 3*(A - B)*a*c^2*d + 3*(A - B)*a*c*d^2 - (A - B)*a*d^3)*sin(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))/sqrt(a) + 4*(15*B*d^3*cos(f*x + e)^4 - 105*B*c^3 - 105*(3*A - 2*B)*c^2*d + 21*(10*A - 17*B)*c*d^2 - (119*A - 92*B)*d^3 + 3*(21*B*c*d^2 + (7*A - B)*d^3)*cos(f*x + e)^3 - (105*B*c^2*d + 21*(5*A - 4*B)*c*d^2 - 4*(7*A - 16*B)*d^3)*cos(f*x + e)^2 - (105*B*c^3 + 105*(3*A - B)*c^2*d - 21*(5*A - 16*B)*c*d^2 + 2*(56*A - 23*B)*d^3)*cos(f*x + e) + (15*B*d^3*cos(f*x + e)^3 + 105*B*c^3 + 105*(3*A - 2*B)*c^2*d - 21*(10*A - 17*B)*c*d^2 + (119*A - 92*B)*d^3 - 3*(21*B*c*d^2 + (7*A - 6*B)*d^3)*cos(f*x + e)^2 - (105*B*c^2*d + 21*(5*A - B)*c*d^2 - (7*A - 46*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","B",0
308,1,448,0,0.836340," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{\frac{15 \, \sqrt{2} {\left({\left(A - B\right)} a c^{2} - 2 \, {\left(A - B\right)} a c d + {\left(A - B\right)} a d^{2} + {\left({\left(A - B\right)} a c^{2} - 2 \, {\left(A - B\right)} a c d + {\left(A - B\right)} a d^{2}\right)} \cos\left(f x + e\right) + {\left({\left(A - B\right)} a c^{2} - 2 \, {\left(A - B\right)} a c d + {\left(A - B\right)} a d^{2}\right)} \sin\left(f x + e\right)\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)}{\sqrt{a}} - 4 \, {\left(3 \, B d^{2} \cos\left(f x + e\right)^{3} - 15 \, B c^{2} - 10 \, {\left(3 \, A - 2 \, B\right)} c d + {\left(10 \, A - 17 \, B\right)} d^{2} - {\left(10 \, B c d + {\left(5 \, A - 4 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(15 \, B c^{2} + 10 \, {\left(3 \, A - B\right)} c d - {\left(5 \, A - 16 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left(3 \, B d^{2} \cos\left(f x + e\right)^{2} - 15 \, B c^{2} - 10 \, {\left(3 \, A - 2 \, B\right)} c d + {\left(10 \, A - 17 \, B\right)} d^{2} + {\left(10 \, B c d + {\left(5 \, A - B\right)} 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}}{30 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"-1/30*(15*sqrt(2)*((A - B)*a*c^2 - 2*(A - B)*a*c*d + (A - B)*a*d^2 + ((A - B)*a*c^2 - 2*(A - B)*a*c*d + (A - B)*a*d^2)*cos(f*x + e) + ((A - B)*a*c^2 - 2*(A - B)*a*c*d + (A - B)*a*d^2)*sin(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))/sqrt(a) - 4*(3*B*d^2*cos(f*x + e)^3 - 15*B*c^2 - 10*(3*A - 2*B)*c*d + (10*A - 17*B)*d^2 - (10*B*c*d + (5*A - 4*B)*d^2)*cos(f*x + e)^2 - (15*B*c^2 + 10*(3*A - B)*c*d - (5*A - 16*B)*d^2)*cos(f*x + e) - (3*B*d^2*cos(f*x + e)^2 - 15*B*c^2 - 10*(3*A - 2*B)*c*d + (10*A - 17*B)*d^2 + (10*B*c*d + (5*A - B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","B",0
309,1,303,0,0.645193," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\frac{\frac{3 \, \sqrt{2} {\left({\left(A - B\right)} a c - {\left(A - B\right)} a d + {\left({\left(A - B\right)} a c - {\left(A - B\right)} a d\right)} \cos\left(f x + e\right) + {\left({\left(A - B\right)} a c - {\left(A - B\right)} a d\right)} \sin\left(f x + e\right)\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)}{\sqrt{a}} - 4 \, {\left(B d \cos\left(f x + e\right)^{2} + 3 \, B c + {\left(3 \, A - 2 \, B\right)} d + {\left(3 \, B c + {\left(3 \, A - B\right)} d\right)} \cos\left(f x + e\right) + {\left(B d \cos\left(f x + e\right) - 3 \, B c - {\left(3 \, A - 2 \, B\right)} d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{6 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"1/6*(3*sqrt(2)*((A - B)*a*c - (A - B)*a*d + ((A - B)*a*c - (A - B)*a*d)*cos(f*x + e) + ((A - B)*a*c - (A - B)*a*d)*sin(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))/sqrt(a) - 4*(B*d*cos(f*x + e)^2 + 3*B*c + (3*A - 2*B)*d + (3*B*c + (3*A - B)*d)*cos(f*x + e) + (B*d*cos(f*x + e) - 3*B*c - (3*A - 2*B)*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","B",0
310,1,210,0,0.945270," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","-\frac{\frac{\sqrt{2} {\left({\left(A - B\right)} a \cos\left(f x + e\right) + {\left(A - B\right)} a \sin\left(f x + e\right) + {\left(A - B\right)} a\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)}{\sqrt{a}} + 4 \, {\left(B \cos\left(f x + e\right) - B \sin\left(f x + e\right) + B\right)} \sqrt{a \sin\left(f x + e\right) + a}}{2 \, {\left(a f \cos\left(f x + e\right) + a f \sin\left(f x + e\right) + a f\right)}}"," ",0,"-1/2*(sqrt(2)*((A - B)*a*cos(f*x + e) + (A - B)*a*sin(f*x + e) + (A - B)*a)*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) + 4*(B*cos(f*x + e) - B*sin(f*x + e) + B)*sqrt(a*sin(f*x + e) + a))/(a*f*cos(f*x + e) + a*f*sin(f*x + e) + a*f)","B",0
311,1,744,0,2.037986," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a c d + a d^{2}} {\left(B c - A d\right)} \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 \, \sqrt{a c d + a d^{2}} {\left(d \cos\left(f x + e\right)^{2} - {\left(c + 2 \, d\right)} \cos\left(f x + e\right) + {\left(d \cos\left(f x + e\right) + c + 3 \, d\right)} \sin\left(f x + e\right) - c - 3 \, d\right)} \sqrt{a \sin\left(f x + e\right) + a} - {\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) + \frac{\sqrt{2} {\left({\left(A - B\right)} a c d + {\left(A - B\right)} a d^{2}\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)}{\sqrt{a}}}{2 \, {\left(a c^{2} d - a d^{3}\right)} f}, -\frac{2 \, \sqrt{-a c d - a d^{2}} {\left(B c - A d\right)} \arctan\left(\frac{\sqrt{-a c d - a d^{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) - c - 2 \, d\right)}}{2 \, {\left(a c d + a d^{2}\right)} \cos\left(f x + e\right)}\right) - \frac{\sqrt{2} {\left({\left(A - B\right)} a c d + {\left(A - B\right)} a d^{2}\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)}{\sqrt{a}}}{2 \, {\left(a c^{2} d - a d^{3}\right)} f}\right]"," ",0,"[1/2*(sqrt(a*c*d + a*d^2)*(B*c - A*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*sqrt(a*c*d + a*d^2)*(d*cos(f*x + e)^2 - (c + 2*d)*cos(f*x + e) + (d*cos(f*x + e) + c + 3*d)*sin(f*x + e) - c - 3*d)*sqrt(a*sin(f*x + e) + a) - (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(2)*((A - B)*a*c*d + (A - B)*a*d^2)*log(-(cos(f*x + e)^2 - (cos(f*x + e) - 2)*sin(f*x + e) - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*(cos(f*x + e) - sin(f*x + e) + 1)/sqrt(a) + 3*cos(f*x + e) + 2)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2))/sqrt(a))/((a*c^2*d - a*d^3)*f), -1/2*(2*sqrt(-a*c*d - a*d^2)*(B*c - A*d)*arctan(1/2*sqrt(-a*c*d - a*d^2)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)/((a*c*d + a*d^2)*cos(f*x + e))) - sqrt(2)*((A - B)*a*c*d + (A - B)*a*d^2)*log(-(cos(f*x + e)^2 - (cos(f*x + e) - 2)*sin(f*x + e) - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*(cos(f*x + e) - sin(f*x + e) + 1)/sqrt(a) + 3*cos(f*x + e) + 2)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2))/sqrt(a))/((a*c^2*d - a*d^3)*f)]","B",0
312,1,2159,0,5.541372," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(B c^{3} - {\left(3 \, A - 2 \, B\right)} c^{2} d - {\left(4 \, A - 3 \, B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3} - {\left(B c^{2} d - {\left(3 \, A - B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{3} - {\left(3 \, A - B\right)} c^{2} d - {\left(A - 2 \, B\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(B c^{3} - {\left(3 \, A - 2 \, B\right)} c^{2} d - {\left(4 \, A - 3 \, B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3} + {\left(B c^{2} d - {\left(3 \, A - B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a c d + a d^{2}} \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 \, \sqrt{a c d + a d^{2}} {\left(d \cos\left(f x + e\right)^{2} - {\left(c + 2 \, d\right)} \cos\left(f x + e\right) + {\left(d \cos\left(f x + e\right) + c + 3 \, d\right)} \sin\left(f x + e\right) - c - 3 \, d\right)} \sqrt{a \sin\left(f x + e\right) + a} - {\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) - \frac{2 \, \sqrt{2} {\left({\left(A - B\right)} a c^{3} d + 3 \, {\left(A - B\right)} a c^{2} d^{2} + 3 \, {\left(A - B\right)} a c d^{3} + {\left(A - B\right)} a d^{4} - {\left({\left(A - B\right)} a c^{2} d^{2} + 2 \, {\left(A - B\right)} a c d^{3} + {\left(A - B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A - B\right)} a c^{3} d + 2 \, {\left(A - B\right)} a c^{2} d^{2} + {\left(A - B\right)} a c d^{3}\right)} \cos\left(f x + e\right) + {\left({\left(A - B\right)} a c^{3} d + 3 \, {\left(A - B\right)} a c^{2} d^{2} + 3 \, {\left(A - B\right)} a c d^{3} + {\left(A - B\right)} a d^{4} + {\left({\left(A - B\right)} a c^{2} d^{2} + 2 \, {\left(A - B\right)} a c d^{3} + {\left(A - B\right)} a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\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)}{\sqrt{a}} - 4 \, {\left(B c^{3} d - A c^{2} d^{2} - B c d^{3} + A d^{4} + {\left(B c^{3} d - A c^{2} d^{2} - B c d^{3} + A d^{4}\right)} \cos\left(f x + e\right) - {\left(B c^{3} d - A c^{2} d^{2} - B c d^{3} + A d^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{4 \, {\left({\left(a c^{4} d^{2} - 2 \, a c^{2} d^{4} + a d^{6}\right)} f \cos\left(f x + e\right)^{2} - {\left(a c^{5} d - 2 \, a c^{3} d^{3} + a c d^{5}\right)} f \cos\left(f x + e\right) - {\left(a c^{5} d + a c^{4} d^{2} - 2 \, a c^{3} d^{3} - 2 \, a c^{2} d^{4} + a c d^{5} + a d^{6}\right)} f - {\left({\left(a c^{4} d^{2} - 2 \, a c^{2} d^{4} + a d^{6}\right)} f \cos\left(f x + e\right) + {\left(a c^{5} d + a c^{4} d^{2} - 2 \, a c^{3} d^{3} - 2 \, a c^{2} d^{4} + a c d^{5} + a d^{6}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{{\left(B c^{3} - {\left(3 \, A - 2 \, B\right)} c^{2} d - {\left(4 \, A - 3 \, B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3} - {\left(B c^{2} d - {\left(3 \, A - B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(B c^{3} - {\left(3 \, A - B\right)} c^{2} d - {\left(A - 2 \, B\right)} c d^{2}\right)} \cos\left(f x + e\right) + {\left(B c^{3} - {\left(3 \, A - 2 \, B\right)} c^{2} d - {\left(4 \, A - 3 \, B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3} + {\left(B c^{2} d - {\left(3 \, A - B\right)} c d^{2} - {\left(A - 2 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-a c d - a d^{2}} \arctan\left(\frac{\sqrt{-a c d - a d^{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) - c - 2 \, d\right)}}{2 \, {\left(a c d + a d^{2}\right)} \cos\left(f x + e\right)}\right) + \frac{\sqrt{2} {\left({\left(A - B\right)} a c^{3} d + 3 \, {\left(A - B\right)} a c^{2} d^{2} + 3 \, {\left(A - B\right)} a c d^{3} + {\left(A - B\right)} a d^{4} - {\left({\left(A - B\right)} a c^{2} d^{2} + 2 \, {\left(A - B\right)} a c d^{3} + {\left(A - B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A - B\right)} a c^{3} d + 2 \, {\left(A - B\right)} a c^{2} d^{2} + {\left(A - B\right)} a c d^{3}\right)} \cos\left(f x + e\right) + {\left({\left(A - B\right)} a c^{3} d + 3 \, {\left(A - B\right)} a c^{2} d^{2} + 3 \, {\left(A - B\right)} a c d^{3} + {\left(A - B\right)} a d^{4} + {\left({\left(A - B\right)} a c^{2} d^{2} + 2 \, {\left(A - B\right)} a c d^{3} + {\left(A - B\right)} a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\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)}{\sqrt{a}} + 2 \, {\left(B c^{3} d - A c^{2} d^{2} - B c d^{3} + A d^{4} + {\left(B c^{3} d - A c^{2} d^{2} - B c d^{3} + A d^{4}\right)} \cos\left(f x + e\right) - {\left(B c^{3} d - A c^{2} d^{2} - B c d^{3} + A d^{4}\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{2 \, {\left({\left(a c^{4} d^{2} - 2 \, a c^{2} d^{4} + a d^{6}\right)} f \cos\left(f x + e\right)^{2} - {\left(a c^{5} d - 2 \, a c^{3} d^{3} + a c d^{5}\right)} f \cos\left(f x + e\right) - {\left(a c^{5} d + a c^{4} d^{2} - 2 \, a c^{3} d^{3} - 2 \, a c^{2} d^{4} + a c d^{5} + a d^{6}\right)} f - {\left({\left(a c^{4} d^{2} - 2 \, a c^{2} d^{4} + a d^{6}\right)} f \cos\left(f x + e\right) + {\left(a c^{5} d + a c^{4} d^{2} - 2 \, a c^{3} d^{3} - 2 \, a c^{2} d^{4} + a c d^{5} + a d^{6}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*((B*c^3 - (3*A - 2*B)*c^2*d - (4*A - 3*B)*c*d^2 - (A - 2*B)*d^3 - (B*c^2*d - (3*A - B)*c*d^2 - (A - 2*B)*d^3)*cos(f*x + e)^2 + (B*c^3 - (3*A - B)*c^2*d - (A - 2*B)*c*d^2)*cos(f*x + e) + (B*c^3 - (3*A - 2*B)*c^2*d - (4*A - 3*B)*c*d^2 - (A - 2*B)*d^3 + (B*c^2*d - (3*A - B)*c*d^2 - (A - 2*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*c*d + a*d^2)*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*sqrt(a*c*d + a*d^2)*(d*cos(f*x + e)^2 - (c + 2*d)*cos(f*x + e) + (d*cos(f*x + e) + c + 3*d)*sin(f*x + e) - c - 3*d)*sqrt(a*sin(f*x + e) + a) - (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))) - 2*sqrt(2)*((A - B)*a*c^3*d + 3*(A - B)*a*c^2*d^2 + 3*(A - B)*a*c*d^3 + (A - B)*a*d^4 - ((A - B)*a*c^2*d^2 + 2*(A - B)*a*c*d^3 + (A - B)*a*d^4)*cos(f*x + e)^2 + ((A - B)*a*c^3*d + 2*(A - B)*a*c^2*d^2 + (A - B)*a*c*d^3)*cos(f*x + e) + ((A - B)*a*c^3*d + 3*(A - B)*a*c^2*d^2 + 3*(A - B)*a*c*d^3 + (A - B)*a*d^4 + ((A - B)*a*c^2*d^2 + 2*(A - B)*a*c*d^3 + (A - B)*a*d^4)*cos(f*x + e))*sin(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))/sqrt(a) - 4*(B*c^3*d - A*c^2*d^2 - B*c*d^3 + A*d^4 + (B*c^3*d - A*c^2*d^2 - B*c*d^3 + A*d^4)*cos(f*x + e) - (B*c^3*d - A*c^2*d^2 - B*c*d^3 + A*d^4)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a*c^4*d^2 - 2*a*c^2*d^4 + a*d^6)*f*cos(f*x + e)^2 - (a*c^5*d - 2*a*c^3*d^3 + a*c*d^5)*f*cos(f*x + e) - (a*c^5*d + a*c^4*d^2 - 2*a*c^3*d^3 - 2*a*c^2*d^4 + a*c*d^5 + a*d^6)*f - ((a*c^4*d^2 - 2*a*c^2*d^4 + a*d^6)*f*cos(f*x + e) + (a*c^5*d + a*c^4*d^2 - 2*a*c^3*d^3 - 2*a*c^2*d^4 + a*c*d^5 + a*d^6)*f)*sin(f*x + e)), 1/2*((B*c^3 - (3*A - 2*B)*c^2*d - (4*A - 3*B)*c*d^2 - (A - 2*B)*d^3 - (B*c^2*d - (3*A - B)*c*d^2 - (A - 2*B)*d^3)*cos(f*x + e)^2 + (B*c^3 - (3*A - B)*c^2*d - (A - 2*B)*c*d^2)*cos(f*x + e) + (B*c^3 - (3*A - 2*B)*c^2*d - (4*A - 3*B)*c*d^2 - (A - 2*B)*d^3 + (B*c^2*d - (3*A - B)*c*d^2 - (A - 2*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(-a*c*d - a*d^2)*arctan(1/2*sqrt(-a*c*d - a*d^2)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)/((a*c*d + a*d^2)*cos(f*x + e))) + sqrt(2)*((A - B)*a*c^3*d + 3*(A - B)*a*c^2*d^2 + 3*(A - B)*a*c*d^3 + (A - B)*a*d^4 - ((A - B)*a*c^2*d^2 + 2*(A - B)*a*c*d^3 + (A - B)*a*d^4)*cos(f*x + e)^2 + ((A - B)*a*c^3*d + 2*(A - B)*a*c^2*d^2 + (A - B)*a*c*d^3)*cos(f*x + e) + ((A - B)*a*c^3*d + 3*(A - B)*a*c^2*d^2 + 3*(A - B)*a*c*d^3 + (A - B)*a*d^4 + ((A - B)*a*c^2*d^2 + 2*(A - B)*a*c*d^3 + (A - B)*a*d^4)*cos(f*x + e))*sin(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))/sqrt(a) + 2*(B*c^3*d - A*c^2*d^2 - B*c*d^3 + A*d^4 + (B*c^3*d - A*c^2*d^2 - B*c*d^3 + A*d^4)*cos(f*x + e) - (B*c^3*d - A*c^2*d^2 - B*c*d^3 + A*d^4)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a*c^4*d^2 - 2*a*c^2*d^4 + a*d^6)*f*cos(f*x + e)^2 - (a*c^5*d - 2*a*c^3*d^3 + a*c*d^5)*f*cos(f*x + e) - (a*c^5*d + a*c^4*d^2 - 2*a*c^3*d^3 - 2*a*c^2*d^4 + a*c*d^5 + a*d^6)*f - ((a*c^4*d^2 - 2*a*c^2*d^4 + a*d^6)*f*cos(f*x + e) + (a*c^5*d + a*c^4*d^2 - 2*a*c^3*d^3 - 2*a*c^2*d^4 + a*c*d^5 + a*d^6)*f)*sin(f*x + e))]","B",0
313,1,4180,0,11.756060," ","integrate((A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, B c^{5} - 3 \, {\left(5 \, A - 4 \, B\right)} c^{4} d - 2 \, {\left(20 \, A - 17 \, B\right)} c^{3} d^{2} - 6 \, {\left(7 \, A - 8 \, B\right)} c^{2} d^{3} - 3 \, {\left(8 \, A - 9 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5} - {\left(3 \, B c^{3} d^{2} - 3 \, {\left(5 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(10 \, A - 19 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(6 \, B c^{4} d - 15 \, {\left(2 \, A - B\right)} c^{3} d^{2} - {\left(35 \, A - 44 \, B\right)} c^{2} d^{3} - 3 \, {\left(8 \, A - 9 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B c^{5} - 3 \, {\left(5 \, A - 2 \, B\right)} c^{4} d - 2 \, {\left(5 \, A - 11 \, B\right)} c^{3} d^{2} - 2 \, {\left(11 \, A - 5 \, B\right)} c^{2} d^{3} - {\left(10 \, A - 19 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) + {\left(3 \, B c^{5} - 3 \, {\left(5 \, A - 4 \, B\right)} c^{4} d - 2 \, {\left(20 \, A - 17 \, B\right)} c^{3} d^{2} - 6 \, {\left(7 \, A - 8 \, B\right)} c^{2} d^{3} - 3 \, {\left(8 \, A - 9 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5} - {\left(3 \, B c^{3} d^{2} - 3 \, {\left(5 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(10 \, A - 19 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, B c^{4} d - 3 \, {\left(5 \, A - 2 \, B\right)} c^{3} d^{2} - {\left(10 \, A - 19 \, B\right)} c^{2} d^{3} - {\left(7 \, A - 4 \, B\right)} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a c d + a d^{2}} \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 \, \sqrt{a c d + a d^{2}} {\left(d \cos\left(f x + e\right)^{2} - {\left(c + 2 \, d\right)} \cos\left(f x + e\right) + {\left(d \cos\left(f x + e\right) + c + 3 \, d\right)} \sin\left(f x + e\right) - c - 3 \, d\right)} \sqrt{a \sin\left(f x + e\right) + a} - {\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) - \frac{8 \, \sqrt{2} {\left({\left(A - B\right)} a c^{5} d + 5 \, {\left(A - B\right)} a c^{4} d^{2} + 10 \, {\left(A - B\right)} a c^{3} d^{3} + 10 \, {\left(A - B\right)} a c^{2} d^{4} + 5 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6} - {\left({\left(A - B\right)} a c^{3} d^{3} + 3 \, {\left(A - B\right)} a c^{2} d^{4} + 3 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(2 \, {\left(A - B\right)} a c^{4} d^{2} + 7 \, {\left(A - B\right)} a c^{3} d^{3} + 9 \, {\left(A - B\right)} a c^{2} d^{4} + 5 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A - B\right)} a c^{5} d + 3 \, {\left(A - B\right)} a c^{4} d^{2} + 4 \, {\left(A - B\right)} a c^{3} d^{3} + 4 \, {\left(A - B\right)} a c^{2} d^{4} + 3 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6}\right)} \cos\left(f x + e\right) + {\left({\left(A - B\right)} a c^{5} d + 5 \, {\left(A - B\right)} a c^{4} d^{2} + 10 \, {\left(A - B\right)} a c^{3} d^{3} + 10 \, {\left(A - B\right)} a c^{2} d^{4} + 5 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6} - {\left({\left(A - B\right)} a c^{3} d^{3} + 3 \, {\left(A - B\right)} a c^{2} d^{4} + 3 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(A - B\right)} a c^{4} d^{2} + 3 \, {\left(A - B\right)} a c^{3} d^{3} + 3 \, {\left(A - B\right)} a c^{2} d^{4} + {\left(A - B\right)} a c d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\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)}{\sqrt{a}} + 4 \, {\left(5 \, B c^{5} d - {\left(9 \, A + 2 \, B\right)} c^{4} d^{2} + 2 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{3} + 2 \, {\left(6 \, A - B\right)} c^{2} d^{4} - {\left(6 \, A + B\right)} c d^{5} - {\left(3 \, A - 4 \, B\right)} d^{6} + {\left(3 \, B c^{4} d^{2} - {\left(7 \, A - B\right)} c^{3} d^{3} - {\left(A - B\right)} c^{2} d^{4} + {\left(7 \, A - B\right)} c d^{5} + {\left(A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(5 \, B c^{5} d - {\left(9 \, A - B\right)} c^{4} d^{2} - {\left(A + 3 \, B\right)} c^{3} d^{3} + {\left(11 \, A - B\right)} c^{2} d^{4} + {\left(A - 2 \, B\right)} c d^{5} - 2 \, A d^{6}\right)} \cos\left(f x + e\right) - {\left(5 \, B c^{5} d - {\left(9 \, A + 2 \, B\right)} c^{4} d^{2} + 2 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{3} + 2 \, {\left(6 \, A - B\right)} c^{2} d^{4} - {\left(6 \, A + B\right)} c d^{5} - {\left(3 \, A - 4 \, B\right)} d^{6} - {\left(3 \, B c^{4} d^{2} - {\left(7 \, A - B\right)} c^{3} d^{3} - {\left(A - B\right)} c^{2} d^{4} + {\left(7 \, A - B\right)} c d^{5} + {\left(A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{16 \, {\left({\left(a c^{6} d^{3} - 3 \, a c^{4} d^{5} + 3 \, a c^{2} d^{7} - a d^{9}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, a c^{7} d^{2} + a c^{6} d^{3} - 6 \, a c^{5} d^{4} - 3 \, a c^{4} d^{5} + 6 \, a c^{3} d^{6} + 3 \, a c^{2} d^{7} - 2 \, a c d^{8} - a d^{9}\right)} f \cos\left(f x + e\right)^{2} - {\left(a c^{8} d - 2 \, a c^{6} d^{3} + 2 \, a c^{2} d^{7} - a d^{9}\right)} f \cos\left(f x + e\right) - {\left(a c^{8} d + 2 \, a c^{7} d^{2} - 2 \, a c^{6} d^{3} - 6 \, a c^{5} d^{4} + 6 \, a c^{3} d^{6} + 2 \, a c^{2} d^{7} - 2 \, a c d^{8} - a d^{9}\right)} f + {\left({\left(a c^{6} d^{3} - 3 \, a c^{4} d^{5} + 3 \, a c^{2} d^{7} - a d^{9}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a c^{7} d^{2} - 3 \, a c^{5} d^{4} + 3 \, a c^{3} d^{6} - a c d^{8}\right)} f \cos\left(f x + e\right) - {\left(a c^{8} d + 2 \, a c^{7} d^{2} - 2 \, a c^{6} d^{3} - 6 \, a c^{5} d^{4} + 6 \, a c^{3} d^{6} + 2 \, a c^{2} d^{7} - 2 \, a c d^{8} - a d^{9}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{{\left(3 \, B c^{5} - 3 \, {\left(5 \, A - 4 \, B\right)} c^{4} d - 2 \, {\left(20 \, A - 17 \, B\right)} c^{3} d^{2} - 6 \, {\left(7 \, A - 8 \, B\right)} c^{2} d^{3} - 3 \, {\left(8 \, A - 9 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5} - {\left(3 \, B c^{3} d^{2} - 3 \, {\left(5 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(10 \, A - 19 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(6 \, B c^{4} d - 15 \, {\left(2 \, A - B\right)} c^{3} d^{2} - {\left(35 \, A - 44 \, B\right)} c^{2} d^{3} - 3 \, {\left(8 \, A - 9 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B c^{5} - 3 \, {\left(5 \, A - 2 \, B\right)} c^{4} d - 2 \, {\left(5 \, A - 11 \, B\right)} c^{3} d^{2} - 2 \, {\left(11 \, A - 5 \, B\right)} c^{2} d^{3} - {\left(10 \, A - 19 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) + {\left(3 \, B c^{5} - 3 \, {\left(5 \, A - 4 \, B\right)} c^{4} d - 2 \, {\left(20 \, A - 17 \, B\right)} c^{3} d^{2} - 6 \, {\left(7 \, A - 8 \, B\right)} c^{2} d^{3} - 3 \, {\left(8 \, A - 9 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5} - {\left(3 \, B c^{3} d^{2} - 3 \, {\left(5 \, A - 2 \, B\right)} c^{2} d^{3} - {\left(10 \, A - 19 \, B\right)} c d^{4} - {\left(7 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(3 \, B c^{4} d - 3 \, {\left(5 \, A - 2 \, B\right)} c^{3} d^{2} - {\left(10 \, A - 19 \, B\right)} c^{2} d^{3} - {\left(7 \, A - 4 \, B\right)} c d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{-a c d - a d^{2}} \arctan\left(\frac{\sqrt{-a c d - a d^{2}} \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) - c - 2 \, d\right)}}{2 \, {\left(a c d + a d^{2}\right)} \cos\left(f x + e\right)}\right) - \frac{4 \, \sqrt{2} {\left({\left(A - B\right)} a c^{5} d + 5 \, {\left(A - B\right)} a c^{4} d^{2} + 10 \, {\left(A - B\right)} a c^{3} d^{3} + 10 \, {\left(A - B\right)} a c^{2} d^{4} + 5 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6} - {\left({\left(A - B\right)} a c^{3} d^{3} + 3 \, {\left(A - B\right)} a c^{2} d^{4} + 3 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(2 \, {\left(A - B\right)} a c^{4} d^{2} + 7 \, {\left(A - B\right)} a c^{3} d^{3} + 9 \, {\left(A - B\right)} a c^{2} d^{4} + 5 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A - B\right)} a c^{5} d + 3 \, {\left(A - B\right)} a c^{4} d^{2} + 4 \, {\left(A - B\right)} a c^{3} d^{3} + 4 \, {\left(A - B\right)} a c^{2} d^{4} + 3 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6}\right)} \cos\left(f x + e\right) + {\left({\left(A - B\right)} a c^{5} d + 5 \, {\left(A - B\right)} a c^{4} d^{2} + 10 \, {\left(A - B\right)} a c^{3} d^{3} + 10 \, {\left(A - B\right)} a c^{2} d^{4} + 5 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6} - {\left({\left(A - B\right)} a c^{3} d^{3} + 3 \, {\left(A - B\right)} a c^{2} d^{4} + 3 \, {\left(A - B\right)} a c d^{5} + {\left(A - B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(A - B\right)} a c^{4} d^{2} + 3 \, {\left(A - B\right)} a c^{3} d^{3} + 3 \, {\left(A - B\right)} a c^{2} d^{4} + {\left(A - B\right)} a c d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\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)}{\sqrt{a}} + 2 \, {\left(5 \, B c^{5} d - {\left(9 \, A + 2 \, B\right)} c^{4} d^{2} + 2 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{3} + 2 \, {\left(6 \, A - B\right)} c^{2} d^{4} - {\left(6 \, A + B\right)} c d^{5} - {\left(3 \, A - 4 \, B\right)} d^{6} + {\left(3 \, B c^{4} d^{2} - {\left(7 \, A - B\right)} c^{3} d^{3} - {\left(A - B\right)} c^{2} d^{4} + {\left(7 \, A - B\right)} c d^{5} + {\left(A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left(5 \, B c^{5} d - {\left(9 \, A - B\right)} c^{4} d^{2} - {\left(A + 3 \, B\right)} c^{3} d^{3} + {\left(11 \, A - B\right)} c^{2} d^{4} + {\left(A - 2 \, B\right)} c d^{5} - 2 \, A d^{6}\right)} \cos\left(f x + e\right) - {\left(5 \, B c^{5} d - {\left(9 \, A + 2 \, B\right)} c^{4} d^{2} + 2 \, {\left(3 \, A - 2 \, B\right)} c^{3} d^{3} + 2 \, {\left(6 \, A - B\right)} c^{2} d^{4} - {\left(6 \, A + B\right)} c d^{5} - {\left(3 \, A - 4 \, B\right)} d^{6} - {\left(3 \, B c^{4} d^{2} - {\left(7 \, A - B\right)} c^{3} d^{3} - {\left(A - B\right)} c^{2} d^{4} + {\left(7 \, A - B\right)} c d^{5} + {\left(A - 4 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{8 \, {\left({\left(a c^{6} d^{3} - 3 \, a c^{4} d^{5} + 3 \, a c^{2} d^{7} - a d^{9}\right)} f \cos\left(f x + e\right)^{3} + {\left(2 \, a c^{7} d^{2} + a c^{6} d^{3} - 6 \, a c^{5} d^{4} - 3 \, a c^{4} d^{5} + 6 \, a c^{3} d^{6} + 3 \, a c^{2} d^{7} - 2 \, a c d^{8} - a d^{9}\right)} f \cos\left(f x + e\right)^{2} - {\left(a c^{8} d - 2 \, a c^{6} d^{3} + 2 \, a c^{2} d^{7} - a d^{9}\right)} f \cos\left(f x + e\right) - {\left(a c^{8} d + 2 \, a c^{7} d^{2} - 2 \, a c^{6} d^{3} - 6 \, a c^{5} d^{4} + 6 \, a c^{3} d^{6} + 2 \, a c^{2} d^{7} - 2 \, a c d^{8} - a d^{9}\right)} f + {\left({\left(a c^{6} d^{3} - 3 \, a c^{4} d^{5} + 3 \, a c^{2} d^{7} - a d^{9}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a c^{7} d^{2} - 3 \, a c^{5} d^{4} + 3 \, a c^{3} d^{6} - a c d^{8}\right)} f \cos\left(f x + e\right) - {\left(a c^{8} d + 2 \, a c^{7} d^{2} - 2 \, a c^{6} d^{3} - 6 \, a c^{5} d^{4} + 6 \, a c^{3} d^{6} + 2 \, a c^{2} d^{7} - 2 \, a c d^{8} - a d^{9}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*((3*B*c^5 - 3*(5*A - 4*B)*c^4*d - 2*(20*A - 17*B)*c^3*d^2 - 6*(7*A - 8*B)*c^2*d^3 - 3*(8*A - 9*B)*c*d^4 - (7*A - 4*B)*d^5 - (3*B*c^3*d^2 - 3*(5*A - 2*B)*c^2*d^3 - (10*A - 19*B)*c*d^4 - (7*A - 4*B)*d^5)*cos(f*x + e)^3 - (6*B*c^4*d - 15*(2*A - B)*c^3*d^2 - (35*A - 44*B)*c^2*d^3 - 3*(8*A - 9*B)*c*d^4 - (7*A - 4*B)*d^5)*cos(f*x + e)^2 + (3*B*c^5 - 3*(5*A - 2*B)*c^4*d - 2*(5*A - 11*B)*c^3*d^2 - 2*(11*A - 5*B)*c^2*d^3 - (10*A - 19*B)*c*d^4 - (7*A - 4*B)*d^5)*cos(f*x + e) + (3*B*c^5 - 3*(5*A - 4*B)*c^4*d - 2*(20*A - 17*B)*c^3*d^2 - 6*(7*A - 8*B)*c^2*d^3 - 3*(8*A - 9*B)*c*d^4 - (7*A - 4*B)*d^5 - (3*B*c^3*d^2 - 3*(5*A - 2*B)*c^2*d^3 - (10*A - 19*B)*c*d^4 - (7*A - 4*B)*d^5)*cos(f*x + e)^2 + 2*(3*B*c^4*d - 3*(5*A - 2*B)*c^3*d^2 - (10*A - 19*B)*c^2*d^3 - (7*A - 4*B)*c*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a*c*d + a*d^2)*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*sqrt(a*c*d + a*d^2)*(d*cos(f*x + e)^2 - (c + 2*d)*cos(f*x + e) + (d*cos(f*x + e) + c + 3*d)*sin(f*x + e) - c - 3*d)*sqrt(a*sin(f*x + e) + a) - (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))) - 8*sqrt(2)*((A - B)*a*c^5*d + 5*(A - B)*a*c^4*d^2 + 10*(A - B)*a*c^3*d^3 + 10*(A - B)*a*c^2*d^4 + 5*(A - B)*a*c*d^5 + (A - B)*a*d^6 - ((A - B)*a*c^3*d^3 + 3*(A - B)*a*c^2*d^4 + 3*(A - B)*a*c*d^5 + (A - B)*a*d^6)*cos(f*x + e)^3 - (2*(A - B)*a*c^4*d^2 + 7*(A - B)*a*c^3*d^3 + 9*(A - B)*a*c^2*d^4 + 5*(A - B)*a*c*d^5 + (A - B)*a*d^6)*cos(f*x + e)^2 + ((A - B)*a*c^5*d + 3*(A - B)*a*c^4*d^2 + 4*(A - B)*a*c^3*d^3 + 4*(A - B)*a*c^2*d^4 + 3*(A - B)*a*c*d^5 + (A - B)*a*d^6)*cos(f*x + e) + ((A - B)*a*c^5*d + 5*(A - B)*a*c^4*d^2 + 10*(A - B)*a*c^3*d^3 + 10*(A - B)*a*c^2*d^4 + 5*(A - B)*a*c*d^5 + (A - B)*a*d^6 - ((A - B)*a*c^3*d^3 + 3*(A - B)*a*c^2*d^4 + 3*(A - B)*a*c*d^5 + (A - B)*a*d^6)*cos(f*x + e)^2 + 2*((A - B)*a*c^4*d^2 + 3*(A - B)*a*c^3*d^3 + 3*(A - B)*a*c^2*d^4 + (A - B)*a*c*d^5)*cos(f*x + e))*sin(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))/sqrt(a) + 4*(5*B*c^5*d - (9*A + 2*B)*c^4*d^2 + 2*(3*A - 2*B)*c^3*d^3 + 2*(6*A - B)*c^2*d^4 - (6*A + B)*c*d^5 - (3*A - 4*B)*d^6 + (3*B*c^4*d^2 - (7*A - B)*c^3*d^3 - (A - B)*c^2*d^4 + (7*A - B)*c*d^5 + (A - 4*B)*d^6)*cos(f*x + e)^2 + (5*B*c^5*d - (9*A - B)*c^4*d^2 - (A + 3*B)*c^3*d^3 + (11*A - B)*c^2*d^4 + (A - 2*B)*c*d^5 - 2*A*d^6)*cos(f*x + e) - (5*B*c^5*d - (9*A + 2*B)*c^4*d^2 + 2*(3*A - 2*B)*c^3*d^3 + 2*(6*A - B)*c^2*d^4 - (6*A + B)*c*d^5 - (3*A - 4*B)*d^6 - (3*B*c^4*d^2 - (7*A - B)*c^3*d^3 - (A - B)*c^2*d^4 + (7*A - B)*c*d^5 + (A - 4*B)*d^6)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a*c^6*d^3 - 3*a*c^4*d^5 + 3*a*c^2*d^7 - a*d^9)*f*cos(f*x + e)^3 + (2*a*c^7*d^2 + a*c^6*d^3 - 6*a*c^5*d^4 - 3*a*c^4*d^5 + 6*a*c^3*d^6 + 3*a*c^2*d^7 - 2*a*c*d^8 - a*d^9)*f*cos(f*x + e)^2 - (a*c^8*d - 2*a*c^6*d^3 + 2*a*c^2*d^7 - a*d^9)*f*cos(f*x + e) - (a*c^8*d + 2*a*c^7*d^2 - 2*a*c^6*d^3 - 6*a*c^5*d^4 + 6*a*c^3*d^6 + 2*a*c^2*d^7 - 2*a*c*d^8 - a*d^9)*f + ((a*c^6*d^3 - 3*a*c^4*d^5 + 3*a*c^2*d^7 - a*d^9)*f*cos(f*x + e)^2 - 2*(a*c^7*d^2 - 3*a*c^5*d^4 + 3*a*c^3*d^6 - a*c*d^8)*f*cos(f*x + e) - (a*c^8*d + 2*a*c^7*d^2 - 2*a*c^6*d^3 - 6*a*c^5*d^4 + 6*a*c^3*d^6 + 2*a*c^2*d^7 - 2*a*c*d^8 - a*d^9)*f)*sin(f*x + e)), 1/8*((3*B*c^5 - 3*(5*A - 4*B)*c^4*d - 2*(20*A - 17*B)*c^3*d^2 - 6*(7*A - 8*B)*c^2*d^3 - 3*(8*A - 9*B)*c*d^4 - (7*A - 4*B)*d^5 - (3*B*c^3*d^2 - 3*(5*A - 2*B)*c^2*d^3 - (10*A - 19*B)*c*d^4 - (7*A - 4*B)*d^5)*cos(f*x + e)^3 - (6*B*c^4*d - 15*(2*A - B)*c^3*d^2 - (35*A - 44*B)*c^2*d^3 - 3*(8*A - 9*B)*c*d^4 - (7*A - 4*B)*d^5)*cos(f*x + e)^2 + (3*B*c^5 - 3*(5*A - 2*B)*c^4*d - 2*(5*A - 11*B)*c^3*d^2 - 2*(11*A - 5*B)*c^2*d^3 - (10*A - 19*B)*c*d^4 - (7*A - 4*B)*d^5)*cos(f*x + e) + (3*B*c^5 - 3*(5*A - 4*B)*c^4*d - 2*(20*A - 17*B)*c^3*d^2 - 6*(7*A - 8*B)*c^2*d^3 - 3*(8*A - 9*B)*c*d^4 - (7*A - 4*B)*d^5 - (3*B*c^3*d^2 - 3*(5*A - 2*B)*c^2*d^3 - (10*A - 19*B)*c*d^4 - (7*A - 4*B)*d^5)*cos(f*x + e)^2 + 2*(3*B*c^4*d - 3*(5*A - 2*B)*c^3*d^2 - (10*A - 19*B)*c^2*d^3 - (7*A - 4*B)*c*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(-a*c*d - a*d^2)*arctan(1/2*sqrt(-a*c*d - a*d^2)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) - c - 2*d)/((a*c*d + a*d^2)*cos(f*x + e))) - 4*sqrt(2)*((A - B)*a*c^5*d + 5*(A - B)*a*c^4*d^2 + 10*(A - B)*a*c^3*d^3 + 10*(A - B)*a*c^2*d^4 + 5*(A - B)*a*c*d^5 + (A - B)*a*d^6 - ((A - B)*a*c^3*d^3 + 3*(A - B)*a*c^2*d^4 + 3*(A - B)*a*c*d^5 + (A - B)*a*d^6)*cos(f*x + e)^3 - (2*(A - B)*a*c^4*d^2 + 7*(A - B)*a*c^3*d^3 + 9*(A - B)*a*c^2*d^4 + 5*(A - B)*a*c*d^5 + (A - B)*a*d^6)*cos(f*x + e)^2 + ((A - B)*a*c^5*d + 3*(A - B)*a*c^4*d^2 + 4*(A - B)*a*c^3*d^3 + 4*(A - B)*a*c^2*d^4 + 3*(A - B)*a*c*d^5 + (A - B)*a*d^6)*cos(f*x + e) + ((A - B)*a*c^5*d + 5*(A - B)*a*c^4*d^2 + 10*(A - B)*a*c^3*d^3 + 10*(A - B)*a*c^2*d^4 + 5*(A - B)*a*c*d^5 + (A - B)*a*d^6 - ((A - B)*a*c^3*d^3 + 3*(A - B)*a*c^2*d^4 + 3*(A - B)*a*c*d^5 + (A - B)*a*d^6)*cos(f*x + e)^2 + 2*((A - B)*a*c^4*d^2 + 3*(A - B)*a*c^3*d^3 + 3*(A - B)*a*c^2*d^4 + (A - B)*a*c*d^5)*cos(f*x + e))*sin(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))/sqrt(a) + 2*(5*B*c^5*d - (9*A + 2*B)*c^4*d^2 + 2*(3*A - 2*B)*c^3*d^3 + 2*(6*A - B)*c^2*d^4 - (6*A + B)*c*d^5 - (3*A - 4*B)*d^6 + (3*B*c^4*d^2 - (7*A - B)*c^3*d^3 - (A - B)*c^2*d^4 + (7*A - B)*c*d^5 + (A - 4*B)*d^6)*cos(f*x + e)^2 + (5*B*c^5*d - (9*A - B)*c^4*d^2 - (A + 3*B)*c^3*d^3 + (11*A - B)*c^2*d^4 + (A - 2*B)*c*d^5 - 2*A*d^6)*cos(f*x + e) - (5*B*c^5*d - (9*A + 2*B)*c^4*d^2 + 2*(3*A - 2*B)*c^3*d^3 + 2*(6*A - B)*c^2*d^4 - (6*A + B)*c*d^5 - (3*A - 4*B)*d^6 - (3*B*c^4*d^2 - (7*A - B)*c^3*d^3 - (A - B)*c^2*d^4 + (7*A - B)*c*d^5 + (A - 4*B)*d^6)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a*c^6*d^3 - 3*a*c^4*d^5 + 3*a*c^2*d^7 - a*d^9)*f*cos(f*x + e)^3 + (2*a*c^7*d^2 + a*c^6*d^3 - 6*a*c^5*d^4 - 3*a*c^4*d^5 + 6*a*c^3*d^6 + 3*a*c^2*d^7 - 2*a*c*d^8 - a*d^9)*f*cos(f*x + e)^2 - (a*c^8*d - 2*a*c^6*d^3 + 2*a*c^2*d^7 - a*d^9)*f*cos(f*x + e) - (a*c^8*d + 2*a*c^7*d^2 - 2*a*c^6*d^3 - 6*a*c^5*d^4 + 6*a*c^3*d^6 + 2*a*c^2*d^7 - 2*a*c*d^8 - a*d^9)*f + ((a*c^6*d^3 - 3*a*c^4*d^5 + 3*a*c^2*d^7 - a*d^9)*f*cos(f*x + e)^2 - 2*(a*c^7*d^2 - 3*a*c^5*d^4 + 3*a*c^3*d^6 - a*c*d^8)*f*cos(f*x + e) - (a*c^8*d + 2*a*c^7*d^2 - 2*a*c^6*d^3 - 6*a*c^5*d^4 + 6*a*c^3*d^6 + 2*a*c^2*d^7 - 2*a*c*d^8 - a*d^9)*f)*sin(f*x + e))]","B",0
314,1,784,0,0.829984," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{15 \, \sqrt{2} {\left(2 \, {\left(A + 3 \, B\right)} c^{3} + 6 \, {\left(3 \, A - 7 \, B\right)} c^{2} d - 6 \, {\left(7 \, A - 11 \, B\right)} c d^{2} + 2 \, {\left(11 \, A - 15 \, B\right)} d^{3} - {\left({\left(A + 3 \, B\right)} c^{3} + 3 \, {\left(3 \, A - 7 \, B\right)} c^{2} d - 3 \, {\left(7 \, A - 11 \, B\right)} c d^{2} + {\left(11 \, A - 15 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{3} + 3 \, {\left(3 \, A - 7 \, B\right)} c^{2} d - 3 \, {\left(7 \, A - 11 \, B\right)} c d^{2} + {\left(11 \, A - 15 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(2 \, {\left(A + 3 \, B\right)} c^{3} + 6 \, {\left(3 \, A - 7 \, B\right)} c^{2} d - 6 \, {\left(7 \, A - 11 \, B\right)} c d^{2} + 2 \, {\left(11 \, A - 15 \, B\right)} d^{3} + {\left({\left(A + 3 \, B\right)} c^{3} + 3 \, {\left(3 \, A - 7 \, B\right)} c^{2} d - 3 \, {\left(7 \, A - 11 \, B\right)} c d^{2} + {\left(11 \, A - 15 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) - 4 \, {\left(12 \, B d^{3} \cos\left(f x + e\right)^{4} - 15 \, {\left(A - B\right)} c^{3} + 45 \, {\left(A - B\right)} c^{2} d - 45 \, {\left(A - B\right)} c d^{2} + 15 \, {\left(A - B\right)} d^{3} + 4 \, {\left(15 \, B c d^{2} + {\left(5 \, A - 3 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - 4 \, {\left(45 \, B c^{2} d + 15 \, {\left(3 \, A - 4 \, B\right)} c d^{2} - 4 \, {\left(5 \, A - 9 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - 15 \, {\left({\left(A - B\right)} c^{3} - 3 \, {\left(A - 5 \, B\right)} c^{2} d + 15 \, {\left(A - B\right)} c d^{2} - {\left(5 \, A - 9 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(12 \, B d^{3} \cos\left(f x + e\right)^{3} + 15 \, {\left(A - B\right)} c^{3} - 45 \, {\left(A - B\right)} c^{2} d + 45 \, {\left(A - B\right)} c d^{2} - 15 \, {\left(A - B\right)} d^{3} - 4 \, {\left(15 \, B c d^{2} + {\left(5 \, A - 6 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - 60 \, {\left(3 \, B c^{2} d + 3 \, {\left(A - B\right)} c d^{2} - {\left(A - 2 \, B\right)} 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}}{120 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/120*(15*sqrt(2)*(2*(A + 3*B)*c^3 + 6*(3*A - 7*B)*c^2*d - 6*(7*A - 11*B)*c*d^2 + 2*(11*A - 15*B)*d^3 - ((A + 3*B)*c^3 + 3*(3*A - 7*B)*c^2*d - 3*(7*A - 11*B)*c*d^2 + (11*A - 15*B)*d^3)*cos(f*x + e)^2 + ((A + 3*B)*c^3 + 3*(3*A - 7*B)*c^2*d - 3*(7*A - 11*B)*c*d^2 + (11*A - 15*B)*d^3)*cos(f*x + e) + (2*(A + 3*B)*c^3 + 6*(3*A - 7*B)*c^2*d - 6*(7*A - 11*B)*c*d^2 + 2*(11*A - 15*B)*d^3 + ((A + 3*B)*c^3 + 3*(3*A - 7*B)*c^2*d - 3*(7*A - 11*B)*c*d^2 + (11*A - 15*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(12*B*d^3*cos(f*x + e)^4 - 15*(A - B)*c^3 + 45*(A - B)*c^2*d - 45*(A - B)*c*d^2 + 15*(A - B)*d^3 + 4*(15*B*c*d^2 + (5*A - 3*B)*d^3)*cos(f*x + e)^3 - 4*(45*B*c^2*d + 15*(3*A - 4*B)*c*d^2 - 4*(5*A - 9*B)*d^3)*cos(f*x + e)^2 - 15*((A - B)*c^3 - 3*(A - 5*B)*c^2*d + 15*(A - B)*c*d^2 - (5*A - 9*B)*d^3)*cos(f*x + e) + (12*B*d^3*cos(f*x + e)^3 + 15*(A - B)*c^3 - 45*(A - B)*c^2*d + 45*(A - B)*c*d^2 - 15*(A - B)*d^3 - 4*(15*B*c*d^2 + (5*A - 6*B)*d^3)*cos(f*x + e)^2 - 60*(3*B*c^2*d + 3*(A - B)*c*d^2 - (A - 2*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
315,1,584,0,0.702607," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left(2 \, {\left(A + 3 \, B\right)} c^{2} + 4 \, {\left(3 \, A - 7 \, B\right)} c d - 2 \, {\left(7 \, A - 11 \, B\right)} d^{2} - {\left({\left(A + 3 \, B\right)} c^{2} + 2 \, {\left(3 \, A - 7 \, B\right)} c d - {\left(7 \, A - 11 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{2} + 2 \, {\left(3 \, A - 7 \, B\right)} c d - {\left(7 \, A - 11 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) + {\left(2 \, {\left(A + 3 \, B\right)} c^{2} + 4 \, {\left(3 \, A - 7 \, B\right)} c d - 2 \, {\left(7 \, A - 11 \, B\right)} d^{2} + {\left({\left(A + 3 \, B\right)} c^{2} + 2 \, {\left(3 \, A - 7 \, B\right)} c d - {\left(7 \, A - 11 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 4 \, {\left(4 \, B d^{2} \cos\left(f x + e\right)^{3} - 3 \, {\left(A - B\right)} c^{2} + 6 \, {\left(A - B\right)} c d - 3 \, {\left(A - B\right)} d^{2} - 4 \, {\left(6 \, B c d + {\left(3 \, A - 4 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(A - B\right)} c^{2} - 2 \, {\left(A - 5 \, B\right)} c d + 5 \, {\left(A - B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left(4 \, B d^{2} \cos\left(f x + e\right)^{2} - 3 \, {\left(A - B\right)} c^{2} + 6 \, {\left(A - B\right)} c d - 3 \, {\left(A - B\right)} d^{2} + 12 \, {\left(2 \, B c d + {\left(A - B\right)} 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}}{24 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/24*(3*sqrt(2)*(2*(A + 3*B)*c^2 + 4*(3*A - 7*B)*c*d - 2*(7*A - 11*B)*d^2 - ((A + 3*B)*c^2 + 2*(3*A - 7*B)*c*d - (7*A - 11*B)*d^2)*cos(f*x + e)^2 + ((A + 3*B)*c^2 + 2*(3*A - 7*B)*c*d - (7*A - 11*B)*d^2)*cos(f*x + e) + (2*(A + 3*B)*c^2 + 4*(3*A - 7*B)*c*d - 2*(7*A - 11*B)*d^2 + ((A + 3*B)*c^2 + 2*(3*A - 7*B)*c*d - (7*A - 11*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(4*B*d^2*cos(f*x + e)^3 - 3*(A - B)*c^2 + 6*(A - B)*c*d - 3*(A - B)*d^2 - 4*(6*B*c*d + (3*A - 4*B)*d^2)*cos(f*x + e)^2 - 3*((A - B)*c^2 - 2*(A - 5*B)*c*d + 5*(A - B)*d^2)*cos(f*x + e) - (4*B*d^2*cos(f*x + e)^2 - 3*(A - B)*c^2 + 6*(A - B)*c*d - 3*(A - B)*d^2 + 12*(2*B*c*d + (A - B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
316,1,407,0,0.703165," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left({\left(A + 3 \, B\right)} c + {\left(3 \, A - 7 \, B\right)} d\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + 3 \, B\right)} c - 2 \, {\left(3 \, A - 7 \, B\right)} d - {\left({\left(A + 3 \, B\right)} c + {\left(3 \, A - 7 \, B\right)} d\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(A + 3 \, B\right)} c + 2 \, {\left(3 \, A - 7 \, B\right)} d + {\left({\left(A + 3 \, B\right)} c + {\left(3 \, A - 7 \, B\right)} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) - 4 \, {\left(4 \, B d \cos\left(f x + e\right)^{2} + {\left(A - B\right)} c - {\left(A - B\right)} d + {\left({\left(A - B\right)} c - {\left(A - 5 \, B\right)} d\right)} \cos\left(f x + e\right) + {\left(4 \, B d \cos\left(f x + e\right) - {\left(A - B\right)} c + {\left(A - B\right)} d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{8 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/8*(sqrt(2)*(((A + 3*B)*c + (3*A - 7*B)*d)*cos(f*x + e)^2 - 2*(A + 3*B)*c - 2*(3*A - 7*B)*d - ((A + 3*B)*c + (3*A - 7*B)*d)*cos(f*x + e) - (2*(A + 3*B)*c + 2*(3*A - 7*B)*d + ((A + 3*B)*c + (3*A - 7*B)*d)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(4*B*d*cos(f*x + e)^2 + (A - B)*c - (A - B)*d + ((A - B)*c - (A - 5*B)*d)*cos(f*x + e) + (4*B*d*cos(f*x + e) - (A - B)*c + (A - B)*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
317,1,293,0,0.621980," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(A + 3 \, B\right)} \cos\left(f x + e\right)^{2} - {\left(A + 3 \, B\right)} \cos\left(f x + e\right) - {\left({\left(A + 3 \, B\right)} \cos\left(f x + e\right) + 2 \, A + 6 \, B\right)} \sin\left(f x + e\right) - 2 \, A - 6 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 4 \, {\left({\left(A - B\right)} \cos\left(f x + e\right) - {\left(A - B\right)} \sin\left(f x + e\right) + A - B\right)} \sqrt{a \sin\left(f x + e\right) + a}}{8 \, {\left(a^{2} f \cos\left(f x + e\right)^{2} - a^{2} f \cos\left(f x + e\right) - 2 \, a^{2} f - {\left(a^{2} f \cos\left(f x + e\right) + 2 \, a^{2} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/8*(sqrt(2)*((A + 3*B)*cos(f*x + e)^2 - (A + 3*B)*cos(f*x + e) - ((A + 3*B)*cos(f*x + e) + 2*A + 6*B)*sin(f*x + e) - 2*A - 6*B)*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*((A - B)*cos(f*x + e) - (A - B)*sin(f*x + e) + A - B)*sqrt(a*sin(f*x + e) + a))/(a^2*f*cos(f*x + e)^2 - a^2*f*cos(f*x + e) - 2*a^2*f - (a^2*f*cos(f*x + e) + 2*a^2*f)*sin(f*x + e))","B",0
318,1,1561,0,4.476704," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left({\left(A + 3 \, B\right)} c - {\left(5 \, A - B\right)} d\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + 3 \, B\right)} c + 2 \, {\left(5 \, A - B\right)} d - {\left({\left(A + 3 \, B\right)} c - {\left(5 \, A - B\right)} d\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(A + 3 \, B\right)} c - 2 \, {\left(5 \, A - B\right)} d + {\left({\left(A + 3 \, B\right)} c - {\left(5 \, A - B\right)} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 4 \, {\left(2 \, B a c - 2 \, A a d - {\left(B a c - A a d\right)} \cos\left(f x + e\right)^{2} + {\left(B a c - A a d\right)} \cos\left(f x + e\right) + {\left(2 \, B a c - 2 \, A a d + {\left(B a c - A a d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) + 4 \, {\left({\left(A - B\right)} c - {\left(A - B\right)} d + {\left({\left(A - B\right)} c - {\left(A - B\right)} d\right)} \cos\left(f x + e\right) - {\left({\left(A - B\right)} c - {\left(A - B\right)} d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{8 \, {\left({\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f - {\left({\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{\sqrt{2} {\left({\left({\left(A + 3 \, B\right)} c - {\left(5 \, A - B\right)} d\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + 3 \, B\right)} c + 2 \, {\left(5 \, A - B\right)} d - {\left({\left(A + 3 \, B\right)} c - {\left(5 \, A - B\right)} d\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(A + 3 \, B\right)} c - 2 \, {\left(5 \, A - B\right)} d + {\left({\left(A + 3 \, B\right)} c - {\left(5 \, A - B\right)} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) - 8 \, {\left(2 \, B a c - 2 \, A a d - {\left(B a c - A a d\right)} \cos\left(f x + e\right)^{2} + {\left(B a c - A a d\right)} \cos\left(f x + e\right) + {\left(2 \, B a c - 2 \, A a d + {\left(B a c - A a d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) + 4 \, {\left({\left(A - B\right)} c - {\left(A - B\right)} d + {\left({\left(A - B\right)} c - {\left(A - B\right)} d\right)} \cos\left(f x + e\right) - {\left({\left(A - B\right)} c - {\left(A - B\right)} d\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{8 \, {\left({\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f - {\left({\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{2} - 2 \, a^{2} c d + a^{2} d^{2}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/8*(sqrt(2)*(((A + 3*B)*c - (5*A - B)*d)*cos(f*x + e)^2 - 2*(A + 3*B)*c + 2*(5*A - B)*d - ((A + 3*B)*c - (5*A - B)*d)*cos(f*x + e) - (2*(A + 3*B)*c - 2*(5*A - B)*d + ((A + 3*B)*c - (5*A - B)*d)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(2*B*a*c - 2*A*a*d - (B*a*c - A*a*d)*cos(f*x + e)^2 + (B*a*c - A*a*d)*cos(f*x + e) + (2*B*a*c - 2*A*a*d + (B*a*c - A*a*d)*cos(f*x + e))*sin(f*x + e))*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))) + 4*((A - B)*c - (A - B)*d + ((A - B)*c - (A - B)*d)*cos(f*x + e) - ((A - B)*c - (A - B)*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f*cos(f*x + e)^2 - (a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f*cos(f*x + e) - 2*(a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f - ((a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f*cos(f*x + e) + 2*(a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f)*sin(f*x + e)), 1/8*(sqrt(2)*(((A + 3*B)*c - (5*A - B)*d)*cos(f*x + e)^2 - 2*(A + 3*B)*c + 2*(5*A - B)*d - ((A + 3*B)*c - (5*A - B)*d)*cos(f*x + e) - (2*(A + 3*B)*c - 2*(5*A - B)*d + ((A + 3*B)*c - (5*A - B)*d)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 8*(2*B*a*c - 2*A*a*d - (B*a*c - A*a*d)*cos(f*x + e)^2 + (B*a*c - A*a*d)*cos(f*x + e) + (2*B*a*c - 2*A*a*d + (B*a*c - A*a*d)*cos(f*x + e))*sin(f*x + e))*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))) + 4*((A - B)*c - (A - B)*d + ((A - B)*c - (A - B)*d)*cos(f*x + e) - ((A - B)*c - (A - B)*d)*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f*cos(f*x + e)^2 - (a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f*cos(f*x + e) - 2*(a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f - ((a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f*cos(f*x + e) + 2*(a^2*c^2 - 2*a^2*c*d + a^2*d^2)*f)*sin(f*x + e))]","B",0
319,1,3403,0,10.833533," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(2 \, {\left(A + 3 \, B\right)} c^{3} - 2 \, {\left(7 \, A - 11 \, B\right)} c^{2} d - 2 \, {\left(17 \, A - 13 \, B\right)} c d^{2} - 2 \, {\left(9 \, A - 5 \, B\right)} d^{3} - {\left({\left(A + 3 \, B\right)} c^{2} d - 8 \, {\left(A - B\right)} c d^{2} - {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(A + 3 \, B\right)} c^{3} - 2 \, {\left(3 \, A - 7 \, B\right)} c^{2} d - {\left(25 \, A - 21 \, B\right)} c d^{2} - 2 \, {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{3} - {\left(7 \, A - 11 \, B\right)} c^{2} d - {\left(17 \, A - 13 \, B\right)} c d^{2} - {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(2 \, {\left(A + 3 \, B\right)} c^{3} - 2 \, {\left(7 \, A - 11 \, B\right)} c^{2} d - 2 \, {\left(17 \, A - 13 \, B\right)} c d^{2} - 2 \, {\left(9 \, A - 5 \, B\right)} d^{3} - {\left({\left(A + 3 \, B\right)} c^{2} d - 8 \, {\left(A - B\right)} c d^{2} - {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{3} - {\left(7 \, A - 11 \, B\right)} c^{2} d - {\left(17 \, A - 13 \, B\right)} c d^{2} - {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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 \, {\left(6 \, B a c^{3} - 2 \, {\left(5 \, A - 6 \, B\right)} a c^{2} d - 2 \, {\left(8 \, A - 5 \, B\right)} a c d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} a d^{3} - {\left(3 \, B a c^{2} d - {\left(5 \, A - 3 \, B\right)} a c d^{2} - {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(3 \, B a c^{3} - {\left(5 \, A - 9 \, B\right)} a c^{2} d - {\left(13 \, A - 8 \, B\right)} a c d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{3} - {\left(5 \, A - 6 \, B\right)} a c^{2} d - {\left(8 \, A - 5 \, B\right)} a c d^{2} - {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right) + {\left(6 \, B a c^{3} - 2 \, {\left(5 \, A - 6 \, B\right)} a c^{2} d - 2 \, {\left(8 \, A - 5 \, B\right)} a c d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} a d^{3} - {\left(3 \, B a c^{2} d - {\left(5 \, A - 3 \, B\right)} a c d^{2} - {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{3} - {\left(5 \, A - 6 \, B\right)} a c^{2} d - {\left(8 \, A - 5 \, B\right)} a c d^{2} - {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) + 4 \, {\left({\left(A - B\right)} c^{3} - {\left(A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2} + {\left(A - B\right)} d^{3} + {\left({\left(A - 3 \, B\right)} c^{2} d + 2 \, {\left(A + B\right)} c d^{2} - {\left(3 \, A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A - B\right)} c^{3} - 2 \, B c^{2} d + {\left(A + 3 \, B\right)} c d^{2} - 2 \, A d^{3}\right)} \cos\left(f x + e\right) - {\left({\left(A - B\right)} c^{3} - {\left(A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2} + {\left(A - B\right)} d^{3} - {\left({\left(A - 3 \, B\right)} c^{2} d + 2 \, {\left(A + B\right)} c d^{2} - {\left(3 \, A - B\right)} 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}}{8 \, {\left({\left(a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c d^{4} - a^{2} d^{5}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{5} - 4 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + 3 \, a^{2} c d^{4} - 2 \, a^{2} d^{5}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{5} - a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + a^{2} c d^{4} - a^{2} d^{5}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{5} - a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + a^{2} c d^{4} - a^{2} d^{5}\right)} f + {\left({\left(a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c d^{4} - a^{2} d^{5}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{5} - a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + a^{2} c d^{4} - a^{2} d^{5}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{5} - a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + a^{2} c d^{4} - a^{2} d^{5}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{\sqrt{2} {\left(2 \, {\left(A + 3 \, B\right)} c^{3} - 2 \, {\left(7 \, A - 11 \, B\right)} c^{2} d - 2 \, {\left(17 \, A - 13 \, B\right)} c d^{2} - 2 \, {\left(9 \, A - 5 \, B\right)} d^{3} - {\left({\left(A + 3 \, B\right)} c^{2} d - 8 \, {\left(A - B\right)} c d^{2} - {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(A + 3 \, B\right)} c^{3} - 2 \, {\left(3 \, A - 7 \, B\right)} c^{2} d - {\left(25 \, A - 21 \, B\right)} c d^{2} - 2 \, {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{3} - {\left(7 \, A - 11 \, B\right)} c^{2} d - {\left(17 \, A - 13 \, B\right)} c d^{2} - {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(2 \, {\left(A + 3 \, B\right)} c^{3} - 2 \, {\left(7 \, A - 11 \, B\right)} c^{2} d - 2 \, {\left(17 \, A - 13 \, B\right)} c d^{2} - 2 \, {\left(9 \, A - 5 \, B\right)} d^{3} - {\left({\left(A + 3 \, B\right)} c^{2} d - 8 \, {\left(A - B\right)} c d^{2} - {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{3} - {\left(7 \, A - 11 \, B\right)} c^{2} d - {\left(17 \, A - 13 \, B\right)} c d^{2} - {\left(9 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) - 4 \, {\left(6 \, B a c^{3} - 2 \, {\left(5 \, A - 6 \, B\right)} a c^{2} d - 2 \, {\left(8 \, A - 5 \, B\right)} a c d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} a d^{3} - {\left(3 \, B a c^{2} d - {\left(5 \, A - 3 \, B\right)} a c d^{2} - {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{3} - {\left(3 \, B a c^{3} - {\left(5 \, A - 9 \, B\right)} a c^{2} d - {\left(13 \, A - 8 \, B\right)} a c d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{3} - {\left(5 \, A - 6 \, B\right)} a c^{2} d - {\left(8 \, A - 5 \, B\right)} a c d^{2} - {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right) + {\left(6 \, B a c^{3} - 2 \, {\left(5 \, A - 6 \, B\right)} a c^{2} d - 2 \, {\left(8 \, A - 5 \, B\right)} a c d^{2} - 2 \, {\left(3 \, A - 2 \, B\right)} a d^{3} - {\left(3 \, B a c^{2} d - {\left(5 \, A - 3 \, B\right)} a c d^{2} - {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left(3 \, B a c^{3} - {\left(5 \, A - 6 \, B\right)} a c^{2} d - {\left(8 \, A - 5 \, B\right)} a c d^{2} - {\left(3 \, A - 2 \, B\right)} a d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) + 4 \, {\left({\left(A - B\right)} c^{3} - {\left(A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2} + {\left(A - B\right)} d^{3} + {\left({\left(A - 3 \, B\right)} c^{2} d + 2 \, {\left(A + B\right)} c d^{2} - {\left(3 \, A - B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A - B\right)} c^{3} - 2 \, B c^{2} d + {\left(A + 3 \, B\right)} c d^{2} - 2 \, A d^{3}\right)} \cos\left(f x + e\right) - {\left({\left(A - B\right)} c^{3} - {\left(A - B\right)} c^{2} d - {\left(A - B\right)} c d^{2} + {\left(A - B\right)} d^{3} - {\left({\left(A - 3 \, B\right)} c^{2} d + 2 \, {\left(A + B\right)} c d^{2} - {\left(3 \, A - B\right)} 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}}{8 \, {\left({\left(a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c d^{4} - a^{2} d^{5}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{2} c^{5} - 4 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + 3 \, a^{2} c d^{4} - 2 \, a^{2} d^{5}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{5} - a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + a^{2} c d^{4} - a^{2} d^{5}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{5} - a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + a^{2} c d^{4} - a^{2} d^{5}\right)} f + {\left({\left(a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c d^{4} - a^{2} d^{5}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{5} - a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + a^{2} c d^{4} - a^{2} d^{5}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{5} - a^{2} c^{4} d - 2 \, a^{2} c^{3} d^{2} + 2 \, a^{2} c^{2} d^{3} + a^{2} c d^{4} - a^{2} d^{5}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/8*(sqrt(2)*(2*(A + 3*B)*c^3 - 2*(7*A - 11*B)*c^2*d - 2*(17*A - 13*B)*c*d^2 - 2*(9*A - 5*B)*d^3 - ((A + 3*B)*c^2*d - 8*(A - B)*c*d^2 - (9*A - 5*B)*d^3)*cos(f*x + e)^3 - ((A + 3*B)*c^3 - 2*(3*A - 7*B)*c^2*d - (25*A - 21*B)*c*d^2 - 2*(9*A - 5*B)*d^3)*cos(f*x + e)^2 + ((A + 3*B)*c^3 - (7*A - 11*B)*c^2*d - (17*A - 13*B)*c*d^2 - (9*A - 5*B)*d^3)*cos(f*x + e) + (2*(A + 3*B)*c^3 - 2*(7*A - 11*B)*c^2*d - 2*(17*A - 13*B)*c*d^2 - 2*(9*A - 5*B)*d^3 - ((A + 3*B)*c^2*d - 8*(A - B)*c*d^2 - (9*A - 5*B)*d^3)*cos(f*x + e)^2 + ((A + 3*B)*c^3 - (7*A - 11*B)*c^2*d - (17*A - 13*B)*c*d^2 - (9*A - 5*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 2*(6*B*a*c^3 - 2*(5*A - 6*B)*a*c^2*d - 2*(8*A - 5*B)*a*c*d^2 - 2*(3*A - 2*B)*a*d^3 - (3*B*a*c^2*d - (5*A - 3*B)*a*c*d^2 - (3*A - 2*B)*a*d^3)*cos(f*x + e)^3 - (3*B*a*c^3 - (5*A - 9*B)*a*c^2*d - (13*A - 8*B)*a*c*d^2 - 2*(3*A - 2*B)*a*d^3)*cos(f*x + e)^2 + (3*B*a*c^3 - (5*A - 6*B)*a*c^2*d - (8*A - 5*B)*a*c*d^2 - (3*A - 2*B)*a*d^3)*cos(f*x + e) + (6*B*a*c^3 - 2*(5*A - 6*B)*a*c^2*d - 2*(8*A - 5*B)*a*c*d^2 - 2*(3*A - 2*B)*a*d^3 - (3*B*a*c^2*d - (5*A - 3*B)*a*c*d^2 - (3*A - 2*B)*a*d^3)*cos(f*x + e)^2 + (3*B*a*c^3 - (5*A - 6*B)*a*c^2*d - (8*A - 5*B)*a*c*d^2 - (3*A - 2*B)*a*d^3)*cos(f*x + e))*sin(f*x + e))*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))) + 4*((A - B)*c^3 - (A - B)*c^2*d - (A - B)*c*d^2 + (A - B)*d^3 + ((A - 3*B)*c^2*d + 2*(A + B)*c*d^2 - (3*A - B)*d^3)*cos(f*x + e)^2 + ((A - B)*c^3 - 2*B*c^2*d + (A + 3*B)*c*d^2 - 2*A*d^3)*cos(f*x + e) - ((A - B)*c^3 - (A - B)*c^2*d - (A - B)*c*d^2 + (A - B)*d^3 - ((A - 3*B)*c^2*d + 2*(A + B)*c*d^2 - (3*A - B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c*d^4 - a^2*d^5)*f*cos(f*x + e)^3 + (a^2*c^5 - 4*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + 3*a^2*c*d^4 - 2*a^2*d^5)*f*cos(f*x + e)^2 - (a^2*c^5 - a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + a^2*c*d^4 - a^2*d^5)*f*cos(f*x + e) - 2*(a^2*c^5 - a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + a^2*c*d^4 - a^2*d^5)*f + ((a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c*d^4 - a^2*d^5)*f*cos(f*x + e)^2 - (a^2*c^5 - a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + a^2*c*d^4 - a^2*d^5)*f*cos(f*x + e) - 2*(a^2*c^5 - a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + a^2*c*d^4 - a^2*d^5)*f)*sin(f*x + e)), 1/8*(sqrt(2)*(2*(A + 3*B)*c^3 - 2*(7*A - 11*B)*c^2*d - 2*(17*A - 13*B)*c*d^2 - 2*(9*A - 5*B)*d^3 - ((A + 3*B)*c^2*d - 8*(A - B)*c*d^2 - (9*A - 5*B)*d^3)*cos(f*x + e)^3 - ((A + 3*B)*c^3 - 2*(3*A - 7*B)*c^2*d - (25*A - 21*B)*c*d^2 - 2*(9*A - 5*B)*d^3)*cos(f*x + e)^2 + ((A + 3*B)*c^3 - (7*A - 11*B)*c^2*d - (17*A - 13*B)*c*d^2 - (9*A - 5*B)*d^3)*cos(f*x + e) + (2*(A + 3*B)*c^3 - 2*(7*A - 11*B)*c^2*d - 2*(17*A - 13*B)*c*d^2 - 2*(9*A - 5*B)*d^3 - ((A + 3*B)*c^2*d - 8*(A - B)*c*d^2 - (9*A - 5*B)*d^3)*cos(f*x + e)^2 + ((A + 3*B)*c^3 - (7*A - 11*B)*c^2*d - (17*A - 13*B)*c*d^2 - (9*A - 5*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(6*B*a*c^3 - 2*(5*A - 6*B)*a*c^2*d - 2*(8*A - 5*B)*a*c*d^2 - 2*(3*A - 2*B)*a*d^3 - (3*B*a*c^2*d - (5*A - 3*B)*a*c*d^2 - (3*A - 2*B)*a*d^3)*cos(f*x + e)^3 - (3*B*a*c^3 - (5*A - 9*B)*a*c^2*d - (13*A - 8*B)*a*c*d^2 - 2*(3*A - 2*B)*a*d^3)*cos(f*x + e)^2 + (3*B*a*c^3 - (5*A - 6*B)*a*c^2*d - (8*A - 5*B)*a*c*d^2 - (3*A - 2*B)*a*d^3)*cos(f*x + e) + (6*B*a*c^3 - 2*(5*A - 6*B)*a*c^2*d - 2*(8*A - 5*B)*a*c*d^2 - 2*(3*A - 2*B)*a*d^3 - (3*B*a*c^2*d - (5*A - 3*B)*a*c*d^2 - (3*A - 2*B)*a*d^3)*cos(f*x + e)^2 + (3*B*a*c^3 - (5*A - 6*B)*a*c^2*d - (8*A - 5*B)*a*c*d^2 - (3*A - 2*B)*a*d^3)*cos(f*x + e))*sin(f*x + e))*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))) + 4*((A - B)*c^3 - (A - B)*c^2*d - (A - B)*c*d^2 + (A - B)*d^3 + ((A - 3*B)*c^2*d + 2*(A + B)*c*d^2 - (3*A - B)*d^3)*cos(f*x + e)^2 + ((A - B)*c^3 - 2*B*c^2*d + (A + 3*B)*c*d^2 - 2*A*d^3)*cos(f*x + e) - ((A - B)*c^3 - (A - B)*c^2*d - (A - B)*c*d^2 + (A - B)*d^3 - ((A - 3*B)*c^2*d + 2*(A + B)*c*d^2 - (3*A - B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c*d^4 - a^2*d^5)*f*cos(f*x + e)^3 + (a^2*c^5 - 4*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + 3*a^2*c*d^4 - 2*a^2*d^5)*f*cos(f*x + e)^2 - (a^2*c^5 - a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + a^2*c*d^4 - a^2*d^5)*f*cos(f*x + e) - 2*(a^2*c^5 - a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + a^2*c*d^4 - a^2*d^5)*f + ((a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c*d^4 - a^2*d^5)*f*cos(f*x + e)^2 - (a^2*c^5 - a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + a^2*c*d^4 - a^2*d^5)*f*cos(f*x + e) - 2*(a^2*c^5 - a^2*c^4*d - 2*a^2*c^3*d^2 + 2*a^2*c^2*d^3 + a^2*c*d^4 - a^2*d^5)*f)*sin(f*x + e))]","B",0
320,1,5864,0,21.576953," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{2} {\left(2 \, {\left(A + 3 \, B\right)} c^{5} - 6 \, {\left(3 \, A - 7 \, B\right)} c^{4} d - 4 \, {\left(23 \, A - 27 \, B\right)} c^{3} d^{2} - 4 \, {\left(37 \, A - 33 \, B\right)} c^{2} d^{3} - 6 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - 2 \, {\left(13 \, A - 9 \, B\right)} d^{5} + {\left({\left(A + 3 \, B\right)} c^{3} d^{2} - {\left(11 \, A - 15 \, B\right)} c^{2} d^{3} - {\left(25 \, A - 21 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{4} - {\left(2 \, {\left(A + 3 \, B\right)} c^{4} d - 3 \, {\left(7 \, A - 11 \, B\right)} c^{3} d^{2} - {\left(61 \, A - 57 \, B\right)} c^{2} d^{3} - 3 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(A + 3 \, B\right)} c^{5} - {\left(7 \, A - 27 \, B\right)} c^{4} d - 6 \, {\left(11 \, A - 15 \, B\right)} c^{3} d^{2} - 2 \, {\left(73 \, A - 69 \, B\right)} c^{2} d^{3} - {\left(127 \, A - 99 \, B\right)} c d^{4} - 3 \, {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{5} - 3 \, {\left(3 \, A - 7 \, B\right)} c^{4} d - 2 \, {\left(23 \, A - 27 \, B\right)} c^{3} d^{2} - 2 \, {\left(37 \, A - 33 \, B\right)} c^{2} d^{3} - 3 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) + {\left(2 \, {\left(A + 3 \, B\right)} c^{5} - 6 \, {\left(3 \, A - 7 \, B\right)} c^{4} d - 4 \, {\left(23 \, A - 27 \, B\right)} c^{3} d^{2} - 4 \, {\left(37 \, A - 33 \, B\right)} c^{2} d^{3} - 6 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - 2 \, {\left(13 \, A - 9 \, B\right)} d^{5} - {\left({\left(A + 3 \, B\right)} c^{3} d^{2} - {\left(11 \, A - 15 \, B\right)} c^{2} d^{3} - {\left(25 \, A - 21 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left({\left(A + 3 \, B\right)} c^{4} d - 2 \, {\left(5 \, A - 9 \, B\right)} c^{3} d^{2} - 36 \, {\left(A - B\right)} c^{2} d^{3} - 2 \, {\left(19 \, A - 15 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{5} - 3 \, {\left(3 \, A - 7 \, B\right)} c^{4} d - 2 \, {\left(23 \, A - 27 \, B\right)} c^{3} d^{2} - 2 \, {\left(37 \, A - 33 \, B\right)} c^{2} d^{3} - 3 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + {\left(30 \, B a c^{5} - 10 \, {\left(7 \, A - 12 \, B\right)} a c^{4} d - 4 \, {\left(56 \, A - 57 \, B\right)} a c^{3} d^{2} - 12 \, {\left(23 \, A - 20 \, B\right)} a c^{2} d^{3} - 2 \, {\left(80 \, A - 63 \, B\right)} a c d^{4} - 2 \, {\left(19 \, A - 12 \, B\right)} a d^{5} + {\left(15 \, B a c^{3} d^{2} - 5 \, {\left(7 \, A - 6 \, B\right)} a c^{2} d^{3} - 3 \, {\left(14 \, A - 13 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{4} - {\left(30 \, B a c^{4} d - 5 \, {\left(14 \, A - 15 \, B\right)} a c^{3} d^{2} - {\left(119 \, A - 108 \, B\right)} a c^{2} d^{3} - {\left(80 \, A - 63 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(15 \, B a c^{5} - 5 \, {\left(7 \, A - 18 \, B\right)} a c^{4} d - 2 \, {\left(91 \, A - 102 \, B\right)} a c^{3} d^{2} - 2 \, {\left(146 \, A - 129 \, B\right)} a c^{2} d^{3} - {\left(202 \, A - 165 \, B\right)} a c d^{4} - 3 \, {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a c^{5} - 5 \, {\left(7 \, A - 12 \, B\right)} a c^{4} d - 2 \, {\left(56 \, A - 57 \, B\right)} a c^{3} d^{2} - 6 \, {\left(23 \, A - 20 \, B\right)} a c^{2} d^{3} - {\left(80 \, A - 63 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right) + {\left(30 \, B a c^{5} - 10 \, {\left(7 \, A - 12 \, B\right)} a c^{4} d - 4 \, {\left(56 \, A - 57 \, B\right)} a c^{3} d^{2} - 12 \, {\left(23 \, A - 20 \, B\right)} a c^{2} d^{3} - 2 \, {\left(80 \, A - 63 \, B\right)} a c d^{4} - 2 \, {\left(19 \, A - 12 \, B\right)} a d^{5} - {\left(15 \, B a c^{3} d^{2} - 5 \, {\left(7 \, A - 6 \, B\right)} a c^{2} d^{3} - 3 \, {\left(14 \, A - 13 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(15 \, B a c^{4} d - 5 \, {\left(7 \, A - 9 \, B\right)} a c^{3} d^{2} - {\left(77 \, A - 69 \, B\right)} a c^{2} d^{3} - {\left(61 \, A - 51 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a c^{5} - 5 \, {\left(7 \, A - 12 \, B\right)} a c^{4} d - 2 \, {\left(56 \, A - 57 \, B\right)} a c^{3} d^{2} - 6 \, {\left(23 \, A - 20 \, B\right)} a c^{2} d^{3} - {\left(80 \, A - 63 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) - 4 \, {\left(2 \, {\left(A - B\right)} c^{5} - 2 \, {\left(A - B\right)} c^{4} d - 4 \, {\left(A - B\right)} c^{3} d^{2} + 4 \, {\left(A - B\right)} c^{2} d^{3} + 2 \, {\left(A - B\right)} c d^{4} - 2 \, {\left(A - B\right)} d^{5} - {\left({\left(2 \, A - 9 \, B\right)} c^{3} d^{2} + 13 \, A c^{2} d^{3} - {\left(8 \, A - 3 \, B\right)} c d^{4} - {\left(7 \, A - 6 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} + {\left({\left(4 \, A - 13 \, B\right)} c^{4} d + {\left(15 \, A + 2 \, B\right)} c^{3} d^{2} - {\left(14 \, A - 9 \, B\right)} c^{2} d^{3} - {\left(9 \, A - 4 \, B\right)} c d^{4} + 2 \, {\left(2 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, {\left(A - B\right)} c^{5} + {\left(2 \, A - 11 \, B\right)} c^{4} d + {\left(13 \, A - 3 \, B\right)} c^{3} d^{2} + {\left(3 \, A + 5 \, B\right)} c^{2} d^{3} - 5 \, {\left(3 \, A - B\right)} c d^{4} - {\left(5 \, A - 6 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(A - B\right)} c^{5} - 2 \, {\left(A - B\right)} c^{4} d - 4 \, {\left(A - B\right)} c^{3} d^{2} + 4 \, {\left(A - B\right)} c^{2} d^{3} + 2 \, {\left(A - B\right)} c d^{4} - 2 \, {\left(A - B\right)} d^{5} - {\left({\left(2 \, A - 9 \, B\right)} c^{3} d^{2} + 13 \, A c^{2} d^{3} - {\left(8 \, A - 3 \, B\right)} c d^{4} - {\left(7 \, A - 6 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(4 \, A - 13 \, B\right)} c^{4} d + {\left(17 \, A - 7 \, B\right)} c^{3} d^{2} - {\left(A - 9 \, B\right)} c^{2} d^{3} - {\left(17 \, A - 7 \, B\right)} c d^{4} - {\left(3 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{16 \, {\left({\left(a^{2} c^{6} d^{2} - 2 \, a^{2} c^{5} d^{3} - a^{2} c^{4} d^{4} + 4 \, a^{2} c^{3} d^{5} - a^{2} c^{2} d^{6} - 2 \, a^{2} c d^{7} + a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{4} - {\left(2 \, a^{2} c^{7} d - 3 \, a^{2} c^{6} d^{2} - 4 \, a^{2} c^{5} d^{3} + 7 \, a^{2} c^{4} d^{4} + 2 \, a^{2} c^{3} d^{5} - 5 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{3} - {\left(a^{2} c^{8} + 2 \, a^{2} c^{7} d - 6 \, a^{2} c^{6} d^{2} - 6 \, a^{2} c^{5} d^{3} + 12 \, a^{2} c^{4} d^{4} + 6 \, a^{2} c^{3} d^{5} - 10 \, a^{2} c^{2} d^{6} - 2 \, a^{2} c d^{7} + 3 \, a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{8} - 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} - 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{8} - 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} - 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f - {\left({\left(a^{2} c^{6} d^{2} - 2 \, a^{2} c^{5} d^{3} - a^{2} c^{4} d^{4} + 4 \, a^{2} c^{3} d^{5} - a^{2} c^{2} d^{6} - 2 \, a^{2} c d^{7} + a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 2 \, {\left(a^{2} c^{7} d - a^{2} c^{6} d^{2} - 3 \, a^{2} c^{5} d^{3} + 3 \, a^{2} c^{4} d^{4} + 3 \, a^{2} c^{3} d^{5} - 3 \, a^{2} c^{2} d^{6} - a^{2} c d^{7} + a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{8} - 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} - 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{8} - 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} - 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{\sqrt{2} {\left(2 \, {\left(A + 3 \, B\right)} c^{5} - 6 \, {\left(3 \, A - 7 \, B\right)} c^{4} d - 4 \, {\left(23 \, A - 27 \, B\right)} c^{3} d^{2} - 4 \, {\left(37 \, A - 33 \, B\right)} c^{2} d^{3} - 6 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - 2 \, {\left(13 \, A - 9 \, B\right)} d^{5} + {\left({\left(A + 3 \, B\right)} c^{3} d^{2} - {\left(11 \, A - 15 \, B\right)} c^{2} d^{3} - {\left(25 \, A - 21 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{4} - {\left(2 \, {\left(A + 3 \, B\right)} c^{4} d - 3 \, {\left(7 \, A - 11 \, B\right)} c^{3} d^{2} - {\left(61 \, A - 57 \, B\right)} c^{2} d^{3} - 3 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(A + 3 \, B\right)} c^{5} - {\left(7 \, A - 27 \, B\right)} c^{4} d - 6 \, {\left(11 \, A - 15 \, B\right)} c^{3} d^{2} - 2 \, {\left(73 \, A - 69 \, B\right)} c^{2} d^{3} - {\left(127 \, A - 99 \, B\right)} c d^{4} - 3 \, {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{5} - 3 \, {\left(3 \, A - 7 \, B\right)} c^{4} d - 2 \, {\left(23 \, A - 27 \, B\right)} c^{3} d^{2} - 2 \, {\left(37 \, A - 33 \, B\right)} c^{2} d^{3} - 3 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) + {\left(2 \, {\left(A + 3 \, B\right)} c^{5} - 6 \, {\left(3 \, A - 7 \, B\right)} c^{4} d - 4 \, {\left(23 \, A - 27 \, B\right)} c^{3} d^{2} - 4 \, {\left(37 \, A - 33 \, B\right)} c^{2} d^{3} - 6 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - 2 \, {\left(13 \, A - 9 \, B\right)} d^{5} - {\left({\left(A + 3 \, B\right)} c^{3} d^{2} - {\left(11 \, A - 15 \, B\right)} c^{2} d^{3} - {\left(25 \, A - 21 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left({\left(A + 3 \, B\right)} c^{4} d - 2 \, {\left(5 \, A - 9 \, B\right)} c^{3} d^{2} - 36 \, {\left(A - B\right)} c^{2} d^{3} - 2 \, {\left(19 \, A - 15 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(A + 3 \, B\right)} c^{5} - 3 \, {\left(3 \, A - 7 \, B\right)} c^{4} d - 2 \, {\left(23 \, A - 27 \, B\right)} c^{3} d^{2} - 2 \, {\left(37 \, A - 33 \, B\right)} c^{2} d^{3} - 3 \, {\left(17 \, A - 13 \, B\right)} c d^{4} - {\left(13 \, A - 9 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + {\left(30 \, B a c^{5} - 10 \, {\left(7 \, A - 12 \, B\right)} a c^{4} d - 4 \, {\left(56 \, A - 57 \, B\right)} a c^{3} d^{2} - 12 \, {\left(23 \, A - 20 \, B\right)} a c^{2} d^{3} - 2 \, {\left(80 \, A - 63 \, B\right)} a c d^{4} - 2 \, {\left(19 \, A - 12 \, B\right)} a d^{5} + {\left(15 \, B a c^{3} d^{2} - 5 \, {\left(7 \, A - 6 \, B\right)} a c^{2} d^{3} - 3 \, {\left(14 \, A - 13 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{4} - {\left(30 \, B a c^{4} d - 5 \, {\left(14 \, A - 15 \, B\right)} a c^{3} d^{2} - {\left(119 \, A - 108 \, B\right)} a c^{2} d^{3} - {\left(80 \, A - 63 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{3} - {\left(15 \, B a c^{5} - 5 \, {\left(7 \, A - 18 \, B\right)} a c^{4} d - 2 \, {\left(91 \, A - 102 \, B\right)} a c^{3} d^{2} - 2 \, {\left(146 \, A - 129 \, B\right)} a c^{2} d^{3} - {\left(202 \, A - 165 \, B\right)} a c d^{4} - 3 \, {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a c^{5} - 5 \, {\left(7 \, A - 12 \, B\right)} a c^{4} d - 2 \, {\left(56 \, A - 57 \, B\right)} a c^{3} d^{2} - 6 \, {\left(23 \, A - 20 \, B\right)} a c^{2} d^{3} - {\left(80 \, A - 63 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right) + {\left(30 \, B a c^{5} - 10 \, {\left(7 \, A - 12 \, B\right)} a c^{4} d - 4 \, {\left(56 \, A - 57 \, B\right)} a c^{3} d^{2} - 12 \, {\left(23 \, A - 20 \, B\right)} a c^{2} d^{3} - 2 \, {\left(80 \, A - 63 \, B\right)} a c d^{4} - 2 \, {\left(19 \, A - 12 \, B\right)} a d^{5} - {\left(15 \, B a c^{3} d^{2} - 5 \, {\left(7 \, A - 6 \, B\right)} a c^{2} d^{3} - 3 \, {\left(14 \, A - 13 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left(15 \, B a c^{4} d - 5 \, {\left(7 \, A - 9 \, B\right)} a c^{3} d^{2} - {\left(77 \, A - 69 \, B\right)} a c^{2} d^{3} - {\left(61 \, A - 51 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(15 \, B a c^{5} - 5 \, {\left(7 \, A - 12 \, B\right)} a c^{4} d - 2 \, {\left(56 \, A - 57 \, B\right)} a c^{3} d^{2} - 6 \, {\left(23 \, A - 20 \, B\right)} a c^{2} d^{3} - {\left(80 \, A - 63 \, B\right)} a c d^{4} - {\left(19 \, A - 12 \, B\right)} a d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) - 2 \, {\left(2 \, {\left(A - B\right)} c^{5} - 2 \, {\left(A - B\right)} c^{4} d - 4 \, {\left(A - B\right)} c^{3} d^{2} + 4 \, {\left(A - B\right)} c^{2} d^{3} + 2 \, {\left(A - B\right)} c d^{4} - 2 \, {\left(A - B\right)} d^{5} - {\left({\left(2 \, A - 9 \, B\right)} c^{3} d^{2} + 13 \, A c^{2} d^{3} - {\left(8 \, A - 3 \, B\right)} c d^{4} - {\left(7 \, A - 6 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{3} + {\left({\left(4 \, A - 13 \, B\right)} c^{4} d + {\left(15 \, A + 2 \, B\right)} c^{3} d^{2} - {\left(14 \, A - 9 \, B\right)} c^{2} d^{3} - {\left(9 \, A - 4 \, B\right)} c d^{4} + 2 \, {\left(2 \, A - B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} + {\left(2 \, {\left(A - B\right)} c^{5} + {\left(2 \, A - 11 \, B\right)} c^{4} d + {\left(13 \, A - 3 \, B\right)} c^{3} d^{2} + {\left(3 \, A + 5 \, B\right)} c^{2} d^{3} - 5 \, {\left(3 \, A - B\right)} c d^{4} - {\left(5 \, A - 6 \, B\right)} d^{5}\right)} \cos\left(f x + e\right) - {\left(2 \, {\left(A - B\right)} c^{5} - 2 \, {\left(A - B\right)} c^{4} d - 4 \, {\left(A - B\right)} c^{3} d^{2} + 4 \, {\left(A - B\right)} c^{2} d^{3} + 2 \, {\left(A - B\right)} c d^{4} - 2 \, {\left(A - B\right)} d^{5} - {\left({\left(2 \, A - 9 \, B\right)} c^{3} d^{2} + 13 \, A c^{2} d^{3} - {\left(8 \, A - 3 \, B\right)} c d^{4} - {\left(7 \, A - 6 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(4 \, A - 13 \, B\right)} c^{4} d + {\left(17 \, A - 7 \, B\right)} c^{3} d^{2} - {\left(A - 9 \, B\right)} c^{2} d^{3} - {\left(17 \, A - 7 \, B\right)} c d^{4} - {\left(3 \, A - 4 \, B\right)} d^{5}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{8 \, {\left({\left(a^{2} c^{6} d^{2} - 2 \, a^{2} c^{5} d^{3} - a^{2} c^{4} d^{4} + 4 \, a^{2} c^{3} d^{5} - a^{2} c^{2} d^{6} - 2 \, a^{2} c d^{7} + a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{4} - {\left(2 \, a^{2} c^{7} d - 3 \, a^{2} c^{6} d^{2} - 4 \, a^{2} c^{5} d^{3} + 7 \, a^{2} c^{4} d^{4} + 2 \, a^{2} c^{3} d^{5} - 5 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{3} - {\left(a^{2} c^{8} + 2 \, a^{2} c^{7} d - 6 \, a^{2} c^{6} d^{2} - 6 \, a^{2} c^{5} d^{3} + 12 \, a^{2} c^{4} d^{4} + 6 \, a^{2} c^{3} d^{5} - 10 \, a^{2} c^{2} d^{6} - 2 \, a^{2} c d^{7} + 3 \, a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{2} + {\left(a^{2} c^{8} - 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} - 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f \cos\left(f x + e\right) + 2 \, {\left(a^{2} c^{8} - 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} - 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f - {\left({\left(a^{2} c^{6} d^{2} - 2 \, a^{2} c^{5} d^{3} - a^{2} c^{4} d^{4} + 4 \, a^{2} c^{3} d^{5} - a^{2} c^{2} d^{6} - 2 \, a^{2} c d^{7} + a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{3} + 2 \, {\left(a^{2} c^{7} d - a^{2} c^{6} d^{2} - 3 \, a^{2} c^{5} d^{3} + 3 \, a^{2} c^{4} d^{4} + 3 \, a^{2} c^{3} d^{5} - 3 \, a^{2} c^{2} d^{6} - a^{2} c d^{7} + a^{2} d^{8}\right)} f \cos\left(f x + e\right)^{2} - {\left(a^{2} c^{8} - 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} - 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f \cos\left(f x + e\right) - 2 \, {\left(a^{2} c^{8} - 4 \, a^{2} c^{6} d^{2} + 6 \, a^{2} c^{4} d^{4} - 4 \, a^{2} c^{2} d^{6} + a^{2} d^{8}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*(2*sqrt(2)*(2*(A + 3*B)*c^5 - 6*(3*A - 7*B)*c^4*d - 4*(23*A - 27*B)*c^3*d^2 - 4*(37*A - 33*B)*c^2*d^3 - 6*(17*A - 13*B)*c*d^4 - 2*(13*A - 9*B)*d^5 + ((A + 3*B)*c^3*d^2 - (11*A - 15*B)*c^2*d^3 - (25*A - 21*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e)^4 - (2*(A + 3*B)*c^4*d - 3*(7*A - 11*B)*c^3*d^2 - (61*A - 57*B)*c^2*d^3 - 3*(17*A - 13*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e)^3 - ((A + 3*B)*c^5 - (7*A - 27*B)*c^4*d - 6*(11*A - 15*B)*c^3*d^2 - 2*(73*A - 69*B)*c^2*d^3 - (127*A - 99*B)*c*d^4 - 3*(13*A - 9*B)*d^5)*cos(f*x + e)^2 + ((A + 3*B)*c^5 - 3*(3*A - 7*B)*c^4*d - 2*(23*A - 27*B)*c^3*d^2 - 2*(37*A - 33*B)*c^2*d^3 - 3*(17*A - 13*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e) + (2*(A + 3*B)*c^5 - 6*(3*A - 7*B)*c^4*d - 4*(23*A - 27*B)*c^3*d^2 - 4*(37*A - 33*B)*c^2*d^3 - 6*(17*A - 13*B)*c*d^4 - 2*(13*A - 9*B)*d^5 - ((A + 3*B)*c^3*d^2 - (11*A - 15*B)*c^2*d^3 - (25*A - 21*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e)^3 - 2*((A + 3*B)*c^4*d - 2*(5*A - 9*B)*c^3*d^2 - 36*(A - B)*c^2*d^3 - 2*(19*A - 15*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e)^2 + ((A + 3*B)*c^5 - 3*(3*A - 7*B)*c^4*d - 2*(23*A - 27*B)*c^3*d^2 - 2*(37*A - 33*B)*c^2*d^3 - 3*(17*A - 13*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + (30*B*a*c^5 - 10*(7*A - 12*B)*a*c^4*d - 4*(56*A - 57*B)*a*c^3*d^2 - 12*(23*A - 20*B)*a*c^2*d^3 - 2*(80*A - 63*B)*a*c*d^4 - 2*(19*A - 12*B)*a*d^5 + (15*B*a*c^3*d^2 - 5*(7*A - 6*B)*a*c^2*d^3 - 3*(14*A - 13*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e)^4 - (30*B*a*c^4*d - 5*(14*A - 15*B)*a*c^3*d^2 - (119*A - 108*B)*a*c^2*d^3 - (80*A - 63*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e)^3 - (15*B*a*c^5 - 5*(7*A - 18*B)*a*c^4*d - 2*(91*A - 102*B)*a*c^3*d^2 - 2*(146*A - 129*B)*a*c^2*d^3 - (202*A - 165*B)*a*c*d^4 - 3*(19*A - 12*B)*a*d^5)*cos(f*x + e)^2 + (15*B*a*c^5 - 5*(7*A - 12*B)*a*c^4*d - 2*(56*A - 57*B)*a*c^3*d^2 - 6*(23*A - 20*B)*a*c^2*d^3 - (80*A - 63*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e) + (30*B*a*c^5 - 10*(7*A - 12*B)*a*c^4*d - 4*(56*A - 57*B)*a*c^3*d^2 - 12*(23*A - 20*B)*a*c^2*d^3 - 2*(80*A - 63*B)*a*c*d^4 - 2*(19*A - 12*B)*a*d^5 - (15*B*a*c^3*d^2 - 5*(7*A - 6*B)*a*c^2*d^3 - 3*(14*A - 13*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e)^3 - 2*(15*B*a*c^4*d - 5*(7*A - 9*B)*a*c^3*d^2 - (77*A - 69*B)*a*c^2*d^3 - (61*A - 51*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e)^2 + (15*B*a*c^5 - 5*(7*A - 12*B)*a*c^4*d - 2*(56*A - 57*B)*a*c^3*d^2 - 6*(23*A - 20*B)*a*c^2*d^3 - (80*A - 63*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e))*sin(f*x + e))*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))) - 4*(2*(A - B)*c^5 - 2*(A - B)*c^4*d - 4*(A - B)*c^3*d^2 + 4*(A - B)*c^2*d^3 + 2*(A - B)*c*d^4 - 2*(A - B)*d^5 - ((2*A - 9*B)*c^3*d^2 + 13*A*c^2*d^3 - (8*A - 3*B)*c*d^4 - (7*A - 6*B)*d^5)*cos(f*x + e)^3 + ((4*A - 13*B)*c^4*d + (15*A + 2*B)*c^3*d^2 - (14*A - 9*B)*c^2*d^3 - (9*A - 4*B)*c*d^4 + 2*(2*A - B)*d^5)*cos(f*x + e)^2 + (2*(A - B)*c^5 + (2*A - 11*B)*c^4*d + (13*A - 3*B)*c^3*d^2 + (3*A + 5*B)*c^2*d^3 - 5*(3*A - B)*c*d^4 - (5*A - 6*B)*d^5)*cos(f*x + e) - (2*(A - B)*c^5 - 2*(A - B)*c^4*d - 4*(A - B)*c^3*d^2 + 4*(A - B)*c^2*d^3 + 2*(A - B)*c*d^4 - 2*(A - B)*d^5 - ((2*A - 9*B)*c^3*d^2 + 13*A*c^2*d^3 - (8*A - 3*B)*c*d^4 - (7*A - 6*B)*d^5)*cos(f*x + e)^2 - ((4*A - 13*B)*c^4*d + (17*A - 7*B)*c^3*d^2 - (A - 9*B)*c^2*d^3 - (17*A - 7*B)*c*d^4 - (3*A - 4*B)*d^5)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^2*c^6*d^2 - 2*a^2*c^5*d^3 - a^2*c^4*d^4 + 4*a^2*c^3*d^5 - a^2*c^2*d^6 - 2*a^2*c*d^7 + a^2*d^8)*f*cos(f*x + e)^4 - (2*a^2*c^7*d - 3*a^2*c^6*d^2 - 4*a^2*c^5*d^3 + 7*a^2*c^4*d^4 + 2*a^2*c^3*d^5 - 5*a^2*c^2*d^6 + a^2*d^8)*f*cos(f*x + e)^3 - (a^2*c^8 + 2*a^2*c^7*d - 6*a^2*c^6*d^2 - 6*a^2*c^5*d^3 + 12*a^2*c^4*d^4 + 6*a^2*c^3*d^5 - 10*a^2*c^2*d^6 - 2*a^2*c*d^7 + 3*a^2*d^8)*f*cos(f*x + e)^2 + (a^2*c^8 - 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 - 4*a^2*c^2*d^6 + a^2*d^8)*f*cos(f*x + e) + 2*(a^2*c^8 - 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 - 4*a^2*c^2*d^6 + a^2*d^8)*f - ((a^2*c^6*d^2 - 2*a^2*c^5*d^3 - a^2*c^4*d^4 + 4*a^2*c^3*d^5 - a^2*c^2*d^6 - 2*a^2*c*d^7 + a^2*d^8)*f*cos(f*x + e)^3 + 2*(a^2*c^7*d - a^2*c^6*d^2 - 3*a^2*c^5*d^3 + 3*a^2*c^4*d^4 + 3*a^2*c^3*d^5 - 3*a^2*c^2*d^6 - a^2*c*d^7 + a^2*d^8)*f*cos(f*x + e)^2 - (a^2*c^8 - 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 - 4*a^2*c^2*d^6 + a^2*d^8)*f*cos(f*x + e) - 2*(a^2*c^8 - 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 - 4*a^2*c^2*d^6 + a^2*d^8)*f)*sin(f*x + e)), 1/8*(sqrt(2)*(2*(A + 3*B)*c^5 - 6*(3*A - 7*B)*c^4*d - 4*(23*A - 27*B)*c^3*d^2 - 4*(37*A - 33*B)*c^2*d^3 - 6*(17*A - 13*B)*c*d^4 - 2*(13*A - 9*B)*d^5 + ((A + 3*B)*c^3*d^2 - (11*A - 15*B)*c^2*d^3 - (25*A - 21*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e)^4 - (2*(A + 3*B)*c^4*d - 3*(7*A - 11*B)*c^3*d^2 - (61*A - 57*B)*c^2*d^3 - 3*(17*A - 13*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e)^3 - ((A + 3*B)*c^5 - (7*A - 27*B)*c^4*d - 6*(11*A - 15*B)*c^3*d^2 - 2*(73*A - 69*B)*c^2*d^3 - (127*A - 99*B)*c*d^4 - 3*(13*A - 9*B)*d^5)*cos(f*x + e)^2 + ((A + 3*B)*c^5 - 3*(3*A - 7*B)*c^4*d - 2*(23*A - 27*B)*c^3*d^2 - 2*(37*A - 33*B)*c^2*d^3 - 3*(17*A - 13*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e) + (2*(A + 3*B)*c^5 - 6*(3*A - 7*B)*c^4*d - 4*(23*A - 27*B)*c^3*d^2 - 4*(37*A - 33*B)*c^2*d^3 - 6*(17*A - 13*B)*c*d^4 - 2*(13*A - 9*B)*d^5 - ((A + 3*B)*c^3*d^2 - (11*A - 15*B)*c^2*d^3 - (25*A - 21*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e)^3 - 2*((A + 3*B)*c^4*d - 2*(5*A - 9*B)*c^3*d^2 - 36*(A - B)*c^2*d^3 - 2*(19*A - 15*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e)^2 + ((A + 3*B)*c^5 - 3*(3*A - 7*B)*c^4*d - 2*(23*A - 27*B)*c^3*d^2 - 2*(37*A - 33*B)*c^2*d^3 - 3*(17*A - 13*B)*c*d^4 - (13*A - 9*B)*d^5)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + (30*B*a*c^5 - 10*(7*A - 12*B)*a*c^4*d - 4*(56*A - 57*B)*a*c^3*d^2 - 12*(23*A - 20*B)*a*c^2*d^3 - 2*(80*A - 63*B)*a*c*d^4 - 2*(19*A - 12*B)*a*d^5 + (15*B*a*c^3*d^2 - 5*(7*A - 6*B)*a*c^2*d^3 - 3*(14*A - 13*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e)^4 - (30*B*a*c^4*d - 5*(14*A - 15*B)*a*c^3*d^2 - (119*A - 108*B)*a*c^2*d^3 - (80*A - 63*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e)^3 - (15*B*a*c^5 - 5*(7*A - 18*B)*a*c^4*d - 2*(91*A - 102*B)*a*c^3*d^2 - 2*(146*A - 129*B)*a*c^2*d^3 - (202*A - 165*B)*a*c*d^4 - 3*(19*A - 12*B)*a*d^5)*cos(f*x + e)^2 + (15*B*a*c^5 - 5*(7*A - 12*B)*a*c^4*d - 2*(56*A - 57*B)*a*c^3*d^2 - 6*(23*A - 20*B)*a*c^2*d^3 - (80*A - 63*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e) + (30*B*a*c^5 - 10*(7*A - 12*B)*a*c^4*d - 4*(56*A - 57*B)*a*c^3*d^2 - 12*(23*A - 20*B)*a*c^2*d^3 - 2*(80*A - 63*B)*a*c*d^4 - 2*(19*A - 12*B)*a*d^5 - (15*B*a*c^3*d^2 - 5*(7*A - 6*B)*a*c^2*d^3 - 3*(14*A - 13*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e)^3 - 2*(15*B*a*c^4*d - 5*(7*A - 9*B)*a*c^3*d^2 - (77*A - 69*B)*a*c^2*d^3 - (61*A - 51*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e)^2 + (15*B*a*c^5 - 5*(7*A - 12*B)*a*c^4*d - 2*(56*A - 57*B)*a*c^3*d^2 - 6*(23*A - 20*B)*a*c^2*d^3 - (80*A - 63*B)*a*c*d^4 - (19*A - 12*B)*a*d^5)*cos(f*x + e))*sin(f*x + e))*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))) - 2*(2*(A - B)*c^5 - 2*(A - B)*c^4*d - 4*(A - B)*c^3*d^2 + 4*(A - B)*c^2*d^3 + 2*(A - B)*c*d^4 - 2*(A - B)*d^5 - ((2*A - 9*B)*c^3*d^2 + 13*A*c^2*d^3 - (8*A - 3*B)*c*d^4 - (7*A - 6*B)*d^5)*cos(f*x + e)^3 + ((4*A - 13*B)*c^4*d + (15*A + 2*B)*c^3*d^2 - (14*A - 9*B)*c^2*d^3 - (9*A - 4*B)*c*d^4 + 2*(2*A - B)*d^5)*cos(f*x + e)^2 + (2*(A - B)*c^5 + (2*A - 11*B)*c^4*d + (13*A - 3*B)*c^3*d^2 + (3*A + 5*B)*c^2*d^3 - 5*(3*A - B)*c*d^4 - (5*A - 6*B)*d^5)*cos(f*x + e) - (2*(A - B)*c^5 - 2*(A - B)*c^4*d - 4*(A - B)*c^3*d^2 + 4*(A - B)*c^2*d^3 + 2*(A - B)*c*d^4 - 2*(A - B)*d^5 - ((2*A - 9*B)*c^3*d^2 + 13*A*c^2*d^3 - (8*A - 3*B)*c*d^4 - (7*A - 6*B)*d^5)*cos(f*x + e)^2 - ((4*A - 13*B)*c^4*d + (17*A - 7*B)*c^3*d^2 - (A - 9*B)*c^2*d^3 - (17*A - 7*B)*c*d^4 - (3*A - 4*B)*d^5)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^2*c^6*d^2 - 2*a^2*c^5*d^3 - a^2*c^4*d^4 + 4*a^2*c^3*d^5 - a^2*c^2*d^6 - 2*a^2*c*d^7 + a^2*d^8)*f*cos(f*x + e)^4 - (2*a^2*c^7*d - 3*a^2*c^6*d^2 - 4*a^2*c^5*d^3 + 7*a^2*c^4*d^4 + 2*a^2*c^3*d^5 - 5*a^2*c^2*d^6 + a^2*d^8)*f*cos(f*x + e)^3 - (a^2*c^8 + 2*a^2*c^7*d - 6*a^2*c^6*d^2 - 6*a^2*c^5*d^3 + 12*a^2*c^4*d^4 + 6*a^2*c^3*d^5 - 10*a^2*c^2*d^6 - 2*a^2*c*d^7 + 3*a^2*d^8)*f*cos(f*x + e)^2 + (a^2*c^8 - 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 - 4*a^2*c^2*d^6 + a^2*d^8)*f*cos(f*x + e) + 2*(a^2*c^8 - 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 - 4*a^2*c^2*d^6 + a^2*d^8)*f - ((a^2*c^6*d^2 - 2*a^2*c^5*d^3 - a^2*c^4*d^4 + 4*a^2*c^3*d^5 - a^2*c^2*d^6 - 2*a^2*c*d^7 + a^2*d^8)*f*cos(f*x + e)^3 + 2*(a^2*c^7*d - a^2*c^6*d^2 - 3*a^2*c^5*d^3 + 3*a^2*c^4*d^4 + 3*a^2*c^3*d^5 - 3*a^2*c^2*d^6 - a^2*c*d^7 + a^2*d^8)*f*cos(f*x + e)^2 - (a^2*c^8 - 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 - 4*a^2*c^2*d^6 + a^2*d^8)*f*cos(f*x + e) - 2*(a^2*c^8 - 4*a^2*c^6*d^2 + 6*a^2*c^4*d^4 - 4*a^2*c^2*d^6 + a^2*d^8)*f)*sin(f*x + e))]","B",0
321,1,980,0,0.650757," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^3/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{3 \, \sqrt{2} {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{3} + 12 \, {\left(5 \, A + 19 \, B\right)} c^{2} d + 12 \, {\left(19 \, A - 75 \, B\right)} c d^{2} - 4 \, {\left(75 \, A - 163 \, B\right)} d^{3} - {\left({\left(3 \, A + 5 \, B\right)} c^{3} + 3 \, {\left(5 \, A + 19 \, B\right)} c^{2} d + 3 \, {\left(19 \, A - 75 \, B\right)} c d^{2} - {\left(75 \, A - 163 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left({\left(3 \, A + 5 \, B\right)} c^{3} + 3 \, {\left(5 \, A + 19 \, B\right)} c^{2} d + 3 \, {\left(19 \, A - 75 \, B\right)} c d^{2} - {\left(75 \, A - 163 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{3} + 3 \, {\left(5 \, A + 19 \, B\right)} c^{2} d + 3 \, {\left(19 \, A - 75 \, B\right)} c d^{2} - {\left(75 \, A - 163 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{3} + 12 \, {\left(5 \, A + 19 \, B\right)} c^{2} d + 12 \, {\left(19 \, A - 75 \, B\right)} c d^{2} - 4 \, {\left(75 \, A - 163 \, B\right)} d^{3} - {\left({\left(3 \, A + 5 \, B\right)} c^{3} + 3 \, {\left(5 \, A + 19 \, B\right)} c^{2} d + 3 \, {\left(19 \, A - 75 \, B\right)} c d^{2} - {\left(75 \, A - 163 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{3} + 3 \, {\left(5 \, A + 19 \, B\right)} c^{2} d + 3 \, {\left(19 \, A - 75 \, B\right)} c d^{2} - {\left(75 \, A - 163 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 4 \, {\left(32 \, B d^{3} \cos\left(f x + e\right)^{4} - 12 \, {\left(A - B\right)} c^{3} + 36 \, {\left(A - B\right)} c^{2} d - 36 \, {\left(A - B\right)} c d^{2} + 12 \, {\left(A - B\right)} d^{3} + 32 \, {\left(9 \, B c d^{2} + {\left(3 \, A - 5 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left({\left(3 \, A + 5 \, B\right)} c^{3} + 3 \, {\left(5 \, A - 13 \, B\right)} c^{2} d - 3 \, {\left(13 \, A - 53 \, B\right)} c d^{2} + {\left(53 \, A - 93 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(7 \, A + B\right)} c^{3} + 3 \, {\left(A - 9 \, B\right)} c^{2} d - 27 \, {\left(A - 9 \, B\right)} c d^{2} + 9 \, {\left(9 \, A - 17 \, B\right)} d^{3}\right)} \cos\left(f x + e\right) + {\left(32 \, B d^{3} \cos\left(f x + e\right)^{3} + 12 \, {\left(A - B\right)} c^{3} - 36 \, {\left(A - B\right)} c^{2} d + 36 \, {\left(A - B\right)} c d^{2} - 12 \, {\left(A - B\right)} d^{3} - 96 \, {\left(3 \, B c d^{2} + {\left(A - 2 \, B\right)} d^{3}\right)} \cos\left(f x + e\right)^{2} - 3 \, {\left({\left(3 \, A + 5 \, B\right)} c^{3} + 3 \, {\left(5 \, A - 13 \, B\right)} c^{2} d - 3 \, {\left(13 \, A - 85 \, B\right)} c d^{2} + {\left(85 \, A - 157 \, B\right)} 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}}{192 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/192*(3*sqrt(2)*(4*(3*A + 5*B)*c^3 + 12*(5*A + 19*B)*c^2*d + 12*(19*A - 75*B)*c*d^2 - 4*(75*A - 163*B)*d^3 - ((3*A + 5*B)*c^3 + 3*(5*A + 19*B)*c^2*d + 3*(19*A - 75*B)*c*d^2 - (75*A - 163*B)*d^3)*cos(f*x + e)^3 - 3*((3*A + 5*B)*c^3 + 3*(5*A + 19*B)*c^2*d + 3*(19*A - 75*B)*c*d^2 - (75*A - 163*B)*d^3)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^3 + 3*(5*A + 19*B)*c^2*d + 3*(19*A - 75*B)*c*d^2 - (75*A - 163*B)*d^3)*cos(f*x + e) + (4*(3*A + 5*B)*c^3 + 12*(5*A + 19*B)*c^2*d + 12*(19*A - 75*B)*c*d^2 - 4*(75*A - 163*B)*d^3 - ((3*A + 5*B)*c^3 + 3*(5*A + 19*B)*c^2*d + 3*(19*A - 75*B)*c*d^2 - (75*A - 163*B)*d^3)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^3 + 3*(5*A + 19*B)*c^2*d + 3*(19*A - 75*B)*c*d^2 - (75*A - 163*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(32*B*d^3*cos(f*x + e)^4 - 12*(A - B)*c^3 + 36*(A - B)*c^2*d - 36*(A - B)*c*d^2 + 12*(A - B)*d^3 + 32*(9*B*c*d^2 + (3*A - 5*B)*d^3)*cos(f*x + e)^3 - 3*((3*A + 5*B)*c^3 + 3*(5*A - 13*B)*c^2*d - 3*(13*A - 53*B)*c*d^2 + (53*A - 93*B)*d^3)*cos(f*x + e)^2 - 3*((7*A + B)*c^3 + 3*(A - 9*B)*c^2*d - 27*(A - 9*B)*c*d^2 + 9*(9*A - 17*B)*d^3)*cos(f*x + e) + (32*B*d^3*cos(f*x + e)^3 + 12*(A - B)*c^3 - 36*(A - B)*c^2*d + 36*(A - B)*c*d^2 - 12*(A - B)*d^3 - 96*(3*B*c*d^2 + (A - 2*B)*d^3)*cos(f*x + e)^2 - 3*((3*A + 5*B)*c^3 + 3*(5*A - 13*B)*c^2*d - 3*(13*A - 85*B)*c*d^2 + (85*A - 157*B)*d^3)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
322,1,744,0,0.848643," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","-\frac{\sqrt{2} {\left({\left({\left(3 \, A + 5 \, B\right)} c^{2} + 2 \, {\left(5 \, A + 19 \, B\right)} c d + {\left(19 \, A - 75 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{3} - 4 \, {\left(3 \, A + 5 \, B\right)} c^{2} - 8 \, {\left(5 \, A + 19 \, B\right)} c d - 4 \, {\left(19 \, A - 75 \, B\right)} d^{2} + 3 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} + 2 \, {\left(5 \, A + 19 \, B\right)} c d + {\left(19 \, A - 75 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} + 2 \, {\left(5 \, A + 19 \, B\right)} c d + {\left(19 \, A - 75 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{2} + 8 \, {\left(5 \, A + 19 \, B\right)} c d + 4 \, {\left(19 \, A - 75 \, B\right)} d^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{2} + 2 \, {\left(5 \, A + 19 \, B\right)} c d + {\left(19 \, A - 75 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} + 2 \, {\left(5 \, A + 19 \, B\right)} c d + {\left(19 \, A - 75 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 4 \, {\left(32 \, B d^{2} \cos\left(f x + e\right)^{3} - 4 \, {\left(A - B\right)} c^{2} + 8 \, {\left(A - B\right)} c d - 4 \, {\left(A - B\right)} d^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{2} + 2 \, {\left(5 \, A - 13 \, B\right)} c d - {\left(13 \, A - 53 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(7 \, A + B\right)} c^{2} + 2 \, {\left(A - 9 \, B\right)} c d - 9 \, {\left(A - 9 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left(32 \, B d^{2} \cos\left(f x + e\right)^{2} - 4 \, {\left(A - B\right)} c^{2} + 8 \, {\left(A - B\right)} c d - 4 \, {\left(A - B\right)} d^{2} + {\left({\left(3 \, A + 5 \, B\right)} c^{2} + 2 \, {\left(5 \, A - 13 \, B\right)} c d - {\left(13 \, A - 85 \, B\right)} 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}}{64 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"-1/64*(sqrt(2)*(((3*A + 5*B)*c^2 + 2*(5*A + 19*B)*c*d + (19*A - 75*B)*d^2)*cos(f*x + e)^3 - 4*(3*A + 5*B)*c^2 - 8*(5*A + 19*B)*c*d - 4*(19*A - 75*B)*d^2 + 3*((3*A + 5*B)*c^2 + 2*(5*A + 19*B)*c*d + (19*A - 75*B)*d^2)*cos(f*x + e)^2 - 2*((3*A + 5*B)*c^2 + 2*(5*A + 19*B)*c*d + (19*A - 75*B)*d^2)*cos(f*x + e) - (4*(3*A + 5*B)*c^2 + 8*(5*A + 19*B)*c*d + 4*(19*A - 75*B)*d^2 - ((3*A + 5*B)*c^2 + 2*(5*A + 19*B)*c*d + (19*A - 75*B)*d^2)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^2 + 2*(5*A + 19*B)*c*d + (19*A - 75*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(32*B*d^2*cos(f*x + e)^3 - 4*(A - B)*c^2 + 8*(A - B)*c*d - 4*(A - B)*d^2 - ((3*A + 5*B)*c^2 + 2*(5*A - 13*B)*c*d - (13*A - 53*B)*d^2)*cos(f*x + e)^2 - ((7*A + B)*c^2 + 2*(A - 9*B)*c*d - 9*(A - 9*B)*d^2)*cos(f*x + e) - (32*B*d^2*cos(f*x + e)^2 - 4*(A - B)*c^2 + 8*(A - B)*c*d - 4*(A - B)*d^2 + ((3*A + 5*B)*c^2 + 2*(5*A - 13*B)*c*d - (13*A - 85*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
323,1,536,0,0.588432," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left({\left(3 \, A + 5 \, B\right)} c + {\left(5 \, A + 19 \, B\right)} d\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left({\left(3 \, A + 5 \, B\right)} c + {\left(5 \, A + 19 \, B\right)} d\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left(3 \, A + 5 \, B\right)} c - 4 \, {\left(5 \, A + 19 \, B\right)} d - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c + {\left(5 \, A + 19 \, B\right)} d\right)} \cos\left(f x + e\right) + {\left({\left({\left(3 \, A + 5 \, B\right)} c + {\left(5 \, A + 19 \, B\right)} d\right)} \cos\left(f x + e\right)^{2} - 4 \, {\left(3 \, A + 5 \, B\right)} c - 4 \, {\left(5 \, A + 19 \, B\right)} d - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c + {\left(5 \, A + 19 \, B\right)} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 4 \, {\left({\left({\left(3 \, A + 5 \, B\right)} c + {\left(5 \, A - 13 \, B\right)} d\right)} \cos\left(f x + e\right)^{2} + 4 \, {\left(A - B\right)} c - 4 \, {\left(A - B\right)} d + {\left({\left(7 \, A + B\right)} c + {\left(A - 9 \, B\right)} d\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A - B\right)} c - 4 \, {\left(A - B\right)} d - {\left({\left(3 \, A + 5 \, B\right)} c + {\left(5 \, A - 13 \, B\right)} d\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{64 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/64*(sqrt(2)*(((3*A + 5*B)*c + (5*A + 19*B)*d)*cos(f*x + e)^3 + 3*((3*A + 5*B)*c + (5*A + 19*B)*d)*cos(f*x + e)^2 - 4*(3*A + 5*B)*c - 4*(5*A + 19*B)*d - 2*((3*A + 5*B)*c + (5*A + 19*B)*d)*cos(f*x + e) + (((3*A + 5*B)*c + (5*A + 19*B)*d)*cos(f*x + e)^2 - 4*(3*A + 5*B)*c - 4*(5*A + 19*B)*d - 2*((3*A + 5*B)*c + (5*A + 19*B)*d)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*(((3*A + 5*B)*c + (5*A - 13*B)*d)*cos(f*x + e)^2 + 4*(A - B)*c - 4*(A - B)*d + ((7*A + B)*c + (A - 9*B)*d)*cos(f*x + e) - (4*(A - B)*c - 4*(A - B)*d - ((3*A + 5*B)*c + (5*A - 13*B)*d)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
324,1,392,0,0.640966," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(3 \, A + 5 \, B\right)} \cos\left(f x + e\right)^{3} + 3 \, {\left(3 \, A + 5 \, B\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, A + 5 \, B\right)} \cos\left(f x + e\right) + {\left({\left(3 \, A + 5 \, B\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left(3 \, A + 5 \, B\right)} \cos\left(f x + e\right) - 12 \, A - 20 \, B\right)} \sin\left(f x + e\right) - 12 \, A - 20 \, B\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 4 \, {\left({\left(3 \, A + 5 \, B\right)} \cos\left(f x + e\right)^{2} + {\left(7 \, A + B\right)} \cos\left(f x + e\right) + {\left({\left(3 \, A + 5 \, B\right)} \cos\left(f x + e\right) - 4 \, A + 4 \, B\right)} \sin\left(f x + e\right) + 4 \, A - 4 \, B\right)} \sqrt{a \sin\left(f x + e\right) + a}}{64 \, {\left(a^{3} f \cos\left(f x + e\right)^{3} + 3 \, a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f + {\left(a^{3} f \cos\left(f x + e\right)^{2} - 2 \, a^{3} f \cos\left(f x + e\right) - 4 \, a^{3} f\right)} \sin\left(f x + e\right)\right)}}"," ",0,"1/64*(sqrt(2)*((3*A + 5*B)*cos(f*x + e)^3 + 3*(3*A + 5*B)*cos(f*x + e)^2 - 2*(3*A + 5*B)*cos(f*x + e) + ((3*A + 5*B)*cos(f*x + e)^2 - 2*(3*A + 5*B)*cos(f*x + e) - 12*A - 20*B)*sin(f*x + e) - 12*A - 20*B)*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 4*((3*A + 5*B)*cos(f*x + e)^2 + (7*A + B)*cos(f*x + e) + ((3*A + 5*B)*cos(f*x + e) - 4*A + 4*B)*sin(f*x + e) + 4*A - 4*B)*sqrt(a*sin(f*x + e) + a))/(a^3*f*cos(f*x + e)^3 + 3*a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f + (a^3*f*cos(f*x + e)^2 - 2*a^3*f*cos(f*x + e) - 4*a^3*f)*sin(f*x + e))","B",0
325,1,2577,0,10.232906," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left({\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{3} - 4 \, {\left(3 \, A + 5 \, B\right)} c^{2} + 8 \, {\left(7 \, A + 17 \, B\right)} c d - 4 \, {\left(43 \, A - 3 \, B\right)} d^{2} + 3 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{2} - 8 \, {\left(7 \, A + 17 \, B\right)} c d + 4 \, {\left(43 \, A - 3 \, B\right)} d^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) - 32 \, {\left(4 \, B a c d - 4 \, A a d^{2} - {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right) + {\left(4 \, B a c d - 4 \, A a d^{2} - {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) + 4 \, {\left(4 \, {\left(A - B\right)} c^{2} - 8 \, {\left(A - B\right)} c d + 4 \, {\left(A - B\right)} d^{2} + {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + B\right)} c d + {\left(11 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(7 \, A + B\right)} c^{2} - 2 \, {\left(11 \, A - 3 \, B\right)} c d + {\left(15 \, A - 7 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A - B\right)} c^{2} - 8 \, {\left(A - B\right)} c d + 4 \, {\left(A - B\right)} d^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + B\right)} c d + {\left(11 \, A - 3 \, B\right)} 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}}{64 \, {\left({\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f + {\left({\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{\sqrt{2} {\left({\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{3} - 4 \, {\left(3 \, A + 5 \, B\right)} c^{2} + 8 \, {\left(7 \, A + 17 \, B\right)} c d - 4 \, {\left(43 \, A - 3 \, B\right)} d^{2} + 3 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{2} - 8 \, {\left(7 \, A + 17 \, B\right)} c d + 4 \, {\left(43 \, A - 3 \, B\right)} d^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + 17 \, B\right)} c d + {\left(43 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 64 \, {\left(4 \, B a c d - 4 \, A a d^{2} - {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right)^{3} - 3 \, {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right) + {\left(4 \, B a c d - 4 \, A a d^{2} - {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(B a c d - A a d^{2}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) + 4 \, {\left(4 \, {\left(A - B\right)} c^{2} - 8 \, {\left(A - B\right)} c d + 4 \, {\left(A - B\right)} d^{2} + {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + B\right)} c d + {\left(11 \, A - 3 \, B\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(7 \, A + B\right)} c^{2} - 2 \, {\left(11 \, A - 3 \, B\right)} c d + {\left(15 \, A - 7 \, B\right)} d^{2}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A - B\right)} c^{2} - 8 \, {\left(A - B\right)} c d + 4 \, {\left(A - B\right)} d^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{2} - 2 \, {\left(7 \, A + B\right)} c d + {\left(11 \, A - 3 \, B\right)} 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}}{64 \, {\left({\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right)^{3} + 3 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f + {\left({\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{3} - 3 \, a^{3} c^{2} d + 3 \, a^{3} c d^{2} - a^{3} d^{3}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/64*(sqrt(2)*(((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e)^3 - 4*(3*A + 5*B)*c^2 + 8*(7*A + 17*B)*c*d - 4*(43*A - 3*B)*d^2 + 3*((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e)^2 - 2*((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e) - (4*(3*A + 5*B)*c^2 - 8*(7*A + 17*B)*c*d + 4*(43*A - 3*B)*d^2 - ((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 32*(4*B*a*c*d - 4*A*a*d^2 - (B*a*c*d - A*a*d^2)*cos(f*x + e)^3 - 3*(B*a*c*d - A*a*d^2)*cos(f*x + e)^2 + 2*(B*a*c*d - A*a*d^2)*cos(f*x + e) + (4*B*a*c*d - 4*A*a*d^2 - (B*a*c*d - A*a*d^2)*cos(f*x + e)^2 + 2*(B*a*c*d - A*a*d^2)*cos(f*x + e))*sin(f*x + e))*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))) + 4*(4*(A - B)*c^2 - 8*(A - B)*c*d + 4*(A - B)*d^2 + ((3*A + 5*B)*c^2 - 2*(7*A + B)*c*d + (11*A - 3*B)*d^2)*cos(f*x + e)^2 + ((7*A + B)*c^2 - 2*(11*A - 3*B)*c*d + (15*A - 7*B)*d^2)*cos(f*x + e) - (4*(A - B)*c^2 - 8*(A - B)*c*d + 4*(A - B)*d^2 - ((3*A + 5*B)*c^2 - 2*(7*A + B)*c*d + (11*A - 3*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e)^3 + 3*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e)^2 - 2*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e) - 4*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f + ((a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e)^2 - 2*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e) - 4*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f)*sin(f*x + e)), 1/64*(sqrt(2)*(((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e)^3 - 4*(3*A + 5*B)*c^2 + 8*(7*A + 17*B)*c*d - 4*(43*A - 3*B)*d^2 + 3*((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e)^2 - 2*((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e) - (4*(3*A + 5*B)*c^2 - 8*(7*A + 17*B)*c*d + 4*(43*A - 3*B)*d^2 - ((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^2 - 2*(7*A + 17*B)*c*d + (43*A - 3*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 64*(4*B*a*c*d - 4*A*a*d^2 - (B*a*c*d - A*a*d^2)*cos(f*x + e)^3 - 3*(B*a*c*d - A*a*d^2)*cos(f*x + e)^2 + 2*(B*a*c*d - A*a*d^2)*cos(f*x + e) + (4*B*a*c*d - 4*A*a*d^2 - (B*a*c*d - A*a*d^2)*cos(f*x + e)^2 + 2*(B*a*c*d - A*a*d^2)*cos(f*x + e))*sin(f*x + e))*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))) + 4*(4*(A - B)*c^2 - 8*(A - B)*c*d + 4*(A - B)*d^2 + ((3*A + 5*B)*c^2 - 2*(7*A + B)*c*d + (11*A - 3*B)*d^2)*cos(f*x + e)^2 + ((7*A + B)*c^2 - 2*(11*A - 3*B)*c*d + (15*A - 7*B)*d^2)*cos(f*x + e) - (4*(A - B)*c^2 - 8*(A - B)*c*d + 4*(A - B)*d^2 - ((3*A + 5*B)*c^2 - 2*(7*A + B)*c*d + (11*A - 3*B)*d^2)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e)^3 + 3*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e)^2 - 2*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e) - 4*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f + ((a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e)^2 - 2*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f*cos(f*x + e) - 4*(a^3*c^3 - 3*a^3*c^2*d + 3*a^3*c*d^2 - a^3*d^3)*f)*sin(f*x + e))]","B",0
326,1,5151,0,22.513638," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{4} - 64 \, {\left(A + 3 \, B\right)} c^{3} d + 8 \, {\left(37 \, A - 77 \, B\right)} c^{2} d^{2} + 64 \, {\left(13 \, A - 9 \, B\right)} c d^{3} + 4 \, {\left(115 \, A - 43 \, B\right)} d^{4} + {\left({\left(3 \, A + 5 \, B\right)} c^{3} d - {\left(19 \, A + 53 \, B\right)} c^{2} d^{2} + {\left(93 \, A - 101 \, B\right)} c d^{3} + {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{4} - {\left(13 \, A + 43 \, B\right)} c^{3} d + {\left(55 \, A - 207 \, B\right)} c^{2} d^{2} + 7 \, {\left(43 \, A - 35 \, B\right)} c d^{3} + 2 \, {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(3 \, {\left(3 \, A + 5 \, B\right)} c^{4} - 2 \, {\left(21 \, A + 67 \, B\right)} c^{3} d + 8 \, {\left(23 \, A - 71 \, B\right)} c^{2} d^{2} + 2 \, {\left(405 \, A - 317 \, B\right)} c d^{3} + 5 \, {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{4} - 16 \, {\left(A + 3 \, B\right)} c^{3} d + 2 \, {\left(37 \, A - 77 \, B\right)} c^{2} d^{2} + 16 \, {\left(13 \, A - 9 \, B\right)} c d^{3} + {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{4} - 64 \, {\left(A + 3 \, B\right)} c^{3} d + 8 \, {\left(37 \, A - 77 \, B\right)} c^{2} d^{2} + 64 \, {\left(13 \, A - 9 \, B\right)} c d^{3} + 4 \, {\left(115 \, A - 43 \, B\right)} d^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{3} d - {\left(19 \, A + 53 \, B\right)} c^{2} d^{2} + {\left(93 \, A - 101 \, B\right)} c d^{3} + {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(3 \, A + 5 \, B\right)} c^{4} - 2 \, {\left(5 \, A + 19 \, B\right)} c^{3} d + 4 \, {\left(9 \, A - 65 \, B\right)} c^{2} d^{2} + 2 \, {\left(197 \, A - 173 \, B\right)} c d^{3} + 3 \, {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{4} - 16 \, {\left(A + 3 \, B\right)} c^{3} d + 2 \, {\left(37 \, A - 77 \, B\right)} c^{2} d^{2} + 16 \, {\left(13 \, A - 9 \, B\right)} c d^{3} + {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) - 16 \, {\left(20 \, B a c^{3} d - 4 \, {\left(7 \, A - 10 \, B\right)} a c^{2} d^{2} - 4 \, {\left(12 \, A - 7 \, B\right)} a c d^{3} - 4 \, {\left(5 \, A - 2 \, B\right)} a d^{4} + {\left(5 \, B a c^{2} d^{2} - {\left(7 \, A - 5 \, B\right)} a c d^{3} - {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{4} - {\left(5 \, B a c^{3} d - {\left(7 \, A - 15 \, B\right)} a c^{2} d^{2} - {\left(19 \, A - 12 \, B\right)} a c d^{3} - 2 \, {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(15 \, B a c^{3} d - {\left(21 \, A - 40 \, B\right)} a c^{2} d^{2} - {\left(50 \, A - 31 \, B\right)} a c d^{3} - 5 \, {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, B a c^{3} d - {\left(7 \, A - 10 \, B\right)} a c^{2} d^{2} - {\left(12 \, A - 7 \, B\right)} a c d^{3} - {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right) + {\left(20 \, B a c^{3} d - 4 \, {\left(7 \, A - 10 \, B\right)} a c^{2} d^{2} - 4 \, {\left(12 \, A - 7 \, B\right)} a c d^{3} - 4 \, {\left(5 \, A - 2 \, B\right)} a d^{4} - {\left(5 \, B a c^{2} d^{2} - {\left(7 \, A - 5 \, B\right)} a c d^{3} - {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(5 \, B a c^{3} d - {\left(7 \, A - 20 \, B\right)} a c^{2} d^{2} - {\left(26 \, A - 17 \, B\right)} a c d^{3} - 3 \, {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, B a c^{3} d - {\left(7 \, A - 10 \, B\right)} a c^{2} d^{2} - {\left(12 \, A - 7 \, B\right)} a c d^{3} - {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) + 4 \, {\left(4 \, {\left(A - B\right)} c^{4} - 8 \, {\left(A - B\right)} c^{3} d + 8 \, {\left(A - B\right)} c d^{3} - 4 \, {\left(A - B\right)} d^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{3} d - {\left(19 \, A - 27 \, B\right)} c^{2} d^{2} - {\left(19 \, A + 21 \, B\right)} c d^{3} + {\left(35 \, A - 11 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left({\left(3 \, A + 5 \, B\right)} c^{4} - {\left(15 \, A - 7 \, B\right)} c^{3} d - {\left(7 \, A - 15 \, B\right)} c^{2} d^{2} - {\left(A + 23 \, B\right)} c d^{3} + 4 \, {\left(5 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(7 \, A + B\right)} c^{4} - 20 \, {\left(A - B\right)} c^{3} d - 2 \, {\left(13 \, A - 21 \, B\right)} c^{2} d^{2} - 4 \, {\left(3 \, A + 13 \, B\right)} c d^{3} + {\left(51 \, A - 11 \, B\right)} d^{4}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A - B\right)} c^{4} - 8 \, {\left(A - B\right)} c^{3} d + 8 \, {\left(A - B\right)} c d^{3} - 4 \, {\left(A - B\right)} d^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{3} d - {\left(19 \, A - 27 \, B\right)} c^{2} d^{2} - {\left(19 \, A + 21 \, B\right)} c d^{3} + {\left(35 \, A - 11 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{4} - 12 \, {\left(A - B\right)} c^{3} d - 2 \, {\left(13 \, A - 21 \, B\right)} c^{2} d^{2} - 4 \, {\left(5 \, A + 11 \, B\right)} c d^{3} + 5 \, {\left(11 \, A - 3 \, B\right)} 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}}{64 \, {\left({\left(a^{3} c^{5} d - 3 \, a^{3} c^{4} d^{2} + 2 \, a^{3} c^{3} d^{3} + 2 \, a^{3} c^{2} d^{4} - 3 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{4} - {\left(a^{3} c^{6} - a^{3} c^{5} d - 4 \, a^{3} c^{4} d^{2} + 6 \, a^{3} c^{3} d^{3} + a^{3} c^{2} d^{4} - 5 \, a^{3} c d^{5} + 2 \, a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{3} - {\left(3 \, a^{3} c^{6} - 4 \, a^{3} c^{5} d - 9 \, a^{3} c^{4} d^{2} + 16 \, a^{3} c^{3} d^{3} + a^{3} c^{2} d^{4} - 12 \, a^{3} c d^{5} + 5 \, a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{6} - 2 \, a^{3} c^{5} d - a^{3} c^{4} d^{2} + 4 \, a^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 2 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{6} - 2 \, a^{3} c^{5} d - a^{3} c^{4} d^{2} + 4 \, a^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 2 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f - {\left({\left(a^{3} c^{5} d - 3 \, a^{3} c^{4} d^{2} + 2 \, a^{3} c^{3} d^{3} + 2 \, a^{3} c^{2} d^{4} - 3 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{3} c^{6} - 7 \, a^{3} c^{4} d^{2} + 8 \, a^{3} c^{3} d^{3} + 3 \, a^{3} c^{2} d^{4} - 8 \, a^{3} c d^{5} + 3 \, a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{6} - 2 \, a^{3} c^{5} d - a^{3} c^{4} d^{2} + 4 \, a^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 2 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{6} - 2 \, a^{3} c^{5} d - a^{3} c^{4} d^{2} + 4 \, a^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 2 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f\right)} \sin\left(f x + e\right)\right)}}, -\frac{\sqrt{2} {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{4} - 64 \, {\left(A + 3 \, B\right)} c^{3} d + 8 \, {\left(37 \, A - 77 \, B\right)} c^{2} d^{2} + 64 \, {\left(13 \, A - 9 \, B\right)} c d^{3} + 4 \, {\left(115 \, A - 43 \, B\right)} d^{4} + {\left({\left(3 \, A + 5 \, B\right)} c^{3} d - {\left(19 \, A + 53 \, B\right)} c^{2} d^{2} + {\left(93 \, A - 101 \, B\right)} c d^{3} + {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{4} - {\left(13 \, A + 43 \, B\right)} c^{3} d + {\left(55 \, A - 207 \, B\right)} c^{2} d^{2} + 7 \, {\left(43 \, A - 35 \, B\right)} c d^{3} + 2 \, {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(3 \, {\left(3 \, A + 5 \, B\right)} c^{4} - 2 \, {\left(21 \, A + 67 \, B\right)} c^{3} d + 8 \, {\left(23 \, A - 71 \, B\right)} c^{2} d^{2} + 2 \, {\left(405 \, A - 317 \, B\right)} c d^{3} + 5 \, {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{4} - 16 \, {\left(A + 3 \, B\right)} c^{3} d + 2 \, {\left(37 \, A - 77 \, B\right)} c^{2} d^{2} + 16 \, {\left(13 \, A - 9 \, B\right)} c d^{3} + {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{4} - 64 \, {\left(A + 3 \, B\right)} c^{3} d + 8 \, {\left(37 \, A - 77 \, B\right)} c^{2} d^{2} + 64 \, {\left(13 \, A - 9 \, B\right)} c d^{3} + 4 \, {\left(115 \, A - 43 \, B\right)} d^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{3} d - {\left(19 \, A + 53 \, B\right)} c^{2} d^{2} + {\left(93 \, A - 101 \, B\right)} c d^{3} + {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(3 \, A + 5 \, B\right)} c^{4} - 2 \, {\left(5 \, A + 19 \, B\right)} c^{3} d + 4 \, {\left(9 \, A - 65 \, B\right)} c^{2} d^{2} + 2 \, {\left(197 \, A - 173 \, B\right)} c d^{3} + 3 \, {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{4} - 16 \, {\left(A + 3 \, B\right)} c^{3} d + 2 \, {\left(37 \, A - 77 \, B\right)} c^{2} d^{2} + 16 \, {\left(13 \, A - 9 \, B\right)} c d^{3} + {\left(115 \, A - 43 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} + 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) + 32 \, {\left(20 \, B a c^{3} d - 4 \, {\left(7 \, A - 10 \, B\right)} a c^{2} d^{2} - 4 \, {\left(12 \, A - 7 \, B\right)} a c d^{3} - 4 \, {\left(5 \, A - 2 \, B\right)} a d^{4} + {\left(5 \, B a c^{2} d^{2} - {\left(7 \, A - 5 \, B\right)} a c d^{3} - {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{4} - {\left(5 \, B a c^{3} d - {\left(7 \, A - 15 \, B\right)} a c^{2} d^{2} - {\left(19 \, A - 12 \, B\right)} a c d^{3} - 2 \, {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(15 \, B a c^{3} d - {\left(21 \, A - 40 \, B\right)} a c^{2} d^{2} - {\left(50 \, A - 31 \, B\right)} a c d^{3} - 5 \, {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, B a c^{3} d - {\left(7 \, A - 10 \, B\right)} a c^{2} d^{2} - {\left(12 \, A - 7 \, B\right)} a c d^{3} - {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right) + {\left(20 \, B a c^{3} d - 4 \, {\left(7 \, A - 10 \, B\right)} a c^{2} d^{2} - 4 \, {\left(12 \, A - 7 \, B\right)} a c d^{3} - 4 \, {\left(5 \, A - 2 \, B\right)} a d^{4} - {\left(5 \, B a c^{2} d^{2} - {\left(7 \, A - 5 \, B\right)} a c d^{3} - {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{3} - {\left(5 \, B a c^{3} d - {\left(7 \, A - 20 \, B\right)} a c^{2} d^{2} - {\left(26 \, A - 17 \, B\right)} a c d^{3} - 3 \, {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(5 \, B a c^{3} d - {\left(7 \, A - 10 \, B\right)} a c^{2} d^{2} - {\left(12 \, A - 7 \, B\right)} a c d^{3} - {\left(5 \, A - 2 \, B\right)} a d^{4}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) + 4 \, {\left(4 \, {\left(A - B\right)} c^{4} - 8 \, {\left(A - B\right)} c^{3} d + 8 \, {\left(A - B\right)} c d^{3} - 4 \, {\left(A - B\right)} d^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{3} d - {\left(19 \, A - 27 \, B\right)} c^{2} d^{2} - {\left(19 \, A + 21 \, B\right)} c d^{3} + {\left(35 \, A - 11 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{3} + {\left({\left(3 \, A + 5 \, B\right)} c^{4} - {\left(15 \, A - 7 \, B\right)} c^{3} d - {\left(7 \, A - 15 \, B\right)} c^{2} d^{2} - {\left(A + 23 \, B\right)} c d^{3} + 4 \, {\left(5 \, A - B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(7 \, A + B\right)} c^{4} - 20 \, {\left(A - B\right)} c^{3} d - 2 \, {\left(13 \, A - 21 \, B\right)} c^{2} d^{2} - 4 \, {\left(3 \, A + 13 \, B\right)} c d^{3} + {\left(51 \, A - 11 \, B\right)} d^{4}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A - B\right)} c^{4} - 8 \, {\left(A - B\right)} c^{3} d + 8 \, {\left(A - B\right)} c d^{3} - 4 \, {\left(A - B\right)} d^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{3} d - {\left(19 \, A - 27 \, B\right)} c^{2} d^{2} - {\left(19 \, A + 21 \, B\right)} c d^{3} + {\left(35 \, A - 11 \, B\right)} d^{4}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{4} - 12 \, {\left(A - B\right)} c^{3} d - 2 \, {\left(13 \, A - 21 \, B\right)} c^{2} d^{2} - 4 \, {\left(5 \, A + 11 \, B\right)} c d^{3} + 5 \, {\left(11 \, A - 3 \, B\right)} 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}}{64 \, {\left({\left(a^{3} c^{5} d - 3 \, a^{3} c^{4} d^{2} + 2 \, a^{3} c^{3} d^{3} + 2 \, a^{3} c^{2} d^{4} - 3 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{4} - {\left(a^{3} c^{6} - a^{3} c^{5} d - 4 \, a^{3} c^{4} d^{2} + 6 \, a^{3} c^{3} d^{3} + a^{3} c^{2} d^{4} - 5 \, a^{3} c d^{5} + 2 \, a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{3} - {\left(3 \, a^{3} c^{6} - 4 \, a^{3} c^{5} d - 9 \, a^{3} c^{4} d^{2} + 16 \, a^{3} c^{3} d^{3} + a^{3} c^{2} d^{4} - 12 \, a^{3} c d^{5} + 5 \, a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{6} - 2 \, a^{3} c^{5} d - a^{3} c^{4} d^{2} + 4 \, a^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 2 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{6} - 2 \, a^{3} c^{5} d - a^{3} c^{4} d^{2} + 4 \, a^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 2 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f - {\left({\left(a^{3} c^{5} d - 3 \, a^{3} c^{4} d^{2} + 2 \, a^{3} c^{3} d^{3} + 2 \, a^{3} c^{2} d^{4} - 3 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{3} + {\left(a^{3} c^{6} - 7 \, a^{3} c^{4} d^{2} + 8 \, a^{3} c^{3} d^{3} + 3 \, a^{3} c^{2} d^{4} - 8 \, a^{3} c d^{5} + 3 \, a^{3} d^{6}\right)} f \cos\left(f x + e\right)^{2} - 2 \, {\left(a^{3} c^{6} - 2 \, a^{3} c^{5} d - a^{3} c^{4} d^{2} + 4 \, a^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 2 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f \cos\left(f x + e\right) - 4 \, {\left(a^{3} c^{6} - 2 \, a^{3} c^{5} d - a^{3} c^{4} d^{2} + 4 \, a^{3} c^{3} d^{3} - a^{3} c^{2} d^{4} - 2 \, a^{3} c d^{5} + a^{3} d^{6}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[-1/64*(sqrt(2)*(4*(3*A + 5*B)*c^4 - 64*(A + 3*B)*c^3*d + 8*(37*A - 77*B)*c^2*d^2 + 64*(13*A - 9*B)*c*d^3 + 4*(115*A - 43*B)*d^4 + ((3*A + 5*B)*c^3*d - (19*A + 53*B)*c^2*d^2 + (93*A - 101*B)*c*d^3 + (115*A - 43*B)*d^4)*cos(f*x + e)^4 - ((3*A + 5*B)*c^4 - (13*A + 43*B)*c^3*d + (55*A - 207*B)*c^2*d^2 + 7*(43*A - 35*B)*c*d^3 + 2*(115*A - 43*B)*d^4)*cos(f*x + e)^3 - (3*(3*A + 5*B)*c^4 - 2*(21*A + 67*B)*c^3*d + 8*(23*A - 71*B)*c^2*d^2 + 2*(405*A - 317*B)*c*d^3 + 5*(115*A - 43*B)*d^4)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^4 - 16*(A + 3*B)*c^3*d + 2*(37*A - 77*B)*c^2*d^2 + 16*(13*A - 9*B)*c*d^3 + (115*A - 43*B)*d^4)*cos(f*x + e) + (4*(3*A + 5*B)*c^4 - 64*(A + 3*B)*c^3*d + 8*(37*A - 77*B)*c^2*d^2 + 64*(13*A - 9*B)*c*d^3 + 4*(115*A - 43*B)*d^4 - ((3*A + 5*B)*c^3*d - (19*A + 53*B)*c^2*d^2 + (93*A - 101*B)*c*d^3 + (115*A - 43*B)*d^4)*cos(f*x + e)^3 - ((3*A + 5*B)*c^4 - 2*(5*A + 19*B)*c^3*d + 4*(9*A - 65*B)*c^2*d^2 + 2*(197*A - 173*B)*c*d^3 + 3*(115*A - 43*B)*d^4)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^4 - 16*(A + 3*B)*c^3*d + 2*(37*A - 77*B)*c^2*d^2 + 16*(13*A - 9*B)*c*d^3 + (115*A - 43*B)*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 16*(20*B*a*c^3*d - 4*(7*A - 10*B)*a*c^2*d^2 - 4*(12*A - 7*B)*a*c*d^3 - 4*(5*A - 2*B)*a*d^4 + (5*B*a*c^2*d^2 - (7*A - 5*B)*a*c*d^3 - (5*A - 2*B)*a*d^4)*cos(f*x + e)^4 - (5*B*a*c^3*d - (7*A - 15*B)*a*c^2*d^2 - (19*A - 12*B)*a*c*d^3 - 2*(5*A - 2*B)*a*d^4)*cos(f*x + e)^3 - (15*B*a*c^3*d - (21*A - 40*B)*a*c^2*d^2 - (50*A - 31*B)*a*c*d^3 - 5*(5*A - 2*B)*a*d^4)*cos(f*x + e)^2 + 2*(5*B*a*c^3*d - (7*A - 10*B)*a*c^2*d^2 - (12*A - 7*B)*a*c*d^3 - (5*A - 2*B)*a*d^4)*cos(f*x + e) + (20*B*a*c^3*d - 4*(7*A - 10*B)*a*c^2*d^2 - 4*(12*A - 7*B)*a*c*d^3 - 4*(5*A - 2*B)*a*d^4 - (5*B*a*c^2*d^2 - (7*A - 5*B)*a*c*d^3 - (5*A - 2*B)*a*d^4)*cos(f*x + e)^3 - (5*B*a*c^3*d - (7*A - 20*B)*a*c^2*d^2 - (26*A - 17*B)*a*c*d^3 - 3*(5*A - 2*B)*a*d^4)*cos(f*x + e)^2 + 2*(5*B*a*c^3*d - (7*A - 10*B)*a*c^2*d^2 - (12*A - 7*B)*a*c*d^3 - (5*A - 2*B)*a*d^4)*cos(f*x + e))*sin(f*x + e))*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))) + 4*(4*(A - B)*c^4 - 8*(A - B)*c^3*d + 8*(A - B)*c*d^3 - 4*(A - B)*d^4 - ((3*A + 5*B)*c^3*d - (19*A - 27*B)*c^2*d^2 - (19*A + 21*B)*c*d^3 + (35*A - 11*B)*d^4)*cos(f*x + e)^3 + ((3*A + 5*B)*c^4 - (15*A - 7*B)*c^3*d - (7*A - 15*B)*c^2*d^2 - (A + 23*B)*c*d^3 + 4*(5*A - B)*d^4)*cos(f*x + e)^2 + ((7*A + B)*c^4 - 20*(A - B)*c^3*d - 2*(13*A - 21*B)*c^2*d^2 - 4*(3*A + 13*B)*c*d^3 + (51*A - 11*B)*d^4)*cos(f*x + e) - (4*(A - B)*c^4 - 8*(A - B)*c^3*d + 8*(A - B)*c*d^3 - 4*(A - B)*d^4 - ((3*A + 5*B)*c^3*d - (19*A - 27*B)*c^2*d^2 - (19*A + 21*B)*c*d^3 + (35*A - 11*B)*d^4)*cos(f*x + e)^2 - ((3*A + 5*B)*c^4 - 12*(A - B)*c^3*d - 2*(13*A - 21*B)*c^2*d^2 - 4*(5*A + 11*B)*c*d^3 + 5*(11*A - 3*B)*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^3*c^5*d - 3*a^3*c^4*d^2 + 2*a^3*c^3*d^3 + 2*a^3*c^2*d^4 - 3*a^3*c*d^5 + a^3*d^6)*f*cos(f*x + e)^4 - (a^3*c^6 - a^3*c^5*d - 4*a^3*c^4*d^2 + 6*a^3*c^3*d^3 + a^3*c^2*d^4 - 5*a^3*c*d^5 + 2*a^3*d^6)*f*cos(f*x + e)^3 - (3*a^3*c^6 - 4*a^3*c^5*d - 9*a^3*c^4*d^2 + 16*a^3*c^3*d^3 + a^3*c^2*d^4 - 12*a^3*c*d^5 + 5*a^3*d^6)*f*cos(f*x + e)^2 + 2*(a^3*c^6 - 2*a^3*c^5*d - a^3*c^4*d^2 + 4*a^3*c^3*d^3 - a^3*c^2*d^4 - 2*a^3*c*d^5 + a^3*d^6)*f*cos(f*x + e) + 4*(a^3*c^6 - 2*a^3*c^5*d - a^3*c^4*d^2 + 4*a^3*c^3*d^3 - a^3*c^2*d^4 - 2*a^3*c*d^5 + a^3*d^6)*f - ((a^3*c^5*d - 3*a^3*c^4*d^2 + 2*a^3*c^3*d^3 + 2*a^3*c^2*d^4 - 3*a^3*c*d^5 + a^3*d^6)*f*cos(f*x + e)^3 + (a^3*c^6 - 7*a^3*c^4*d^2 + 8*a^3*c^3*d^3 + 3*a^3*c^2*d^4 - 8*a^3*c*d^5 + 3*a^3*d^6)*f*cos(f*x + e)^2 - 2*(a^3*c^6 - 2*a^3*c^5*d - a^3*c^4*d^2 + 4*a^3*c^3*d^3 - a^3*c^2*d^4 - 2*a^3*c*d^5 + a^3*d^6)*f*cos(f*x + e) - 4*(a^3*c^6 - 2*a^3*c^5*d - a^3*c^4*d^2 + 4*a^3*c^3*d^3 - a^3*c^2*d^4 - 2*a^3*c*d^5 + a^3*d^6)*f)*sin(f*x + e)), -1/64*(sqrt(2)*(4*(3*A + 5*B)*c^4 - 64*(A + 3*B)*c^3*d + 8*(37*A - 77*B)*c^2*d^2 + 64*(13*A - 9*B)*c*d^3 + 4*(115*A - 43*B)*d^4 + ((3*A + 5*B)*c^3*d - (19*A + 53*B)*c^2*d^2 + (93*A - 101*B)*c*d^3 + (115*A - 43*B)*d^4)*cos(f*x + e)^4 - ((3*A + 5*B)*c^4 - (13*A + 43*B)*c^3*d + (55*A - 207*B)*c^2*d^2 + 7*(43*A - 35*B)*c*d^3 + 2*(115*A - 43*B)*d^4)*cos(f*x + e)^3 - (3*(3*A + 5*B)*c^4 - 2*(21*A + 67*B)*c^3*d + 8*(23*A - 71*B)*c^2*d^2 + 2*(405*A - 317*B)*c*d^3 + 5*(115*A - 43*B)*d^4)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^4 - 16*(A + 3*B)*c^3*d + 2*(37*A - 77*B)*c^2*d^2 + 16*(13*A - 9*B)*c*d^3 + (115*A - 43*B)*d^4)*cos(f*x + e) + (4*(3*A + 5*B)*c^4 - 64*(A + 3*B)*c^3*d + 8*(37*A - 77*B)*c^2*d^2 + 64*(13*A - 9*B)*c*d^3 + 4*(115*A - 43*B)*d^4 - ((3*A + 5*B)*c^3*d - (19*A + 53*B)*c^2*d^2 + (93*A - 101*B)*c*d^3 + (115*A - 43*B)*d^4)*cos(f*x + e)^3 - ((3*A + 5*B)*c^4 - 2*(5*A + 19*B)*c^3*d + 4*(9*A - 65*B)*c^2*d^2 + 2*(197*A - 173*B)*c*d^3 + 3*(115*A - 43*B)*d^4)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^4 - 16*(A + 3*B)*c^3*d + 2*(37*A - 77*B)*c^2*d^2 + 16*(13*A - 9*B)*c*d^3 + (115*A - 43*B)*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 + 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) + 32*(20*B*a*c^3*d - 4*(7*A - 10*B)*a*c^2*d^2 - 4*(12*A - 7*B)*a*c*d^3 - 4*(5*A - 2*B)*a*d^4 + (5*B*a*c^2*d^2 - (7*A - 5*B)*a*c*d^3 - (5*A - 2*B)*a*d^4)*cos(f*x + e)^4 - (5*B*a*c^3*d - (7*A - 15*B)*a*c^2*d^2 - (19*A - 12*B)*a*c*d^3 - 2*(5*A - 2*B)*a*d^4)*cos(f*x + e)^3 - (15*B*a*c^3*d - (21*A - 40*B)*a*c^2*d^2 - (50*A - 31*B)*a*c*d^3 - 5*(5*A - 2*B)*a*d^4)*cos(f*x + e)^2 + 2*(5*B*a*c^3*d - (7*A - 10*B)*a*c^2*d^2 - (12*A - 7*B)*a*c*d^3 - (5*A - 2*B)*a*d^4)*cos(f*x + e) + (20*B*a*c^3*d - 4*(7*A - 10*B)*a*c^2*d^2 - 4*(12*A - 7*B)*a*c*d^3 - 4*(5*A - 2*B)*a*d^4 - (5*B*a*c^2*d^2 - (7*A - 5*B)*a*c*d^3 - (5*A - 2*B)*a*d^4)*cos(f*x + e)^3 - (5*B*a*c^3*d - (7*A - 20*B)*a*c^2*d^2 - (26*A - 17*B)*a*c*d^3 - 3*(5*A - 2*B)*a*d^4)*cos(f*x + e)^2 + 2*(5*B*a*c^3*d - (7*A - 10*B)*a*c^2*d^2 - (12*A - 7*B)*a*c*d^3 - (5*A - 2*B)*a*d^4)*cos(f*x + e))*sin(f*x + e))*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))) + 4*(4*(A - B)*c^4 - 8*(A - B)*c^3*d + 8*(A - B)*c*d^3 - 4*(A - B)*d^4 - ((3*A + 5*B)*c^3*d - (19*A - 27*B)*c^2*d^2 - (19*A + 21*B)*c*d^3 + (35*A - 11*B)*d^4)*cos(f*x + e)^3 + ((3*A + 5*B)*c^4 - (15*A - 7*B)*c^3*d - (7*A - 15*B)*c^2*d^2 - (A + 23*B)*c*d^3 + 4*(5*A - B)*d^4)*cos(f*x + e)^2 + ((7*A + B)*c^4 - 20*(A - B)*c^3*d - 2*(13*A - 21*B)*c^2*d^2 - 4*(3*A + 13*B)*c*d^3 + (51*A - 11*B)*d^4)*cos(f*x + e) - (4*(A - B)*c^4 - 8*(A - B)*c^3*d + 8*(A - B)*c*d^3 - 4*(A - B)*d^4 - ((3*A + 5*B)*c^3*d - (19*A - 27*B)*c^2*d^2 - (19*A + 21*B)*c*d^3 + (35*A - 11*B)*d^4)*cos(f*x + e)^2 - ((3*A + 5*B)*c^4 - 12*(A - B)*c^3*d - 2*(13*A - 21*B)*c^2*d^2 - 4*(5*A + 11*B)*c*d^3 + 5*(11*A - 3*B)*d^4)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^3*c^5*d - 3*a^3*c^4*d^2 + 2*a^3*c^3*d^3 + 2*a^3*c^2*d^4 - 3*a^3*c*d^5 + a^3*d^6)*f*cos(f*x + e)^4 - (a^3*c^6 - a^3*c^5*d - 4*a^3*c^4*d^2 + 6*a^3*c^3*d^3 + a^3*c^2*d^4 - 5*a^3*c*d^5 + 2*a^3*d^6)*f*cos(f*x + e)^3 - (3*a^3*c^6 - 4*a^3*c^5*d - 9*a^3*c^4*d^2 + 16*a^3*c^3*d^3 + a^3*c^2*d^4 - 12*a^3*c*d^5 + 5*a^3*d^6)*f*cos(f*x + e)^2 + 2*(a^3*c^6 - 2*a^3*c^5*d - a^3*c^4*d^2 + 4*a^3*c^3*d^3 - a^3*c^2*d^4 - 2*a^3*c*d^5 + a^3*d^6)*f*cos(f*x + e) + 4*(a^3*c^6 - 2*a^3*c^5*d - a^3*c^4*d^2 + 4*a^3*c^3*d^3 - a^3*c^2*d^4 - 2*a^3*c*d^5 + a^3*d^6)*f - ((a^3*c^5*d - 3*a^3*c^4*d^2 + 2*a^3*c^3*d^3 + 2*a^3*c^2*d^4 - 3*a^3*c*d^5 + a^3*d^6)*f*cos(f*x + e)^3 + (a^3*c^6 - 7*a^3*c^4*d^2 + 8*a^3*c^3*d^3 + 3*a^3*c^2*d^4 - 8*a^3*c*d^5 + 3*a^3*d^6)*f*cos(f*x + e)^2 - 2*(a^3*c^6 - 2*a^3*c^5*d - a^3*c^4*d^2 + 4*a^3*c^3*d^3 - a^3*c^2*d^4 - 2*a^3*c*d^5 + a^3*d^6)*f*cos(f*x + e) - 4*(a^3*c^6 - 2*a^3*c^5*d - a^3*c^4*d^2 + 4*a^3*c^3*d^3 - a^3*c^2*d^4 - 2*a^3*c*d^5 + a^3*d^6)*f)*sin(f*x + e))]","B",0
327,1,8555,0,77.475779," ","integrate((A+B*sin(f*x+e))/(a+a*sin(f*x+e))^(5/2)/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{6} - 8 \, {\left(9 \, A + 31 \, B\right)} c^{5} d + 4 \, {\left(117 \, A - 413 \, B\right)} c^{4} d^{2} + 16 \, {\left(177 \, A - 233 \, B\right)} c^{3} d^{3} + 4 \, {\left(1197 \, A - 1013 \, B\right)} c^{2} d^{4} + 8 \, {\left(423 \, A - 271 \, B\right)} c d^{5} + 4 \, {\left(219 \, A - 115 \, B\right)} d^{6} + {\left({\left(3 \, A + 5 \, B\right)} c^{4} d^{2} - 24 \, {\left(A + 3 \, B\right)} c^{3} d^{3} + 2 \, {\left(81 \, A - 137 \, B\right)} c^{2} d^{4} + 24 \, {\left(17 \, A - 13 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{5} + {\left(2 \, {\left(3 \, A + 5 \, B\right)} c^{5} d - 3 \, {\left(13 \, A + 43 \, B\right)} c^{4} d^{2} + 4 \, {\left(63 \, A - 191 \, B\right)} c^{3} d^{3} + 6 \, {\left(217 \, A - 241 \, B\right)} c^{2} d^{4} + 2 \, {\left(831 \, A - 583 \, B\right)} c d^{5} + 3 \, {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 4 \, {\left(3 \, A + 13 \, B\right)} c^{5} d + {\left(75 \, A - 547 \, B\right)} c^{4} d^{2} + 8 \, {\left(123 \, A - 203 \, B\right)} c^{3} d^{3} + 19 \, {\left(123 \, A - 115 \, B\right)} c^{2} d^{4} + 4 \, {\left(525 \, A - 349 \, B\right)} c d^{5} + 3 \, {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(3 \, {\left(3 \, A + 5 \, B\right)} c^{6} - 2 \, {\left(21 \, A + 83 \, B\right)} c^{5} d + {\left(267 \, A - 1507 \, B\right)} c^{4} d^{2} + 4 \, {\left(669 \, A - 1045 \, B\right)} c^{3} d^{3} + {\left(5871 \, A - 5383 \, B\right)} c^{2} d^{4} + 2 \, {\left(2523 \, A - 1667 \, B\right)} c d^{5} + 7 \, {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 2 \, {\left(9 \, A + 31 \, B\right)} c^{5} d + {\left(117 \, A - 413 \, B\right)} c^{4} d^{2} + 4 \, {\left(177 \, A - 233 \, B\right)} c^{3} d^{3} + {\left(1197 \, A - 1013 \, B\right)} c^{2} d^{4} + 2 \, {\left(423 \, A - 271 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{6} - 8 \, {\left(9 \, A + 31 \, B\right)} c^{5} d + 4 \, {\left(117 \, A - 413 \, B\right)} c^{4} d^{2} + 16 \, {\left(177 \, A - 233 \, B\right)} c^{3} d^{3} + 4 \, {\left(1197 \, A - 1013 \, B\right)} c^{2} d^{4} + 8 \, {\left(423 \, A - 271 \, B\right)} c d^{5} + 4 \, {\left(219 \, A - 115 \, B\right)} d^{6} + {\left({\left(3 \, A + 5 \, B\right)} c^{4} d^{2} - 24 \, {\left(A + 3 \, B\right)} c^{3} d^{3} + 2 \, {\left(81 \, A - 137 \, B\right)} c^{2} d^{4} + 24 \, {\left(17 \, A - 13 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{5} d - {\left(21 \, A + 67 \, B\right)} c^{4} d^{2} + 2 \, {\left(69 \, A - 173 \, B\right)} c^{3} d^{3} + 2 \, {\left(285 \, A - 293 \, B\right)} c^{2} d^{4} + {\left(627 \, A - 427 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 6 \, {\left(A + 7 \, B\right)} c^{5} d + 3 \, {\left(11 \, A - 227 \, B\right)} c^{4} d^{2} + 12 \, {\left(105 \, A - 193 \, B\right)} c^{3} d^{3} + 3 \, {\left(1159 \, A - 1119 \, B\right)} c^{2} d^{4} + 6 \, {\left(559 \, A - 375 \, B\right)} c d^{5} + 5 \, {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 2 \, {\left(9 \, A + 31 \, B\right)} c^{5} d + {\left(117 \, A - 413 \, B\right)} c^{4} d^{2} + 4 \, {\left(177 \, A - 233 \, B\right)} c^{3} d^{3} + {\left(1197 \, A - 1013 \, B\right)} c^{2} d^{4} + 2 \, {\left(423 \, A - 271 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) - 4 \, {\left(140 \, B a c^{5} d - 28 \, {\left(9 \, A - 20 \, B\right)} a c^{4} d^{2} - 8 \, {\left(108 \, A - 121 \, B\right)} a c^{3} d^{3} - 8 \, {\left(141 \, A - 112 \, B\right)} a c^{2} d^{4} - 4 \, {\left(168 \, A - 107 \, B\right)} a c d^{5} - 4 \, {\left(39 \, A - 20 \, B\right)} a d^{6} + {\left(35 \, B a c^{3} d^{3} - 7 \, {\left(9 \, A - 10 \, B\right)} a c^{2} d^{4} - {\left(90 \, A - 67 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{5} + {\left(70 \, B a c^{4} d^{2} - 7 \, {\left(18 \, A - 35 \, B\right)} a c^{3} d^{3} - {\left(369 \, A - 344 \, B\right)} a c^{2} d^{4} - {\left(348 \, A - 241 \, B\right)} a c d^{5} - 3 \, {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left(35 \, B a c^{5} d - 21 \, {\left(3 \, A - 10 \, B\right)} a c^{4} d^{2} - 2 \, {\left(171 \, A - 226 \, B\right)} a c^{3} d^{3} - 6 \, {\left(98 \, A - 83 \, B\right)} a c^{2} d^{4} - {\left(426 \, A - 281 \, B\right)} a c d^{5} - 3 \, {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(105 \, B a c^{5} d - 7 \, {\left(27 \, A - 80 \, B\right)} a c^{4} d^{2} - 6 \, {\left(150 \, A - 191 \, B\right)} a c^{3} d^{3} - 2 \, {\left(729 \, A - 610 \, B\right)} a c^{2} d^{4} - 3 \, {\left(340 \, A - 223 \, B\right)} a c d^{5} - 7 \, {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(35 \, B a c^{5} d - 7 \, {\left(9 \, A - 20 \, B\right)} a c^{4} d^{2} - 2 \, {\left(108 \, A - 121 \, B\right)} a c^{3} d^{3} - 2 \, {\left(141 \, A - 112 \, B\right)} a c^{2} d^{4} - {\left(168 \, A - 107 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right) + {\left(140 \, B a c^{5} d - 28 \, {\left(9 \, A - 20 \, B\right)} a c^{4} d^{2} - 8 \, {\left(108 \, A - 121 \, B\right)} a c^{3} d^{3} - 8 \, {\left(141 \, A - 112 \, B\right)} a c^{2} d^{4} - 4 \, {\left(168 \, A - 107 \, B\right)} a c d^{5} - 4 \, {\left(39 \, A - 20 \, B\right)} a d^{6} + {\left(35 \, B a c^{3} d^{3} - 7 \, {\left(9 \, A - 10 \, B\right)} a c^{2} d^{4} - {\left(90 \, A - 67 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(35 \, B a c^{4} d^{2} - 21 \, {\left(3 \, A - 5 \, B\right)} a c^{3} d^{3} - {\left(153 \, A - 137 \, B\right)} a c^{2} d^{4} - 3 \, {\left(43 \, A - 29 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(35 \, B a c^{5} d - 7 \, {\left(9 \, A - 40 \, B\right)} a c^{4} d^{2} - 2 \, {\left(234 \, A - 331 \, B\right)} a c^{3} d^{3} - 2 \, {\left(447 \, A - 386 \, B\right)} a c^{2} d^{4} - {\left(684 \, A - 455 \, B\right)} a c d^{5} - 5 \, {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(35 \, B a c^{5} d - 7 \, {\left(9 \, A - 20 \, B\right)} a c^{4} d^{2} - 2 \, {\left(108 \, A - 121 \, B\right)} a c^{3} d^{3} - 2 \, {\left(141 \, A - 112 \, B\right)} a c^{2} d^{4} - {\left(168 \, A - 107 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) - 4 \, {\left(4 \, {\left(A - B\right)} c^{6} - 8 \, {\left(A - B\right)} c^{5} d - 4 \, {\left(A - B\right)} c^{4} d^{2} + 16 \, {\left(A - B\right)} c^{3} d^{3} - 4 \, {\left(A - B\right)} c^{2} d^{4} - 8 \, {\left(A - B\right)} c d^{5} + 4 \, {\left(A - B\right)} d^{6} - {\left({\left(3 \, A + 5 \, B\right)} c^{4} d^{2} - 4 \, {\left(6 \, A - 17 \, B\right)} c^{3} d^{3} - 6 \, {\left(15 \, A - B\right)} c^{2} d^{4} + 4 \, {\left(12 \, A - 11 \, B\right)} c d^{5} + 7 \, {\left(9 \, A - 5 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left(2 \, {\left(3 \, A + 5 \, B\right)} c^{5} d - {\left(41 \, A - 101 \, B\right)} c^{4} d^{2} - 4 \, {\left(38 \, A - 31 \, B\right)} c^{3} d^{3} - 2 \, {\left(39 \, A + 35 \, B\right)} c^{2} d^{4} + 10 \, {\left(17 \, A - 11 \, B\right)} c d^{5} + 5 \, {\left(19 \, A - 11 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} + {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 16 \, {\left(A - B\right)} c^{5} d - {\left(31 \, A - 75 \, B\right)} c^{4} d^{2} - 4 \, {\left(21 \, A - 11 \, B\right)} c^{3} d^{3} - {\left(23 \, A + 49 \, B\right)} c^{2} d^{4} + 20 \, {\left(5 \, A - 3 \, B\right)} c d^{5} + {\left(51 \, A - 31 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(7 \, A + B\right)} c^{6} - 2 \, {\left(9 \, A - 17 \, B\right)} c^{5} d - {\left(79 \, A - 175 \, B\right)} c^{4} d^{2} - 28 \, {\left(7 \, A - 3 \, B\right)} c^{3} d^{3} - {\left(15 \, A + 121 \, B\right)} c^{2} d^{4} + 2 \, {\left(107 \, A - 59 \, B\right)} c d^{5} + {\left(87 \, A - 55 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A - B\right)} c^{6} - 8 \, {\left(A - B\right)} c^{5} d - 4 \, {\left(A - B\right)} c^{4} d^{2} + 16 \, {\left(A - B\right)} c^{3} d^{3} - 4 \, {\left(A - B\right)} c^{2} d^{4} - 8 \, {\left(A - B\right)} c d^{5} + 4 \, {\left(A - B\right)} d^{6} + {\left({\left(3 \, A + 5 \, B\right)} c^{4} d^{2} - 4 \, {\left(6 \, A - 17 \, B\right)} c^{3} d^{3} - 6 \, {\left(15 \, A - B\right)} c^{2} d^{4} + 4 \, {\left(12 \, A - 11 \, B\right)} c d^{5} + 7 \, {\left(9 \, A - 5 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{5} d - 2 \, {\left(11 \, A - 24 \, B\right)} c^{4} d^{2} - 4 \, {\left(16 \, A - 7 \, B\right)} c^{3} d^{3} + 2 \, {\left(3 \, A - 19 \, B\right)} c^{2} d^{4} + {\left(61 \, A - 33 \, B\right)} c d^{5} + 2 \, {\left(8 \, A - 5 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 2 \, {\left(5 \, A - 13 \, B\right)} c^{5} d - 3 \, {\left(25 \, A - 57 \, B\right)} c^{4} d^{2} - 4 \, {\left(53 \, A - 25 \, B\right)} c^{3} d^{3} - {\left(11 \, A + 125 \, B\right)} c^{2} d^{4} + 6 \, {\left(37 \, A - 21 \, B\right)} c d^{5} + {\left(83 \, A - 51 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{64 \, {\left({\left(a^{3} c^{7} d^{2} - 3 \, a^{3} c^{6} d^{3} + a^{3} c^{5} d^{4} + 5 \, a^{3} c^{4} d^{5} - 5 \, a^{3} c^{3} d^{6} - a^{3} c^{2} d^{7} + 3 \, a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{5} + {\left(2 \, a^{3} c^{8} d - 3 \, a^{3} c^{7} d^{2} - 7 \, a^{3} c^{6} d^{3} + 13 \, a^{3} c^{5} d^{4} + 5 \, a^{3} c^{4} d^{5} - 17 \, a^{3} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{7} + 7 \, a^{3} c d^{8} - 3 \, a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{4} - {\left(a^{3} c^{9} + a^{3} c^{8} d - 8 \, a^{3} c^{7} d^{2} + 18 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 16 \, a^{3} c^{3} d^{6} + 8 \, a^{3} c^{2} d^{7} + 5 \, a^{3} c d^{8} - 3 \, a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{3} - {\left(3 \, a^{3} c^{9} + a^{3} c^{8} d - 20 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 42 \, a^{3} c^{5} d^{4} - 18 \, a^{3} c^{4} d^{5} - 36 \, a^{3} c^{3} d^{6} + 20 \, a^{3} c^{2} d^{7} + 11 \, a^{3} c d^{8} - 7 \, a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{9} - a^{3} c^{8} d - 4 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 4 \, a^{3} c^{3} d^{6} + 4 \, a^{3} c^{2} d^{7} + a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{9} - a^{3} c^{8} d - 4 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 4 \, a^{3} c^{3} d^{6} + 4 \, a^{3} c^{2} d^{7} + a^{3} c d^{8} - a^{3} d^{9}\right)} f + {\left({\left(a^{3} c^{7} d^{2} - 3 \, a^{3} c^{6} d^{3} + a^{3} c^{5} d^{4} + 5 \, a^{3} c^{4} d^{5} - 5 \, a^{3} c^{3} d^{6} - a^{3} c^{2} d^{7} + 3 \, a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{4} - 2 \, {\left(a^{3} c^{8} d - 2 \, a^{3} c^{7} d^{2} - 2 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{3} d^{6} + 2 \, a^{3} c^{2} d^{7} + 2 \, a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{3} - {\left(a^{3} c^{9} + 3 \, a^{3} c^{8} d - 12 \, a^{3} c^{7} d^{2} - 4 \, a^{3} c^{6} d^{3} + 30 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 28 \, a^{3} c^{3} d^{6} + 12 \, a^{3} c^{2} d^{7} + 9 \, a^{3} c d^{8} - 5 \, a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{9} - a^{3} c^{8} d - 4 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 4 \, a^{3} c^{3} d^{6} + 4 \, a^{3} c^{2} d^{7} + a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{9} - a^{3} c^{8} d - 4 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 4 \, a^{3} c^{3} d^{6} + 4 \, a^{3} c^{2} d^{7} + a^{3} c d^{8} - a^{3} d^{9}\right)} f\right)} \sin\left(f x + e\right)\right)}}, \frac{\sqrt{2} {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{6} - 8 \, {\left(9 \, A + 31 \, B\right)} c^{5} d + 4 \, {\left(117 \, A - 413 \, B\right)} c^{4} d^{2} + 16 \, {\left(177 \, A - 233 \, B\right)} c^{3} d^{3} + 4 \, {\left(1197 \, A - 1013 \, B\right)} c^{2} d^{4} + 8 \, {\left(423 \, A - 271 \, B\right)} c d^{5} + 4 \, {\left(219 \, A - 115 \, B\right)} d^{6} + {\left({\left(3 \, A + 5 \, B\right)} c^{4} d^{2} - 24 \, {\left(A + 3 \, B\right)} c^{3} d^{3} + 2 \, {\left(81 \, A - 137 \, B\right)} c^{2} d^{4} + 24 \, {\left(17 \, A - 13 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{5} + {\left(2 \, {\left(3 \, A + 5 \, B\right)} c^{5} d - 3 \, {\left(13 \, A + 43 \, B\right)} c^{4} d^{2} + 4 \, {\left(63 \, A - 191 \, B\right)} c^{3} d^{3} + 6 \, {\left(217 \, A - 241 \, B\right)} c^{2} d^{4} + 2 \, {\left(831 \, A - 583 \, B\right)} c d^{5} + 3 \, {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 4 \, {\left(3 \, A + 13 \, B\right)} c^{5} d + {\left(75 \, A - 547 \, B\right)} c^{4} d^{2} + 8 \, {\left(123 \, A - 203 \, B\right)} c^{3} d^{3} + 19 \, {\left(123 \, A - 115 \, B\right)} c^{2} d^{4} + 4 \, {\left(525 \, A - 349 \, B\right)} c d^{5} + 3 \, {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(3 \, {\left(3 \, A + 5 \, B\right)} c^{6} - 2 \, {\left(21 \, A + 83 \, B\right)} c^{5} d + {\left(267 \, A - 1507 \, B\right)} c^{4} d^{2} + 4 \, {\left(669 \, A - 1045 \, B\right)} c^{3} d^{3} + {\left(5871 \, A - 5383 \, B\right)} c^{2} d^{4} + 2 \, {\left(2523 \, A - 1667 \, B\right)} c d^{5} + 7 \, {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 2 \, {\left(9 \, A + 31 \, B\right)} c^{5} d + {\left(117 \, A - 413 \, B\right)} c^{4} d^{2} + 4 \, {\left(177 \, A - 233 \, B\right)} c^{3} d^{3} + {\left(1197 \, A - 1013 \, B\right)} c^{2} d^{4} + 2 \, {\left(423 \, A - 271 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) + {\left(4 \, {\left(3 \, A + 5 \, B\right)} c^{6} - 8 \, {\left(9 \, A + 31 \, B\right)} c^{5} d + 4 \, {\left(117 \, A - 413 \, B\right)} c^{4} d^{2} + 16 \, {\left(177 \, A - 233 \, B\right)} c^{3} d^{3} + 4 \, {\left(1197 \, A - 1013 \, B\right)} c^{2} d^{4} + 8 \, {\left(423 \, A - 271 \, B\right)} c d^{5} + 4 \, {\left(219 \, A - 115 \, B\right)} d^{6} + {\left({\left(3 \, A + 5 \, B\right)} c^{4} d^{2} - 24 \, {\left(A + 3 \, B\right)} c^{3} d^{3} + 2 \, {\left(81 \, A - 137 \, B\right)} c^{2} d^{4} + 24 \, {\left(17 \, A - 13 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{5} d - {\left(21 \, A + 67 \, B\right)} c^{4} d^{2} + 2 \, {\left(69 \, A - 173 \, B\right)} c^{3} d^{3} + 2 \, {\left(285 \, A - 293 \, B\right)} c^{2} d^{4} + {\left(627 \, A - 427 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 6 \, {\left(A + 7 \, B\right)} c^{5} d + 3 \, {\left(11 \, A - 227 \, B\right)} c^{4} d^{2} + 12 \, {\left(105 \, A - 193 \, B\right)} c^{3} d^{3} + 3 \, {\left(1159 \, A - 1119 \, B\right)} c^{2} d^{4} + 6 \, {\left(559 \, A - 375 \, B\right)} c d^{5} + 5 \, {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 2 \, {\left(9 \, A + 31 \, B\right)} c^{5} d + {\left(117 \, A - 413 \, B\right)} c^{4} d^{2} + 4 \, {\left(177 \, A - 233 \, B\right)} c^{3} d^{3} + {\left(1197 \, A - 1013 \, B\right)} c^{2} d^{4} + 2 \, {\left(423 \, A - 271 \, B\right)} c d^{5} + {\left(219 \, A - 115 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{a \cos\left(f x + e\right)^{2} - 2 \, \sqrt{2} \sqrt{a \sin\left(f x + e\right) + a} \sqrt{a} {\left(\cos\left(f x + e\right) - \sin\left(f x + e\right) + 1\right)} + 3 \, a \cos\left(f x + e\right) - {\left(a \cos\left(f x + e\right) - 2 \, a\right)} \sin\left(f x + e\right) + 2 \, a}{\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) - 8 \, {\left(140 \, B a c^{5} d - 28 \, {\left(9 \, A - 20 \, B\right)} a c^{4} d^{2} - 8 \, {\left(108 \, A - 121 \, B\right)} a c^{3} d^{3} - 8 \, {\left(141 \, A - 112 \, B\right)} a c^{2} d^{4} - 4 \, {\left(168 \, A - 107 \, B\right)} a c d^{5} - 4 \, {\left(39 \, A - 20 \, B\right)} a d^{6} + {\left(35 \, B a c^{3} d^{3} - 7 \, {\left(9 \, A - 10 \, B\right)} a c^{2} d^{4} - {\left(90 \, A - 67 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{5} + {\left(70 \, B a c^{4} d^{2} - 7 \, {\left(18 \, A - 35 \, B\right)} a c^{3} d^{3} - {\left(369 \, A - 344 \, B\right)} a c^{2} d^{4} - {\left(348 \, A - 241 \, B\right)} a c d^{5} - 3 \, {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left(35 \, B a c^{5} d - 21 \, {\left(3 \, A - 10 \, B\right)} a c^{4} d^{2} - 2 \, {\left(171 \, A - 226 \, B\right)} a c^{3} d^{3} - 6 \, {\left(98 \, A - 83 \, B\right)} a c^{2} d^{4} - {\left(426 \, A - 281 \, B\right)} a c d^{5} - 3 \, {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(105 \, B a c^{5} d - 7 \, {\left(27 \, A - 80 \, B\right)} a c^{4} d^{2} - 6 \, {\left(150 \, A - 191 \, B\right)} a c^{3} d^{3} - 2 \, {\left(729 \, A - 610 \, B\right)} a c^{2} d^{4} - 3 \, {\left(340 \, A - 223 \, B\right)} a c d^{5} - 7 \, {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(35 \, B a c^{5} d - 7 \, {\left(9 \, A - 20 \, B\right)} a c^{4} d^{2} - 2 \, {\left(108 \, A - 121 \, B\right)} a c^{3} d^{3} - 2 \, {\left(141 \, A - 112 \, B\right)} a c^{2} d^{4} - {\left(168 \, A - 107 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right) + {\left(140 \, B a c^{5} d - 28 \, {\left(9 \, A - 20 \, B\right)} a c^{4} d^{2} - 8 \, {\left(108 \, A - 121 \, B\right)} a c^{3} d^{3} - 8 \, {\left(141 \, A - 112 \, B\right)} a c^{2} d^{4} - 4 \, {\left(168 \, A - 107 \, B\right)} a c d^{5} - 4 \, {\left(39 \, A - 20 \, B\right)} a d^{6} + {\left(35 \, B a c^{3} d^{3} - 7 \, {\left(9 \, A - 10 \, B\right)} a c^{2} d^{4} - {\left(90 \, A - 67 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{4} - 2 \, {\left(35 \, B a c^{4} d^{2} - 21 \, {\left(3 \, A - 5 \, B\right)} a c^{3} d^{3} - {\left(153 \, A - 137 \, B\right)} a c^{2} d^{4} - 3 \, {\left(43 \, A - 29 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{3} - {\left(35 \, B a c^{5} d - 7 \, {\left(9 \, A - 40 \, B\right)} a c^{4} d^{2} - 2 \, {\left(234 \, A - 331 \, B\right)} a c^{3} d^{3} - 2 \, {\left(447 \, A - 386 \, B\right)} a c^{2} d^{4} - {\left(684 \, A - 455 \, B\right)} a c d^{5} - 5 \, {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(35 \, B a c^{5} d - 7 \, {\left(9 \, A - 20 \, B\right)} a c^{4} d^{2} - 2 \, {\left(108 \, A - 121 \, B\right)} a c^{3} d^{3} - 2 \, {\left(141 \, A - 112 \, B\right)} a c^{2} d^{4} - {\left(168 \, A - 107 \, B\right)} a c d^{5} - {\left(39 \, A - 20 \, B\right)} a d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \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) - 4 \, {\left(4 \, {\left(A - B\right)} c^{6} - 8 \, {\left(A - B\right)} c^{5} d - 4 \, {\left(A - B\right)} c^{4} d^{2} + 16 \, {\left(A - B\right)} c^{3} d^{3} - 4 \, {\left(A - B\right)} c^{2} d^{4} - 8 \, {\left(A - B\right)} c d^{5} + 4 \, {\left(A - B\right)} d^{6} - {\left({\left(3 \, A + 5 \, B\right)} c^{4} d^{2} - 4 \, {\left(6 \, A - 17 \, B\right)} c^{3} d^{3} - 6 \, {\left(15 \, A - B\right)} c^{2} d^{4} + 4 \, {\left(12 \, A - 11 \, B\right)} c d^{5} + 7 \, {\left(9 \, A - 5 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{4} - {\left(2 \, {\left(3 \, A + 5 \, B\right)} c^{5} d - {\left(41 \, A - 101 \, B\right)} c^{4} d^{2} - 4 \, {\left(38 \, A - 31 \, B\right)} c^{3} d^{3} - 2 \, {\left(39 \, A + 35 \, B\right)} c^{2} d^{4} + 10 \, {\left(17 \, A - 11 \, B\right)} c d^{5} + 5 \, {\left(19 \, A - 11 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} + {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 16 \, {\left(A - B\right)} c^{5} d - {\left(31 \, A - 75 \, B\right)} c^{4} d^{2} - 4 \, {\left(21 \, A - 11 \, B\right)} c^{3} d^{3} - {\left(23 \, A + 49 \, B\right)} c^{2} d^{4} + 20 \, {\left(5 \, A - 3 \, B\right)} c d^{5} + {\left(51 \, A - 31 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} + {\left({\left(7 \, A + B\right)} c^{6} - 2 \, {\left(9 \, A - 17 \, B\right)} c^{5} d - {\left(79 \, A - 175 \, B\right)} c^{4} d^{2} - 28 \, {\left(7 \, A - 3 \, B\right)} c^{3} d^{3} - {\left(15 \, A + 121 \, B\right)} c^{2} d^{4} + 2 \, {\left(107 \, A - 59 \, B\right)} c d^{5} + {\left(87 \, A - 55 \, B\right)} d^{6}\right)} \cos\left(f x + e\right) - {\left(4 \, {\left(A - B\right)} c^{6} - 8 \, {\left(A - B\right)} c^{5} d - 4 \, {\left(A - B\right)} c^{4} d^{2} + 16 \, {\left(A - B\right)} c^{3} d^{3} - 4 \, {\left(A - B\right)} c^{2} d^{4} - 8 \, {\left(A - B\right)} c d^{5} + 4 \, {\left(A - B\right)} d^{6} + {\left({\left(3 \, A + 5 \, B\right)} c^{4} d^{2} - 4 \, {\left(6 \, A - 17 \, B\right)} c^{3} d^{3} - 6 \, {\left(15 \, A - B\right)} c^{2} d^{4} + 4 \, {\left(12 \, A - 11 \, B\right)} c d^{5} + 7 \, {\left(9 \, A - 5 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{3} - 2 \, {\left({\left(3 \, A + 5 \, B\right)} c^{5} d - 2 \, {\left(11 \, A - 24 \, B\right)} c^{4} d^{2} - 4 \, {\left(16 \, A - 7 \, B\right)} c^{3} d^{3} + 2 \, {\left(3 \, A - 19 \, B\right)} c^{2} d^{4} + {\left(61 \, A - 33 \, B\right)} c d^{5} + 2 \, {\left(8 \, A - 5 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)^{2} - {\left({\left(3 \, A + 5 \, B\right)} c^{6} - 2 \, {\left(5 \, A - 13 \, B\right)} c^{5} d - 3 \, {\left(25 \, A - 57 \, B\right)} c^{4} d^{2} - 4 \, {\left(53 \, A - 25 \, B\right)} c^{3} d^{3} - {\left(11 \, A + 125 \, B\right)} c^{2} d^{4} + 6 \, {\left(37 \, A - 21 \, B\right)} c d^{5} + {\left(83 \, A - 51 \, B\right)} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)\right)} \sqrt{a \sin\left(f x + e\right) + a}}{64 \, {\left({\left(a^{3} c^{7} d^{2} - 3 \, a^{3} c^{6} d^{3} + a^{3} c^{5} d^{4} + 5 \, a^{3} c^{4} d^{5} - 5 \, a^{3} c^{3} d^{6} - a^{3} c^{2} d^{7} + 3 \, a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{5} + {\left(2 \, a^{3} c^{8} d - 3 \, a^{3} c^{7} d^{2} - 7 \, a^{3} c^{6} d^{3} + 13 \, a^{3} c^{5} d^{4} + 5 \, a^{3} c^{4} d^{5} - 17 \, a^{3} c^{3} d^{6} + 3 \, a^{3} c^{2} d^{7} + 7 \, a^{3} c d^{8} - 3 \, a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{4} - {\left(a^{3} c^{9} + a^{3} c^{8} d - 8 \, a^{3} c^{7} d^{2} + 18 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 16 \, a^{3} c^{3} d^{6} + 8 \, a^{3} c^{2} d^{7} + 5 \, a^{3} c d^{8} - 3 \, a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{3} - {\left(3 \, a^{3} c^{9} + a^{3} c^{8} d - 20 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 42 \, a^{3} c^{5} d^{4} - 18 \, a^{3} c^{4} d^{5} - 36 \, a^{3} c^{3} d^{6} + 20 \, a^{3} c^{2} d^{7} + 11 \, a^{3} c d^{8} - 7 \, a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{9} - a^{3} c^{8} d - 4 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 4 \, a^{3} c^{3} d^{6} + 4 \, a^{3} c^{2} d^{7} + a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{9} - a^{3} c^{8} d - 4 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 4 \, a^{3} c^{3} d^{6} + 4 \, a^{3} c^{2} d^{7} + a^{3} c d^{8} - a^{3} d^{9}\right)} f + {\left({\left(a^{3} c^{7} d^{2} - 3 \, a^{3} c^{6} d^{3} + a^{3} c^{5} d^{4} + 5 \, a^{3} c^{4} d^{5} - 5 \, a^{3} c^{3} d^{6} - a^{3} c^{2} d^{7} + 3 \, a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{4} - 2 \, {\left(a^{3} c^{8} d - 2 \, a^{3} c^{7} d^{2} - 2 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{3} d^{6} + 2 \, a^{3} c^{2} d^{7} + 2 \, a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{3} - {\left(a^{3} c^{9} + 3 \, a^{3} c^{8} d - 12 \, a^{3} c^{7} d^{2} - 4 \, a^{3} c^{6} d^{3} + 30 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 28 \, a^{3} c^{3} d^{6} + 12 \, a^{3} c^{2} d^{7} + 9 \, a^{3} c d^{8} - 5 \, a^{3} d^{9}\right)} f \cos\left(f x + e\right)^{2} + 2 \, {\left(a^{3} c^{9} - a^{3} c^{8} d - 4 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 4 \, a^{3} c^{3} d^{6} + 4 \, a^{3} c^{2} d^{7} + a^{3} c d^{8} - a^{3} d^{9}\right)} f \cos\left(f x + e\right) + 4 \, {\left(a^{3} c^{9} - a^{3} c^{8} d - 4 \, a^{3} c^{7} d^{2} + 4 \, a^{3} c^{6} d^{3} + 6 \, a^{3} c^{5} d^{4} - 6 \, a^{3} c^{4} d^{5} - 4 \, a^{3} c^{3} d^{6} + 4 \, a^{3} c^{2} d^{7} + a^{3} c d^{8} - a^{3} d^{9}\right)} f\right)} \sin\left(f x + e\right)\right)}}\right]"," ",0,"[1/64*(sqrt(2)*(4*(3*A + 5*B)*c^6 - 8*(9*A + 31*B)*c^5*d + 4*(117*A - 413*B)*c^4*d^2 + 16*(177*A - 233*B)*c^3*d^3 + 4*(1197*A - 1013*B)*c^2*d^4 + 8*(423*A - 271*B)*c*d^5 + 4*(219*A - 115*B)*d^6 + ((3*A + 5*B)*c^4*d^2 - 24*(A + 3*B)*c^3*d^3 + 2*(81*A - 137*B)*c^2*d^4 + 24*(17*A - 13*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e)^5 + (2*(3*A + 5*B)*c^5*d - 3*(13*A + 43*B)*c^4*d^2 + 4*(63*A - 191*B)*c^3*d^3 + 6*(217*A - 241*B)*c^2*d^4 + 2*(831*A - 583*B)*c*d^5 + 3*(219*A - 115*B)*d^6)*cos(f*x + e)^4 - ((3*A + 5*B)*c^6 - 4*(3*A + 13*B)*c^5*d + (75*A - 547*B)*c^4*d^2 + 8*(123*A - 203*B)*c^3*d^3 + 19*(123*A - 115*B)*c^2*d^4 + 4*(525*A - 349*B)*c*d^5 + 3*(219*A - 115*B)*d^6)*cos(f*x + e)^3 - (3*(3*A + 5*B)*c^6 - 2*(21*A + 83*B)*c^5*d + (267*A - 1507*B)*c^4*d^2 + 4*(669*A - 1045*B)*c^3*d^3 + (5871*A - 5383*B)*c^2*d^4 + 2*(2523*A - 1667*B)*c*d^5 + 7*(219*A - 115*B)*d^6)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^6 - 2*(9*A + 31*B)*c^5*d + (117*A - 413*B)*c^4*d^2 + 4*(177*A - 233*B)*c^3*d^3 + (1197*A - 1013*B)*c^2*d^4 + 2*(423*A - 271*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e) + (4*(3*A + 5*B)*c^6 - 8*(9*A + 31*B)*c^5*d + 4*(117*A - 413*B)*c^4*d^2 + 16*(177*A - 233*B)*c^3*d^3 + 4*(1197*A - 1013*B)*c^2*d^4 + 8*(423*A - 271*B)*c*d^5 + 4*(219*A - 115*B)*d^6 + ((3*A + 5*B)*c^4*d^2 - 24*(A + 3*B)*c^3*d^3 + 2*(81*A - 137*B)*c^2*d^4 + 24*(17*A - 13*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e)^4 - 2*((3*A + 5*B)*c^5*d - (21*A + 67*B)*c^4*d^2 + 2*(69*A - 173*B)*c^3*d^3 + 2*(285*A - 293*B)*c^2*d^4 + (627*A - 427*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e)^3 - ((3*A + 5*B)*c^6 - 6*(A + 7*B)*c^5*d + 3*(11*A - 227*B)*c^4*d^2 + 12*(105*A - 193*B)*c^3*d^3 + 3*(1159*A - 1119*B)*c^2*d^4 + 6*(559*A - 375*B)*c*d^5 + 5*(219*A - 115*B)*d^6)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^6 - 2*(9*A + 31*B)*c^5*d + (117*A - 413*B)*c^4*d^2 + 4*(177*A - 233*B)*c^3*d^3 + (1197*A - 1013*B)*c^2*d^4 + 2*(423*A - 271*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 4*(140*B*a*c^5*d - 28*(9*A - 20*B)*a*c^4*d^2 - 8*(108*A - 121*B)*a*c^3*d^3 - 8*(141*A - 112*B)*a*c^2*d^4 - 4*(168*A - 107*B)*a*c*d^5 - 4*(39*A - 20*B)*a*d^6 + (35*B*a*c^3*d^3 - 7*(9*A - 10*B)*a*c^2*d^4 - (90*A - 67*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e)^5 + (70*B*a*c^4*d^2 - 7*(18*A - 35*B)*a*c^3*d^3 - (369*A - 344*B)*a*c^2*d^4 - (348*A - 241*B)*a*c*d^5 - 3*(39*A - 20*B)*a*d^6)*cos(f*x + e)^4 - (35*B*a*c^5*d - 21*(3*A - 10*B)*a*c^4*d^2 - 2*(171*A - 226*B)*a*c^3*d^3 - 6*(98*A - 83*B)*a*c^2*d^4 - (426*A - 281*B)*a*c*d^5 - 3*(39*A - 20*B)*a*d^6)*cos(f*x + e)^3 - (105*B*a*c^5*d - 7*(27*A - 80*B)*a*c^4*d^2 - 6*(150*A - 191*B)*a*c^3*d^3 - 2*(729*A - 610*B)*a*c^2*d^4 - 3*(340*A - 223*B)*a*c*d^5 - 7*(39*A - 20*B)*a*d^6)*cos(f*x + e)^2 + 2*(35*B*a*c^5*d - 7*(9*A - 20*B)*a*c^4*d^2 - 2*(108*A - 121*B)*a*c^3*d^3 - 2*(141*A - 112*B)*a*c^2*d^4 - (168*A - 107*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e) + (140*B*a*c^5*d - 28*(9*A - 20*B)*a*c^4*d^2 - 8*(108*A - 121*B)*a*c^3*d^3 - 8*(141*A - 112*B)*a*c^2*d^4 - 4*(168*A - 107*B)*a*c*d^5 - 4*(39*A - 20*B)*a*d^6 + (35*B*a*c^3*d^3 - 7*(9*A - 10*B)*a*c^2*d^4 - (90*A - 67*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e)^4 - 2*(35*B*a*c^4*d^2 - 21*(3*A - 5*B)*a*c^3*d^3 - (153*A - 137*B)*a*c^2*d^4 - 3*(43*A - 29*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e)^3 - (35*B*a*c^5*d - 7*(9*A - 40*B)*a*c^4*d^2 - 2*(234*A - 331*B)*a*c^3*d^3 - 2*(447*A - 386*B)*a*c^2*d^4 - (684*A - 455*B)*a*c*d^5 - 5*(39*A - 20*B)*a*d^6)*cos(f*x + e)^2 + 2*(35*B*a*c^5*d - 7*(9*A - 20*B)*a*c^4*d^2 - 2*(108*A - 121*B)*a*c^3*d^3 - 2*(141*A - 112*B)*a*c^2*d^4 - (168*A - 107*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e))*sin(f*x + e))*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))) - 4*(4*(A - B)*c^6 - 8*(A - B)*c^5*d - 4*(A - B)*c^4*d^2 + 16*(A - B)*c^3*d^3 - 4*(A - B)*c^2*d^4 - 8*(A - B)*c*d^5 + 4*(A - B)*d^6 - ((3*A + 5*B)*c^4*d^2 - 4*(6*A - 17*B)*c^3*d^3 - 6*(15*A - B)*c^2*d^4 + 4*(12*A - 11*B)*c*d^5 + 7*(9*A - 5*B)*d^6)*cos(f*x + e)^4 - (2*(3*A + 5*B)*c^5*d - (41*A - 101*B)*c^4*d^2 - 4*(38*A - 31*B)*c^3*d^3 - 2*(39*A + 35*B)*c^2*d^4 + 10*(17*A - 11*B)*c*d^5 + 5*(19*A - 11*B)*d^6)*cos(f*x + e)^3 + ((3*A + 5*B)*c^6 - 16*(A - B)*c^5*d - (31*A - 75*B)*c^4*d^2 - 4*(21*A - 11*B)*c^3*d^3 - (23*A + 49*B)*c^2*d^4 + 20*(5*A - 3*B)*c*d^5 + (51*A - 31*B)*d^6)*cos(f*x + e)^2 + ((7*A + B)*c^6 - 2*(9*A - 17*B)*c^5*d - (79*A - 175*B)*c^4*d^2 - 28*(7*A - 3*B)*c^3*d^3 - (15*A + 121*B)*c^2*d^4 + 2*(107*A - 59*B)*c*d^5 + (87*A - 55*B)*d^6)*cos(f*x + e) - (4*(A - B)*c^6 - 8*(A - B)*c^5*d - 4*(A - B)*c^4*d^2 + 16*(A - B)*c^3*d^3 - 4*(A - B)*c^2*d^4 - 8*(A - B)*c*d^5 + 4*(A - B)*d^6 + ((3*A + 5*B)*c^4*d^2 - 4*(6*A - 17*B)*c^3*d^3 - 6*(15*A - B)*c^2*d^4 + 4*(12*A - 11*B)*c*d^5 + 7*(9*A - 5*B)*d^6)*cos(f*x + e)^3 - 2*((3*A + 5*B)*c^5*d - 2*(11*A - 24*B)*c^4*d^2 - 4*(16*A - 7*B)*c^3*d^3 + 2*(3*A - 19*B)*c^2*d^4 + (61*A - 33*B)*c*d^5 + 2*(8*A - 5*B)*d^6)*cos(f*x + e)^2 - ((3*A + 5*B)*c^6 - 2*(5*A - 13*B)*c^5*d - 3*(25*A - 57*B)*c^4*d^2 - 4*(53*A - 25*B)*c^3*d^3 - (11*A + 125*B)*c^2*d^4 + 6*(37*A - 21*B)*c*d^5 + (83*A - 51*B)*d^6)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^3*c^7*d^2 - 3*a^3*c^6*d^3 + a^3*c^5*d^4 + 5*a^3*c^4*d^5 - 5*a^3*c^3*d^6 - a^3*c^2*d^7 + 3*a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e)^5 + (2*a^3*c^8*d - 3*a^3*c^7*d^2 - 7*a^3*c^6*d^3 + 13*a^3*c^5*d^4 + 5*a^3*c^4*d^5 - 17*a^3*c^3*d^6 + 3*a^3*c^2*d^7 + 7*a^3*c*d^8 - 3*a^3*d^9)*f*cos(f*x + e)^4 - (a^3*c^9 + a^3*c^8*d - 8*a^3*c^7*d^2 + 18*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 16*a^3*c^3*d^6 + 8*a^3*c^2*d^7 + 5*a^3*c*d^8 - 3*a^3*d^9)*f*cos(f*x + e)^3 - (3*a^3*c^9 + a^3*c^8*d - 20*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 42*a^3*c^5*d^4 - 18*a^3*c^4*d^5 - 36*a^3*c^3*d^6 + 20*a^3*c^2*d^7 + 11*a^3*c*d^8 - 7*a^3*d^9)*f*cos(f*x + e)^2 + 2*(a^3*c^9 - a^3*c^8*d - 4*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 4*a^3*c^3*d^6 + 4*a^3*c^2*d^7 + a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e) + 4*(a^3*c^9 - a^3*c^8*d - 4*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 4*a^3*c^3*d^6 + 4*a^3*c^2*d^7 + a^3*c*d^8 - a^3*d^9)*f + ((a^3*c^7*d^2 - 3*a^3*c^6*d^3 + a^3*c^5*d^4 + 5*a^3*c^4*d^5 - 5*a^3*c^3*d^6 - a^3*c^2*d^7 + 3*a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e)^4 - 2*(a^3*c^8*d - 2*a^3*c^7*d^2 - 2*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^3*d^6 + 2*a^3*c^2*d^7 + 2*a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e)^3 - (a^3*c^9 + 3*a^3*c^8*d - 12*a^3*c^7*d^2 - 4*a^3*c^6*d^3 + 30*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 28*a^3*c^3*d^6 + 12*a^3*c^2*d^7 + 9*a^3*c*d^8 - 5*a^3*d^9)*f*cos(f*x + e)^2 + 2*(a^3*c^9 - a^3*c^8*d - 4*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 4*a^3*c^3*d^6 + 4*a^3*c^2*d^7 + a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e) + 4*(a^3*c^9 - a^3*c^8*d - 4*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 4*a^3*c^3*d^6 + 4*a^3*c^2*d^7 + a^3*c*d^8 - a^3*d^9)*f)*sin(f*x + e)), 1/64*(sqrt(2)*(4*(3*A + 5*B)*c^6 - 8*(9*A + 31*B)*c^5*d + 4*(117*A - 413*B)*c^4*d^2 + 16*(177*A - 233*B)*c^3*d^3 + 4*(1197*A - 1013*B)*c^2*d^4 + 8*(423*A - 271*B)*c*d^5 + 4*(219*A - 115*B)*d^6 + ((3*A + 5*B)*c^4*d^2 - 24*(A + 3*B)*c^3*d^3 + 2*(81*A - 137*B)*c^2*d^4 + 24*(17*A - 13*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e)^5 + (2*(3*A + 5*B)*c^5*d - 3*(13*A + 43*B)*c^4*d^2 + 4*(63*A - 191*B)*c^3*d^3 + 6*(217*A - 241*B)*c^2*d^4 + 2*(831*A - 583*B)*c*d^5 + 3*(219*A - 115*B)*d^6)*cos(f*x + e)^4 - ((3*A + 5*B)*c^6 - 4*(3*A + 13*B)*c^5*d + (75*A - 547*B)*c^4*d^2 + 8*(123*A - 203*B)*c^3*d^3 + 19*(123*A - 115*B)*c^2*d^4 + 4*(525*A - 349*B)*c*d^5 + 3*(219*A - 115*B)*d^6)*cos(f*x + e)^3 - (3*(3*A + 5*B)*c^6 - 2*(21*A + 83*B)*c^5*d + (267*A - 1507*B)*c^4*d^2 + 4*(669*A - 1045*B)*c^3*d^3 + (5871*A - 5383*B)*c^2*d^4 + 2*(2523*A - 1667*B)*c*d^5 + 7*(219*A - 115*B)*d^6)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^6 - 2*(9*A + 31*B)*c^5*d + (117*A - 413*B)*c^4*d^2 + 4*(177*A - 233*B)*c^3*d^3 + (1197*A - 1013*B)*c^2*d^4 + 2*(423*A - 271*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e) + (4*(3*A + 5*B)*c^6 - 8*(9*A + 31*B)*c^5*d + 4*(117*A - 413*B)*c^4*d^2 + 16*(177*A - 233*B)*c^3*d^3 + 4*(1197*A - 1013*B)*c^2*d^4 + 8*(423*A - 271*B)*c*d^5 + 4*(219*A - 115*B)*d^6 + ((3*A + 5*B)*c^4*d^2 - 24*(A + 3*B)*c^3*d^3 + 2*(81*A - 137*B)*c^2*d^4 + 24*(17*A - 13*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e)^4 - 2*((3*A + 5*B)*c^5*d - (21*A + 67*B)*c^4*d^2 + 2*(69*A - 173*B)*c^3*d^3 + 2*(285*A - 293*B)*c^2*d^4 + (627*A - 427*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e)^3 - ((3*A + 5*B)*c^6 - 6*(A + 7*B)*c^5*d + 3*(11*A - 227*B)*c^4*d^2 + 12*(105*A - 193*B)*c^3*d^3 + 3*(1159*A - 1119*B)*c^2*d^4 + 6*(559*A - 375*B)*c*d^5 + 5*(219*A - 115*B)*d^6)*cos(f*x + e)^2 + 2*((3*A + 5*B)*c^6 - 2*(9*A + 31*B)*c^5*d + (117*A - 413*B)*c^4*d^2 + 4*(177*A - 233*B)*c^3*d^3 + (1197*A - 1013*B)*c^2*d^4 + 2*(423*A - 271*B)*c*d^5 + (219*A - 115*B)*d^6)*cos(f*x + e))*sin(f*x + e))*sqrt(a)*log(-(a*cos(f*x + e)^2 - 2*sqrt(2)*sqrt(a*sin(f*x + e) + a)*sqrt(a)*(cos(f*x + e) - sin(f*x + e) + 1) + 3*a*cos(f*x + e) - (a*cos(f*x + e) - 2*a)*sin(f*x + e) + 2*a)/(cos(f*x + e)^2 - (cos(f*x + e) + 2)*sin(f*x + e) - cos(f*x + e) - 2)) - 8*(140*B*a*c^5*d - 28*(9*A - 20*B)*a*c^4*d^2 - 8*(108*A - 121*B)*a*c^3*d^3 - 8*(141*A - 112*B)*a*c^2*d^4 - 4*(168*A - 107*B)*a*c*d^5 - 4*(39*A - 20*B)*a*d^6 + (35*B*a*c^3*d^3 - 7*(9*A - 10*B)*a*c^2*d^4 - (90*A - 67*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e)^5 + (70*B*a*c^4*d^2 - 7*(18*A - 35*B)*a*c^3*d^3 - (369*A - 344*B)*a*c^2*d^4 - (348*A - 241*B)*a*c*d^5 - 3*(39*A - 20*B)*a*d^6)*cos(f*x + e)^4 - (35*B*a*c^5*d - 21*(3*A - 10*B)*a*c^4*d^2 - 2*(171*A - 226*B)*a*c^3*d^3 - 6*(98*A - 83*B)*a*c^2*d^4 - (426*A - 281*B)*a*c*d^5 - 3*(39*A - 20*B)*a*d^6)*cos(f*x + e)^3 - (105*B*a*c^5*d - 7*(27*A - 80*B)*a*c^4*d^2 - 6*(150*A - 191*B)*a*c^3*d^3 - 2*(729*A - 610*B)*a*c^2*d^4 - 3*(340*A - 223*B)*a*c*d^5 - 7*(39*A - 20*B)*a*d^6)*cos(f*x + e)^2 + 2*(35*B*a*c^5*d - 7*(9*A - 20*B)*a*c^4*d^2 - 2*(108*A - 121*B)*a*c^3*d^3 - 2*(141*A - 112*B)*a*c^2*d^4 - (168*A - 107*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e) + (140*B*a*c^5*d - 28*(9*A - 20*B)*a*c^4*d^2 - 8*(108*A - 121*B)*a*c^3*d^3 - 8*(141*A - 112*B)*a*c^2*d^4 - 4*(168*A - 107*B)*a*c*d^5 - 4*(39*A - 20*B)*a*d^6 + (35*B*a*c^3*d^3 - 7*(9*A - 10*B)*a*c^2*d^4 - (90*A - 67*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e)^4 - 2*(35*B*a*c^4*d^2 - 21*(3*A - 5*B)*a*c^3*d^3 - (153*A - 137*B)*a*c^2*d^4 - 3*(43*A - 29*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e)^3 - (35*B*a*c^5*d - 7*(9*A - 40*B)*a*c^4*d^2 - 2*(234*A - 331*B)*a*c^3*d^3 - 2*(447*A - 386*B)*a*c^2*d^4 - (684*A - 455*B)*a*c*d^5 - 5*(39*A - 20*B)*a*d^6)*cos(f*x + e)^2 + 2*(35*B*a*c^5*d - 7*(9*A - 20*B)*a*c^4*d^2 - 2*(108*A - 121*B)*a*c^3*d^3 - 2*(141*A - 112*B)*a*c^2*d^4 - (168*A - 107*B)*a*c*d^5 - (39*A - 20*B)*a*d^6)*cos(f*x + e))*sin(f*x + e))*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))) - 4*(4*(A - B)*c^6 - 8*(A - B)*c^5*d - 4*(A - B)*c^4*d^2 + 16*(A - B)*c^3*d^3 - 4*(A - B)*c^2*d^4 - 8*(A - B)*c*d^5 + 4*(A - B)*d^6 - ((3*A + 5*B)*c^4*d^2 - 4*(6*A - 17*B)*c^3*d^3 - 6*(15*A - B)*c^2*d^4 + 4*(12*A - 11*B)*c*d^5 + 7*(9*A - 5*B)*d^6)*cos(f*x + e)^4 - (2*(3*A + 5*B)*c^5*d - (41*A - 101*B)*c^4*d^2 - 4*(38*A - 31*B)*c^3*d^3 - 2*(39*A + 35*B)*c^2*d^4 + 10*(17*A - 11*B)*c*d^5 + 5*(19*A - 11*B)*d^6)*cos(f*x + e)^3 + ((3*A + 5*B)*c^6 - 16*(A - B)*c^5*d - (31*A - 75*B)*c^4*d^2 - 4*(21*A - 11*B)*c^3*d^3 - (23*A + 49*B)*c^2*d^4 + 20*(5*A - 3*B)*c*d^5 + (51*A - 31*B)*d^6)*cos(f*x + e)^2 + ((7*A + B)*c^6 - 2*(9*A - 17*B)*c^5*d - (79*A - 175*B)*c^4*d^2 - 28*(7*A - 3*B)*c^3*d^3 - (15*A + 121*B)*c^2*d^4 + 2*(107*A - 59*B)*c*d^5 + (87*A - 55*B)*d^6)*cos(f*x + e) - (4*(A - B)*c^6 - 8*(A - B)*c^5*d - 4*(A - B)*c^4*d^2 + 16*(A - B)*c^3*d^3 - 4*(A - B)*c^2*d^4 - 8*(A - B)*c*d^5 + 4*(A - B)*d^6 + ((3*A + 5*B)*c^4*d^2 - 4*(6*A - 17*B)*c^3*d^3 - 6*(15*A - B)*c^2*d^4 + 4*(12*A - 11*B)*c*d^5 + 7*(9*A - 5*B)*d^6)*cos(f*x + e)^3 - 2*((3*A + 5*B)*c^5*d - 2*(11*A - 24*B)*c^4*d^2 - 4*(16*A - 7*B)*c^3*d^3 + 2*(3*A - 19*B)*c^2*d^4 + (61*A - 33*B)*c*d^5 + 2*(8*A - 5*B)*d^6)*cos(f*x + e)^2 - ((3*A + 5*B)*c^6 - 2*(5*A - 13*B)*c^5*d - 3*(25*A - 57*B)*c^4*d^2 - 4*(53*A - 25*B)*c^3*d^3 - (11*A + 125*B)*c^2*d^4 + 6*(37*A - 21*B)*c*d^5 + (83*A - 51*B)*d^6)*cos(f*x + e))*sin(f*x + e))*sqrt(a*sin(f*x + e) + a))/((a^3*c^7*d^2 - 3*a^3*c^6*d^3 + a^3*c^5*d^4 + 5*a^3*c^4*d^5 - 5*a^3*c^3*d^6 - a^3*c^2*d^7 + 3*a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e)^5 + (2*a^3*c^8*d - 3*a^3*c^7*d^2 - 7*a^3*c^6*d^3 + 13*a^3*c^5*d^4 + 5*a^3*c^4*d^5 - 17*a^3*c^3*d^6 + 3*a^3*c^2*d^7 + 7*a^3*c*d^8 - 3*a^3*d^9)*f*cos(f*x + e)^4 - (a^3*c^9 + a^3*c^8*d - 8*a^3*c^7*d^2 + 18*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 16*a^3*c^3*d^6 + 8*a^3*c^2*d^7 + 5*a^3*c*d^8 - 3*a^3*d^9)*f*cos(f*x + e)^3 - (3*a^3*c^9 + a^3*c^8*d - 20*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 42*a^3*c^5*d^4 - 18*a^3*c^4*d^5 - 36*a^3*c^3*d^6 + 20*a^3*c^2*d^7 + 11*a^3*c*d^8 - 7*a^3*d^9)*f*cos(f*x + e)^2 + 2*(a^3*c^9 - a^3*c^8*d - 4*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 4*a^3*c^3*d^6 + 4*a^3*c^2*d^7 + a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e) + 4*(a^3*c^9 - a^3*c^8*d - 4*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 4*a^3*c^3*d^6 + 4*a^3*c^2*d^7 + a^3*c*d^8 - a^3*d^9)*f + ((a^3*c^7*d^2 - 3*a^3*c^6*d^3 + a^3*c^5*d^4 + 5*a^3*c^4*d^5 - 5*a^3*c^3*d^6 - a^3*c^2*d^7 + 3*a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e)^4 - 2*(a^3*c^8*d - 2*a^3*c^7*d^2 - 2*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^3*d^6 + 2*a^3*c^2*d^7 + 2*a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e)^3 - (a^3*c^9 + 3*a^3*c^8*d - 12*a^3*c^7*d^2 - 4*a^3*c^6*d^3 + 30*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 28*a^3*c^3*d^6 + 12*a^3*c^2*d^7 + 9*a^3*c*d^8 - 5*a^3*d^9)*f*cos(f*x + e)^2 + 2*(a^3*c^9 - a^3*c^8*d - 4*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 4*a^3*c^3*d^6 + 4*a^3*c^2*d^7 + a^3*c*d^8 - a^3*d^9)*f*cos(f*x + e) + 4*(a^3*c^9 - a^3*c^8*d - 4*a^3*c^7*d^2 + 4*a^3*c^6*d^3 + 6*a^3*c^5*d^4 - 6*a^3*c^4*d^5 - 4*a^3*c^3*d^6 + 4*a^3*c^2*d^7 + a^3*c*d^8 - a^3*d^9)*f)*sin(f*x + e))]","B",0
328,0,0,0,1.034409," ","integrate((a+a*sin(f*x+e))^2*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left({\left(A + 2 \, B\right)} a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2} + {\left(B a^{2} \cos\left(f x + e\right)^{2} - 2 \, {\left(A + B\right)} a^{2}\right)} \sin\left(f x + e\right)\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-((A + 2*B)*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2 + (B*a^2*cos(f*x + e)^2 - 2*(A + B)*a^2)*sin(f*x + e))*(d*sin(f*x + e) + c)^n, x)","F",0
329,0,0,0,1.169281," ","integrate((a+a*sin(f*x+e))*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(B a \cos\left(f x + e\right)^{2} - {\left(A + B\right)} a \sin\left(f x + e\right) - {\left(A + B\right)} a\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(B*a*cos(f*x + e)^2 - (A + B)*a*sin(f*x + e) - (A + B)*a)*(d*sin(f*x + e) + c)^n, x)","F",0
330,0,0,0,0.753605," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a \sin\left(f x + e\right) + a}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^n/(a*sin(f*x + e) + a), x)","F",0
331,0,0,0,1.003291," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^n/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
332,0,0,0,1.179899," ","integrate((a+a*sin(f*x+e))^(3/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(B a \cos\left(f x + e\right)^{2} - {\left(A + B\right)} a \sin\left(f x + e\right) - {\left(A + B\right)} a\right)} \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(B*a*cos(f*x + e)^2 - (A + B)*a*sin(f*x + e) - (A + B)*a)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n, x)","F",0
333,0,0,0,1.084058," ","integrate((a+a*sin(f*x+e))^(1/2)*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n, x)","F",0
334,0,0,0,1.095630," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{\sqrt{a \sin\left(f x + e\right) + a}}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(d*sin(f*x + e) + c)^n/sqrt(a*sin(f*x + e) + a), x)","F",0
335,0,0,0,1.164441," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n/(a+a*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{a \sin\left(f x + e\right) + a} {\left(d \sin\left(f x + e\right) + c\right)}^{n}}{a^{2} \cos\left(f x + e\right)^{2} - 2 \, a^{2} \sin\left(f x + e\right) - 2 \, a^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(a*sin(f*x + e) + a)*(d*sin(f*x + e) + c)^n/(a^2*cos(f*x + e)^2 - 2*a^2*sin(f*x + e) - 2*a^2), x)","F",0
336,0,0,0,0.889678," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(A c^{2} + 2 \, B c d + A d^{2} - {\left(2 \, B c d + A d^{2}\right)} \cos\left(f x + e\right)^{2} - {\left(B d^{2} \cos\left(f x + e\right)^{2} - B c^{2} - 2 \, A c d - B d^{2}\right)} \sin\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((A*c^2 + 2*B*c*d + A*d^2 - (2*B*c*d + A*d^2)*cos(f*x + e)^2 - (B*d^2*cos(f*x + e)^2 - B*c^2 - 2*A*c*d - B*d^2)*sin(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
337,0,0,0,1.049376," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(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)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(B*d*cos(f*x + e)^2 - A*c - B*d - (B*c + A*d)*sin(f*x + e))*(a*sin(f*x + e) + a)^m, x)","F",0
338,0,0,0,1.016319," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m, x)","F",0
339,0,0,0,0.980669," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{d \sin\left(f x + e\right) + c}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(d*sin(f*x + e) + c), x)","F",0
340,0,0,0,0.918280," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2), x)","F",0
341,0,0,0,1.232523," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{3 \, c d^{2} \cos\left(f x + e\right)^{2} - c^{3} - 3 \, c d^{2} + {\left(d^{3} \cos\left(f x + e\right)^{2} - 3 \, c^{2} d - d^{3}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/(3*c*d^2*cos(f*x + e)^2 - c^3 - 3*c*d^2 + (d^3*cos(f*x + e)^2 - 3*c^2*d - d^3)*sin(f*x + e)), x)","F",0
342,0,0,0,1.282763," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(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)\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral(-(B*d*cos(f*x + e)^2 - A*c - B*d - (B*c + A*d)*sin(f*x + e))*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
343,0,0,0,1.256108," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m, x)","F",0
344,0,0,0,1.325861," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{\sqrt{d \sin\left(f x + e\right) + c}}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m/sqrt(d*sin(f*x + e) + c), x)","F",0
345,0,0,0,1.146155," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{d \sin\left(f x + e\right) + c} {\left(a \sin\left(f x + e\right) + a\right)}^{m}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(d*sin(f*x + e) + c)*(a*sin(f*x + e) + a)^m/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2), x)","F",0
346,0,0,0,1.199228," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
347,0,0,0,1.215364," ","integrate((a+a*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(-1-m),x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 1}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 1), x)","F",0
348,0,0,0,1.203732," ","integrate((a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a \sin\left(f x + e\right) - a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral(-(a*sin(f*x + e) - a)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
349,0,0,0,1.100399," ","integrate((a-a*sin(f*x+e))*(a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-1-m),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(a \sin\left(f x + e\right) - a\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 1}, x\right)"," ",0,"integral(-(a*sin(f*x + e) - a)*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 1), x)","F",0
350,1,56,0,1.160997," ","integrate((a+a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(d-(c-d)*m+(c+(c-d)*m)*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(d \cos\left(f x + e\right) \sin\left(f x + e\right) + c \cos\left(f x + e\right)\right)} {\left(a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 2}}{f}"," ",0,"-(d*cos(f*x + e)*sin(f*x + e) + c*cos(f*x + e))*(a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 2)/f","A",0
351,1,57,0,1.241806," ","integrate((a-a*sin(f*x+e))^m*(c+d*sin(f*x+e))^(-2-m)*(d+(c+d)*m+(c+(c+d)*m)*sin(f*x+e)),x, algorithm=""fricas"")","-\frac{{\left(d \cos\left(f x + e\right) \sin\left(f x + e\right) + c \cos\left(f x + e\right)\right)} {\left(-a \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{-m - 2}}{f}"," ",0,"-(d*cos(f*x + e)*sin(f*x + e) + c*cos(f*x + e))*(-a*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^(-m - 2)/f","A",0
352,1,1308,0,1.335152," ","integrate((a+b*sin(f*x+e))^2*(A+B*sin(f*x+e))/(c+d*sin(f*x+e))^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(2 \, B b^{2} c^{6} - 4 \, B b^{2} c^{4} d^{2} + 2 \, B b^{2} c^{2} d^{4} - {\left(2 \, B a b + A b^{2}\right)} c^{5} d + 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{3} d^{3} - {\left(2 \, B a b + A b^{2}\right)} c d^{5}\right)} f x + {\left(2 \, B b^{2} c^{5} - 3 \, B b^{2} c^{3} d^{2} - {\left(2 \, B a b + A b^{2}\right)} c^{4} d + {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} c^{2} d^{3} - {\left(B a^{2} + 2 \, A a b\right)} c d^{4} + {\left(2 \, B b^{2} c^{4} d - 3 \, B b^{2} c^{2} d^{3} - {\left(2 \, B a b + A b^{2}\right)} c^{3} d^{2} + {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} c d^{4} - {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} \sin\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}} \log\left(\frac{{\left(2 \, c^{2} - d^{2}\right)} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2} + 2 \, {\left(c \cos\left(f x + e\right) \sin\left(f x + e\right) + d \cos\left(f x + e\right)\right)} \sqrt{-c^{2} + d^{2}}}{d^{2} \cos\left(f x + e\right)^{2} - 2 \, c d \sin\left(f x + e\right) - c^{2} - d^{2}}\right) + 2 \, {\left(2 \, B b^{2} c^{5} d + A a^{2} d^{6} - {\left(2 \, B a b + A b^{2}\right)} c^{4} d^{2} + {\left(B a^{2} + 2 \, A a b - 3 \, B b^{2}\right)} c^{3} d^{3} - {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} c^{2} d^{4} - {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} c d^{5}\right)} \cos\left(f x + e\right) + 2 \, {\left({\left(2 \, B b^{2} c^{5} d - 4 \, B b^{2} c^{3} d^{3} + 2 \, B b^{2} c d^{5} - {\left(2 \, B a b + A b^{2}\right)} c^{4} d^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d^{4} - {\left(2 \, B a b + A b^{2}\right)} d^{6}\right)} f x + {\left(B b^{2} c^{4} d^{2} - 2 \, B b^{2} c^{2} d^{4} + B b^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{2 \, {\left({\left(c^{4} d^{4} - 2 \, c^{2} d^{6} + d^{8}\right)} f \sin\left(f x + e\right) + {\left(c^{5} d^{3} - 2 \, c^{3} d^{5} + c d^{7}\right)} f\right)}}, -\frac{{\left(2 \, B b^{2} c^{6} - 4 \, B b^{2} c^{4} d^{2} + 2 \, B b^{2} c^{2} d^{4} - {\left(2 \, B a b + A b^{2}\right)} c^{5} d + 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{3} d^{3} - {\left(2 \, B a b + A b^{2}\right)} c d^{5}\right)} f x + {\left(2 \, B b^{2} c^{5} - 3 \, B b^{2} c^{3} d^{2} - {\left(2 \, B a b + A b^{2}\right)} c^{4} d + {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} c^{2} d^{3} - {\left(B a^{2} + 2 \, A a b\right)} c d^{4} + {\left(2 \, B b^{2} c^{4} d - 3 \, B b^{2} c^{2} d^{3} - {\left(2 \, B a b + A b^{2}\right)} c^{3} d^{2} + {\left(A a^{2} + 4 \, B a b + 2 \, A b^{2}\right)} c d^{4} - {\left(B a^{2} + 2 \, A a b\right)} d^{5}\right)} \sin\left(f x + e\right)\right)} \sqrt{c^{2} - d^{2}} \arctan\left(-\frac{c \sin\left(f x + e\right) + d}{\sqrt{c^{2} - d^{2}} \cos\left(f x + e\right)}\right) + {\left(2 \, B b^{2} c^{5} d + A a^{2} d^{6} - {\left(2 \, B a b + A b^{2}\right)} c^{4} d^{2} + {\left(B a^{2} + 2 \, A a b - 3 \, B b^{2}\right)} c^{3} d^{3} - {\left(A a^{2} - 2 \, B a b - A b^{2}\right)} c^{2} d^{4} - {\left(B a^{2} + 2 \, A a b - B b^{2}\right)} c d^{5}\right)} \cos\left(f x + e\right) + {\left({\left(2 \, B b^{2} c^{5} d - 4 \, B b^{2} c^{3} d^{3} + 2 \, B b^{2} c d^{5} - {\left(2 \, B a b + A b^{2}\right)} c^{4} d^{2} + 2 \, {\left(2 \, B a b + A b^{2}\right)} c^{2} d^{4} - {\left(2 \, B a b + A b^{2}\right)} d^{6}\right)} f x + {\left(B b^{2} c^{4} d^{2} - 2 \, B b^{2} c^{2} d^{4} + B b^{2} d^{6}\right)} \cos\left(f x + e\right)\right)} \sin\left(f x + e\right)}{{\left(c^{4} d^{4} - 2 \, c^{2} d^{6} + d^{8}\right)} f \sin\left(f x + e\right) + {\left(c^{5} d^{3} - 2 \, c^{3} d^{5} + c d^{7}\right)} f}\right]"," ",0,"[-1/2*(2*(2*B*b^2*c^6 - 4*B*b^2*c^4*d^2 + 2*B*b^2*c^2*d^4 - (2*B*a*b + A*b^2)*c^5*d + 2*(2*B*a*b + A*b^2)*c^3*d^3 - (2*B*a*b + A*b^2)*c*d^5)*f*x + (2*B*b^2*c^5 - 3*B*b^2*c^3*d^2 - (2*B*a*b + A*b^2)*c^4*d + (A*a^2 + 4*B*a*b + 2*A*b^2)*c^2*d^3 - (B*a^2 + 2*A*a*b)*c*d^4 + (2*B*b^2*c^4*d - 3*B*b^2*c^2*d^3 - (2*B*a*b + A*b^2)*c^3*d^2 + (A*a^2 + 4*B*a*b + 2*A*b^2)*c*d^4 - (B*a^2 + 2*A*a*b)*d^5)*sin(f*x + e))*sqrt(-c^2 + d^2)*log(((2*c^2 - d^2)*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2 + 2*(c*cos(f*x + e)*sin(f*x + e) + d*cos(f*x + e))*sqrt(-c^2 + d^2))/(d^2*cos(f*x + e)^2 - 2*c*d*sin(f*x + e) - c^2 - d^2)) + 2*(2*B*b^2*c^5*d + A*a^2*d^6 - (2*B*a*b + A*b^2)*c^4*d^2 + (B*a^2 + 2*A*a*b - 3*B*b^2)*c^3*d^3 - (A*a^2 - 2*B*a*b - A*b^2)*c^2*d^4 - (B*a^2 + 2*A*a*b - B*b^2)*c*d^5)*cos(f*x + e) + 2*((2*B*b^2*c^5*d - 4*B*b^2*c^3*d^3 + 2*B*b^2*c*d^5 - (2*B*a*b + A*b^2)*c^4*d^2 + 2*(2*B*a*b + A*b^2)*c^2*d^4 - (2*B*a*b + A*b^2)*d^6)*f*x + (B*b^2*c^4*d^2 - 2*B*b^2*c^2*d^4 + B*b^2*d^6)*cos(f*x + e))*sin(f*x + e))/((c^4*d^4 - 2*c^2*d^6 + d^8)*f*sin(f*x + e) + (c^5*d^3 - 2*c^3*d^5 + c*d^7)*f), -((2*B*b^2*c^6 - 4*B*b^2*c^4*d^2 + 2*B*b^2*c^2*d^4 - (2*B*a*b + A*b^2)*c^5*d + 2*(2*B*a*b + A*b^2)*c^3*d^3 - (2*B*a*b + A*b^2)*c*d^5)*f*x + (2*B*b^2*c^5 - 3*B*b^2*c^3*d^2 - (2*B*a*b + A*b^2)*c^4*d + (A*a^2 + 4*B*a*b + 2*A*b^2)*c^2*d^3 - (B*a^2 + 2*A*a*b)*c*d^4 + (2*B*b^2*c^4*d - 3*B*b^2*c^2*d^3 - (2*B*a*b + A*b^2)*c^3*d^2 + (A*a^2 + 4*B*a*b + 2*A*b^2)*c*d^4 - (B*a^2 + 2*A*a*b)*d^5)*sin(f*x + e))*sqrt(c^2 - d^2)*arctan(-(c*sin(f*x + e) + d)/(sqrt(c^2 - d^2)*cos(f*x + e))) + (2*B*b^2*c^5*d + A*a^2*d^6 - (2*B*a*b + A*b^2)*c^4*d^2 + (B*a^2 + 2*A*a*b - 3*B*b^2)*c^3*d^3 - (A*a^2 - 2*B*a*b - A*b^2)*c^2*d^4 - (B*a^2 + 2*A*a*b - B*b^2)*c*d^5)*cos(f*x + e) + ((2*B*b^2*c^5*d - 4*B*b^2*c^3*d^3 + 2*B*b^2*c*d^5 - (2*B*a*b + A*b^2)*c^4*d^2 + 2*(2*B*a*b + A*b^2)*c^2*d^4 - (2*B*a*b + A*b^2)*d^6)*f*x + (B*b^2*c^4*d^2 - 2*B*b^2*c^2*d^4 + B*b^2*d^6)*cos(f*x + e))*sin(f*x + e))/((c^4*d^4 - 2*c^2*d^6 + d^8)*f*sin(f*x + e) + (c^5*d^3 - 2*c^3*d^5 + c*d^7)*f)]","B",0
353,-2,0,0,0.000000," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(3/2)/(a+b*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   Curve not irreducible after change of variable 0 -> infinity","F(-2)",0
354,0,0,0,5.625996," ","integrate((A+B*sin(f*x+e))*(c+d*sin(f*x+e))^(1/2)/(a+b*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{b^{2} \cos\left(f x + e\right)^{2} - 2 \, a b \sin\left(f x + e\right) - a^{2} - b^{2}}, x\right)"," ",0,"integral(-(B*sin(f*x + e) + A)*sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(b^2*cos(f*x + e)^2 - 2*a*b*sin(f*x + e) - a^2 - b^2), x)","F",0
355,0,0,0,1.187776," ","integrate((A+B*sin(f*x+e))/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{2 \, a b d - {\left(b^{2} c + 2 \, a b d\right)} \cos\left(f x + e\right)^{2} + {\left(a^{2} + b^{2}\right)} c - {\left(b^{2} d \cos\left(f x + e\right)^{2} - 2 \, a b c - {\left(a^{2} + b^{2}\right)} d\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(2*a*b*d - (b^2*c + 2*a*b*d)*cos(f*x + e)^2 + (a^2 + b^2)*c - (b^2*d*cos(f*x + e)^2 - 2*a*b*c - (a^2 + b^2)*d)*sin(f*x + e)), x)","F",0
356,0,0,0,1.579340," ","integrate((A+B*sin(f*x+e))/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{b^{2} d^{2} \cos\left(f x + e\right)^{4} + 4 \, a b c d + {\left(a^{2} + b^{2}\right)} c^{2} + {\left(a^{2} + b^{2}\right)} d^{2} - {\left(b^{2} c^{2} + 4 \, a b c d + {\left(a^{2} + 2 \, b^{2}\right)} d^{2}\right)} \cos\left(f x + e\right)^{2} + 2 \, {\left(a b c^{2} + a b d^{2} + {\left(a^{2} + b^{2}\right)} c d - {\left(b^{2} c d + a b d^{2}\right)} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(b^2*d^2*cos(f*x + e)^4 + 4*a*b*c*d + (a^2 + b^2)*c^2 + (a^2 + b^2)*d^2 - (b^2*c^2 + 4*a*b*c*d + (a^2 + 2*b^2)*d^2)*cos(f*x + e)^2 + 2*(a*b*c^2 + a*b*d^2 + (a^2 + b^2)*c*d - (b^2*c*d + a*b*d^2)*cos(f*x + e)^2)*sin(f*x + e)), x)","F",0
357,0,0,0,1.889456," ","integrate((A+B*sin(f*x+e))/(a+b*sin(f*x+e))^(3/2)/(c+d*sin(f*x+e))^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B \sin\left(f x + e\right) + A\right)} \sqrt{b \sin\left(f x + e\right) + a} \sqrt{d \sin\left(f x + e\right) + c}}{6 \, a b c^{2} d + 2 \, a b d^{3} + {\left(3 \, b^{2} c d^{2} + 2 \, a b d^{3}\right)} \cos\left(f x + e\right)^{4} + {\left(a^{2} + b^{2}\right)} c^{3} + 3 \, {\left(a^{2} + b^{2}\right)} c d^{2} - {\left(b^{2} c^{3} + 6 \, a b c^{2} d + 4 \, a b d^{3} + 3 \, {\left(a^{2} + 2 \, b^{2}\right)} c d^{2}\right)} \cos\left(f x + e\right)^{2} + {\left(b^{2} d^{3} \cos\left(f x + e\right)^{4} + 2 \, a b c^{3} + 6 \, a b c d^{2} + 3 \, {\left(a^{2} + b^{2}\right)} c^{2} d + {\left(a^{2} + b^{2}\right)} d^{3} - {\left(3 \, b^{2} c^{2} d + 6 \, a b c d^{2} + {\left(a^{2} + 2 \, b^{2}\right)} d^{3}\right)} \cos\left(f x + e\right)^{2}\right)} \sin\left(f x + e\right)}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*sqrt(b*sin(f*x + e) + a)*sqrt(d*sin(f*x + e) + c)/(6*a*b*c^2*d + 2*a*b*d^3 + (3*b^2*c*d^2 + 2*a*b*d^3)*cos(f*x + e)^4 + (a^2 + b^2)*c^3 + 3*(a^2 + b^2)*c*d^2 - (b^2*c^3 + 6*a*b*c^2*d + 4*a*b*d^3 + 3*(a^2 + 2*b^2)*c*d^2)*cos(f*x + e)^2 + (b^2*d^3*cos(f*x + e)^4 + 2*a*b*c^3 + 6*a*b*c*d^2 + 3*(a^2 + b^2)*c^2*d + (a^2 + b^2)*d^3 - (3*b^2*c^2*d + 6*a*b*c*d^2 + (a^2 + 2*b^2)*d^3)*cos(f*x + e)^2)*sin(f*x + e)), x)","F",0
358,0,0,0,1.891441," ","integrate((a+b*sin(f*x+e))^m*(A+B*sin(f*x+e))*(c+d*sin(f*x+e))^n,x, algorithm=""fricas"")","{\rm integral}\left({\left(B \sin\left(f x + e\right) + A\right)} {\left(b \sin\left(f x + e\right) + a\right)}^{m} {\left(d \sin\left(f x + e\right) + c\right)}^{n}, x\right)"," ",0,"integral((B*sin(f*x + e) + A)*(b*sin(f*x + e) + a)^m*(d*sin(f*x + e) + c)^n, x)","F",0
